Transcript Accretion

Accretion in astrophysics
Gas falls onto a star or a compact object (neutron star, white dwarf, black holes)
Gravitational potential energy converted into thermal energy
Gas radiates as it heats up, produces a luminosity proportional to the loss of
gravitational energy as it falls down
This “accretion luminosity” is enormous in the case of compact objects
because gas has to lose enormous amount of gravitational potential
energy to fall onto them (E ~ GM2/r, r ~ 0 for a black hole!)
Accretion onto compact objects is most powerful energy source in the Universe,
more powerful than nuclear reactions! Emission typically in X-rays band
It produces active galactic nuclei (AGNS) and QUASARS, the highest luminosity
objects that we know in the Universe (100 times more luminous than galaxies)!
QUASARS are believed to be the result of accretion onto supermassive
black holes (SMBHs) with masses 108-109 Mo ----> huge GM2/R
Galactic compact X-ray sources – from white dwarfs/neutron stars/stellar BHs,
usually in binary system with main sequence star (< 100 Mo) Lx ~ 1037-1038 erg/s
AGNs/ QUASARS
- from SMBHs (> 106 Mo) Lx ~ 1042-1046 erg/s
Ultraluminous X-ray sources (ULXs)– from intermediate mass BHs (100-105 Mo)
Lx ~ 1040 erg/s
Two types of accretion
-spherical---- gas has no angular momentum
-from a disk (accretion disk) --- gas has angular momentum
Accretion disks are the most common mode of accretion in astrophytsics.
Examples
Accretion disk around a protostar – this is essentially the protostellar/protoplanetary disk.
Accretion disk in a binary system made of a neutron star/white dwarf around
a main sequence star (or some other combination). Gas flows from the star to
the compact object (gas infall produces cataclysmic variables or supernovae
type II)
Accretion around a single compact object, e.g. neutron star, stellar black hole or
supermassive black hole
A little digression - What is the “radius” of a black hole?
Stellar black holes form from collapse of very massive stars (M > 8 Mo)
Neither degenerate electron or degenerate neutron gas pressure can
stop the collapse.
Star collapses into a singularity, i.e. a region of space-time with infinite
Density.
Black holes are a prediction of General Relativity.
Black hole is “black” because not even photons can escape
If that is true it means GM/r > 1/2 ve2 = 1/2c2, and so there exists a minimum
radius rs at which photons can orbit the black hole while still being able
to escape
rs = 2GM/c2 = 3km x M/Mo (Schwarzschild radius) rs = 30 km for 10 Mo BH
From studying equation of motion of matter around a black hole in General
Relativity one finds that radius of last stable orbit is 3rs ---> this is the
“radius” of a black hole relevant for accretion since inside this radius matter
has no potential energy in the newtonian sense.
Accretion disks
Suppose matter (gas) moves in a disk around a star or compact object?
Then it means matter is in centrifugal equilibrium.
How can it fall onto the star or compact object?
Answer: there must be a non-conservative force that “extracts” angular
momentum and rotational energy from some of the matter in the disk (can
happen even if the disk conserves angular momentum globally)
Assumption: viscous force (same meaning as friction in mechanics)
Note: not the same as molecular viscosity because macroscopic force
Examples of viscosity
1- spiral waves in disk (gravitational disturbance)
2- turbulence in a clumpy medium = medium made of clouds and
clouds collide anelastically transferring energy and angular momentum
2 – magnetic field can also extract energy and angular momentum from the
gas. Important especially around compact objects because gas is very hot
and ionized (so many charged particles, needed to maintain magnetic field)
Hard to know which mechanism produces viscosity in a given situation,
observations of accretion disks are not detailed enough to study directly
the role of turbulence or the interaction between gas and magnetic field
Simple “heuristic” model is the a-disk model (Shakura & Sunyaev 1977)
ff ~ arvvisc2 ~ aP (last equality holds if vvisc ~ aT)
ff =
viscous stress (=viscous force per unit area), enters both
momentum and energy equation for disk fluid  opposite
sign of thermal pressure force (pulls gas inward)
Since viscosity drives accretion a ~ dM/dt - one determines a by measuring
the accretion rate using observations of accretion disk luminosity/spectrum.
It turns out that typically a ~ 10-1– 1 for accretion disks around compact
objects (e.g. black holes), 10-3 – 10-2 for protostellar disks.
----->
viscous force removes angular momentum locally and
converts kinetic (rotational) into thermal energy
Viscosity does something to
energy as well…
Disk + Viscosity -> Accretion Disk
 Converts rotational energy in to heat
Gravitational
potential energy
Viscosity
 Heat radiated away
(important, otherwise
rising pressure
would stop accretion
again!)
 Energy being lost in heated gas
ultimaltely depends on potential
energy lost (DEth ~ DT ~ hn ~ DEpot
~ Mbh)  typically X-rays
Radiation
 Gas sinks deeper in
the potential well if
it cools efficiently
Accretion luminosity and accretion efficency
Total accretion luminosity does not depend on viscosity or details of radiation
physics it is simply (as for protostellar disks L = G x M x dM/dt /rin
Efficiency = h= L / (dM/dt x c2) = ½ GM / c2 rin
dM/dt x c2 = maximum possible luminosity =
power emitted if all mass converted into
energy
Neutron Star – rin ~ 10 km  h= 0.1
Black Hole - rin = 3rs  h ~ 0.08
But from GR different for non rotating (h= 0.057) and rotating black holes
(h = 0.42)
For nuclear reactions in stars h ~ 0.007 , much smaller!!
Plus all mass participates to accretion in disk, only a fraction to nuclear
burning in stars
Eddington Limit
Radiation coming from the disk produces radiation pressure  the higher the
accretion flow the hotter the disk and the stronger the effect of radiation pressure
Radiation pressure is felt by accreting matter -- eventually radiation pressure
becomes higher than gravitational pull of compact object/star and accretion stops.
Radiation pressure force will be proportional to luminosity (more photons=more
radiation pressure) and luminosity is proportional to accretion rate.
The limiting luminosity at which an object can accrete in “steady state” is:
Ledd =
4pcGMmp
sT = Thomson cross section
sT
Derived for spherical accretion but approximately correct also for accretion disk
(photons emitted mostly perpendicular from the disk)
L > Le still possible (e.g. supernovae type Ia and novae) but only transient and
outflow occurs!
Energy of typical photon = pc
(gas hot and ionized  free
electrons)
The number of photons crossing unit area in unit time at
radius r is:
L/4pr2pc
Number of collisions per electron per unit time= L sT/4pr2pc
Force per electron = rate at which momentum is deposited per
unit time
= Frad = LsT/4pr2pc X p = LsT/4pr2c
For accretion to occur it must be Frad < Fgrav
Fgrav (gravitational force per electron) = GMmp/r2
(protons and electrons coupled by Coulomb interaction so
gravitational force communicated via protons)
Obtain Ledd by setting Fgrav=Frad.
Unique phenomena produced by accretion in binaries
Nova – white dwarf + main sequence
star
outbursts of luminosity produced by
thermonuclear burning of hydrogen
rich accreted material
systems brightens for about a month
with L >> Ledd
Enova ~ 1046 erg
Supernova Type Ia
White dwarf + main sequence star but much stronger outburst because 1 Mo of
helium/carbon is ignited and synthesized into iron group elements
Esup ~ 1051 – 1052 erg.
Small range of luminosities, standard candles important for cosmology!
How do we know that black holes exist?
How can we prove existence? Example: measure velocity of gas or stars on
the last stable orbit because GR makes accurate predictions on the equations
of motions that are valid only for black holes
Unfortunately no instrument has enough resolution to take measurements so
close to a BH.
In general, we think that black holes exist because gas accretion onto black holes
is the only way to explain X-ray luminosity of the most powerful sources that we
see in the Universe, from some Galactic X-ray sources to AGNs and QUASARS in
distant galaxies
AGNs and QUASARS like powered by supermassive black holes (SMBHs). These
were probably born in the early Universe from collapse of Supermassive Stars
(> 100 Mo) and then accrete gas from the galaxy in which they were born:
connection between galaxy formation and supermassive black holes, hot topic
of current research!
AGNs as indirect evidence for SMBHs
Active Galactic Nuclei (AGNs) are some of the most powerful energy
outbursts in the Universe (X-ray, radio, optical)
The most powerful AGNs, distant QUASARS, have X-ray luminosities
up to 1046 erg/s (>100 times brighter than our Milky Way)
A nearby QUASAR
Associated with galaxies, powered
by a central SMBH
M87
Radio jets produced by electrons accelerated by strong magnetic field
produced in accretion disk (synchrotron radiation)
FIRST QUASAR DISCOVERED in 1964, 3C 273
HOST GALAXY OF 3C273
AGNs: indirect evidence for SMBHs
Magnetic field entangles and
accelerates part of the infalling
gas into powerful jets
Accretion disk
~0.01 pc
Now do the SMBHs feed?
With large reservoirs of gas in galaxies at kpc scales
(108-109 Mo, same mass as SMBHs!)
How does the gas get to the SMBHs that sit at the
center?
Merging galaxies are often associated with AGNs……
X - rays
Evolution of the gas component in major
merger
Accretion disks: structure equations
One can solve the a system of structure equations for accretion disks around
compact object assuming (1) steady state, (2) neglecting gas infall
(no protostellar envelope in this case although gas inflow may occur as gas
comes from the donor star in a binary system), (3) thin axisymmetric and
(4) viscosity is the only source of heating in the disk - determines the disk
temperature together with cooling processes and pressure law.
Self-gravity neglected for AGN/X-ray binaries accretion discs, not necessarily
for protostellar disks (self-gravity can be coupled with viscosity there).
Equations to solve; momentum (Euler + viscosity), continuity, equation of state
(e.g. polytropic), energy equation (gives luminosity, source is viscosity rather
than nuclear reactions as in the case of stars), energy transport equation (e.g.
diffusion equation in optically thick regions).
In addition auxiliary equations for viscosity law and for opacity law.
Final result; M (mass of compact object) and dM/dt (accretion rate of gas from
disk to star, related to viscous mass transport, constant by assumption of
steady-state) determine completely disk structure (in the case of stars was
just M).
The full solution of the disk structure equation shows the the accretion disk can
be divided into three regions;
(1) an outer region, a radius r >> rI, rI = inner radius of the disk, where
gas pressure dominates over radiation pressure and in which the opacity is controlled
by free-free absorption (inverse brehmsstrahlung)
(2) a middle region, at small r, in which gas pressure dominates radiation pressure
but the opacity is mainly due to electron (Thomson) scattering
(3) an inner region, at very small r, r ~ rI, at which radiation pressure dominates
gas pressure and electron scattering dominates absorption in the opacity
Important: at the inner radius of the disk rI , i.e. closest to the compact object,
most of the gravitational energy is released -- most of the viscous heating is
generated - most of the radiation is emitted
Therefore the inner region is what one needs to study in order to understand
the observed spectrum of an accretion disk. For this the steady state solution
gives the disk interior temperature as (note the dependence on a);
T = (5 x 107 K)(aM) -1/4 r
– 3/8
Spectrum of accretion disk
To compute the spectrum (power/luminosity per frequency) one needs to take into
account that the different regions of the accretion disk will produce a different
specific flux Fn depending on the local properties, i.e.;
(1) Optical depth – optically thick vs. optically thin regions
(2) Source of opacity (in optically thick regions). Scattering or absorption, which scattering
or absorption process?
In optically thick regions (no matter the opacity source) one can use the usual
diffusion approximation for vertical radiation transport to calculate F(r,z).
replacing differentials with finite differences and integrating on z one obtains
flux at the surface, i.e F(r,z = h) = F(r)
F(r) ~ acT4/t ~ acT4/<k>S
At sufficiently high altitude above the disk midplane, quite soon if the disk is thin, the disk
will become optically thin. In a thin disk the transition will be sharp - the surface of
the disk emits as a blackbody. So the emitted flux Fe will be:
Fe = aTs4,
where Ts (surface temperature)= [4F(r)/a]1/4
In optically thin regions (t < 1 in an entire column above the midplane –
this happens at disk inner and outer edge for example)
the emitted flux will be equal to the emergent flux and will be equal to;
F(r) = Fe ~ hL(r,T)
L(r, T) average photon emissivity, depends
on specific radiative process (erg s-1 cm-3)
But middle and inner region of the disk belongs to a third regime; disk is
optically thick (so diffusion equation ok for radiation transport) but opacity is
mostly due to scattering of photons rather than absorption -- cannot assume
blackbody for emergent flux, valid only when absorption dominates!
In this case, the emergent flux is that of a “modified blackbody”. Scattering
near the surface increases absorption probability before photon can escape
at the surface so that the intensity goes down compared to blackbody case.
The specific intensity is given by:
In ~ jnff/knffr(knff/kes) ~ Bn(Ts)(knff/kes)1/2
Note that absorption opacity is due to free-free (and emission as well) in this
region (high midplane temperature, gas is ionized -> see expression for Ts).
Scattering is due to electron scattering instead
The total emitted flux follows from In and is given by;
(*) Fe ~ (6.2 x 1019 erg cm2 s -1)r1/2Ts9/4
(<kff>
<< kes )
rather than Fe ~ aTs4 (blackbody)
(<kff> >> kes)
<kff> = Rosseland mean absorption opacity
Using Rosseland mean opacities and Fe = sTeff4 (Stefan-Boltzmann’s law)
one obtains the relation between the emission temperature and the
blackbody effective temperature.
Teff ~ Ts(<kff>/kes)1/8
rather than Teff ~ Ts
Ts = surface temperature, characterizes the energy of emitted photons
The effect of scattering is thus to increase the mean energy of the emergent
photons, kBTs, above the value it would have been if the radiation occurred in
thermodynamical equilibrium (i.e. the blackbody case).
One can then use equation (*) in combination with the structure equation that
relates the emergent flux to the mass (M) and mass accretion flow (dM/dt)
to express the surface temperature Ts as a function of M and dM/dt;
Ts = (2 x 109 K) a2/9(M/Mo)-10/9( (dM/dt)17)8/9(r/rs)-17/9 f8/9
rs = Schwarzschild radius
(dM/dt)17= mass accretion rate measured in units of 1017 g s-1 ~ 10-9 Mo/yr
f = 1 – (6/r)1/2
For a blackbody (see 14.5.38) the temperature constant would be much lower
~5 x 107 K --- the photons emitted have higher energy (“harder”) than
if the disk radiated as a true blackbody. Photons are “hard” X rays, i.e. X-rays
with very high energies (10-100 keV, more for SMBHs).
This is a very good feature because it allows to distinguish emission by accretion
disks around compact objects from other astrophysical objects that produce
lower energy “softer” X-rays (e.g. galaxy clusters, protostellar outflows, emission
at 0.1-1 keV)
The total spectrum of the accretion disk emission is the superposition of the
flux coming from the different regions of the disk but, as anticipated, the
highest flux (so most of the luminosity) is produced by the middle/inner region
that gives rise to the modified blackbody shape (scattering dominates).
The outer region is optically thick and absorption dominated and is well
described by a blackbody spectrum.
The innermost region is optically thin and the emission is dominated by free-free
emission and inverse Compton scattering – inverse Compton is the process by
which photons gain energy by scattering off electrons at very high speed and
produces the high energy tail in the spectrum (hottest region).