AST4320 - Cosmology and extragalactic astronomy
Lecture 20
Black Holes Part II
1 AST4320 - Cosmology and extragalactic astronomy
Outline: Black Holes Part II
• Gas accretion disks around black holes, and their spectra.
• Eddington Accretion
• Super Massive Black Holes (SMBHs) & Active Galactic Nuclei (AGN)
• Origin of SMBHs
2 Properties of Thin Accretion Disks around Black Holes
Disk is geometrically thin. Assume it is optically thick to radiation. This assumption corresponds to assuming that the gas radiates like a black-body.
We can showed that gas on circular orbits slowly moving inward gives rise to temperature gradient:
mass accretion rate onto BH M is mass of central BH. T An interesting implication is that accretion disks are hotter for lower mass black holes! (see board) r
3 Properties of Thin Accretion Disks around Black Holes
Disk is geometrically thin. Assume it is optically thick to radiation. This assumption corresponds to assuming that the gas radiates like a black-body.
We can showed that gas on circular orbits slowly moving inward gives rise to temperature gradient:
mass accretion rate onto BH M is mass of central BH. T An interesting implication is that accretion disks are hotter for lower mass black holes! (see notes) r
4 Properties of Thin Accretion Disks around Black Holes
With the temperature profile determined, we can predict the spectrum emerging from an accretion disk [see board]
R+dR T(R)
R
5 Properties of Thin Accretion Disks around Black Holes
With the temperature profile determined, we can predict the spectrum emerging from an accretion disk [see notes]
Rout
Rin
6 Properties of Thin Accretion Disks around Black Holes
With the temperature profile determined, we can predict the spectrum emerging from an accretion disk [see notes]
log
log v
7 Properties of Thin Accretion Disks around Black Holes
With the temperature profile determined, we can predict the spectrum emerging from an accretion disk [see notes]
log
log v Temperature of gas at innermost radius of accretion disk much higher than that of stellar atmosphere, which is why accreting black holes emit well into X-rays! 8 Properties of Thin Accretion Disks around Black Holes
With the temperature profile determined, we can predict the spectrum emerging from an accretion disk [see notes]
log
log v Temperature of gas at innermost radius of accretion disk much higher than that of stellar atmosphere, which is why accreting black holes emit well into X-rays! 9 Inner Most Stable Orbit around Black Holes
In Newtonian gravity, particles can be in a stable orbit around the BH at any radius R > Rs
However, in general relativity particles cannot be in stable orbits at radii R < 3 Rs. This radius is inner `ISCO’ [Innermost Stable Circular Orbit] radius
RISCO depends on black hole spin: a=0 [no spin], a=1 [maximal spin]
At R < RISCO gas flows in without dissipating energy.
10 Maximum Luminosity: The Eddington Limit
We have characterized the spectrum emerging from an accretion disk.
We derived that
The total luminosity would then be
As we increase m-dot, we increase the luminosity. However, the increased luminosity exert an outward pressure which prevents mass from coming in.
Radiation pressure sets a maximum mass-accretion rate, and hence luminosity. These rates are known as the Eddington luminosity/accretion rate.
The Eddington luminosity is given by [board]
11 Maximum Luminosity: The Eddington Limit
We have characterized the spectrum emerging from an accretion disk.
We derived that
The total luminosity would then be
As we increase m-dot, we increase the luminosity. However, the increased luminosity exert an outward pressure which prevents mass from coming in.
Radiation pressure sets a maximum mass-accretion rate, and hence luminosity. These rates are known as the Eddington luminosity.
The Eddington luminosity is given by [notes]
Compare with
12 Maximum Luminosity: The Eddington Limit
The Eddington luminosity is given by
Solar mass black holes have hottest accretion disks, expected to emit the bulk of their accretion luminosity in X-rays.
13 Maximum Luminosity: The Eddington Limit
The Eddington luminosity is given by
Solar mass black holes have hottest accretion disks, expected to emit the bulk of their accretion luminosity in X-rays.
X-ray picture of Milky Way. Red: low E X-ray. Blue: high E X-rays. Green: intermediate All X-ray point sources correspond to accreting compact objects. 14 Maximum Luminosity: The Eddington Limit
The Eddington luminosity is given by
Solar mass black holes have hottest accretion disks, expected to emit the bulk of their accretion luminosity in X-rays.
External galaxies M83 (left) and NGC 4697 (right)
15 Maximum Luminosity: The Eddington Limit
The Eddington luminosity is given by
Solar mass black holes have hottest accretion disks, expected to emit the bulk of their accretion luminosity in X-rays.
`low’ mass X-ray binaries, Mdonor < 5Msun `high’ mass X-ray binaries, Mdonor > 5Msun
Number counts/X-ray luminosity function 16 Maximum Luminosity: The Eddington Limit
The Eddington luminosity is given by
Solar mass black holes have hottest accretion disks, expected to emit the bulk of their accretion luminosity in X-rays.
`low’ mass X-ray binaries, Mdonor < 5Msun `high’ mass X-ray binaries, Mdonor > 5Msun
Luminosity functions truncated at Ledd for few solar mass BH 17 Maximum Luminosity: The Eddington Limit
The Eddington luminosity is given by Most recent high-mass X-ray binary (HMXB) luminosity function (each color, represents different galaxy).
Normalization of different curves related From Mineo et al. 2012 to total star formation rate in galaxy.
Shape similar. HMXB appears to cut off at a few 1040 erg/s
X-ray binaries with LX >1039 erg/s are called `ultraluminous’ X-ray sources (ULXs)
Eddington accretion of MBH > 10 Msun, or `Super-Eddington’ accretion?
18 Maximum Luminosity: The Eddington Limit
The Eddington luminosity is given by
X-ray binaries trace gas accretion onto black holes. Most luminous ULXs seem to trace black holes with masses of ~ 100 Msun
These black hole masses are tiny compared to black holes masses that appear to power active galactic nuclei (AGN).
Througout I will also refer to AGN as `quasars’.
Quasar: `Quasi Stellar Radio Objects’
`stellar’ because they appeared compact/unresolved like stars. `quasi’ because they contain broad emission lines, unlike stars.
19 Maximum Luminosity: The Eddington Limit
The Eddington luminosity is given by
Quasar bolometric luminosity (incl. all frequencies) function.
From Hopkins et al. 2007
log L/Lsun 20 Maximum Luminosity: The Eddington Limit
The Eddington luminosity is given by
Quasar bolometric luminosity (incl. all frequencies) function.
From Hopkins et al. 2007
log L/Lsun 20 Maximum Luminosity: The Eddington Limit
The Eddington luminosity is given by
Quasar bolometric luminosity (incl. all frequencies) function.
From Hopkins et al. 2007
log L/Lsun 20 Independent BH Mass Constraints.
Quasar luminosities indicate of black holes masses up to 10 billion solar mass.
Are there other ways to probe black hole masses?
21 Independent BH Mass Constraints.
Quasar luminosities indicate of black holes masses up to 10 billion solar mass.
Are there other ways to probe black hole masses?
Yes. • stellar & gas kinematics • `reverberation mapping.
21 Independent BH Mass Constraints.
Observed (in Infrared) stellar kinematics around the center of our Milky-Way
6 Stellar kinematics constrains mass of central region at ~ MBH~4x10 Msun 22 Independent BH Mass Constraints.
In nearby galaxies, stellar kinematics can also be studied in detail.
Carefully measure stellar velocity dispersion as a function of R.
Model observed dispersion with different models for gravitational R potential.
See if you need a massive point source.
23 Independent BH Mass Constraints.
In nearby galaxies, stellar kinematics can also be studied in detail.
Example of measured velocity dispersion at three R. Black solid line + triangles are models that include massive black hole. Favored by data.
24 Independent BH Mass Constraints.
In nearby galaxies, stellar kinematics can also be studied in detail.
Example of measured velocity dispersion at three R. Black solid line + triangles are models that include massive black hole. Favored by data.
24 `Virial Relationship’/`Reverberation Mapping’
Reverberation mapping uses the fact that time changes in (recombination) line- flux follow those of the continuum, but with a delay.
From Peterson. 2001
25 `Virial Relationship’/`Reverberation Mapping’
Reverberation mapping uses the fact that time changes in (recombination) line- flux follow those of the continuum, but with a delay.
26 `Virial Relationship’/`Reverberation Mapping’
Reverberation mapping uses the fact that time changes in (recombination) line- flux follow those of the continuum, but with a delay.
continuum source
26 `Virial Relationship’/`Reverberation Mapping’
Reverberation mapping uses the fact that time changes in (recombination) line- flux follow those of the continuum, but with a delay.
1. Continuum flux has variable luminosity which we detect directly.
continuum source
26 `Virial Relationship’/`Reverberation Mapping’
Reverberation mapping uses the fact that time changes in (recombination) line- flux follow those of the continuum, but with a delay.
27 `Virial Relationship’/`Reverberation Mapping’
Reverberation mapping uses the fact that time changes in (recombination) line- flux follow those of the continuum, but with a delay.
continuum source
27 `Virial Relationship’/`Reverberation Mapping’
Reverberation mapping uses the fact that time changes in (recombination) line- flux follow those of the continuum, but with a delay. 2. Variation in continuum flux is also present in variations in ionizing flux. Gas in so-called `broad line’ clouds responds to fluctuations in ionizing flux via a change in ionization state.
continuum source
27 `Virial Relationship’/`Reverberation Mapping’
Reverberation mapping uses the fact that time changes in (recombination) line- flux follow those of the continuum, but with a delay.
28 `Virial Relationship’/`Reverberation Mapping’
Reverberation mapping uses the fact that time changes in (recombination) line- flux follow those of the continuum, but with a delay.
continuum source
28 `Virial Relationship’/`Reverberation Mapping’
Reverberation mapping uses the fact that time changes in (recombination) line- flux follow those of the continuum, but with a delay.
3. Ionization state changes in`broad line’ clouds boosts recombination emission.
continuum source
28 `Virial Relationship’/`Reverberation Mapping’
Reverberation mapping uses the fact that time changes in (recombination) line- flux follow those of the continuum, but with a delay.
3. Ionization state changes in`broad line’ clouds boosts recombination emission.
Note: at the high densities in the broad line clouds, and intense radiation field near the accretion disk, photoionization + recombination time very short.
continuum source
28 `Virial Relationship’/`Reverberation Mapping’
Reverberation mapping uses the fact that time changes in (recombination) line- flux follow those of the continuum, but with a delay.
R
29 `Virial Relationship’/`Reverberation Mapping’
Reverberation mapping uses the fact that time changes in (recombination) line- flux follow those of the continuum, but with a delay.
R
continuum source
29 `Virial Relationship’/`Reverberation Mapping’
Reverberation mapping uses the fact that time changes in (recombination) line- flux follow those of the continuum, but with a delay.
3. Ionization state changes in`broad line’ clouds boosts recombination emission.
R
continuum source
29 `Virial Relationship’/`Reverberation Mapping’
Reverberation mapping uses the fact that time changes in (recombination) line- flux follow those of the continuum, but with a delay.
3. Ionization state changes in`broad line’ clouds boosts recombination emission.
R
Delay time is dominated by added light travel time continuum source
29 `Virial Relationship’/`Reverberation Mapping’
Reverberation mapping uses the fact that time changes in (recombination) line- flux follow those of the continuum, but with a delay.
3. Ionization state changes in`broad line’ clouds boosts recombination emission.
R
Delay time is dominated by added light travel time continuum source
R is characteristic distance to broad line clouds. 29 `Virial Relationship’/`Reverberation Mapping’
Mass of black hole can be inferred from
Where Delta V denotes the line width of the line used to measure the time delay. R is characteristic distance to broad line clouds (inferred from delay), f is a factor of order unity, which depends on detailed geometry of broad-line region.
These mass estimates are (generally) consistent with those obtained from e.g. stellar kinematics.
30 Eddington Ratios
The Eddington luminosity is given by If we measure luminosity L, and independently infer MBH, then we can infer the Eddington ratio: L/L edd
KollmeierKollmeier et et al. al. 2006 2006
Number sample of most luminous quasars
log L/Ledd 31 Eddington Ratios
The Eddington luminosity is given by If we measure luminosity L, and independently infer MBH, then we can infer the Eddington ratio: L/L edd
KollmeierKollmeier et et al. al. 2006 2006
Number sample of most luminous quasars
log L/Ledd 31 Eddington Ratios
The Eddington luminosity is given by
Kollmeier et al. 2006
Number sample of most luminous quasars
The most luminous quasars are powered by 108-1010 solar mass black holes accreting close to their Eddington rate.
log L/Ledd 32 Eddington Ratios
The Eddington luminosity is given by
Kollmeier et al. 2006
Number sample of most luminous quasars
The most luminous quasars are powered by 108-1010 solar mass black holes accreting close to their Eddington rate.
log L/Ledd 32 The MBH–σ Relation
Mass of black holes correlates with velocity dispersion of stars in bulges of galaxies.
33 The MBH–σ Relation
Mass of black holes correlates with velocity dispersion of stars in bulges of galaxies.
34 The MBH–σ Relation
Mass of black holes correlates with velocity dispersion of stars in bulges of galaxies.
Origin of this relation likely linked to the formation & co-evolution of the galaxies and their supermassive black holes.
35 Where are the Intermediate Mass Black Holes?
6 There are no accurate BH mass determinations below MBH~ 10 Msun.
2 Recall from the X-ray binaries, there is no evidence for BHs with MBH>10 Msun. Little is known about black holes at intermediate masses. The black holes are referred to as `intermediate mass black holes’ (IMBHs).
Understanding IMBHs is likely connected to understanding the 6 formation of super-massive black holes (MBH>10 Msun.) 36 The Origin of Super Massive Black Holes is still unclear.
Could super massive black holes have grown from stellar seed black holes via gas accretion?
The Eddington luminosity was the maximum luminosity emerging from an accreting disk before radiation pressure halts inflow of gas.
Recall that the luminosity from the accretion disk is powered by mass inflow rate, i.e.
The total binding energy that any proton/atom must radiate away before reaching RISCO equals [board]
37 The Origin of Super Massive Black Holes is still unclear.
Could super massive black holes have grown from stellar seed black holes via gas accretion?
The Eddington luminosity was the maximum luminosity emerging from an accreting disk before radiation pressure halts inflow of gas.
Recall that the luminosity from the accretion disk is powered by mass inflow rate, i.e.
The total binding energy that any proton/atom must radiate away before reaching RISCO equals [notes]
The total accretion luminosity is then
38 Maximum Luminosity: The Eddington Limit
The growth of the mass of a black hole accretion at Eddington luminosity grows by a factor of e(=2.72....) each 4.5e7 yrs [see board].
Suppose we start with a 100 Msun black hole. Growth to 1 billion solar masses, would require ~ 0.72 Gyr << age of Universe today.
But......
1. should we not see the intermediate stages of formation [i.e. an actively accreting 1e4, 1e5, 1e6 IMBHs] (?)
2. super massive black holes existed at z>7, when the Universe was ~0.77 Gyr old.
39 The Most Distant z=7 Quasar
.....ULAS J1120+0641 has a luminosity of 6.3 × 1013L⊙ and hosts a black hole with a mass of 2 × 109M⊙ (where L⊙ and M⊙ are the luminosity and mass of the Sun)......
40 High-z vs Low-z Quasars
Red: stacked spectrum z=6 quasars. Black: stacked spectrum low-z quasars.
Suggests that whatever process is making SMBHs operates fast, and seems not to know much about age of Universe! 41 High-z vs Low-z Quasars
Black: z=7 quasar. Red: stacked spectrum low-z (z=2.3-2.6)quasars.
Mortlock et al. 2011
Suggests that whatever process is making SMBHs operates fast, and seems not to know much about age of Universe! 42 Origin of SMBHs
Formation of super massive black holes is a very active research field, with many open questions.
credit: Regan & Haehnelt 2009
43 Origin of SMBHs
Formation of super massive black holes is a very active research field, with many open questions.
credit: Regan & Haehnelt 2009
43 Origin of SMBHs
Formation of super massive black holes is a very active research field, with many open questions.
credit: Regan & Haehnelt 2009
4 6 So-called `direct-collapse-black-hole’ scenario, a 10 -10 msun gas cloud collapses directly into a super massive black hole (no intermediate star formation) 44 Origin of SMBHs
Formation of super massive black holes is a very active research field, with many open questions.
credit: Regan & Haehnelt 2009
4 6 So-called `direct-collapse-black-hole’ scenario, a 10 -10 msun gas cloud collapses directly into a super massive black hole (no intermediate star formation) 44 Origin of SMBHs
Other mechanisms have been proposed
Growth of stellar mass seeds: continuous accretion at Eddington rate occurs in rare cases. Possible especially at higher-z because enhanced density of DM halos, merger rates etc.
(SMBHs are rare)
Super-Eddington accretion?
45