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.