Accretion in astrophysics

1
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!
• 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 ----gt
  huge GM2/R
• Galactic compact X-ray sources from white
  dwarfs/neutron stars/stellar BHs,
• usually in binary system with main sequence star
  (lt 100 Mo) Lx 1037-1038 erg/s
• AGNs/ QUASARS - from SMBHs (gt 106 Mo) Lx
  1042-1046 erg/s

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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/proto-
• planetary disk (see previous lectures).
• 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 compact object, e.g. neutron
  star, stellar black hole or
• supermassive black hole

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A little digression -
What is the radius of a black hole?
Stellar black holes form from collapse of very
massive stars (M gt 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 and infinite gravitational
force. 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 gt 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
GM/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 ---gt this is the radius of
a black hole relevant for accretion since inside
this radius matter has no potential energy in
the newtonian sense.
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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 orbital
energy from the matter in the disk Assumption
viscous force (same meaning as friction) Examples
of viscosity 1- spiral waves generated by
gravitational instability (recall
protostellar disks) 2- turbulence in a clumpy
medium medium made of clouds and clouds collide
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)
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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)
f?? ???vvisc2 ?P (last equality
holds if vvisc ?aT) f?? viscous
stress (viscous force per unit area), enters
both momentum and energy equation for disk
fluid Since viscosity drives accretion ?
dM/dt -? one determines ? by measuring the
accretion rate using observations of accretion
disk luminosity/spectrum. It turns out that
typically ? 10-1 1 for accretion disks around
compact Objects, 10-3 10-2 for protostellar
disks. Recall viscous force removes angular
momentum and heats up the gas due to
energy conservation
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Accretion disks structure equations
As for stars, 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 disk and (4) viscosity is the only
source of heating in the disk -? determines the
disk temperature together with cooling processes
and pressure law 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).
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• The full solution of the disk structure equation
  shows the the accretion disk can
• be divided into three regions
• an outer region, a radius r gtgt 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

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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 F? depending on the local
  properties, i.e.
• 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/? acT4/lt?gt?
• 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

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In optically thin regions (? lt 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 h?(r,T)
?(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 I?
j?ff/??ff?(??ff/?es) B?(Ts)(??ff/?es)1/2 Note
that absorption opacity is due to free-free (and
emission as well) in this region (high midplane
temperature, gas is ionized -gt see expression for
Ts). Scattering is due to electron scattering
instead
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The total emitted flux follows from I? and is
given by () Fe (6.2 x 1019 erg cm2 s
-1)?1/2Ts9/4 rather than Fe aTs4
(blackbody) (lt?ffgt ltlt ??es
) (lt?ffgt
gtgt??es) lt?ffgt Rosseland mean absorption
opacity Using Rosseland mean opacities and Fe
?Teff4 (Stefan-Boltzmanns law) one obtains the
relation between the emission temperature and
the blackbody effective temperature.
Teff Ts(lt?ffgt/?es)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).
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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) ?2/9(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)
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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).
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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 ?? 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 ??? 0.1 Black
Hole - rin 3rs ? ? 0.08 But from GR
different for rotating (? 0.057) and
non-rotating black holes (? 0.42) For nuclear
reactions in stars ? 0.007 , much smaller!!
Plus all mass participates to accretion in disk,
only a fraction to nuclear burning in stars
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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
photonsmore radiation pressure) and luminosity
is proportional to accretion rate. The limiting
luminosity at which an object can accrete in
steady state is
4pcGMmp
??? Thomson cross section
Ledd
?T
Derived for spherical accretion but approximately
correct also for accretion disk (photons emitted
mostly perpendicular from the disk) L gt Le still
possible (e.g. supernovae type Ia and novae) but
only transient and outflow occurs!
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Energy of typical photon pc The number of
photons crossing unit area in unit time at radius
r is L/4?r2pc Number of collisions per
electron per unit time L ?T/4?r2pc Force per
electron rate at which momentum is deposited
per unit time Frad L?T/4?r2pc X p
L?T/4?r2c For accretion to occur it must be Frad
lt 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
FgravFrad.
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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 gtgt 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!
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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 (gt
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!
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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 (gt100 times brighter than our Milky
Way) Associated with galaxies, powered by a
central SMBH Radio jets produced by electrons
accelerated by strong magnetic field produced in
accretion disk (synchrotron radiation)
A nearby QUASAR M87
FIRST QUASAR DISCOVERED in 1964, 3C 273
HOST GALAXY OF 3C273
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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
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AGNs indirect evidence for SMBHs
Magnetic field entangles and accelerates part of
the infalling gas into a powerful jets
Accretion disk
0.01 pc
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Evolution of the gas component in major merger