The central engine: energetics and demographics

The central engine: energetics and demographics Overview Global properties Total energy output Efficiency Mass Energy and black-hole mass densities Formation scenarios Determining BH masses from observations Demographics Questions AGN-4: HR-2007 p. 1 Energy output Luminous quasar: Lifetime: Total energy output: AGN-4: HR-2007 p. 2 1

Variability and Size of Central engine Higher ν continuum varies faster than lower ν continuum Lower luminosity objects vary more rapidly than do higher luminosity objects Variability observed on many timescales (Δ T : seconds to years) Light-travel time: size R < c (Δ T/3 hours) < 10-4 pc (see K8.1.4) EXO-sat observations of the 1.2-10 kev flux from the Type 1 Seyfert galaxy MCG 6-30-15 (Krolik et al. 1993) No obvious preferred timescale A power law spectra of frequencies P(f) f b with 1<b<2 AGN-4: HR-2007 p. 3 Efficiency of energy generation I Ratio of the two times spend in the medium Due to large optical depth Increased time spend in medium c/(1+τ c ) Restriction on source size based on light variations Mass involved in emission M 4/3 π R 3 n m p With n: number density and m p : proton mass Luminosity L = η M c 2 / Δ t, with η<1 energy conversion efficiency Using τ ν =nσ Τ R we get (note mistake in KN, see Fabian 1979): AGN-4: HR-2007 p. 4 2

Energy generation II Potential energy U of mass m a distance r from a central mass M U = G m M /r Rate at which U can be converted Event horizon for a non-rotation blackhole Schwarzschild radius R s AGN-4: HR-2007 p. 5 Energy Generation II Ignoring relativistic effects, energy available for particle mass m to fall to 5 R_S (where most of optical/uv emission comes from: Compare to derivation from light variations Other energy sources not very efficient: Chemical reactions: Nuclear reactions: Binding energy per nucleon Conclusion: Most likely energy source of AGN: accretion in relativistic potential AGN-4: HR-2007 p. 6 3

Mass of central object Outward momentum flux Where L is the luminosity of the source Outward radiation force (*) Inward gravitation force (**) Eddington limit (*) = (**) Eddington luminosity/mass M E 10 8 L 46 M 0 AGN-4: HR-2007 p. 7 Eddington accretion rate So the energy requirement is not the major issue But Angular moment is! Angular moment per unit mass L/m = (GMr) 1/2 Consider A particle at r =10 kpc in a galaxy with M= 10 11 M 0 A particle at 0.01 pc of a 10 7 M 0 black hole Due to viscous forces a fraction of 10 5 in angular momentum needs to be lost! AGN-4: HR-2007 p. 8 4

Last week Luminous quasar: Lifetime: Total energy output: Efficiency conversion mass -> energy ~10% Eddington accretion rate Today: -- Energy and black-hole mass densities Formation scenarios Determining BH masses from observations Demographics Note: bol.com AGN-4: HR-2007 p. 9 Mean energy density of Quasar light I Consider QSO luminosity function QSO LF(L,z, ) is the comoving space density of qsos as a function of z Note 1. Bright quasars are rare 2. Locally quasars are rare Croom et al. 2004, MNRAS, Volume 349, pp. 1397 KN 7.2 AGN-4: HR-2007 p. 10 5

3. Space density luminous quasars peak at z 2-3 AGN-4: HR-2007 p. 11 Mean energy density of Quasar light - Soltan A., 1982, MNRAS, 200, 115--122 - Chokshi A., Turner E.L., 1992, MNRAS, 259, 421--424 (CT92) Energy density of quasar light Here t is cosmic time, and is the luminosity function of quasars CT92 take, where, and With,and follows from for Result: For comparison: - - 6

To note Detailed calculation Photon energy diminishes by factor (1+z) Observed ν emitted at ν(1+z) Bolometric corrections Extrapolating to faint levels using a shape of the (redshift dependent) luminosity function Uses updated qso LF Dust and neutral gas absorption In hard X-ray band AGN dominant source of photons. AGN-4: HR-2007 p. 13 mass density in black holes of Mean luminosity in galaxies: Ratio of mass in relic black holes to luminosity in galaxies Average mass in relic BH per galaxy if η is low (e.g. Non-gravitational) an unrealistic large fraction of the galaxy mass involved in providing energy to have AGN radiate Recent determination based on SDSS gives similar numbers - Yu & Tremaine 2002, MNRAS, 335, 965 - Aller & Richstone 2002, AJ, 124, 3035 AGN-4: HR-2007 p. 14 7

Gravitational potential energy of mass M, radius R Unstable system Formation of supermassive black hole `inevitable' Rees, Black Hole Models for Active Galactic Nuclei, 1984, Annual review of astronomy and astrophysics. Volume 22. p. 471 AGN-4: HR-2007 p. 15 Observable effects of (inactive) central black hole (K 4.4) Observable inside radius of influence: the distance at which its potential significantly affects the orbital motions of stars: Requires high spatial resolution Example: AGN-4: HR-2007 p. 16 8

Approach -Measure -kinematics -scale size -Constrain mass black hole Observations -Kinematics of individual stars - Galactic Center - globular clusters Kinematics of centers of galaxies Stellar absorption-line kinematics - for normal galaxies Gas emission-line kinematics - for spirals and radio-loud early-type galaxies (e.g., Hα) Fe Kα line in Seyferts (X-rays) VLBI kinematics of Masers Reverberation mapping of broad emission lines for Seyfert galaxies de Zeeuw 2001, In Black Holes in Binaries and Galactic Nuclei, eds Kaper & van den Heuvel, 78--87 (astro-ph/0009249) AGN-4: HR-2007 p. 17 AGN-4: HR-2007 p. 18 9

p. 19 AGN-4: HR-2007 An infrared NACO image of a ~ 2 x 2 arcsec2 area, centred on the position of the compact radio source "SgrA*" at the centre of the Milky Way Galaxy; it is marked by a small cross. The image was obtained in the Ks-band at wavelength 2.1 µm in May 2002 and the angular resolution (image sharpness) is about 0.060 arcsec. At about the same time, the star designated "S2" came within 0.015 arcsec of the radio source. At the distance of the Milky Way Center, 1 arcsec on the sky corresponds to 46 light-days [5]; the bar is 20 light-days long (0.44 arcsec). http://www.eso.org/outreach/pressrel/pr-2002/pr-17-02.html AGN-4: HR-2007 p. 20 10

Pericenter : 5000 km/s 124 AU, 2100 * Schwarzschild radius AGN-4: HR-2007 p. 21 AGN-4: HR-2007 p. 22 11

The BH in the center of the Galaxy - Compact non-thermal radio source Sgr A * West - Distance»8.5 kpc: very high spatial resolution - CO-bandhead at 2.2 µ: stellar radial velocities - Near-IR imaging )proper motions - enclosed mass: -Inferred density -At this density there is no stable configuration of normal stars, stellar remnants or substellar entities If one accepts these arguments it is hard to escape the conclusion that there must be a massive black hole at the core of the Milky Way (Genzel R., et al., 1997, MNRAS, 291, 219) AGN-4: HR-2007 p. 23 AGN-4: HR-2007 p. 24 12

Have a look at: Assignment What is their advocated mass for the central black hole? What are the dominant random and systematic errors in this determination? In the future, how could we significantly improve on the mass determination? AGN-4: HR-2007 p. 25 Stellar dynamical modeling of centers of galaxies Requirements - no restriction on form of potential - arbitrary intrinsic shape - multiple components - no restriction on distribution function (but ) - full range of velocity anisotropy - no need to know analytic integrals of motion - This can all be done for flattened models by Schwarzschild's numerical orbit superposition method including all kinematic observables V,σ, VP shapes) General codes for axisymmetric shapes used to derive masses of central black holes in nearly twenty galaxies - van der Marel et al. 1997, 1998; Cretton & van den Bosch 1998; Cappellari et al. 2002; Verolme et al. 2002; Gebhardt et al. 2003 - One or more FOS pointings for small number of galaxies - STIS absorption-line measurements for more than a dozen nuclei (`Nuker group, Rutgers team, ) } - Two-dimensional kinematic coverage important AGN-4: HR-2007 p. 26 13

The E3 galaxy M32 - Small, inactive companion of the Andromeda nebula This false-color UV image of the M32 center uses a logarithmic scaling to enhance the faintest stars. The STIS/HST field is 25 25 arcsec (Brown et al. 2000) AGN-4: HR-2007 p. 27 Integral field spectroscopy of M32: Verolme et al. 2002 MNRAS, 335, 517 V σ h3 h4 Top: The kinematic maps of M32 (from left to right: the mean velocity, velocity dispersion and Gauss Hermite moments h3 and h4), as observed with the integral-field spectrograph SAURON. The field of view is 9 11 arcsec2. Bottom: The best-fitting kinematic maps, obtained by adding the weighted contributions of the best-fitting set of orbits in the SAURON apertures. AGN-4: HR-2007 p. 28 14

Long slit HST spectroscopy of M32 The major axis velocity, dispersion, third- and fourth-order Gauss Hermite moments of M32 obtained with the high-resolution spectrograph STIS on board HST (diamonds, Joseph et al. 2001), together with the predictions at the STIS apertures of the best-fitting model (solid line). AGN-4: HR-2007 p. 29 Emission-line gas kinematics -High spatial resolution emission-line kinematics using HST Two-dimensional kinematics via exposures with parallel slits: measure deviations from simple circular motion Gas kinematics is `clean' in small fraction of the cases - often gas kinematics influenced by AGN activity Example: S0 galaxy NGC 3245 -circum nuclear disk of ionized gas and dust with a radius of 1 arcsec (110 pc) -a mildly active nucleus AGN-4: HR-2007 p. 30 15

Emission-line gas in the S0 galaxy NGC 3245 Barth et al. 2001, ApJ, 555, 685 HST WFPC2/PC images of the nuclear region of NGC 3245. The rectangles overplotted on the F702W images show the slit positions used in the spectroscopic exposures. Each successive spectroscopic observation moved the slit aperture 0.25 arecsec. In the V-R image, dark regions are redder and light regions are bluer than the surrounding starlight. The darkest regions correspond to a reddening of E(V-R) 0.3 mag relative to the unreddened regions. Each box is 54arcsec on a side. p. 31 AGN-4: HR-2007 Emission-line gas in the S0 galaxy NGC 3245 Barth et al. 2001, ApJ, 555, 685 The STIS spectra showing the H + [N ] emission blend. The spatial axis is vertical with the same orientation as on the previous page and wavelength increases to the right. Continuum emission from the galaxy bulge has been subtracted. Each box has dimensions 4 arcsec in the spatial direction and 83 Å in the dispersion direction. Right panels: Two-dimensional synthetic spectra for each slit position for the best-fitting disk model. AGN-4: HR-2007 p. 32 16

X-ray emission of Seyferts - Very broad Fe Kα line in MCG--6--30--15 and NGC 3516 - width of order c - Must originate near black hole (» 10 R S ) - Since we do not know R, no measurement of M AGN-4: HR-2007 p. 33 X-ray emission of a Seyfert 1 MCG--6--30--15 with XMM-Newton (Fabian et al. 2002, MNRAS, 335, L1) Relativistic iron line profile, shown in (F) flux units, obtained from the ratio of the MOS data to best-fitting underlying continuum model (model 4), multiplied by the continuum model in flux units (as opposed to an 'unfolded' plot). The crosses mark the data points and the solid line marks the line model. AGN-4: HR-2007 p. 34 17

VLBI measurements of maser emission - Very high spatial resolution - Keplerian increase of velocities to smaller radii - Three cases so far: NGC 4258, NGC 4945, and NGC 1068 Spectrum of the water maser emission from the nucleus of NGC 4945 made at the Parkes radiotelescope of the CSIRO. The maser is variable on timescales of months, but the spectrum shown is typical. Greenhill et al., 1997, ApJ, 481, L23 AGN-4: HR-2007 p. 35 Cartoon Maser emission From NGC 4945 Greenhill et al. 1995 AGN-4: HR-2007 p. 36 18

H 2 0 maser emission Greenhill et al 1996 Warm (400K), high density (10 8 10 10 ) molecular gas Self gravitating disk model (Lodata and Bertin 2003) M disk ~ 8 10 6 M 0 1 0.5 0 0.5 1 Radius (pc) M BH ~ 8 10 6 M 0 AGN-4: HR-2007 p. 37 Reverberation mapping in Seyfert galaxies -Time-variation of broad Hβ emission lines infer used to radius R of broad-line region - Combination with simple kinematic models for motion of broad-line clouds gives -Derived black hole masses for Seyferts agree with kinematic estimates (Gebhardt et al. 2000, ApJ, 543, L5) - Significant uncertainties include: - Geometry broad-line region - Distribution of distances of line-emitting gas - Nongravitational motions AGN-4: HR-2007 p. 38 19

Demographics Ferrarese and Ford 2005 -Rough correlation of M BH with spheroid luminosity L -Observational bias against small black holes in big galaxies -Why this relation?? AGN-4: HR-2007 p. 39 Expected results in next few years - Black hole demographics as a function of Hubble type, radio properties, shapes, and internal dynamics - Rate of occurrence of gaseous and stellar nuclear disks, and of nuclear starclusters, connection with AGN - Properties of nuclear stellar populations AGN-4: HR-2007 p. 40 20

Literature Khembavi & Narlikar 5.1 de Zeeuw 2001, In Black Holes in Binaries and Galactic Nuclei, eds Kaper & van den Heuvel, 78--87 (astro-ph/0009249) AGN-4: HR-2007 p. 41 Determining Black Hole Mass by Reverberation Mapping Adriaan Kroonenberg AGN-4: HR-2007 p. 42 21

Mass determination by reverberation mapping Basic context Determining black hole mass by reverberation mapping is based around finding the virial mass 2 r! M = G While the velocity dispersion can be measured directly from spectra, the determination of r is problematic Reverberation mapping provides a way to ascertain the distance of the emitting region to the central object AGN-4: HR-2007 p. 43 Reverberation mapping Principles Simple BLR model: a compact central source, surrounded by a spherical shell of gas clouds The clouds are photoionised by the central source, and show line emission Line emission Continuum Cloud shell Source AGN-4: HR-2007 p. 44 22

Reverberation mapping Principles Continuum flux r The photoionising continuum emission from the source shows flux variations, which will lead to variations in the emission-line flux The variations will reach the emission line cloud at a time delay r/c AGN-4: HR-2007 p. 45 Reverberation mapping Principles Extra path For a single burst of emission, we can easily calculate the time delay: r " = ( 1+ cos! ) c The emission line response to the burst at the observer 2 is given by: $ (! ) = 2"# r sin! d! The transfer function: d$ %(! ) d! = %( $ ) d! = 2"# rc d! d! AGN-4: HR-2007 p. 46 23

The transfer function In reality this simple picture is more complex as: Continuum flux variation is continuous Geometry of the BLR is not this simple In general, the emission-line line flux is given by the transfer equation: # L ( t) = " %(! ) C( t $! ) d! $# The goal is to find the transfer function from the observed L(t) and C(t), but deconvolution is not straightforward AGN-4: HR-2007 p. 47 Correlation analysis We can use a relatively simple correlation analysis, defining the cross-correlation and continuum autocorrelation functions as: " F CCF ( $ ) = L( t) C( t # $ ) dt and F ACF ( $ ) =! C( t) C( t # $ ) dt! #" We measure now the temporal shift that maximises the cross-correlation This is called the lag " #" AGN-4: HR-2007 p. 48 24

Results of Reverberation Mapping Continuum Emission lines Netzer & Peterson 1997, astro-ph/9706039 AGN-4: HR-2007 p. 49 Mass determination Virial mass is determined from a mean lag and the velocity dispersion of the responding gas: f" 2 c! M BH = G f is a factor representing geometry, kinematics and orientation of the BLR Assuming that the M σ relation is the same for AGNs and quiescent galaxies we can determine f a mean value AGN-4: HR-2007 p. 50 25

Results of black hole mass determination through Reverberation mapping Onken et al. 2004, ApJ, 615, 645 AGN-4: HR-2007 p. 51 Problems and sources of error Uncertainty in determination of lag and dispersion Irregular and limited sampling of C(t) and L(t) Determination of peak of often asymmetrical and flat CCF can be problematic Assumptions may not always hold! Uncertainty in the value of Any specific BH mass may be off by an order of magnitude, typical uncertainties are around a factor 3 f AGN-4: HR-2007 p. 52 26