AST Cosmology and extragalactic astronomy. Lecture 20. Black Holes Part II

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: T r mass accretion rate onto BH M is mass of central BH. An interesting implication is that accretion disks are hotter for lower mass black holes! (see board) 3

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

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). From Mineo et al. 2012 Normalization of different curves related to total star formation rate in galaxy. Shape similar. HMXB appears to cut off at a few 10 40 erg/s X-ray binaries with LX >10 39 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

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 Stellar kinematics constrains mass of central region at ~ MBH~4x10 6 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. R Model observed dispersion with different models for gravitational 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

`Virial Relationship /`Reverberation Mapping Reverberation mapping uses the fact that time changes in (recombination) lineflux 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) lineflux follow those of the continuum, but with a delay. 26

`Virial Relationship /`Reverberation Mapping Reverberation mapping uses the fact that time changes in (recombination) lineflux 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) lineflux follow those of the continuum, but with a delay. 27

`Virial Relationship /`Reverberation Mapping Reverberation mapping uses the fact that time changes in (recombination) lineflux 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) lineflux 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) lineflux follow those of the continuum, but with a delay. 28

`Virial Relationship /`Reverberation Mapping Reverberation mapping uses the fact that time changes in (recombination) lineflux 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) lineflux 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) lineflux 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) lineflux 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) lineflux follow those of the continuum, but with a delay. 3. Ionization state changes in`broad line clouds boosts recombination emission. R continuum source Delay time is dominated by added light travel time 29

`Virial Relationship /`Reverberation Mapping Reverberation mapping uses the fact that time changes in (recombination) lineflux follow those of the continuum, but with a delay. 3. Ionization state changes in`broad line clouds boosts recombination emission. R continuum source Delay time is dominated by added light travel time 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/Ledd Kollmeier et al. 2006 Kollmeier et al. 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 10 8-10 10 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? There are no accurate BH mass determinations below MBH~ 10 6 Msun. Recall from the X-ray binaries, there is no evidence for BHs with MBH>10 2 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 formation of super-massive black holes (MBH>10 6 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

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 10 13 L and hosts a black hole with a mass of 2 10 9 M (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 So-called `direct-collapse-black-hole scenario, a 10 4-10 6 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