Chapter 4
BLACK
HOLES
4.1. The
role of gravity in the formation and evolution of stars
4.2. The
final stages of stellar evolution.
Gravitational collapse 4.3.
Schwarzschild static black holes
4.4. Rotating
and electrically charged Kerr-Newman black holes
4.5. The
"black hole has no hair" theorem
4.6. Laws
of black hole dynamics
4.7. Quantum
radiation and thermodynamics of black holes
4.8. Astrophysical significance of black holes
4.9. Total
gravitational collapse - the biggest catastrophe in nature
4.8. Astrophysical significance of black holes
In the previous few
chapters, we have built up the theory
of black holes, which are (along with the global
structure and evolution of the entire universe) the most extreme
manifestation of the properties of gravity. It's time to turn to
real nature and ask: Are there
black holes in the universe? And what is
the role do
these black holes in universe?
Note: Only the "outer" part
of the black hole above the event horizon has astrophysical
significance for the processes taking place in space, not the
"inner" asymptotically future area below the horizon (in
connection with the dynamics of gravitational collapse it was
discussed in §4.2, passage "There are "complete"
black holes in space?").
Opinions on the
role of black holes in space have changed radically in recent
decades. Until the
mid-1960s, astronomers did not take the possibility of
gravitational collapse (the term
"black hole" did not exist at that time) too seriously - they believed
that all stars would lose enough mass during their evolution to
avoid gravitational collapse (renowned English astronomer A.S.Eddington sought
natural law or a mechanism that would "prevent the
stars from doing such nonsenses"!). After the discovery of quasars - see note below *) and pulsars
this position began
to change rapidly. In the half of the 1970s, black holes became
so popular, that astrophysicists used them to explain
almost all new or as yet unexplained phenomena - not just X-ray
sources, quasars and active galaxy nuclei, the mystery of missing
matter in spiral galaxies and galaxy clusters etc., but also, for
example, the lack of solar neutrinos, the fall of the Tunguska
meteorite, or even the disappearance of ships in the Bermuda
Triangle...
Later, when a some "sobering up" has
occurred, probable hypotheses about the role of black holes in
space have already separated from unrealistic
fabrications (such as the last three
mentioned above),
which have shifted from the pages of professional treatises to
the field of sci-fi literature. Black hole astrophysics now has
relatively close contact with astronomical observations, so that
black holes are given an increasingly objective and adequate
place and role in space.
*) Quasars
and radio galaxies
In 1960, a strange radio source 3C48 of very
small angular size (less than 1 arcsecond) was observed with a
Jodrell Bank radio telescope, which was identified in the optical
field with a Palomar 5-meter telescope with a faint bluish point
object that looked like a star. But the spectrum of this object
was very strange, its lines were completely different from the
radiation of any star. Over the next few years was discovered a
number of these special objects "like the stars" - quasistelar
objects in short called quasars (quasar
- quasi-stellar object).
The spectra of quasar radiation at first
seemed utterly mysterious. In the end, however, it was found that
the strange spectra of these objects are still formed by standard
spectral lines of hydrogen, oxygen, magnesium, ... etc., which
are emitted by atoms of excited gas in ordinary stars (or on
Earth), which, however, do not have their usual wavelengths, but
they are significantly shifted to the red end of the
spectrum (by tens of %). According to the Doppler
effect, this means that these objects must move away
from us at a speed close to the speed of light (for the first
observed quasars it was about 16% - 40% c ).
Such tremendous speeds indicated that they
could not be stars in our Galaxy, but that
quasars were objects from distant space that are
moving away from us due to the cosmological expansion of the
universe. Since, according to Hubble's law (see §5.1), the
velocity of the distance is directly proportional to the actual
distance of the object, the distance of the first observed
quasars was about 2-5 billion light-years.
This means, however, that in order for
quasars to be as bright as the astronomically
observed from such a vast distance, they must have a huge
radiant power - about 100 times larger than the
brightest galaxies! Furthermore, the brightness of quasars was
found to be variable, changes significantly in
time scales of about 1 month. However, this shows that most of
the light from such a source must be emitted from space smaller
than 1 "light moon", ie from an area about a million
times smaller in diameter than galaxies. The radiation must
therefore come from a very massive compact object
made of hot gases, heated by an extremely powerful energy
source. It turns out that such a "quasar
engine" is probably a giant black hole in
the core of the galaxy. As will be discussed below, a black hole
can act as a "machine" that converts a portion of the
mass of the surrounding absorbed gas into heat in a rotating accretion
disk, which is then converted to radiation. Such a
"gravitational aggregate" could be highly
efficient, significantly more efficient than a fission
nuclear and even a thermonuclear reactors!
Long before that, in fact, from the 1930s,
when radio radiation from space began to be registered, some
objects in distant space emitting radio waves were observed.
Later, when the principle of radio interferometry of signals from
a large number of distant antennas succeeded in significantly
improving the angular resolution, so-called radio
galaxies were discovered - large regions in the distant
universe emitting radio waves. At first it seemed to be a
collision of two galaxies, but further observations showed that
it was the only galaxy from the center of which large clouds
emanate, a kind of "lobes" emitting radio waves. A
detailed atlas of such radiation-active galaxies compiled
by K.Seyfert in the 1940s and therefore galaxies with active
nuclei are sometimes referred to as Seyfert galaxies.
Near the source nuclei of galaxies, these
radio-emitting clouds have the shape of narrowly collimated
jets of very fast particles, which are only braked at
great distances in the intergalactic environment, where they end
in large radio lobes reaching distances of several parsecs to
hundreds of kiloparsecs - Fig.4.29. The observed geometry of the
jets from the active nuclei of galaxies suggests that the
particle beams emitted from the compact source in the galaxy
nucleus have a very stable geometric axis, the
direction of which has remained virtually unchanged for about 106 -108 years. The source of
the jets must therefore be a very massive rotating
structure, the angular momentum of which, with its gyroscopic
effect, guarantees a spatially stable axis of rotation
along which the jets point. Below we will see that there is a
very close connection between the active nuclei of galaxies and
quasars (+ blazars): the common essence is massive jets of
radiation, particles and gas from rotating accretion
disks around giant black holes in the
center of galaxies, with gas and radiation flow tightly bound
with the axis of rotation of the black hole. This is the same
phenomenon, observed only from different angles (discussed below in the section "Mechanism of
quasars and active nuclei of galaxies").
Blazars
Special types of highly luminous quasars with rapid
changes in brightness, which greatly shine even in the
ultraviolet, X-ray or gamma of the spectrum are called blazars
(blazing quasi-stellar object -
blazing, flaming quasar, the name derives also from the
combination of the name of emission galaxy BL Lacertae and
strongly variable quasars). They are some
of the most energetic sources of radiation observed in the
universe. The blazar effect is probably due to the observation of
a quasar rotated by its rotational axis, ie the jet line (see
"Thick accretion disks. Quasars"
below), exactly in the direction of the observer, where clearer
radiation is observed and the variability of radiation intensity
is best seen.
Origin and Occurrence
of Black Holes
Although,
according to current astrophysics, there
should be a large
number of black holes occur in our galaxy (and a significant
percentage of stars should end up as black holes), the existence
of black holes has not been proven immediately and with absolute
certainty for a long time. It is not surprising, because a
black hole with the mass of an average star is an object with
effective dimensions of the order of kilometers to tens of
kilometers, which itself practically does not
glow and is
therefore not observable at large interstellar distances. We have
a no chance to reveal a lone black hole
traveling through empty space. Simply put, no
one has ever seen black holes and will never see the future - noting from them
can be seen, it's just a bizarre empty and dark place in space... We could see, at most, only the "silhouette"
of a black hole (its horizon or photon
sphere) against the background of brighter
cosmic objects, or manifestations of a gravitational lens
(§4.3, passage "Gravitational
lenses. Optics of black holes.").
However, below we will describe
some phenomena where we do not see the black hole itself, but its
existence is pointed out by phenomena occurring in its immediate
vicinity *) - a black hole can be inferred indirectly on the
basis of significant manifestations of its interaction
with the surrounding matter.
*) The black hole itself cannot be
visually observed as it follows from its very essence -
the presence of the event horizon. However, we can observe the
manifestations of the effect of its massive
gravitational field on the surrounding matter,
or to transmitted light. E.g. when stars and gas orbit a massive
invisible object, it is an indication for a black hole. And as
we'll see below, the accretion disks around the massive black
holes may even be the most intense sources of radiation in the
universe!
First, we notice
the situations in
which black holes can be expected to form and the mechanisms by which black holes
are formed.
Black holes of stellar
masses
In §4.2 we showed the easiest way to produce black holes: a star
with enough weight *) after consumption of nuclear
"fuel" collapses nearly spherical, and if the
remaining mass is large enough, neither the collapse of a white dwarf nor the neutron
star will stop (no
equilibrium configuration for such a large mass does not exist), an event horizon is formed
and a black hole is created. In §4.4 (Fig.4.14) a somewhat
more complicated case was mentioned, when the
rapid rotation first led
to fragmentation (thus delaying another collapse for some time)
and only after the excess angular momentum was radiated by the gravitational waves, did the
collapse and the formation of the resulting rotating black hole be
completed. In this way, black holes of stellar masses M ~ (2÷100)M¤ can form both alone and in multiple star
systems.
*) The condition is that the mass after the end of thermonuclear
reactions exceeds ~ 2M¤ (Oppenheimer-Landau limit). According to
today's knowledge about the evolution of stars, it is necessary
for the initial mass of a star to exceed about ~10-20 M¤; lighter stars end their existence mostly
like neutron stars or white dwarfs
(due to the large mass losses of stars during their long
evolution).
In a close binary
system, a
black hole can be formed by an indirect mechanism, so that from
one component (which is a giant star) it flows through the inner
Lagrange point (see §1.2,
Fig.1.1d , passage "Binary system") to the other component, which is
a white dwarf or neutron star, a considerable amount of matter
(the situation is similar to Fig.4.26). After a certain time, the
Oppenheimer-Landau limit is reached by accretion, a complete
collapse occurs and a black hole is formed. The flowing mass is then still absorbed by this black hole, around which
an accretion disk forms, see below.
It is estimated that our Milky
Way could contain ~100 million black holes formed at the end of
the evolutionary path of massive stars.
Medium-sizes and giant
black holes
Furthermore, black holes can form in a system of a large number
of stars - in galactic nuclei or star
clusters If
the stars in such a system is too "crampedly", there will be inelastic interactions and collisions,
which will lead to the merging
of some stars into compact structures.
They can be formed, and gradually increase very
massive objects, that can easily become so thick that it
collapses into a medium-sizes black
holes from
weights from ~102-104 M¤ (in star clusters),
or into a giant black holes up to ~109-1012 M¤ (at galaxies - see
below "Mechanism of
quasars and active nuclei of galaxies").
The whole process can take place in a very diverse way, eg it can
be combined with the normal collapse of some of the participating
stars and subsequent fusion of black holes and the like (the possibilities for the formation of supermassive
black holes in the center of galaxies are briefly discussed below
in the section "How did the central
supermassive black holes form?").
The result of such processes may
be the entire range of masses of black holes - from tens or
hundreds of M¤, over thousands or millions of M¤, to the giant black hole weighing many
billions M¤ located probably in the center
of large galaxies (see "Thick
accretion discs. Quasars"). In terms of astronomical
observations, there are already strong indications (see below)
for black holes of stellar
masses, and supermassive black holes in the cores
of galaxies. The medium-mass black holes (~ 102-104 M¤), expected
in star clusters, have
not yet been observed (certain
indications for a black hole of mass ~5-8x103 M¤ were
observed in the center of the globular star cluster Omega
Centauri).
Black holes in the
center of galaxies
In the center of our Galaxy is observed the object Sagitarius
A, around which the stars of the central star cluster in the
Milky Way and gases orbit at such a high speed (approaching c/3), that a very
massive object with a mass of about 4 millions of M¤ must be in
the center - supermassive black hole. Such black
"giant-holes" probably occur in the center of all
galaxies. Inside some galaxies, there may be even two
large black holes, clogged there in the distant past in the
collision and fusion of two galaxies (galactic
"cannibalism"), which had
previously formed their supermassive black holes at their
centers; they then orbit large distances of tens or hundreds of
light-years in the resulting galaxy.
From an astrophysical point of view, it
can be expected that in the central regions of galaxies, where in
dense gas clouds there are ideal conditions for the formation of
massive stars, which soon collapse into black holes, hundreds or
thousands of smaller black holes (weighing
about tens of M¤) may occur, some of which may orbit the central giant
black hole. And astrophysical estimates suggest that up to 100
million black holes may occur throughout the Milky Way.
In some clusters,
such as the globular cluster NGC 6624, a sharp maximum mass
density at the center and strong X-ray emission have been
observed, indirectly indicating for the presence of a large black hole. In the
cores of many (maybe even most) of galaxies exist conditions for
giant black holes to form, and galactic nuclei activity
observation suggests that similarly
processed are actually taking place there (see below,
"The mechanism
of active cores and quasar galaxies").
Left : Large black holes could be found inside globular clusters. |
Right : Two massive jets flow from the radiation-active elliptical galaxy NGC 4261 (45 million light-years away). |
|
Gigantic black holes could be found in the cores of galaxies. | At the core of this active galaxy, the Hubble Space Telescope has found a gas-dust disk about 400 light-years across, perpendicular to jets. | |
On the possibilities of the existence of black holes in the center of star clusters and in the cores of galaxies. |
Flashes of radiation
during the formation of black holes
Such a high-energy and "catastrophic" phenomenon, such
as the complete gravitational collapse and the formation of a
black hole, is of course accompanied by significant
"accompanying phenomena". In massive stars, which were
born 20 or more times the mass of the Sun, a gravitational
collapse occurs after the depletion of thermonuclear fuel - a supernova
explosion in which the star's core collapses directly
into a black hole, without the formation of a neutron star. In
less massive stars, the product of a supernova explosion is a
neutron star, which may later collapse into a black hole by
accretion of material or fusion with another compact object in a
binary or multiple system. An important side effect of these
processes is the sudden release of a huge amount of
energy - a rapidly expanding "fireball" is
formed from the rapidly accelerated material surrounding the
star. Shock waves often occur in the expanding
material as the faster grouping strikes and precedes the slower
grouping. The vast amount of radiation and energetic particles,
emitted in the form of a massive flash during
this explosion is probably an important source of cosmic
radiation propagating through space. In the case of
rapid rotation, the surrounding material has a disk shape
and usually produces a very strong magnetic field. The
expanding hot gas is then formed into a pair of jets
along the rotational axis of the system.
Additional intense radiation is continuously generated during the
accretion of the substance, as discussed below in the section
"Accretion disks around black holes".
Primordial black holes ?
An interesting hypothesis is the black holes of primordial
origin, which could have formed in large numbers
from the hot, extremely dense plasma that filled the universe
immediately after the Big Bang. Microscopic quantum fluctuations
increase to a macroscopic scale as inflation expands - creating
areas with significantly lower and higher densities of matter and
energy, from which all structures in the universe later emerged (
§5.5 "Microphysics
and Cosmology. Inflation Universe."). In the very early stages
of the universe, soon after the inflationary period, a large
amount of significant densities could be present, which could
collapse locally into black holes. Such a large amount would be
created primordial black holes of various weights.
In this way, primordial black holes of
both high masses and (as opposed to gravitational
collapse) of arbitrarily small
masses
could be formed; this mass would then decide their future. Large
primordial black holes will enlarge due to the accretion of
radiation and matter, so they could now grow into gigantic masses
(perhaps up to 1015 M¤) of observed supermassive black holes in
the center of galaxies (see below "Mechanism of quasars and active
nuclei of galaxies"). For very small primordial black
holes would in turn prevail quantum
evaporation (see §4.7 "Quantum
radiation and thermodynamics of black holes", section "Quantum radiation from black holes"));
all primordial black holes weighing less than about 1015 g would have to evaporate completely to
this day *). The final phase of quantum evaporation will take
place very quickly, it is explosive in nature and a large amount
of energy will be released in the form of a flash of mainly hard
gamma radiation and high-energy particles. For the existence of
primordial black mini-holes are not yet any direct or
indirect evidence (observation trying to register the appropriate
hard gamma bursts were unsuccessful), so their astrophysical
significance is mostly not reflected.
*) With the Hawking effect, in a vacuum every black hole of mass M
evaporates completely in about T ~ 1065.
(M/M¤)3 years.
Dark matter ?
Smaller and medium primordial black holes (~10-18÷10-6 M¤),
formed in the first second after the big bang, possibly in large
quantities, would be stable in the long term and would also occur
in the present universe. Sometimes they are considered as one of
the suitable "candidates" for hidden - dark -
matter in galaxies and clusters of galaxies (§5.6, passage "Future
development of the universe. Hidden-dark matter."). This explanation would be
quite convincing because it would not require looking for unknown
particles outside the standard model. It is not known how many of
them were created at the beginning of the universe, whether their
number is sufficient to explain dark matter. Detecting these
primordial black holes is difficult, perhaps using gravitational
micro-lensing. This origin of dark matter has not yet been
proven...
"Parasitic" black
holes inside stars ?
There were even hypotheses (in the 1970s by
S.Hawking) that "endoparasitic"
primordial black holes could also reside in the interior of
some stars and were "eating" them from the inside. The
direct capture and absorption of a small black hole by an already
"finished" star is unlikely. Due to the high speed and
large impact parameter, they would mostly fly past the star
without being captured. Even those black holes that would hit a
star directly would mostly fly through its material without
significant braking by friction or accretion and fly away; their
speed is usually greater than the escape speed. But small
primordial black holes could occur in clouds of gas and dust,
from which stars formed. By the contraction of these gases, these
black holes could become parts of some emerging stars from the
beginning.
If such an inner black hole had the mass of a smaller
planet, an inner accretion disk would form around it in
the center of the star, and this accretion would generate a large
amount of thermal energy. The radiant energy of such a star would
no longer be powered only by nuclear fusion, but increasingly by
the inner black hole as well. This process could be very
long-term (~106-109 years), with the black hole
growing. In the late stages, this would lead to the cessation of
fusion thermonuclear reactions in the core of the star and the
expansion of the outer layers - establishing a star similar in
appearance to a red giant, with a lower surface temperature. This
star would then not perish in a supernova explosion, but by the
continuous absorption - accretion - of all hydrogen and helium. A
stellar-mass black hole would remain in its place. This
hypothesis has not yet been confirmed...
Virtual black holes ?
As part of investigating the possibilities of the quantum
theory of gravity, the virtual black hole
hypothesis emerged, which exists temporarily due to quantum
fluctuations in spacetime (quantum
fluctuations in spacetime and spacetime foam are mentioned in
§5.5 "Microphysics and cosmology. Inflation universe." and mainly in §B.4 "Quantum
geometrodynamics") - they arise spontaneously and then disappear. Virtual
black holes should have weights of the order of 10-5 grams (Planck's
mass) and would only exist for an extremely short time of
the order of 10-43 seconds (Planck's time). Virtual black
micro-holes have no astrophysical significance; if they existed,
they could perhaps be important in quantum gravity and unitary
field theory (§B6 "Unification
of fundamental interactions. Supergravity. Superstrings."), or in elementary
particle physics (§1.5 "Elementary particles and accelerators" in the book "Nuclear physics and physics
of ionizing radiation") ..?..
What can be the maximum
and minimum sizes of black holes ?
Black holes are very compact objects, so their spatial sizes
(horizon diameters) are much smaller relative to their mass than
other objects in the universe.
The largest black holes - gigantic
"superholes" with masses of ~106-1012 M¤ -
are astronomically observed in the centers of large galaxies (the
possibilities of their formation are discussed in more detail
below "Mechanism of quasars and active galactic nuclei").
Black holes of intermediate
masses ~102-104 M¤
could form in regions with a tight cluster of more stars. They
have not yet been observed, the competing mechanism of pair
instability at the end of the evolution of heavy stars (Gravitace4-1.htm#ElektronPozitronNestabilita) may also apply here.
The minimum mass of a black hole
formed by the gravitational collapse of a star, which is the only
currently known formation mechanism, is around ~2.5-3 solar masses.
......
The very smallest black hole,
according to the currently known laws of physics, could
hypothetically have a Planck mass of about 0.02
milligrams. There is no known mechanism by which it could be
created (quantum fluctuations of space-time are sometimes
considered) and it would be immediately quantum vaporized by
Hawking radiation - it would only be virtual.
Astrophysical behavior
of black holes
We will now turn to the question of astrophysical
behavior
and the meaning of black holes, ie we will briefly
analyze the processes of interaction of black holes with the
environment in various situations that may occur according to
astrophysical knowledge. The simplest effect of a black hole on
the surroundings is the ordinary gravitational
attraction
between the black hole and the surrounding matter and bodies
(stars). At distances substantially greater than 2M, the
gravitational pull of a black hole is exactly the same as that of
an ordinary star of the same mass. Thus, planet
or another star may orbit a black hole along almost Kepler orbits - a black
hole may be a component of a binary
star or a
multiple system. Stars "age" at different speeds
(depending mainly on their mass), so in a binary system, one
component may reach the black hole stage, while the other
component may still be a normal star. At smaller distances from
the black hole, relativistic effects are already evident:
twisting of "perihelium" orbiting bodies, intense
radiation of gravitational waves, possibility of absorbing bodies
flying close enough around the black hole, gravitational lensing
effect for light passing around the black hole, entrainment
effects body by rotation of the black hole and the similarly.
What would happen if
the Sun turned into a black hole
?
Let's imagine in a fictitious thought experiment that our Sun
would immediately turn into a black
hole - peacefully, without an eruption of gases and radiation
or a supernova explosion (according to the
analysis in §4.2, we know that nothing like that is
possible..!..). So
that this black hole has the same
mass (and possibly also the rotational moment of momentum) as the original Sun. What
consequences would this have for our Earth and the planetary
Solar System ?
-> First of all, Earth and the
other planets would continue to orbit in exactly the same orbits as before. Gravitational attraction does
not depend on the nature of matter-energy. which causes it. The
orbit of the planets will not change until the mass of the
central object, here the black hole, changes.
-> The sky would be as dark as the deepest night. Only distant stars
would shine. We would not see the Moon or any planets because
there would be no sunlight to reflect off them.
-> The surfaces of the planets and
their atmospheres would cool down to a temperature of about 3 ºK in a
short period of time, due to the absence of solar
radiation (however, the deeper layers would
retain accumulated heat for a long time and could be heated by
tidal forces and the radioactivity of uranium, thorium, and
potassium).
Atmospheric gases (nitrogen and oxygen on
Earth) would freeze
and fall to the surface as "snow".
On Earth all life would soon end...
However, all this negative freezing changes for us would simply
be due to the lack of solar radiation, but not due to the
action of the black hole !
-> In the place where the Sun was,
we would see nothing but an empty starry sky. The
event horizon of a solar-mass black hole has a diameter of only
about 3 kilometers, and gravitational-optical effects (analyzed in §4.3, passage
"Gravitational lenses. Black hole
optics") are limited to an area of about
4-6 km. They are too small in size to be seen at a given distance
with the naked eye, or even with an ordinary astronomical
telescope. However, precise astronomical measurements of the
position of the stars would clearly register the effect of
bending of the path of light by gravitational field of the
central body - the black hole.
Limited "radius
of action" of black holes
Black holes are locally very effective "vacuum
cleaners" of matter from space - "bottomless
abysses" from space. So we could expect a great
destructive effect of black holes on the surrounding
universe. However, this is not the case: black
holes, due to their compactness, have a very small gravitational
"radius of action" compared to cosmic scales - usually
do not exceed the dimensions of the size of our solar system
(§4.3, text around Fig.4.7). The black hole, as it moves through
space, thus leaves behind only a very narrow trace
"cleaned" of matter. If we compare it with the
mentioned vacuum cleaner from everyday life, it would be an
extremely powerful unit (vacuum pump) with a thin hose and a
millimeter nozzle, which would perfectly vacuum the dust (and
pull out even the carpet fabric), but only in this millimeter
area...
But below we will see (in the section "Accretion
disks, quasars, ..") that some specific phenomena in
the accretion of matter into black holes can significantly
prolong the astrophysical "radius of action" of black
holes - but they are not gravitational action, but high-energy
particles ejected from accretion disks at great distances into
space.
The initially very small gravitational "radius of
action" of black hole increases with time
by two mechanisms :
- Growth in the size of the black hole (the horizon) as a
result of accretion of matter.
- Emission of gravitational waves by
each gravitationally coupled system at orbiting its parts around
a common center of gravity. These gravitational waves carry away
kinetic energy of the orbiting bodies, which are getting closer
and closer until they finally merge.
Friction in the interstellar gas also
contributes to this dissipative effect, by which part of the
kinetic energy of the circulation is converted into heat,
subsequently radiated out by electromagnetic waves, especially in
the infrared range. On very long time scales (~1035 years), all galaxies
will collapse into giant black holes. Only some stars
that manage to gain more momentum will escape the galaxy and
become lone "wandering stars". However, this process
takes place on such large space-time scales that global
cosmological metrics of space-time can be significantly applied
here (some possibilities are discussed in §5.6 "The Future of
the Universe. The Arrow of Time. Hidden Matter.").
Some potential risks from black holes are discussed in
§4.9 "Complete
gravitational collapse - the greatest catastrophe in nature", passage "Can a black hole
engulf us and the whole universe?".
Emissions of gravitational
waves in interactions with black holes
As described in §4.3 (passage "Emissions of gravitational waves when moving
in a black hole field"), a body orbiting in a
"stable" path around a black hole will lose energy by emitting gravitational waves, so it will (initially slowly)
descend gradually in a spiral, until it reaches the innermost (lowest) stable
orbit; then it is quickly absorbed by the black hole. The total
amount of energy emitted by gravitational waves in such a process
can be easily calculated if the mass of the trapped body m is
much less than the mass M of the black hole. If such a body
initially orbits in a distant orbit around a
black hole, the amount of energy radiated by gravitational waves
until the last stable orbit is reached will be given by the
binding energy of this limit innermost stable orbit (we assume that all
braking is caused by gravitational radiation): E1wave = m - Ems, which for Schwarzschild the
black hole is about 0.057 m (relation
(4.21)) and for the
extreme Kerr black hole it is about 0.423 m in the co-rotating
circulation (§4.4, section "Particle motion in the field of a
rotating black hole"). During the actual absorption of
the body, a pulse of gravitational radiation with an energy of E2wave @ 0.01
m2/M is emitted (relation (4.22)). A body falling
directly on a black hole emits in the form of gravitational waves
the total energy of Ewave = E2wave, while a body descending
gradually along a spiral radiates significantly more energy: Ewave ~ E1waves + E2wave. However, the most important
gravitational-wave process is the emission of massive
gravitational waves in close orbit in a binary system of black
holes - it is discussed below in the passage "Binary systems of
gravitationally coupled black holes. Collision and fusion of
black holes .".
Destruction and
absorption of bodies by black holes
The gravitational field in the vicinity of a black hole is
strongly inhomogeneous, so that bodies moving near a black hole
are subjected to large tidal forces, which can significantly
affect the internal structure of these bodies. Stars flying
around a black hole can be torn by tidal forces into parts, some
of which are absorbed by a black hole, others can be ejected by
reaction forces in stellar matter. If the black hole is rotating
and this decay takes place in its ergosphere, the ejected
part can also carry away part of the rotational energy of the
black hole and gain considerable speed. The disruption of stars
by tidal forces is even more effective in giant black holes, but
it does not manifest itself externally, because it takes place already below
the horizon (only there are sufficient tidal forces) - §4.2, section "External and internal view of gravitational
collapse".
Accretion
disks around black holes
The most important process of interaction of black holes with the
environment *) is, however, accretion (lat. Accret = growth, enlargement, weight gain
), during which the
black hole absorbs the surrounding material with its gravity and
thereby increases own mass.
*) On the contrary, the least
significant manifestation of black holes is probably quantum
evaporation (discussed
in detail in §4.7 "Quantum radiation and
thermodynamics of black holes"),
which is completely negligible in physically real situations (if we do not take into account primordial mini-holes,
for which there is nothing does not indicate) and does not manifest itself - it is many times "overcharged"
by the accretion of gases and radiation... Hypothetically,
it can only manifest in the very distant future of the universe
in the "heat death of the universe" scenario (§5.6 "The future of the universe.
The arrow of time. Dark matter. Dark energy.").
Even a "lonely" black hole,
located in the "vacuum" of interstellar or
intergalactic space, absorbs cosmic radiation and slightly
increases its mass. However, this unmeasurable phenomenon is not
considered astrophysically relevant accretion. True accretion
occurs when denser clouds of gas are found around the black hole.
These can be clouds of gas after supernova explosions, large
gas-dust regions in the center of galaxies (Fig.4.30), gas
overflow from a star to a black hole in close binary systems
(Fig.4.26).
Sufficiently dense surrounding matter,
mainly gas, is drawn in by the powerful gravitational field and,
during its fall onto the black hole, is heated
to such a high temperature due to strong adiabatic compression
and braking by viscous friction (this is
accompanied by the formation of turbulence and shock waves), that there is a strong emission of not only infrared and visible light,
but also X-rays from the inner part of the accretion disk. During accretion, an otherwise
non-radiant black hole becomes a brightly
shinning object ! More precisely, the glowing object is
the absorbed gas in its vicinity.
The basic quantity describing the
accretion is the accretion flux dMA/dt, which is the
amount (mass) of gas absorbed per unit time. However, the energy
balance and intensity of radiation emitted during accretion also
depends significantly on the mass and momentum of the black hole
and the absorbed gas, as well as on the presence and intensity of
the magnetic field (will be discussed below
in the passages on thin and thick accretion disks).
The simplest type of accretion is spherical
accretion, which occurs when the Schwarzschild black
hole is surrounded by a non-rotating cloud of matter (gas). If
the accretion flux dMA/dt (which is the amount of gas absorbed per unit time)
is sufficiently high, by adiabatic compression and viscous
dissipation, the gas near the black hole will be heated to a high
temperature and part of the energy will be radiated by
electromagnetic waves. Gravitational radiation does not apply
here, because there is no change in the quadrupole moment of mass
distribution (which is, after all, zero in
the considered spherical case) with time.
In spherical accretion, the efficiency of converting the mass of
the accreting gas to electromagnetic radiation is relatively low,
so spherical accretion cannot be a sufficient source of quasar
energy.
Spherical accretion
is only the simplest idealized model, which is probably practically not realized. In
fact, the particles of the accreting mass will always have a
certain angular momentum with respect to the center of a
black hole, so that the substance does not fall directly on it,
but first orbits around it (if
the particles of matter did not interact with each other, they
would move in circular paths around the black hole). Especially in binaries
systems (Fig.4.26) and galactic nuclei, the accreting gass will have a
considerable specific
angular momentum - significantly larger than it corresponds to circular orbits near the horizon. In this
case, the absorbed gas around the black hole creates a rotating
disc-like formation called an accretion
disk - a
cloud of gas that swirls and gradually
sinks into a black
hole. In this accretion disk, the gas revolves around a black
hole, is braked by viscous friction (and
magnetic braking, see below) and, after gradually decreasing
circular - spiral - orbits, is
directed towards the black
hole. The radial rate of decrease of the gas particles is much
lower than their rotational speed. In this way, a certain dynamic
equilibrium is established in the accretion disk (unlike spherical accretion). The gradual fall of matter onto a
compact object leads to the release of considerable gravitational
energy, the emission of which also regulates the influx of new
matter.
Fig.4.26. The formation of an accretion disk around a black hole,
which is part of a tight "binary star". The
equipotential surfaces that touch at the inner Lagrange point L
form the critical Roche limit,
which is the first common equipotential of a binary system (see
§1.2, Fig.1.1d , passage "Binary system"). From a normal star, a gas stream
can flow to a black hole through the Lagrange liberation point L,
especially when the dimensions of
the stars near the Roche limit.
This gas enters almost circular orbits around the black hole,
loses energy due to viscous friction and gradually descends to
the black hole.
This image is a "top" view, in the direction of the
axis of rotation of the accretion disk. The "side" view
is in Fig.4.31.
If the black hole is rotating with a non-negligible angular momentum
J, then due to the effect of entrainment of
inertial systems (§4.4, section "Influence of black hole
rotation. Ergosphere.") the accretion disk near the black hole will
always be corotating and inclined
into the equatorial plane of the black hole *); the circulating gas, even
when coming from a direction different from the equatorial plane,
is already pulled into the equatorial plane of the rotating black
hole at a considerable distance by the effect of dragging of
inertial systems.
*) The rotating space near the
black hole entrains the inner parts of the accretion disk so that
they are corotating and fixed in the equatorial plane, regardless
of how they were oriented in the outer part of the disk. The
configuration of the inner part of the accretion disk is
independent of the dynamics of the gas trapped in the outer parts
of the disk.
However, the outer areas of the accretion
disk, further away from the black hole, may orbit at other
angles, outside the equatorial plane, or the rotation of the
gases may temporarily occur in the opposite direction -
compare with the particle trajectory in Fig.4.15c in §4.4, section "Influence
of black hole rotation".
These circumstances depend on the direction from which the gas is
coming, its momentum and the impact parameter.
By the way, the gas
absorbed from the circulating accretion disk (which always has a non-zero angular momentum) introduces a certain additional rotational momentum
into the black hole. Even if the black hole hole was originally
non-rotating (static Schwarzschild), the accretion would gradually make it a rotating
Kerr black hole ...
Non-accretion dark matter disks
around black holes ?
The massive gravitational field of black holes affects not only
ordinary matter, but also the ubiquitous hidden-dark
matter (§5.6, section "Future development of the universe.
Hidden-dark matter."). Therefore, a gravitationally bound disk of
rotating dark matter can form around massive compact
objects such as black holes, but with
practically no accretion. Due to the absence of
friction, the orbiting dark matter cannot get rid of excess
angular momentum in any way and therefore cannot descend to
progressively lower orbits to finally be absorbed by a black hole
(cf. "Accretion
discs around black holes" above); will continuously orbit around. This phenomenon can be
expected especially for supermassive black holes in the center of
galaxies, where a greater concentration of dark matter is assumed
and the dark-matter rotating disk can be very massive. Even if it
does not directly contribute to accretion, its gravity can
greatly influence the structure and dynamics of an accretion disk
made of ordinary matter.
Thin
accretion disk
If the total weight of the disk is much less than the weight of
the black hole (ie the own gravity of the mass of the disk
can be neglected) and the accretion flux is not too high, it will
be a thin accretion disk [193], [227] whose thickness is less
smaller than its diameter - Fig.4.27 :
Fig.4.27. When accreting a gas with a specific angular momentum substantially greater than that of circular orbits near the innermost (lowest) stable circular orbit, the absorbed gas forms an accretion disk around the black hole, which is thin at low accretion fluxes. The gas particles move approximately in circular geodesics, being inhibited by viscous friction and gradually decreasing in a spiral up to the limit innermost of stable circular orbit r = rms , from where they are absorbed. |
Braking and transfer of
angular momentum in an accretion disk
The gas particles in the accretion disk move approximately in
circular geodetic orbits. If they moved freely without
interactions (collisions) with surrounding gas particles, they
would orbit like this "forever", no accretion could
occur. However, gas particles move faster
on the inner orbits than on the outer orbits (as follows from
the classical Kepler's laws; there will be even greater velocity
gradients in the relativistic case). During particle collisions on
"adjacent" orbits, the inner particles are braked and
the outer ones are accelerated - the angular
momentum is transferred from the inner part to the outer part of
the disk. The inner particles thus descend
into an orbit closer
to the center, the outer ones rise to a more distant orbit. The
kinetic energy that the particles gain from these collisions
heats the gas, which then emits radiation (discussed below).
Thus, due
to the viscous friction *) between the outer layers, the gas
particles in the inner layers are thus braked, the radius of their orbits
slowly decreases and the mass thus gradually decreases towards
the black hole.
After reaching the limit of innermost stable orbit r = rms , which is the inner edge of the thin
accretion disk, then the gas falls rapidly into the black hole. If there are no major inhomogeneities in the accretion
disk, the emission of gravitational waves does not occur, because
(similarly to spherical accretion) the quadrupole moment does not
change with time. In
this process, there is a current of angular
momentum from the
inner layers of the disk to the outer layers (rotation of the
outer layers is accelerated by friction), where part of the mass
is released and carries away the excess angular
momentum. Viscous
friction heats the disk (especially in the inner
parts) to a high
temperature
and this energy is radiated out by electromagnetic waves.
*) The difference between the velocities
during circulation on the higher and lower orbits leads to a
certain "velocity shear", which according to the laws
of hydrodynamics causes turbulence in the
circulating gas flow. These turbulences lead to even sharper
collisions of larger volumes of gas, more efficient energy
dissipation and higher accretionary flux. Astronomically observed
brightness fluctuations of the respective objects suggest that
turbulence in the accretion disks is indeed taking place.
Magnetic transfer of angular
momentum
The shear friction in the thin gas is relatively weak
and may not be sufficient for the necessary mechanical transfer
of the orbital angular momentum from the interior of the
accretion disk towards the peripheral parts
(however, this friction is probably sufficient to heat the inner
dense and fast regions of the accretion disk to high
temperatures, as discussed below). However,
if the accreting gas is partially ionized (which is generally expected),
there may be a strong magnetic field. The inner,
rapidly rotating parts of the accretion disk act as an "engine"
generating a rotary magnetic field, which then electromagnetically
spin up the outer parts of the accretion disk *). And
the rotation of the internal parts of the disc are adequately braked
by this. The transfer of angular momentum from the inner part to
the outer part of the accretion disk can thus take place
effectively even without direct mechanical contact between these
areas.
*) It is somewhat similar to an
external coil powered by an alternating current, creating a rotating
magnetic field that electromagnetically spins the anode of
the X-ray tube through the vacuum, without mechanical contact
with it (passage "X-ray
tubes" Fig. 3.2.3 in §3.2 in the
monograph "Nuclear Physics and Physics of Ionizing radiation").
Energy release in the
accretion disk
Under the circumstances common in our terrestrial conditions,
friction is not a very powerful source of heat (let's try, for example, to start a fire by rubbing
wood...). In the accretion disk, however,
there is an effective high-speed "friction"
(precipitation) of gas particles accelerated by a enormous
gravitational energy, substantially greater than nuclear energy.
Therefore, friction effectively heats the disk so much, that it
can glow more than stars (even the entire
galaxy, as will be shown below in the section on quasars).
Note: Accretion
disks can also form around neutron stars or white dwarfs, but
their energy efficiency is significantly lower than that of black
holes (the specific binding energy of particle orbits at the
surface of such stars is relatively small).
At equilibrium, the
total radiated power is equal to the amount of energy that all
particles in the disk generate per unit time by internal
friction. Each gas
particle of mass dM as it passes through the whole disk from its
originally large distance (in which we can neglect the
gravitational binding energy) along the spiral path to the
boundary - last - stable orbit r = rms (Fig.4.27) gives the disk
viscous friction energy equal to its binding energy at the limit innermost stable
orbit. The total power emitted by the disk (luminosity) is
therefore equal to
W = ( 1 - ` E ms ) .c 2 . dM A / dt , | (4.66) |
where dMA/dt
is the total accretion flux and` E ms is the specific energy in orbit along the
innermost (lowest) stable circular path. The
"efficiency" of the conversion of the rest mass of the
accreting substance into the radiated energy is thus given by
the specific binding energy 1-`
Ems of the innermost stable orbit. For the non-rotating
Schwarzschild black hole, this efficiency is approximately 5.7%, but for the extremely rotating Kerr black
hole it is about 42.3% (see §4.4)!
Therefore, if the black hole
initially has a slow rotation and the energy efficiency of the
accretion disk is around 5.7%, this efficiency will slowly
increase over time as the black hole is gradually "more-rotated"
by the transmitted angular momentum of the absorbed mass *).
Change of mass and angular momentum black hole into which
the material falls from the innermost stable orbits specific energy` Ems and specific angular momentum` Lm
given by expression (4.39) with r = rms leads to the fact, that a black hole can be spin-up by
the theoretically up to the extreme state J = M2 (limit
given by the 3rd law of Black Hole Mechanics, derived in §4.6
"Laws of Black Hole Dynamics"). In reality, however, part of the radiation
from the accretion disk is absorbed by the black hole, and this
absorbed radiation will somewhat inhibit the rotation of the black hole,
because the effective cross section of capturing
photon moving
against the direction of rotation of the black hole is larger
than for photons corotating. As a
result, the limit rotation
will be slightly slower, about J @ 0.918
M2 [215], and the conversion efficiency
accreting material on the radiation disc will reach a limit
around 30%; such a black hole with the maximum achievable speed
of rotation, driven by transmitted angular
momentum of the accretion
disk, is sometimes called canonical.
*) The gas falling in a spiral into a black
hole brings angular momentum and spins it at
ever-increasing speeds. When the black hole about twice doubles
its weight by this absorption, it reaches almost critical
"extreme" rotational speed; then the already
centrifugal forces prevent further acceleration of the rotation
(§4.4, section "Movement of particles in the field of a
rotating black hole"). Large black
holes that have grown due to accretion should have almost maximum
rotation speed (extreme, more precisely
"canonical").
At large accretion
fluxes and thus large
radiative powers - especially when the radiated
power is close to the limit Eddington
luminosity WEd = 4p G.M.c/O (» 1,3.1031 M/M¤ [J.s-1] (if the
opacity O is caused by classical Thomson scattering in
ionized gas; was derived in §4.1) - in the inner region of the disc the radiation pressure becomes dominant
over the gas
pressure. To meet the condition of mechanical equilibrium, the
flux of radiated energy at each location must be less than the
corresponding "critical" flux (at which the radiation
pressure would equal the resultant of gravitational and
centrifugal forces); this critical radiation flux is directly
proportional to the total gravitational acceleration at a given
location and indirectly proportional to the opacity of the
accreting mass. For high accretion fluxes, the thin accretion
disk model is no longer adequate, the disk with increasing
accretion flux begins to "get fat". Pressure
gradients are significant manifested here, the movement of
gas particles no longer takes place along almost Kepler orbits; it will be a thick accretion disk [145], [1], [227], [37] :
Thick accretion disks. Quasars.
The shape of the accretion disk in this situation is
schematically shown in Fig.4.28. The disk remains thin at great
distances and also at the inner edge, from where the mass
overflows into a black hole. The inner edge of the disk no longer
lies in the limit innermost stable orbit, but is shifted
somewhat deeper; the radius of the inner edge of the disk lies
between the innermost stable circular orbit r = rms and the limit circular orbit r = rf , where it is pushed by the pressure
gradient. The total radiated power is again given by (4.66),
where instead of` Ems a specific energy corresponding
to the orbit of the radius of the inner edge of the disk emerges.
The higher the accretion flux dMA/dt, the "thicker" the
accretion disk, the steeper its inner walls and the more the
inner edge of the disk shifts toward to the boundary (photon) circular
orbit r = rf . With increasing accretion flux, the total radiant luminosity
of disk increases, although the
conversion efficiency of conversion of absorbed material to radiant energy
decreases somewhat, because the absorption of of matter by a black hole occur
from orbits lower
than the innermost stable circular orbit (which has the greatest binding energy, see §4.4) and binding energy is lower here.
Fig.4.28. At high accretion fluxes, the accretion disk around the
black hole becomes thick and its inner edge lies below the
marginal innermost stable circular orbit. Most of the
dissipation energy is radiated by the inner walls of the disk,
which at considerable thicknesses are quite steep and form a
"funnel" around the black hole. At the bottom right is
a directional radiation pattern of a thick accretion disk. The
vast majority of radiation is collimated in the direction of the
axis of rotation (coming from the "funnel" of the
accretion disk).
For very large accretion
flows, considerably thick accretion disks with high and steep
inner walls are formed; these steep walls of the accretion disk
form a kind of double "funnel" around the axis of
rotation, in the center of which lies a black hole
(Fig.4.28). Because most of the energy generated by the disk is
radiated by these inner walls (multiple
absorptions, scattering and re-emission of radiation also occur
on the inner walls),
the resulting disk radiation will be strongly non-isotropic: most radiation will be emitted by a
"funnel" in narrow cones along the axis of rotation. If
such an accretion disk is observed from a direction only slightly different from the direction of the axis
of rotation, its apparent luminosity may exceed the Eddington
limit many times over (super-
Eddington luminosity). In addition, the strong flux of
radiation in the "funnels", by its pressure, can accelerate on the relativistic velocity the gas particles, that got out of the disc walls ("jet effect"). This creates mighty cosmic jets - collimated streams of ionized gas and
high-energy particles, flying in both opposite directions along
the axis of rotation of the accretion disk. Furthermore, the
interaction of high-energy particles can produce gamma radiation, also emitted in a narrow cone along the
axis of rotation. The direction of gas and radiation streams is
thus firmly and long-term tied to
the axis of rotation of the black hole. Cosmic
ray acceleration mechanisms could work in black hole jets.
Turbulence in the accretion disk can lead to shock waves,
in which conditions are created for the acceleration of particles
even to the highest energies. Jets from the interior of rotating
accretion disks of black holes could thus be (in addition to
supernovae) a significant source of cosmic radiation
- high-energy charged particles, especially protons, spreading
over long distances in space.
For the properties of cosmic radiation,
mechanisms of origin, its propagation, possibilities of detection
and influence on life, see §1.6 "Ionizing radiation",
part "Cosmic radiation" of the book "Nuclear
physics and physics of ionizing radiation".
Furthermore, jets
from accretion disks of giant black holes of active nuclei of
galaxies interact with intergalactic matter, containing atoms of
hydrogen, helium, carbon, oxygen, etc. The kinetic energy of jet
particles heats the gas of intergalactic matter
and supplies activation energy for many chemical
reactions water, carbon dioxide, hydrocarbons, etc. It thus
cooperates (together with gas emissions from stars, supernova
explosions, with cosmic radiation) in the chemical
evolution of the universe.
The speed of rotation
of the accretion disk and the intensity of mass jets
The intensity of the jets significantly depends on the speed of
rotation (angular momentum) of the black hole. With slow
rotation, only faint jets are produced, most of the gas from the
accretion disk quickly proceeds to the black hole, where it
disappears forever. However, rapidly rotating black holes eject
up to 25% of the gas that enters the accretion
disk.
Radiation spectrum from accretion disks
It was discussed above how in the accretion disk the gas is drawn
in by a massive gravitational field and as it descends to the
black hole it heats up to such a high
temperature due to strong adiabatic compression and braking by
viscous friction that not only infrared and visible light is
emitted, but from internal parts of the accretion disk even
X-rays. Also, the chaotic turbulence of the plasma, with the
participation of magnetic fields, strongly locally heats the
plasma in the accretion disk, which leads to the emergence of
X-radiation.Above all, intense radiation in the form of
collimated jets is emitted from inside the narrow funnels along
the axis of rotation. UV funnel and high-energy electrons are
also generated in the funnels inside the accretion disk. During
the interactions of photons with electrons, multiple Compton
scattering of photons on fast electrons *) can occur,
during which the energy of UV photons can increase
up to the level of X-rays, the intensity of which is
stronger the stronger the radiation from the accretion
disk. Thus, heavier accretion disks should emit a higher
proportion of harder photon radiation.
*) The standard Compton scattering
of photon radiation (gamma or X) in substances takes place on
electrons that are essentially at rest, while the energy of
scattered photons decreases (see §1.6, passage
"Interaction of gamma and X radiation", paragraph "Compton scattering" in book "Nuclear Physics and Ionizing
Radiation Physics"). However, during scattering on fast
electrons, the energy of some photons may increase,
if the scattering occurs approximately in the direction of
electron motion (referred to as the inverse Compton
effect).
The electromagnetic
radiation emitted by the accretion disk has a basically continuous
spectrum from radio waves, through infrared, visible and
UV radiation, to X-rays. The different parts of the disc have
very different temperatures. In the innermost parts, where the
temperature reaches up to 106-108 °C, there can be no atoms exists and the rapidly moving
electrons in the fully ionized plasma generate braking
X-rays with energies of unit up to tens of keV. In
slightly higher layers, where the temperature is lower than about
3000 °C, atomic nuclei can already keep electrons in the shell.
These electrons are then excited by the primary X-rays from the
inner region of the disk and, upon deexcitation, emit secondary characteristic
X-rays with a line spectrum (lines
Ka,b). However, due to the
gravitational and Doppler frequency redshifts, this line will be
greatly widened, especially to areas with lower frequencies.
Indeed, such an extended spectral line X of the Ka-Fe of
the iron atom was observed in the radiation spectrum of the
galaxy MGC-6-30-15.
Radiation from the inner part of the
accretion disk occurs mainly in the X-ray spectral
region. Thus, X-ray spectrometry may be one of
the ways to determine the rotational speed and other parameters
of the accretion disk. For this analysis, the characteristic
X-radiation of the gas atoms in the accretion disk can
be particularly useful. The spectral lines of the characteristic
X-rays of gas atoms from the inner part of the rotating accretion
disk are significantly wided by Doppler effect by fast orbital
motion (thermal spread of spectral lines
caused by chaotic motion of individual gas particles is much
smaller in this case than Doppler schift by fast motion in
accretion disk). In addition, the
fundamental natural frequency (energy) of the photons wo when reduced from a great distance (A) is reduced by
the gravitational redshift relative to the known laboratory
energy. The remote observer measures the reduced value
of the frequency wA. The
effect of the gravitational frequency shift from the general
point of view of GTR is briefly outlined in §2.4, passage "Gravitational spectral shift". Here, it depends on the angle
at which the accretion disk is oriented relative to the distant
observer :
A remarkable special arrangement is the
"frontal" orientation of the accretion
disk, with the axis oriented to the observer. In this case, the
gravitational redshift from a point at a distance r in the
accretion disk is wo/wA = 1/Ö(1-3M/r). In the inner part of the disc, at the lowest
stable circular orbit r = rms ~ 6M, the gravitational frequency shift is wA = wo/Ö2 = 0,7.wo. Doppler frequency shift is not applied here.
A slightly more complex situation can be
expected for accretion disks tilted towards the observer "from
the side" (with their
"edge"). In addition to the
gravitational spectral shift, the Doppler frequency shift
will also be significantly applied here - by a factor of [1 ± 1/Ö(r/M - 2)], where
the "+" sign applies to the emitting atom moving in the
accretion disk away from the observer and the " -
"corresponds to the emitting atom moving in the opposite
part of the accretion disk towards the observer. In the inner
part of the accretion disk with r = rms ~ 6M this corresponds to the range wA
» (0,93¸0,47).wo. Due to the high rotational speeds, the observed
spectral lines should therefore have a split shape with
two peaks and a drop in the middle. One of the peaks occurs in
the part of the disk where the gas moves towards the observer,
while the other peak comes from the area where the gas moves away
from the observer. The representation and energy spacing of these
split peaks would depend on the inclination of the rotational
plane of the disk with respect to the direction of the observer.
A certain observed spectral line of characteristic
X-rays is composed of photons coming from different regions of
the accretion disk with different radii r. Since the value
of the gravitational redshift depends on the distance r of
the emitting atom from the center of the disk and is different
for different geometric orientations of the accretion disk with
respect to the observer, by analysis the energies and shape of
the measured spectral lines of the characteristic X-radiation we
can approximately determine the size of the accretion disk and
its orientation with respect to the observer.
Astronomical X-ray spectrometry
is still in the beginning. However, future sensitive
spectrometers located on space probes will certainly be able to
measure fine details in the radiation spectra of accretion disks
around black holes (or neutron stars) and thus determine the
rotational parameters of accretion disks and thus the black holes
themselves.
Electromagnetic
extraction of black hole rotational energy
A black hole as such
does not have its own magnetic field (see
§4.5 "A black hole has no hair"). However, the charged particles
swirling in the plasma of the accretion disk around the black
hole represent an effective electric current generating a
magnetic field. The strong magnetic
field
created in this way probably plays an important role in the
formation of jets from the accretion disk of a rotating black
hole.
Its lines
of force are entrained by the rotation
of the black hole and lead to the induction
of intense electric forces acting on charged plasma particles in the
direction along the rotational axis of the black hole. It
accelerates these particles at the relativistic speeds. The
tightly coiled magnetic field that wraps the jet keeps it in the
shape of a narrow beam with little divergence. In this
way, the jet continues by inertia to distances of hundreds and
thousands of light years - it rushes through the interstellar
space of the parent galaxy, leaves it and penetrates into
intergalactic space. Only at very great distances does the jet
slow down, expand, swell and form large glowing
clouds high-energy
particles (Fig.4.29) interacting with the surrounding gas.
Electrons with a velocity close to the speed of light in an
ionized gas orbit in spirals around magnetic field lines and emit
electromagnetic waves - synchrotron
radiation (the mechanism of
synchrotron radiation is outlined in §1.6, passage "Cyclotron and synchrotron radiation" of the book "Nuclear Physics and Ionizing
Radiation Physics", see also Fig.4.3 in §4.2, part "Pulsars
- fast rotating neutron stars").
The mechanism of a
gigantic "MASER" - stimulated emission of
radiation in more distant atoms under the influence of harder
radiation from the central parts of the disk - could also
contribute to the observed massive radio radiation.
In addition, a very
strong magnetic field in the central part of the accretion disk
(which could reach up to 1010 T) can cause fast charged particles, especially
electrons and positrons, point in to negative energy
orbits in the ergosphere of a rotating Kerr black hole,
which could lead to the extraction of the rotational
energy of a black hole by the Penrose process - the
so-called Blandford-Znajek mechanism [20], see
§4.4, part "Penrose process", passage "Electromagnetic
extraction of rotational energy - Blandford-Znajek mechanism".
When a plasma of charged
particles orbits a rotating black hole - the accretion disc,
it creates a strong poloidal magnetic field by rotating toroidal
currents flowing in the equatorial plane. The entrainment of
space, and thus of the magnetic field lines by the rotation of a
black hole, then induces an intense electric
field - a powerful electric generator
is created in the form of a stream of charged particles. Some of
them enter orbits with negative energy in the ergosphere and fall
into a black hole, while the extracted energy strengthens the
electromagnetic field. Other charged particles are then
electromagnetically accelerated by the extracted rotational
energy and transfer this energy to the plasma in the jets by
magnetohydrodynamic effects. Such a "gravito-magnetic
dynamo", driven by the rotation of a black hole,
could supply a considerable amount of energy to the jet from the
accretion disk, contributing to the relativistic jets from inside
the accretion disk.
The rotating
accretion disk around the black hole thus acts as a kind of rotating-linear
"jet engine", converting part
of the mass falling into the black hole into high-energy quantum
and particles, radiated linearly along both axes of the black
hole. The efficiency of this engine can reach up to 30% (from mc2) *) for fast-rotating
black holes; existing jet or rocket engines can only envy this
efficiency! "Mega-jets" from giant black holes in the
center of galaxies, surrounded by massive accretion disks, are
the most energetic processes we observe in the
universe!
*) The energy of the jets is partly drawn
from the rotational energy of the black hole (§4.4, part "Penrose
process"). However, the rotational
energy of a black hole is continuously supplemented
by the accretion of the co-rotating gas, which brings the angular
momentum. The accreting mass can store almost
30% of its rest energy in the rotating gravitational field around
the black hole. And this huge energy can then be pumped
from there via the accretion disk to the kinetic energy of the
high-energy particles in the jets. This is the essence of the
"black hole engine" that supplies
quasars and massive gas currents in the lobes of radiation-active
galaxies :
The mechanism of quasars and active
galactic nuclei
The idea of a thick accretion
disk around
a large black hole (Fig.4.28) so quite naturally
explains the most important peculiarities
observed in quasars and radiation active
galactic nuclei, ie. their extreme
luminosity
(highly super-eddington) and ejected clouds of
relativistic particles in the form of massive jets - Fig.4.29 :
In the 3C449 radio source, jets are about 200,000
light-years long from the core of an elliptical galaxy. The galaxy is about 150 million worlds away from Earth. flight. |
|
In a 3C348 radio source, about 1.5 billion away from the light-years, the jets form a structure as long as 1.5 million light-years! | |
Fig.4.29. Examples of radio astronomically observed jets from active galaxy nuclei. |
In quasars, the central black hole in the
galaxy is intensively "fed" by the surrounding absorbed
gas, and there is great friction in the gas in the massive accretion
disk. The large amount of heat heats the disk so much,
that with its brightness of 100-x and 1000-x it overcomes all
other stars in the galaxy. The innermost part of the disk is so
hot that it emits mostly X-rays, further from the center the disk
is colder and emits UV radiation, then visible light. In the
outer parts, the disk is already relatively cold and emits
infrared radiation. Massive streams of gas, heading from the
accretion disk to the intergalactic environment, radiate energy
in the area of radio waves.
A more detailed
explanation of the astrophysics of accretion disks
goes beyond the scope of this book focused on relativity, gravity
and spacetime (we can refer, for example, to the recently
published review work [37] and the literature mentioned there).
Significantly complicated models of accretion disks are
constantly evolving in an effort to move from phenomenological
character to the application of laws of microphysics leading to
finding the equation of state, viscosity mechanisms, turbulence,
magnetic effects, opacity and other processes of dissipation and
energy transfer, co-determining disk shape and dynamics, flow
distribution radiation and its spectra from the surface and from
inside the "funnel" of the accretion disk.
To summarize, currently the most
realistic model of a quasar is the following notion
(Fig.4.30): A quasar is an extremely active
nucleus of a galaxy that is collapsed into giant black holes weighing ~106 -109 M¤. Around this black hole, a thick accretion disk is formed from the surrounding matter
(interstellar matter and disturbed stars), in which the
gravitational binding energy of the absorbed matter is converted
into radiant energy. These radiation active galactic nucleus may
radiate more intensely than the entire galaxy, wherein the
radiation is strongly anisotropic - directed along the rotation
axis of the disc - and a time
variable
(due to inhomogeneity and turbulence in the accretion disk).
Thanks to the sharp anisotropy of radiation from the thick
accretion disk, a selective effect is manifested: we see mainly
those quasars that are to us inverted by its axis of rotation (observer "A" in
Fig.4.30) :
Fig.4.30. Intense jets of relativistic particles and radiation
gush from a massive accretion disk around a rotating massive
black hole in the center of a young galaxy along the axis of
rotation. The distant observer "A", to which the system
is inclined by the axis of rotation, observes a clear point
source - the quasar. The lateral observer
"B" then sees the radiation - active nucleus of
the galaxy with jets of ionized gas.
Note: In the illustrative drawing, the
dimensions of the black hole and the accretion disk are greatly
enlarged relative to the size of the galaxy (the black
hole and the accretion disk are many billions of times smaller
than the galaxy...).
Their luminosity then appears to us many times
greater than would correspond to isotropic radiation. In
addition, in the case of plasma clouds ejected from the
"funnel" of the accretion disk, a special relativistic
selection effect is also taken in that the radiation of the
fast-flying source appears to the observer in a cone in the
direction of movement; the rapid movement towards the observer is
also related to the seemingly superluminal velocities observed in
the ejected clouds from inside the quasars. The intense flux of
radiation completely overexposes the rest of the galaxy, which is
usually not visible at all, we see only a point object (observer
"A").
If the accretion disk around the
giant black hole is not to us inverted by its axis of rotation,
we do not see closely collimated intense radiation from inside
the accretion disk. In this case, we do not observe a quasar, but
a distant galaxy with a radiation - active
nucleus (such as Seyfert's or
radio galaxies),
from which massive streams of ionized gas gush to opposite sides
(observer "B" in Fig.4.30).
Quasars (+ blazars) and active
nuclei of galaxies probably represent the same
phenomenon
in outer space - radiation from rotating accretion
disks around giant black holes in the
center of galaxies,
which is only observed from a different
angle *),
depending on the inclination of the plane of the accretion disk relative to
the line of sight.
*) Different angles of view:
The difference between the observational perception of the
accretion disk around a massive black hole in the core of a
distant galaxy, when viewed in the direction of the axis of
rotation and in a different direction, can be roughly compared to
the night observation of a car. When the car is driving in the
distance against us, we only see bright spotlights,
which overexpose the faint image of the car. However, if we
observe a glowing car from the side (it goes along a
side road, for example), we see traces of light cones in the air
and the surrounding terrain, sometimes partly the outlines of the
car itself.
Similarly, if we observe a galaxy with an active central black
hole "from the side", at an angle to the axis of
rotation close to 90°, it appears as a radiogalaxy
with jets, at angles around 60° as a Seyfert galaxy.
At angles less than 30°, intense radiation from the jet
overexposes the image of a distant galaxy, and the object appears
as a bright glowing point similar to a star - a quasar.
When viewed at a very small angle almost in the direction of the
axis of rotation, we see the clearest effect, referred to as the blazar
(mentioned above in the passage "Quasars
and active nuclei of galaxies"); the variability of radiation intensity is also best
seen here.
Superluminal velocities of
jets from quasars ?
If there is any astronomically observable distinct structure in
the jet, we can determine the speed of movement of this structure
in the sky by precisely observing its position A, B at
two times t1, t2 (a few
months apart) - in
principle, thus we measure the speed of the gas in the jet.
Detailed measurements of the light (and
electromagnetic radiation in general) of jets from quasars and active galactic
nuclei have shown that in many cases the movement of the glowing
gas structures in the jets appears to be faster
than light.
This deceptive effect occurs when the velocity of the jet is
close to the speed of light (>0.9c) and there is a high
component of the velocity towards the Earth (small jet angle q
approx. 10°-40°). In such a case, as the observed structure in
the jet moves towards the Earth, the distance d2
is shortened compared to d1 and thus the time delay of
detection in both positions A, B by the value (v/c).cosq. As if the observed
structure had managed to overcome the distance between the two
places A-->B earlier. This means that the apparent observed
velocity v´ appears larger than the actual
velocity v, by the ratio 1/[1-(v/c).cosq].
Apparently superluminal velocities in the
inner parts of jets have been observed, for example, in quasars
3C 273, 3C 279, M87, ....
The issue of astronomically
observed apparently superluminal velocities is discussed in
general in §1.6, the passage "Apparently superluminal speeds of
motion?",
from which we reproduce the image here for clarity :
Actual and apparent
velocity of quasar jets. Left: A jet from the accretion disk of the central black hole, directed at an angle q relative to the observer. Right: Trigonometric analysis of the movement of the investigated element in the jet and the observed light rays in two times t1, t2. |
Active and
"starved" quasars
It is likely that very massive black holes "reside" in
the center of most galaxies. However, not
every such
black hole is reflected by the massive radiation of the
surrounding gas, such as a quasar or an active galactic nucleus.
This requires a sufficient supply of material to the accretion
disk. In many cases, the "feed supply" is probably
insufficient and the black hole is "calm", inactive.
From this point of view, it is characteristic that we observe
most quasars in the distant
universe,
which also corresponds to the distant
past when
the universe was only about 2-4 billion years old. In the distant
past, young galaxies contained far more gas and dust than they do
today, so the central black hole had a much greater supply of
material for the massive accretion disk in the long run. After
depletion of this supply of gas and dust in the central part of
the galaxy, the accretion gradually ceased, the massive quasar
"starved" and faded; now the surrounding galaxies,
including ours, are relatively peaceful.
However, such an inactive black
hole, or "starved quasar", may again "wake
up" for a while if a star or a large gas-dust cloud wanders
near it, from which the black hole "sucks" a new supply
of material by gravity. If a normal star
(solar type) gets close to a black hole (mass
~106-9 M¤), will be torn and destroyed by massive
gravitational tidal forces *). As it approaches, the tidal forces
will initially stretch it in the direction of orbit. Upon further
approach, the tidal forces overcome the star's own gravity and
tear it into thin arcuate gas streams. This gas enters an
ever-lower orbit and, before being absorbed, forms a hot
accretion disk from which intense radiation and energetic
particles are emitted along the axis of rotation - for a
"shorter time" a quasar or an active
galactic nucleus is formed again. Something
similar may have happened to our Milky Way galaxy. The observed
giant clouds of gas (so-called Fermi
bubbles) extending to both sides from the
center of the galaxy could have arisen in such a way, that a few
million years ago the intensity of accretion to the central black
hole suddenly increased and the resulting energetic polar jets
interated with the surrounding thin gas and created these
bubbles.
*) However, small and dense compact objects
- white dwarfs and neutron stars, or smaller black holes - are
much more resistant to tidal forces than solar-type gaseous
stars, so they can be absorbed by the black hole "as a
whole". A weaker accretion disk could only arise here from
gases or planets that orbited them.
The most gigantic
black holes of mass > ~1011 M¤ have
gravitational gradients (tidal forces) at their horizon too weak
to rupture incoming stars and form an accretion disk that would
be a source of radiant energy and quasar jets. Such a gigantic
black hole "swallows the stars as a whole", without the
formation of a more massive accretion disk and thus without
quasar effects (after depletion of the
initial gas supply from its surroundings).
The largest black holes are probably not quasars
..?.
The spectrum of quasar radiation
In the section on thick accretion disks ("Thick
Accretion Disks. Quasars."),
it was discussed how intense radiation is
emitted inside narrow funnels along the axis of rotation in the
form of narrow jets. In the funnel inside thick accretion
disk arises also UV radiation and high-energy electrons. When the interactions of photons with electrons may
occur for multiple Compton scattering of photons at fast
electrons *) in which can increase
energy UV photons to the level of X-radiation whose
intensity is higher, the emission from the accretion disk larger.
Thus, brighter quasars should emit a higher proportion of harder
photon radiation.
*) The standard Compton scattering of
photon radiation (gamma or X) in substances takes place on
electrons that are essentially at rest, while the energy of
scattered photons decreases (see §1.6, passage
"Interaction of gamma and X radiation", passage "Compton scattering" in book "Nuclear Physics and Physics of
Ionizing Radiation"). However, during scattering on
fast electrons, the energy of some photons may increase
if the scattering occurs approximately in the direction of
electron motion (referred to as the inverse Compton
effect).
Quasars as "standard candles" in the farthest universe
..?..
Quasars are the only observable objects in the outermost
universe. The absolute magnitude (actual
radiant power) of quasars is different, it
depends on the mass and rotational angular momentum of the black
hole and especially on the amount of absorbed gas - accretion
flow. However, as shown above, this absolute magnitude is
related to the emission spectrum of the quasar,
especially to the ratio of radiation in the ultraviolet and X-ray
fields. At present, these spectrometric measurements are
performed on a number of quasars of different distances, which
will make it possible to determine the calibration dependence
between the spectrum and the absolute magnitude of the quasar.
Once the true luminosity is known, the distance of the quasars
can be determined from the observed radiation intensity. The
quasars can then be used as "standard candles"
for measuring the greatest cosmological distances (where it can supplement and replace type Ia supernovae,
see §41.1, passage "Determining
the distance of space objects")
.
How did central supermassive black holes
form ?
The question remains, by what mechanism
and at what stage of evolution galaxy, these
central supermassive black holes formed? What came first -
galaxies, or their central black holes? There are basically three
standard hypothetical options; a fourth possibility is the
inclusion of hypothetical dark matter :
1. In the dense gas in the center of early
(proto)galaxies originated many massive stars
*), which quickly exhausted its nuclear fuel and collapsed (over supernova explosion ) into
black holes weighing tens to hundreds of M¤ - a kind of
"seed black hole", which have
become "germs" for the formation of supermassive black
holes. These medium-sized black holes then absorbed the
surrounding gas (and possibly the stars) and in a dense environment their orbital motion was
effectively braked. Therefore, they merging
to each other relatively quickly, creating seed black holes
weighing about 10 000 - 100 000 M¤. For several hundred million years, they could grow
into giant masses, which were further increased by accretion.
However, with this scenario of the gradual merger of many small
black holes of stellar masses, the observed supermassive black
holes at the center of galaxies could take many billions of years
to form.
*) At that time there was only hydrogen and
helium in the universe, the stars of the first generation had
zero metallicity and could have formed with masses of tens or
many hundreds of M¤.
2. A very large clouds of dense gas
(and dark matter..?..) in the center of the emerging galaxies could collapse
directly into a large black holes,
without the need for star formation and evolution - without
collapse into black holes of stellar masses. Especially during
the collisions of massive streams of cold gas, large-scale
condensations could form, which could collapse into very massive
black holes. These "gembrinal"
black holes could have masses of many tens of thousands to
several million M¤ and
could be surrounded by a larger number of 1st generation stars -
the star clusters. The collisions and mergers of a
larger number of these seed black holes could have produced
supermassive black holes in a cosmologically relatively short
time (several hundred million years). And in addition, there is a possible scenario that the
gradual fusion of the surrounding star clusters could also have
created the galaxies themselves with a gigantic black hole in
their center..?..
3. In a hypothetical
scenario, there may first have been large primordial
black holes (as mentioned above in
the passage Primordial black holes?"), around which the first
galaxies formed, within which they then increased
with accretion and formed supermassive central black holes..?..
There is no astronomical evidence for this hypothetical scenario.
Many observed quasars are very old,
probably formed about 200 million years after the beginning of
the universe. With the help of commonly observed matter, we
cannot yet convincingly explain how such gigantic black holes
could have formed so soon after the beginning of
the era of substance..?..
4. But
it is likely that in the gravitational collapse of large gas-dust
clouds and possibly merging of the resulting seed black holes was
hidden-dark matter significantly involved (its existence and properties are discussed in §5.6,
section "Future
evolution of the universe. Hidden-dark matter."), whose attractive
gravitational effects prevailed over the repulsive pressure
forces in vast contracting gas clouds..?.. At the time of the
formation of the first galaxies and stars, about 200 million
years after the creation of the universe, the primordial dense
clouds of hydrogen and helium could contain a significant
percentage of dark matter. Dark matter, due to the absence of
pressure, could gravitationally clump together earlier
than the atomic-baryonic matter of hydrogen and helium gases. And
it was only against the background of these dark matter
densities, invisible to us, that the observed large-scale
structures in the universe condensed..?..
It is discussed that, with the
participation of dark matter, the first emerging stars of the 1st
generation could hypothetically reach large masses of up to
millions of M¤.
After their early collapse, they could also be the seeds for the
formation of supermassive black holes..?..
Observation of some
very distant and therefore early galaxies, formed about
500 million years after the big bang (or
even earlier), shows that the mass of their
black holes is comparable to the total mass of their stars. It
indicates that at least some giant black holes were created by
scenario No. 2 (or 4) - the direct
collapse of massive clouds of gas. And these galaxies then
grew around these central black holes.
The occurrence of large black holes and
their role for galaxies
Two questions are sometimes debated :
1. "Does every galaxy have a supermassive
black hole at its center ?"
It is believed to yes, but in a number of
galaxies have failed to detect a black hole astronomically.
Indirectly "observation" the galactic central black
hole, or its manifestations, are possible under two favorable
situations :
-> For relatively close galaxies, where we can
observe the movement of the glowing substance in their center -
an enormously fast rotation around the central object, or the
"silhouette" of the black hole.
-> In active galactic nuclei that produce strong
collimated jets of fast particles and radiation from accretion
disks, while absorbing large amounts of matter.
In many older galaxies, however, the central black holes have
already absorbed everything in their vicinity, they have nothing
to "eat" and no jet is produced. In such a case, the
black hole is practically undetectable astronomically. However,
it does not have to be a permanent condition. After a long enough
time, perhaps thousands or millions of years, some star or a
nebula may come into close proximity to the black hole, the black
hole will begin to absorb it and create a new observable jet.
2.
"Does this
supermassive black hole play a crucial role in the galaxy ?"
Here the answer is no! At least not now. The
supermassive black hole at the center of the galaxy, as well as
other black holes present, make up only a tiny fraction of the
galaxy's total mass. They only add a negligible amount of
gravity, nothing more. If we removed them all, almost nothing
would change in the overall structure or dynamics of the galaxy.
The answer to these two questions evokes another
tertiary question: "Why are black holes, when
their mass is only a small percentage of the total mass of a
large galaxy, usually found in the center of the galaxy?".
In general, most black holes are not located in the central
regions of galaxies, many smaller and medium-sized black holes
are probably distributed in various places. But supermassive
black holes are located in the center, which can basically have
two alternative reasons :
- In the central part of the galaxy, there is the largest
accumulation of stars and interstellar matter, so there are the
best conditions for the formation of black holes and their growth
to giant masses.
- Supermassive black holes were the seeds of large spiral
galaxies. The galaxy thus formed around the black hole, which
remained where it was before - in the central region.
However, if two galaxies collide, penetrate, and their
central cores interact, the massive black holes may no longer
remain at the center. In certain cases they may even be ejected
away from the resulting merged galaxy..?..
Black-hole
in binary systems
Let us now return to stellar black holes. Astronomical observations show
that most stars are not isolated, but are part of a binary or
multiple system - they are gravitationally bound and orbit
(common center of gravity) - §4.2, passage "Binary
stars and multiple systems". If two stars in a binary system do
not orbit too closely around each other, they evolve independently, depending mainly on their mass. At a
given time since their common origin, they could therefore reach various stages of their evolution. Either they can still
be common stars of the main sequence, or one of them could
already consume its thermonuclear fuel and shrink into a white
dwarf or neutron star, or collapse into a black hole at high
mass. For closely orbiting binary stars, the overflow of gases
between the two components can be significantly applied (as discussed in the mentioned passage "Binary
stars and multiple systems"). It can be expected that there
will be a large number of binary systems in space, one component
of which will be a black hole ...
In tight binary
systems, in
which one component is a black hole, the mass flowing from the
other star around the black hole forms an accretion disk in which
the gravitational binding energy (ie part of the mass) of the
accreting mass is converted by dissipative processes into heat, which is
radiated from the disk - Fig.4.26 (view in the
direction of the axis of rotation) and Fig.4.31 (side view). The
inner parts of the disk heat up to a high temperature and also
emit X-rays. Due to instabilities and turbulence in the accretion
disk, the emitted radiation has an irregularly variable
intensity.
Fig.4.31 A close binary star system in which a stream of gas flows into a black hole orbiting a common center of gravity with an ordinary star, forming an accretion disk around the black hole. Narrow cones (jets) of radiation and ionized gas are emitted along the rotational axis of the accretion disk. Note: This is an identical situation as in Fig.4.26, but observed "from the side", perpendicular to the axis of rotation of the accretion disk. |
The best known example
of such a system is the binary X-ray source Cygnus
X-1, which
according to astronomical observations consists of a blue giant
star HDE 226 868 with a mass of about 25 M¤ (distance from Earth about 2.5 kpc) and
an optically invisible "guide" of at least ~6 M¤ (this mass of the invisible
component results from the Doppler measured velocity and period
of the first component). The period of this eclipsing binary is
5.6 days. X-rays are irregularly variable with a characteristic
period of the order of milliseconds, so that the dimensions of
the emitting area are not larger than the order of hundreds of
kilometers. The source of X-rays is the invisible guide, which
cannot be a star, because at this mass an ordinary star would
have a luminosity of ~103 times higher than the Sun and
would therefore be visible. This component cannot be
neither white dwarf or neutron stars, because its weight significantly
exceeds both Chandrasekhar, and Oppenheimer-Landau limit. So it
is most likely a binary system of a normal star and a black hole according to Fig.4.26 or
Fig.4.31, where a stream of matter flowing from a star to a black hole
creates an accretion disk, in which the observed X-radiation are generated. Several similar "serious
candidates" for the black hole are now observed, in addition
to Cyg X-1, for example, the X-ray source Cir X-1, the binary
star V861 Sco, or the object LMC X-3.
Even with a small
blac holes from accretion disk along the rotation axis occurs jets
of relativistic particles are ejected into the surrounding space
(obr.4.31). Due to their geometric arrangement and some of their
properties, the accretion disks around the black holes of stellar
masses resemble much more massive distant quasars and
radiation-active nuclei of galaxies, but as if reduced to much
smaller scales - by a ratio of the order of 106; therefore, these
objects are sometimes called "microquasars"
(compare Figs.4.30 and 4.31). A typical example of such an object
observed in our galaxy is the binary source SS 433 with an
orbital period of 13 days, whose secondary compact component has
a mass of min. 5-10 M¤ and emits from it, in addition to X-rays, two opposite
gas jets at speeds up to 0.26c.
The above-mentioned apparently
superluminal jet velocities were also registered in some
microquasars whose jets were directed at a small angle relative
to the observer. The first such case was the binary object GRS
1915+105 with a standard star and a black hole with an accretion
disk.
Thus, in general, a black hole that forms a binary
system with an ordinary star has the best chance
of being proven. In the optical field in this binary
system, we see only a star, which shows a Doppler spectral shift
which periodically changes into red and blue regions as the star
orbits its invisible companion approaches or moves away from the
observer on Earth. From this measurement of the period and
orbital velocity of the visible component, the mass of the second
invisible component can be determined astronomically; if it is a
compact object with a mass significantly larger than 2M¤
and, in addition, X-rays or jets of relativistic particles come
from there, it is probably a black hole.
Binary systems of gravitationally coupled
black holes. Collisions and fusions of black holes and neutron
stars .
From a mechanical point of view, black holes basically behave as
very massive strongly gravitational
bodies with
relatively very small dimensions, which move evenly in a straight
line in free space and move along curved geodetic paths in the
gravitational fields of other objects. In vast outer space, there
is a very small probability that two independent black holes would collide
directly ("frontally") - it
probably didn't happen anywhere during the entire existence of
the universe. Even
the mutual gravitational capture of two independent flying black
holes is not very probable (they would have
to encounter a low mutual velocity and a very small impact
parameter, but see below "supermassive binary black
holes").
The only real possibility of close mutual interaction ("collision" or fusion) of
black holes is their
common origin in a binary or multiple star
system.
Binary systems of gravitationally coupled black
holes (two or more) are undoubtedly very common in the universe, because they commonly
form during the evolution of stars that are part of binary
systems: when in such a binary (or
multiple) system of
massive stars (masses greater than about
six times the Sun) at
the end of their evolution, the gravitational
collapse
will occur to form compact objects. The mutual
gravitational relation to the orbit will be preserved, so that the original binary system
becomes a binary system of gravitationally bound compact objects,
still orbiting the common center of gravity (we
are mainly interested in the case where black holes formed by
gravitational collapse). According to the laws of the general
theory of relativity of a body in a binary system, gravitational waves radiate during their mutual circulation,
carrying away part of the kinetic energy of the circulation - see §2.7, section "Sources of gravitational waves".
In most cases, the resulting
black holes circulate at great distances. In
conventional binary systems, the orbital distance is at least 106 km (close "spectrometric" binary stars), which is more than 100,000 gravitational radii; at
these distances, the GTR effects are practically not applied.
During their circulation, only very weak gravitational waves (approx. 1025 W) emit - the initial part of the
graph in Fig.4.13. They would not reach the stage of close
circulation by gravitational radiation during the entire
existence of the universe! However, there is a mechanisms that
can significantly "converge" in the foreseeable future:
it's friction and acretion in a
large and dense cloud of gas which, after
collapse, often surrounds the binary system. If the two black
holes approach each other at a distance of several tens of
gravitational (Schwarzschild) radii, the intensity of the radiation of gravitational
waves will increase significantly.
In this situation, the removal of the energy of the
orbital motion by intense gravitational waves leads to the converging
bodies approaching each other, shortening the
orbital period, increasing the velocity of the circulation and increasing
the frequency and intensity of the gravitational waves.
This is shown in Fig.4.13-GW :
Fig.4.13-GW.
Time course of amplitude, frequency and intensity of
gravitational radiation of a binary system of two compact
black holes m1 and m2 orbiting a
common center of gravity. Bodies that begin their orbit at time t = t0 on some large radius r0 descend very slowly in a spiral and continuously emit gravitational waves, initially weak (stage I). Even with tight binary systems, it is a process that lasts hundreds of thousands and millions of years. As you approach, the intensity and frequency of the radiation continue to increase. After reaching the circulation distance of several tens of gravitational radii, there is an avalanche-like increase in the intensity and frequency of gravitational waves (stage II). After reaching the limit innermost of stable orbit, the bodies fuse rapidly, sending a short intense flash of gravitational waves (stage III). In the upper part of the figure, enlarged sections from the last few cycles are symbolically drawn, during which both horizons are deformed and finally they are connected to the deformed horizon of the resulting black hole. The resulting black hole m1+m 2 is rotating and rapidly relaxes to a stationary axially symmetrical configuration of the Kerr black hole (stage IV) by radiating damped gravitational waves. Note: This figure is analogous to Fig.4.13 in §4.3 passage "Emission of gravitational waves during motion in the field of a black hole , related to the circulation of a body in the field of a black hole, but the qualitative character of the dependence is the same. |
At first, the two components slowly, but with
increasing speed, approach each other in a spiral and radiate
more and more intensively by gravity (middle part of the graph in
Fig.4.13). At the
end of this avalanche-shaped "spiral of death", after a
close approach, during the last few orbits and the subsequent
merging of the two black holes, a massive
flash of gravitational waves emits. Gravitational
waves will carry about 5% of the total weight of both merging
compact objects !
To summarize, the dynamics of the orbital binary system
of black holes emitted by gravitational waves can be divided into
4 stages :
I. Distant orbital
along almost Kepler orbits, with weak by
gravitational radiation and very slow spiral approach. This phase
can last several billion years.
II. After approaching
a distance of several tens of gravitational radii, the intensity
of gravitational radiation increases greatly, which leads to a rapid
spiral approach of both bodies, with the emission of
increasingly powerful gravitational waves with rapidly
increasing frequency, from units to several hundred Hz.
In astrophysical jargon, this phase is
sometimes called a "chirp" because the rapid
growth rate of circulation just before the merger of two black
holes resembles a bird chirp.
III. Fusion
(merge, collision) of both black holes into one resulting
rotating black hole, while is emitting a gigantic flash of
gravitational waves.
IV. Relaxation
of the resulting black hole on a stationary axially symmetric
configuration of a Kerr black hole with a rapid
attenuated reverberation of gravitational
radiation.
In terms of the emission of gravitational waves, these processes
are discussed in more detail in §2.7,
section "Sources of
gravitational waves".
More complex scenarios of collisions and
fusion of black holes
From the point of view of black hole physics, we have so far
assumed that a binary (or multiple) system of compact objects is "pure"
- it does not contain any gas or other bodies. After the
gravitational collapse, the resulting black holes around each
other (around a common center of gravity) continue to orbit for millions of years at distances of
several million kilometers - as a binary system of
compact objects. At first, they have accretion disks
from the remaining gases from the cloud around them (as analyzed above in the section "Accretion
disks around black holes"), but gradually they "consume" them or discard
them in the final stages of rapid circulation. In such an idealized case, the
behavior of a "pure" binary system can be analyzed by
the above scenario, in which only gravitational waves
are emitted ( Fig.4.13-GW) .
However, during cataclysmic explosions of supernovae (and "hypernovae") in
the final stages of massive stars, huge amounts of gases
are ejected, some of which remain
gravitationally bound in the source system. The binary system of
collapsed stars is thus "immersed" in a dense cloud of
gases, at least in the initial stage. If the binary system of two
black holes is initially relatively tight, or friction in a dense
gas cloud soon slows down the rotational speeds of both
components, the final phase of aproching and merging will take
place not in a vacuun, but in an environment with a high gas
content. Perhaps there could be a larger and looser
"common accretion disk" around a tight
binary system..?.. In addition to the massive emission of
gravitational waves, the collision-fusion of compact objects in
such a system can also occur gas particles interacting with photon
radiation, predominantly high-energy - a flash
of gamma rays.
Another possible scenario is that it is a
multiple system of two black holes and in addition a white
dwarf or neutron star, which can supply
a substance (gas) to the binary black hole system, which
interacts with the emission of hard photon radiation during the
collision..?..
In these more complex scenarios of black
hole merging-collision dynamics, the massive emission of
gravitational waves may be accompanied by a weaker emission of a flash
of photon radiation .
Binary system supermassive black
hole
Another way interaction and precipitation compact objects could
be binary supermassive black hole at the center
of galaxies (large black hole at the center
of galaxies, the amount paid to the "quasars"
passage "Mechanism of quasars and active
nuclei of galaxies"). According to galactic astrophysics, they could form
during galaxy collisions in situations where
galaxies penetrate each other with a small impact parameter and
at a lower mutual speed. Black holes in the center of both
galaxies can then form a bound binary system as
they "pass". Massive low-frequency
gravitational waves would form as they circulate,
gradually approach, and eventually fuse these giant black holes .
Collisions and fusion of neutron
stars
After a supernova explosion, the neutron stars formed in the
binary system also initially orbit at great distances (Fig.4.13 -FusionNeutronStars.).
Relatively weak gravitational waves are emitted, carrying away
the kinetic energy of the orbital motion (a).
The neutron stars thus slowly approach each other in a spiral,
the gravitational waves increase and the frequency increases, and
the shape deforms during close orbit (b).
Inevitably, finally they will "collide" and merge (c)
- (the time for which this fusion occurs is
given by the formula (2.82c) derived in §2.7, section "Sources of gravitational waves").
Fig.4.13 -FusionNeutronStars.
a) Two
neutron stars orbiting in a binary system at a great distance
descend very slowly in a spiral and continuously emit
gravitational waves, initially faint. b) As you approach, the intensity and
frequency of gravitational radiation continue to increase. c)
During a close approach,
deformation occurs and eventually a collision and fusion of the
two neutron stars occurs. d) With rapid rotation during fusion, a large
amount of neutron substance can be ejected, which immediately
nucleonizes to form predominantly heavy nuclei, followed by
radioactive decay. e) The resulting object, after the instabilities subside, is either a neutron star or a black hole (according to the remaining mass). This
resulting object will have only a small accretion disk around it (since most of the substance has been ejected away by
the enormous energy released during explosive nucleonization).
During a rotational collision (c)
and the merging of two neutron stars (or a neutron star with a black hole) in a binary system, their elliptical deformation occurs,
during which a large amount of neutron material (d)
is ejected by centrifugal forces. As soon as
this neutron substance breaks out of the grip of the massive
gravity of the neutron star, it becomes highly unstable
and immediately explodes - rapid decompression from a nuclear
density of 1014 g /cm3. Neutrons with weak interaction are promptly
transformed into protons: no ® p+ + e- + n (cf. "Radioactivity beta -" in the treatise "Radioactivity"
in the monograph "Nuclear Physics, ionizing radiation"). The dense mixture of protons and neutrons due to the
strong interaction occurs immediately "nucleonization"
- thrown material is converted to the nucleus of heavy elements (in a manner similar r- process
in supernova), which is accompanied
by explosion and gamma-ray bursts. This
heavy nuclei is then already more slowly radioactively
converted into the nucleus of other heavy elements and
glow intensely with longer afterglow. This process can enrich
the surrounding universe with heavy elements,
similar to the previous supernova explosion (which
formed the participating neutron stars a long time ago). The resulting substance (in the
plasma state) is ejected into the
surrounding space mainly in the opposite cones along the
rotational axis of the system.
Collision-fusion of two white dwarfs or
neutron stars (or neutron stars with a
black hole) thus, besides gravitational
waves, accompanied by a strong optical astronomical effect -
emission of intense flash energy photon radiation, short GRB,
with a gradual fading through gamma from radioactivity, UV
radiation, visible light, to radio waves.
*) Such an astronomically
observed event is sometimes called a "kilonova"
- it can be up to 1000-times more powerful than a normal nova,
especially if observed from the direction of the binary system's
rotation axis. Neutron star fusion, however, is a completely
different process that has nothing to do with a nova explosion.
Although the name kilonova is misleading, in the
astronomical literature it has become...
What final
object obtained after merging of a binary system of
neutron stars (after recovery from
transient instabilities )? This probably
depends mainly on the total weight of the
system. When two massive neutron stars merge, a
"supermassive" neutron star is likely to form
initially, which will be unstable and quickly collapse into a black
hole. The fusion of two lighter neutron stars should
result in the formation of a neutron star. The type and weight of
the resulting object will also depend on the rotational angular
momentum and the amount of ejected substance. For more massive
binary systems, there will be a rapid collapse, so it will be
sufficient to create less ejected neutron masses. If the initial
mass is low, a resultant long-surviving or stable neutron star
can be formed with more ejected material, which can radiate more
intensely and for a long time. So we can expect roughly
inverse relationship between photon emissivity (amount
of radiation emitted in the process) and the initial weight of
the binary system.
In most cases, the collision of ordinary
neutron stars is expected to result in an explosion
accompanied by jets of radiation at various wavelengths ("kilonova").
However, when somewhat more massive neutron
stars collide, they can almost immediately collapse into a black
hole, which quickly eats up almost all of the mass of both
neutron stars. Almost no radiation escapes then from the
collision site - the kilonova is not observed...
This process of collision and fusion of
intermediate mass neutron stars was recently observed for the
first time by detecting gravitational waves and at the
same time electromagnetic waves - §2.7, passage GW170817.
This is "good news" in terms of the diversity
of the chemical evolution of the universe: as this
fusion of neutron stars occurs more frequently, a significant
number of heavy elements are continuously formed. And it
will continue to be formed in the distant future - even
decades and hundreds of billions of years, when no more active
stars will shine and no supernovae explode in space (see §5.5 "The future of the universe"), pairs of neutron stars
will still collide and form hot-matter districts rich in heavier
elements. Perphas there will be something to develop from life
and create other complex structures..?..
How
many heavy elements in the universe are formed by collisions and
fusions of neutron stars ?
The mechanism of nucleonization of the ejected neutron substance
represents an "additional" formation of heavier
elements from the substance, which would otherwise be lost due to
the chemical evolution of the universe, would remain permanently
gravitationally trapped in the neutron star. From the point of
view of the chemical evolution of the universe, it is important
how much matter, formed by heavy elements, is formed during the
collisions and fusion of neutron stars. Nuclear-astrophysical
analyzes show that when two neutron stars of usual masses of
about 1.2-2 M¤
merge, the amount of ejected neutron matter is estimated to be
about 0.1 M¤.
Its nucleonization could create about 0.05 M¤ (=~16000MEarth)
elements heavier than iron - of which about 5MEarth
elements from the lanthanide region, about 10MEarth
elements around gold and platinum and about 2MEarth
heaviest elements around uranium.
To assess the extent
to which neutron star fusion contributes to the overall cosmic nucleogenesis
of heavier elements - along with stellar synthesis
and supernova explosions (cf. §4.1, 4
"Evolution of stars" and §4.2, "Astrophysical significance of supernovae") - it is necessary to estimate how
frequent these events of neutron star fusion in space
are. The initial astronomical data here is the number
(percentage) of close massive binary stars with
masses of 2÷8 M¤,
which explode as supernovae at the end of their lives and lead to
the formation of neutron stars. These neutron stars then orbit
each other, emit gravitational waves, and after a time given by
the formula (2.82c) - ranging from about 100 million to more than
10 billion years - combine to eject a portion of the neutron mass
that nucleonizes to form heavy elements (as
mentioned above). The frequency of occurrence of
this neutron star fusion event is estimated at (200 - 1000) Gpc-3year-1
(perhaps in the space of one cubic gigaparsec, max. a thousand
neutron star fusions per year ...) *).
*) The great uncertainty of the expected
frequency of neutron star fusion is due to the fact that we
do not know well enough the initial parameters of neutron star
orbits in the binary system, nor the density of possible braking
gaseous medium in which neutron stars orbit. If the circulation
took place in a vacuum, the frequency of occurrence would be even
lower.
The resulting
analyzes show that the fusion of neutron stars does
not occur often enough to explain globally *) most
of the observed amount of heavy elements in space. It is an
important component, but the main source of heavy elements is
probably stellar nucleosynthesis and supernova
explosions (as discussed in §4.2,
section "Astrophysical significance of supernovae"), including high-performance fast-rotating
supernovae with a strong magnetic field.
*) Locally, however, it can be
an important resource. If neutron stars collide and fuse in the
vicinity of several hundred light-years from the germinal
gas-dust nebula from which protostars and then stars form, the
emerging stars and the planetary systems around them can be
enriched with heavy elements, more than stars in areas where this
process did not occur. Nuclear-analytical methods of studying the
content of isotopes in meteorites suggest that something like
this happened even before the formation of our solar system ...
Gravitational
"Standard Siren"
The detection of gravitational waves from the fusion of
neutron stars, together with the simultaneous detection of
electromagnetic radiation from their optical counterparts, also
has astrophysical-cosmological significance for the independent
determination of the distance of the respective objects.
This measurement makes it possible to combine the determination
of the distance to the source derived from the gravitational wave
analysis with the receding velocity derived from the redshift
measurement using electromagnetic signal spectrometry. This
approach not requires the use of a cosmic distance
"ladder" (discussed in §4.1, passage "Determining
the distance of cosmic objects - a fundamental condition of
astrophysics"). The
analysis of gravitational + electromagnetic waves can thus be a
measurement of the direct determination of the relationship
distance <--> luminosity in cosmological scales,
without the use of intermediate distances, with sometimes
problematic continuity. Gravitational wave detection is therefore
sometimes metaphorically referred to as a "standard
siren" - a gravitational-wave analogue of the
electromagnetic "standard candle" (cepheids,
Ia supernovae) used to determine large cosmological distances...
Influence
of black holes on the surrounding universe
From the general-relativistic theory of black holes, presented in
§4.2-4.7 (in connection to §3.4-3.6), it might seem that :
n 1. Black holes are locally very
effective "vacuum cleaners" of matter from space -
"bottomless abysses" into which matter falls and disappears irretrievably from space;
n 2. However, black holes have, due to their
compactness, a very small "radius of action" compared
to cosmic scales.
However, the properties of rotating accretion disks around black
holes change these conclusions somewhat :
¨ ad 1. Not all
matter that gets close to a black hole is irretrievably lost. If
the black hole rotates rapidly, then a relatively large portion
of the hot gas descending in the vortex of the accretion disk can
be ejected in a pair of jets along the axis
of rotation. With rapidly rotating black holes, up to 25% of the
mass that enters the accretion can be ejected.
¨ ad 2. The jets of
matter and radiation along the rotational axis of the accretion
disks of supermassive black holes extend to great
distances of
many hundreds of thousand light-years (as
seen, for example, in Fig. 4.29), where they can affect the dynamics of
star formation and galaxy evolution. The effective range of black holes - their "radius of action" - thus increases sharply.
Black holes surrounded by an
accretion disk are no longer just small but bottomless and
mysterious "holes in space", but they become dynamic objects, contributing significantly to the
dramatic events observed in outer space. Overall, we can say that
black holes already have
an important place in astrophysics, and so far all indications are that the
importance of black holes in the further development of knowledge
of the structure and evolution of the universe will continue to
grow.
"Holes" in space
Contemporary relativistic astrophysics has come up with the
concept of four types of "holes" - deep
defects in
the structure of spacetime that could, at least theoretically within GTR, exist in space :
¨ Black holes ,
representing an area
in which attractive gravity is so strong, that they do not "let"
even light out - a horizon
of events
will form around this area. Typical black holes are formed by the
gravitational collapse of sufficiently massive stars (§4.2 "The final stages of stellar
evolution. Gravitational collapse. The formation of a black hole."), they are a kind of
"posthumous" remnants. We have dealt with the theory of
black holes extensively throughout the existing chapter 4 " Black
Holes
".
¨ White holes (hypothetical) ,
which are a certain "opposite" of
black holes. Radiation and matter fly out of the
white hole area into the surrounding space. In §4.4 "Rotating
and Electrically Charged Kerr-Newman Black Holes", we showed the theoretical possibility of how
inside a rotating black hole, matter below the inner horizon
could "miss" the singularity and emerge in another
region of space-time - in "another universe";
this place would appear here as a "white hole".
At the same time, we subjected this possibility to a critical
analysis, which revealed a de facto impossibility
this process. Thus, there are no theoretical or
observational indications for white holes of this kind. However,
the final phase of quantum evaporation of a
hypothetical black "micro-holes" could
appear as a white hole (§4.7 "Quantum
radiation and thermodynamics of black holes").
¨ Gray holes ,
which would be a kind of "transition state" between the
absorbing black hole and the radiating white hole. According to
quantum gravity, every black hole would in fact be "gray"
- on the one hand it would irreversibly absorb
matter and radiation, but on the other hand it would quantumly emit other
radiation (§4.7 "Quantum
radiation and the thermodynamics of black holes ").
¨ Wormholes (hypothetical) ,
representing a kind of "topological shortcuts"
in space through which the particles can pass through and
overcome huge spatial distance between distant places
in the universe, or even penetrate into the "other
universes" (discussed in
§4.4, passage "Wormholes").
4.7. Quantum radiation and thermodynamics of black holes |
4.9.Gravitational collapse - - the biggest catastrophe in nature |
Gravity, black holes and space-time physics : | ||
Gravity in physics | General theory of relativity | Geometry and topology |
Black holes | Relativistic cosmology | Unitary field theory |
Anthropic principle or cosmic God | ||
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