Reverberation Mapping of Active Galactic Nuclei Bradley M. Peterson - PowerPoint PPT Presentation

Reverberation Mapping of Active Galactic Nuclei Bradley M. Peterson Department of Astronomy Astronomy 295 4 January 2011 1

Driving Force in AGNs • Simple arguments suggest AGNs are powered by supermassive black holes Eddington limit requires M  – 10 6 M  • Requirement is that self-gravity exceeds radiation pressure – Deep gravitational potential leads to accretion disk that radiates across entire spectrum • Accretion disk around a 10 6 – 10 8 black M  hole emits a thermal spectrum that peaks in the UV 2

How Can We Measure Black-Hole Masses? • Virial mass measurements based on motions of stars and gas in nucleus. – Stars • Advantage: gravitational forces only • Disadvantage: requires high spatial resolution larger distance from nucleus  less critical test – – Gas • Advantage: can be found very close to nucleus • Disadvantage: possible role of non-gravitational forces 3

Mass estimates from the Virial Estimators virial theorem: M = f ( r  V 2 / G ) Source Distance from central source X-Ray Fe K  3-10 R S where Broad-Line Region 200  10 4 R S = scale length of r 4  10 4 R S Megamasers region 8  10 5 R S Gas Dynamics  V = velocity dispersion 10 6 R S Stellar Dynamics = a factor of order f unity, depends on In units of the Schwarzschild radius details of geometry = 2 GM / c 2 = 3 × 10 13 cm . R S M 8 and kinematics 4

Reverberation Mapping • Kinematics and Continuum geometry of the BLR can be tightly constrained by measuring the emission- Emission line line response to continuum variations. NGC 5548, the most closely monitored Seyfert 1 galaxy 5

Reverberation Mapping Concepts: Response of an Edge-On Ring • Suppose line-emitting clouds are on a circular orbit around the central source. • Compared to the signal from the central source,  = r/c the signal from anywhere on the ring is  r cos  = /c delayed by light-travel time. The isodelay surface is a parabola: • Time delay at position ( r ,  ) is   ) r / c τ = (1 + cos c  r  1 cos θ 6

Surfaces ” “Isodelay All points on an “isodelay surface” have the same extra light-travel time to the observer, relative to photons  = r/c from the continuum source.  = r/c 7

Velocity-Delay Map for an Edge-On Ring • Clouds at intersection of isodelay surface and orbit have line-of-sight velocities sin  . V = ± V orb • Response time is   ) r/c = (1 + cos • Circular orbit projects to an ellipse in the ( V ,  ) plane. 8

Thick Geometries • Generalization to a disk or thick shell is trivial. • General result is illustrated with simple two ring system. A multiple-ring system 9

Observed Response of an Emission Line The relationship between the continuum and emission can be taken to be:         ( , ) ( , ) ( ) L V t V C t d  Emission-line “Velocity- Continuum light curve Delay Map” Light Curve Velocity-delay map is observed line response to a  -function outburst Simple velocity-delay map 10

Time after continuum outburst “Isodelay surface” Time delay 20 light days Broad-line region as a disk, 2–20 light days Line profile at Black hole/accretion disk current time delay

Emission-Line Lags • Because the data requirements are relatively modest, it is most common to determine the cross-correlation function and obtain the “lag” (mean response time):            CCF( ) = ( ) ACF( - ) d  -

Reverberation Mapping Results • Reverberation lags have been measured for 36 AGNs, mostly for H  , but in some cases for multiple lines. • AGNs with lags for multiple lines show that highest ionization emission lines respond most rapidly  ionization stratification 14

A Virialized BLR  V  • R –1/2 for every AGN in which it is testable. • Suggests that gravity is the principal dynamical force in the BLR. 15

–  * Relationship The AGN M BH • Assume slope and zero point of most recent quiescent galaxy calibration. • Maximum likelihood places an upper limit on intrinsic scatter  log ~ 0.40 dex M BH (factor of ~2.5) – Consistent with quiescent galaxies. 16

BLR Scaling with Luminosity • To first order, AGN spectra look the same ( H ) Q L   U  2 2 4 r n c n r H H  Same ionization parameter U  Same density n H r  L 1/2 SDSS composites, by luminosity Vanden Berk et al. (2004) 17

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NGC 4051 Mrk 335 PG 0953+414 z = 0.00234 z =0.0256 z = 0.234 log L opt = 41.2 log L opt = 43.8 log L opt = 45.1 Measurement of host-galaxy properties is difficult even for low- z AGNs • Bulge velocity dispersion σ * • Starlight contribution to optical luminosity

ACS HRC images and model residuals 20

Recent Progress in Determining the Radius-Luminosity Relationship Original PG + Seyferts Expanded, reanalyzed Starlight removed (Kaspi et al. 2000) (Kaspi et al. 2005) (Bentz et al. 2009)   2    2    2  7.29 5.04 4.49 R (H  )  L 0.76 R (H  )  L 0.59 R (H  )  L 0.49 21

Estimating Black Hole Masses from Individual Spectra Correlation between BLR radius R (= c  cent ) and luminosity L allows estimate of black hole mass by measuring line width and luminosity only: M = f ( c  cent  line / G )  f L 1/2  line 2 2 Dangers: • blending (incl. narrow lines) • using inappropriate f Typically, the variable part of H  – is 20% narrower than the whole line Radius – luminosity relationship Bentz et al. (2006). 22

Estimating AGN Black Hole Masses Phenomenon: Quiescent Type 2 Type 1 Galaxies AGNs AGNs Primary Stellar, gas Stellar, gas Megamasers Megamasers 2-d 2-d 1-d 1-d Methods: dynamics dynamics RM RM RM RM Fundamental  * AGN –  * – M BH M BH Empirical Relationships: Broad-line width V Secondary Fundamental [O III ] line width & size scaling with V   *  M BH Mass plane: luminosity  e   * Indicators: , r e R  L 1/2  M BH  M BH Application: BL Lac Low- z AGNs High- z AGNs objects