1. SIGRAV Graduate School in Contemporary Relativity and Gravitational Physics Laura Ferrarese Rutgers University Lecture 4: Beyond the Resolution Limit

2. Lecture Outline 1. The Innermost Regions of Active Galactic Nuclei 2. Variability in Active Galactic Nuclei  Continuum variability  Emission line variability 3. Reverberation mapping:  making sense of the continuum-emission line connection 4. Potential problems…. 5. … and how to solve them: the Transfer Function 6. Where the Observations Stand

3. Schematic View of an AGN

4. Reverberation Mapping in a Nutshell  Measuring masses of SBHs using Reverberation Mapping is based on the assumption that the size r and velocity  of the Broad Line Region (BLR) clouds are connected by a simple virial relationship:  According to the standard model, Broad Line Region (BLR) clouds are  many (10 7-8, Arav et al. 1997, 1998, Dietrich et al. 1999)  small, dense (N e ~ 10 9-11 cm -3 )  cold (T e ~ 2  10 4 K)  photoionized (Ferland et al. 1992)  localized within a volume of a few to several tens of light weeks in diameter around the central ionization source.  As such, the BLR is, and will remain, spatially unresolved at optical wavelengths even using space based instrumentation, and its size cannot be determined using conventional images.

5. Reverberation Mapping in a Nutshell  If the BLR is photoionized, the broad lines should respond to continuum variations. The line response contains a wealth of information regarding the spatial and kinematic structure of the BLR; therefore monitoring programs for AGNs started in the early ‘80s in the attempt to quantify the nature of the continuum and emission line variations (if any!)  If everything works as planned, the time delay between continuum and line variation is simply (?) related to the size of the BLR.

6. Reverberation Mapping in a Nutshell  Advantages:  reverberation mapping probes regions very close to the central engine (10 3 R Sch ), a factor at least 1000 smaller than allowed by “traditional’ methods which relay on resolved kinematics.  This leaves little doubt that the measured mass (if correct!) is in the form of a supermassive black hole  Disadvantages:  The observations are difficult. Close time monitoring at very closely spaced intervals and multiple frequencies is necessary.  For the virial approximation to be applicable, the kinematics must be dominated by gravity. The presence of outflows or not gravitational motions (to which gas might be prone) would undermine the method entirely.  The geometry of the BLR are not known.

7. Observational Requirements for Monitoring Programs  Temporal Sampling  observations must be closely spaced in time relative to the physical timescale of interest (generally a problem for the early monitoring programs)  difficulties in scheduling the observations  S/N of the data  S/N must be high relative to the magnitude of the flux variations (i.e. F var must be >> 0)  e.g. S/N=30 is necessary to detect 10% variations in continuum flux at the 3  confidence level.  Aperture effects  variations in seeing at the time of the observations, as well as pointing and guiding errors can cause variations in the amount of light entering the spectrograph, since both the NLR and the host galaxy are extended. This can cause spurious spectral variations.  Datasets must be as homogenous as possible, ideally using a single instrument in a stable configuration

8.  Flux calibration: since it is impossible to rely exclusively on photometric conditions, relative spectrophotometry can be achieved by:  simultaneous observation of the AGN and a nearby (non-variable) field star. the slit response function (sensitivity as a function of position in the slit) must be known very accurately 1-2% spectrophotometric accuracy  using non-variable components of the AGN spectra (e.g. [OIII] 4959,5007 narrow line emission) aperture effects can be difficult to control since the NLR is extended - must know the surface brightness distribution of the extended component and the PSF (as a function of time) 2% spectrophotometric accuracy Observational Requirements for Monitoring Programs

9. Observational Requirements Systematic errors as a function of width of the radial emissivity distribution for several length experiments. Solid line: 900 data points, dashed line: 64 data points. Dotted line: 25 data points (Krolik 2001). N=9000 N=64 N=25

10. Observational Requirements Systematic errors as a function of width of the radial emissivity distribution for four experiments, each with 64 data points, but different time sampling (Krolik 2001). Anisotropic model,  t = (1/24)(r/c) Anisotropic model,  t = (3/8)(r/c) Isotropic model,  t = (1/24)(r/c) Isotropic model,  t = (3/8)(r/c)

11. Monitoring Programs  UV/optical monitoring programs started in the early ‘80s  International AGN Watch (Peterson 1993, PASP, 105, 247) IUE (UV) and ground-based optical monitoring program of NGC 5548. Mostly ground based optical monitoring of 8 nearby Seyfert 1 galaxies. (although only 5 have been monitored extensively; see Wandel, Peterson & Malkan 1999, ApJ, 526, 579 for a compilation)  Ohio State University optical monitoring of 9 Seyfert 1s, manly observed in H   Wise/Steward (Kaspi et al. 2000, ApJ, 533, 631) optical monitoring of 17 quasars (H  and/or H  ).  LAG (Lovers of Active Galaxies), led by M.V. Penston optical monitoring of 8 AGNs and quasars, 3 not previously observed (H  and/or H  ). Sampling patterns of previous and planned AGN multiwavelength programs Time (days)

12. Monitoring Programs  The main results of these programs are:  AGN continua vary on timescales which can be as short as days.  The UV and optical continuum vary with no apparent time lag between them. AGN continuum variability must not be caused by either mechanical disk instabilities or variations in the accretion rates, since these would propagate through the disk slowly enough that the inner, hotter (UV) part of the disk should be seen to vary before the outer, cooler (optical) part. UV/continuum variations might be caused by reprocessing by the disk of the hard X-ray produced along the disk axis.  Variations in the emission line flux correlate with continuum variations.  The highest ionization lines respond most rapidly to continuum changes, implying that there is ionization stratification in the BLR.  The BLR is not in pure radial motion, since there is no obvious difference in the timescale of the response of the red and blue wings of the emission lines.

13. Variability in AGNs  AGNs are variable at all wavelengths at which they have been studied, not only in the continuum, but also in the emission lines.  Typical quasars vary at the 0.3 - 0.5 mag level over timescales of a few months, with extreme cases varying on timescales as short as a few days.  The variability in Seyfert galaxies is less dramatic and was not discovered until the late ‘60s.  Causality arguments imply that the emitting region is less than a few light days across  Periodicity in the light curve have been searched for but never found: variations are aperiodic and have variable amplitudes

14. Variability in AGNs  The continuum variability can be characterized by the mean fractional variation: Difference in optical flux (upper panel) and variability parameter (lower panel) for the Seyfert 1 galaxy NGC 5548, as a function of the time interval between observations.

15. X-Ray Variability in AGNs  Rapid X-ray variability is a staple in all AGNs (Mushotzky et al. 1993, ARAA)  Since X-rays arise near the SBH event horizon, X-ray variability sets the tightest constraints on the AGN size:  the fastest possible variability timescale for a coherent, isotropically emitting region is the crossing time:  The variability timescale is characterized by the fluctuation power density spectrum (PDS), which is the product of the Fourier Transform of the light curve with its complex conjugate.  Observationally, P( )  , with index  ~ 1-2 over timescales of hours to months.  Since the total power (integral of the PDS over all frequencies) must be finite, the PDS must turn over (  < 1) at low frequencies. EXOSAT PDSs for galactic stellar mass X-ray binaries (Belloni & Hasinger 1990, A&A, 103, 119)

16. X-Ray Variability in AGNs RXTE light curve (left) and PDS (up) for NGC 3516. The cutoff frequency  corresponds to a timescale of 27 days, much longer than the light crossing time for a SBH of plausible mass (Edelson & Nandra 1999, ApJ, 514, 682)

17. X-Ray Variability in AGNs  The observed cutoff must be related to the fundamental physics that generate the variability and to the processes by which the X-rays are produced, e.g.  Compton upscattering of ultraviolet "seed" photons that probably arise in an accretion disk (e.g., Haardt & Maraschi 1991,1993; Zdziarski et al. 1994; Stern et al. 1995 ). optical depth effects size of the scattering region  ‘Bright spot’ model (e.g. Bao & Abramowicz 1996). In this model, active regions on the surface of a rotating accretion disk produce the observed variability. The relevant turnover timescale could perhaps be identified with the orbital timescale, marginally consistent with the observed cutoff for the extremes of parameter space mentioned above if the emission is produced very far out in the disk. acceleration mechanism nature of the instabilities that cause the bright spots to form  To first order, the cutoff frequency scale depends on the relevant timescale which controls the variations (light crossing time, orbital timescale, thermal timescale, sound timescale, drift timescale), all of which depend on the physical size of the incriminated region and therefore on the black hole mass. For instance, the cutoff frequency in NGC 3516 is a factor 10 5 -10 6 shorter than in Cyg-X1 (M BH ~ 10 M  ), implying a central SBH of the order 10 6 -10 7 M 

18. Emission Line Variability  Broad Emission lines in AGN spectra can vary in both flux and profile.  Narrow lines fluxes do not vary! This is due to the fact that in the NLR both the light crossing time and the recombination time are large (>100 years), therefore short-term variability is smeared out.

19. Emission Line Variability Mean spectrum formed from 34 individual spectra of NGC 5548 (upper panel). RMS spectrum formed from the same data by computing the rms flux at each wavelength. Constant features, such as narrow emission line and the host galaxy continuum, do not appear in the rms spectrum (Korista et al. 1995, ApJS 97, 285)

20. Line-Continuum Variations H  line flux against the continuum flux measured at the same time (left) and 15 days earlier (right), for the Seyfert 1 galaxy Mrk 335. The emission line fluxes are better correlated with the earlier rather than current continuum fluxes (Peterson et al. 1998, ApJ 501, 82)

21. The Time ‘Lag’  The time lag is commonly measured by cross correlating the line and continuum light curves Emission line light curve Continuum light curve

22. The Time ‘Lag’  Calculating the cross-correlation function can be tricky, in particular:  for larger and larger lags, fewer points contribute to the CCF, since the points at the end of the series drop out. This implies that for the cross-correlation to yield statistically significant results, it is necessary to have a large number of datapoints.  sparse datasets need to be interpolated, with all the uncertainties that follow.

23. Observational Results  AGNs with lags for multiple lines show that highest ionization emission lines respond most rapidly  ionization stratification

24. The Basis of Reverberation Mapping  The fact that emission lines vary in response to the optical/UV continuum variation immediately implies that:  The line emitting clouds are close to the continuum source  the line emitting clouds are optically thick  The ionizing continuum ( < 912Å) is closely related to the observable optical/UV continuum.  Therefore, our hopes are realized: by characterizing the emission line response to continuum variations, the kinematics and geometry of the BLR can be constrained:  the time delay between continuum and emission line variations are ascribed to light travel time effects within the BLR: the emission lines ‘echo’ or ‘reverberate’ to the continuum changes (Blandford & McKee 1982, ApJ, 255, 419).

25. Reverberation Mapping Assumptions  The continuum originates in a single central source. Typical scalelengths are: Accretion disk (for 10 7 – 10 8 M  SBH): 10 13–14 cm Broad Line Region:10 16 cm  To all effects, as seen from the BLR, the continuum source can be treated as point- like  The continuum is not required to be emitted isotropically (although isotropy is usually assumed)  The most important timescale is the light-travel time.  the cloud response to a change in the continuum flux is instantaneous. Light travel time: Timescale to re-establish photoionization equilibrium: Timescale it takes a Lyman  photon to diffuse outward through the BLR: n e = electron density; U = ionization parameter;  B = recombination coefficient; R ion = depth to which the BLR is completely ionized

26. Reverberation Mapping Assumptions  The structure of the BLR does not change on the variability time scale (or the timescale over which the experiment is conducted).  Dynamical (cloud-crossing) time:  There is a simple, though not necessarily linear, relationship between the observed continuum and the ionizing continuum.

27. Reverberation Mapping Assumptions  Once the (responsivity weighted) size r of the BLR is known, the AGN central mass can be obtained through the virial relationship: where f is a dimensionless factor of order unity that depends on the geometry and kinematics of the BLR, and  is the emission line velocity dispersion.  The velocity width  of the lines is measured in the rms spectrum:  the rms spectrum only contains information on the variable part of the lines; constant components do not contribute.

28. Potential Problems  What does reverberation mapping measure?  The flux variations in each line are responsivity-weighted:  Determined by where the physical conditions (mainly flux and particle density) give the largest response for a given continuum increase.  This can vary with time.  Also, this conditions might be verified at different depths for r and  (Krolik 2001, ApJ, 551, 72), potentially leading to systematic errors on the masses. Systematic errors due to the differing moments that define r and , as a function of the width of the radial emissivity distribution. Solid curve: isotropic radiation. Dotted curve: anisotropic radiation (directed towards the center). Masses are systematically overestimated: in the anisotropic case, since we see preferentially the outer regions of the cloud, the measured lag is greater than it would be if the entire emitting region could be observed (Krolik 2001).

29. Potential Problems  What is f?  circular, coplanar orbits: mean-square line-of-sight velocity is GMsin 2 i/(2r), therefore f=2/sin 2 i. f could therefore take any value between 2 and .  random, isotropic circular orbits: mean-square line-of-sight velocity is GM/(3r), therefore f=3  random, isotropic parabolic orbits: mean-square line-of-sight velocity is 2GM/(3r), therefore f=3/2  These potential problems add to the systematics arising from the (generally) inadequate temporal sampling of the observations, and the (generally) short duration of the experiments.

30. Potential Problems: the Virial Hypothesis  How can we test the virial hypothesis?  If the motion of the gas is gravitational, using BLR sizes and velocity derived from different emission lines in the same AGN must produce the same estimate of the central mass.  NGC 5548: highest ionization lines have smallest lags and largest Doppler widths, such that virial product r V 2 is constant.  1989 data from IUE and ground-based telescopes.  1993 data from HST and IUE. Virial relationship with M = 6  10 7 M .

31. Potential Problems: the Virial Hypothesis  There are a total four AGNs for which lag measurements for multiple emission lines exist, all supporting the virial approximation (Onken & Peterson 2002)  NGC 7469: 8.4  10 6 M   NGC 3783: 8.7  10 6 M   NGC 5548: 5.9  10 7 M   3C 390.3: 3.2  10 8 M 

32. Potential Problems: the Virial Hypothesis  In the case of NGC 5548 only, there is sufficient information on the long term behavior of a single line, H , to monitor the variation of the line width and lag as a function of time.  As the continuum brightens, the lag is expected to become longer (since the BLR can be ionized to a greater depth) and the line width is expected to become narrower. This agrees with the observations.

33. Potential Problems  While the time lag measured for different lines agrees with the virial relationship, it does not necessarily exclude other models. For instance, special cases of cloud outflows or disk winds could also explain the observations (Blumenthal & Mathews 1975, ApJ, 198, 517; Murray et al. 1995, ApJ, 451, 498; Emmering, Blandford & Shlosman 1992, ApJ, 385, 460; Chiang & Murray 1996, ApJ, 466, 704; Bottorff et al. 1997, ApJ, 479, 200)

34. Potential Problems  To summarize, all of our problems would be solved if the geometry and kinematics of the broad line region were completely determined:  One of the major remaining mysteries of AGN astrophysics  We need to know this to understand systematic uncertainties in AGN masses.  Can we determine the BLR geometry and kinematics from the observations? YES!  BUT… this will require a leap in data quality.  Accurate mapping requires a number of characteristics (nominal values follow): High time resolution (  0.2 day) Long duration (several months) Moderate spectral resolution (  600 km s-1) High homogeneity and signal-to-noise (~100)  Given these data, we could not just restrict ourselves to measuring time lags, but we could measure the complete transfer function.

35. The Transfer Function Emission-line flux at line of sight velocity V z Transfer Function Continuum Light Curve  The transfer function determines the relation between continuum and emission lines variations:  The transfer function is simply the time-smeared emission-line response to a  function outburst in the continuum. In other words, the transfer function can be interpreted as a ‘velocity delay map’.  Solving for the transfer function is a classical inversion problem. In practice, it requires extremely well sampled, high quality data.

36. The Transfer Function  In the best case, the data so far only allows us to solve for the velocity independent (or 1-d) transfer equation where both  (  ) and L(t) represent integrals over the emission line width: Integrate over time delay to get the line profile Integrate over velocity to get the delay map

37. The Isodelay Surface  Suppose that:  the BLR consists of clouds in a thin spherical shell in orbit around the central source.  the continuum light curve is a  function outburst. Then:  the signal anywhere in the shell is delayed with respect to the continuum outburst by the light travel time r/c.  An observer at the central source will record a variation in the emission lines with a delay 2r/c following the continuum outburst.  An observer at any other location will record time delays in the emission lines which are different for different parts of the cloud.  = r/c Observer

38. The Isodelay Surface  the ‘isodelay surface’ is defined as the locus of points for which the pathlength to the observer is constant.  Emission lines variations arising from the intersection of the isodelay surface to the BLR are recorded simultaneously by the observer.  Isodelay surfaces are conic sections with the observer at one focus and the continuum source at the other: the time delay at position (r,  ) is  = (1 + cos  )r/c Observer Continuum

39. The Isodelay Surface  If the observer is at infinity, the isodelay surfaces are parabolas:

40. Examples of Transfer Functions  Let’s take a look at some specific transfer functions. Geometries of particular relevance are:  Clouds distributed in a shell and in random Keplerian orbits, illuminated by either an isotropic or bipolar continuum.  BLR in biconical outflows: these might be relevant, since they are seen in the NLR and might apply to at least a component of the BLR.  Disks of random orientation in Keplerian motion.

41. Isodelay Surfaces and Transfer Function  The transfer function measures the amount of line emission emitted at a given Doppler shift in the direction of the observer as a function of time delay .  Consider a thin spherical shell. The time delay for a particular isodelay surface is simply the equation of a conic section is polar coordinates:  The intersection of the isodelay surface with the BLR is a ring of radius rsin . The surface area element of the ring is 2  (rsin  )rd . If the response of each area element has the constant value , then the transfer function of the ring can be written as:  (  ) = 2  r 2 sin  d  or, in terms of the time delay  rather than  :  (  )d  =  (  ) (d  /d  ) d  = 2  rc d   Thus the 1-D transfer function for a thin spherical shell is constant over the range 0 <  < 2r/c.

42. Transfer Function of a Thin Spherical Shell To observer

43. Examples of Transfer Functions  A complication is introduced if the line emission is anisotropic.  Physically this can happen if the BLR is optically thick to both continuum and line radiation. In this case, most of the line emission will be from the side of the cloud facing the central continuum source.  The BLR optical depth for different emission lines is different.  The degree of anisotropy in the line emission can be parameterized as  (  ) =  0 (1+Acos  )  with A=0 for isotropic emission, A=1 for completely anisotropic emission. A~1 for Ly , A~0.7 for CIV, A~0.7 for Ly .  The main effect of anisotropic line emission is to increase the measured lag for a given geometry because the apparent response of the near side of the BLR is suppressed.

44. Examples of Transfer Function  Transfer function for a thin, completely anisotropic ( A=1 ) shell To observer

45. Examples of Transfer Functions  Transfer function in the case in which the BLR (again assumed to be a spherical shell) is illuminated by a biconical beam with given opening angle.  Only part of each orbit is illuminated by the continuum source.

46. Examples of Transfer Functions  Consider the simple case of clouds in a circular orbit of radius r and inclination i = 90° (edge on), and orbital speed V orb.  Clouds at the intersection of the isodelay surface and the orbital plane have line-of-sight velocities V z = ±V orb sin .  Therefore, the circular orbit projects to an ellipse in the (V z,  ) plane with semiaxes V orb and r/c.

47. Examples of Transfer Functions  When the orbit is inclined at i < 90°, the range in both time delay and line-of- sight velocity contract:  The range in time delays decreases from [0,2r/c] to [(1-sini)r/c,(1+sini)r/c]  The line of sight velocity decreases from [-V orb, V orb ] to [-V orb sini, V orb sini]  In the limit of i = 0°, the velocity-delay map contracts to a single point at [  = r/c, V z = 0].  A complete thin shell can be constructed by integrating over all inclinations.

48. Transfer Functions: Thick Geometries  The generalization to a disk or thick shell is trivial - simply a matter of integrating over a series of circular orbits (disk) or spherical shells (thick shell).  In thick geometries, the responsivity per unit volume is generally a function of distance, because of geometrical dilution of the continuum and the fact that the BLR covering factor will vary.  (r) =  0 r 

49. Transfer Function: Keplerian Disk  Transfer function for a thin keplerian disk at a 45 degree inclination.

50. r in =2 ld r out =10 ld  =0 r in =2 ld r out =10 ld  =-4 Transfer Functions: Thick Shells  In thick geometries, the responsivity per unit volume is generally a function of distance, because of geometrical dilution of the continuum and the fact that the BLR covering factor will vary.  (r) =  0 r   Transfer functions for two shells with the same geometry, but different responsivity function

51. r in =2 ld r out =10 ld  =-2 A=0 w=75º i=15º r in =2 ld r out =10 ld  =-2 A=0 w=30º i=45º Transfer Functions: Thick Shells  Transfer functions for two thick shells with the same geometry and responsivity functions, but illuminated by a biconical outflow which does not (left) and does (right) point towards the observer. to the observer

52. Transfer Function: BLR Outflows  Transfer functions in the case of a BLR in spherical (left) and biconical (right) outflow.

53. Complex Transfer Functions  Recovering complex transfer functions requires mapping at multiple emission lines.

54. Transfer Functions  Very different scenarios can correspond to very similar 1-D transfer functions, but can be very easily distinguished using the 2D transfer function (or, equivalently, the time delay map and the line profiles). Dashed line: randomly inclined circular Keplerian orbits. Solid line: BLR in spherical outflow

55. Two Simple Velocity-Delay Maps Inclined Keplerian disk Randomly inclined circular Keplerian orbits

56. C IV and He II in NGC 4151. The double peaked appearance in the line is due to a strong absorption feature (Ulrich & Horne 1996, MNRAS, 283, 748) Recovering Velocity-Delay Maps from Real Data  Transfer functions can be recovered from real velocity-delay maps by Fourier inversion.  This requires:  High S/N in each spectrum  High S/N in the light curve  Moderately high spectral resolution  Long monitoring duration  Dense temporal sampling  In no case to date has this been achieved, though in no case has it been a design specification!

57. Transfer function recovered from the CIV emission in NGC 5548. The data has been interpreted as 1) evidence of no outflows; 2) evidence of radial outflows; 3) evidence of radial inflow (!). Recovering Velocity-Delay Maps from Real Data Transfer function recovered from the H  emission in NGC 5548. Caution should be exercised since the data spans a period longer than the BLR dynamical timescale. Notice little response from material along our line of sight to the continuum source

58. Observational Results  Although no experiment yet has recovered a reliable velocity-delay map, emission-line lags have been measured in 37 AGNs, in some cases for multiple emission lines. The H  response in NGC 5548 has been measured for 14 individual observing seasons. Measured lags range from 6 to 26 days.

59. Reverberation Mapped AGNs From Kaspi et al. 2000, ApJ, 533, 631

60. Mass-Luminosity Relationship M  L 0.3±0.1  QSOs (Kaspi et al. 2000)  Seyfert 1s (Wandel, Peterson, Malkan 1999)  Narrow-line AGNs  NGC 4051 (NLS1)  The measured masses correlate, although with very large scatter, with the continuum luminosity, in the sense that brighter AGNs have larger SBHs.

61. “Secondary” Mass Estimators  Reverberation mapping opens the way to calibrate a “secondary” mass estimators since, to first order, we expect the broad line region size to correlate with the ionizing continuum luminosity:  Photoionization equilibrium models are parameterized by the shape of the ionizing continuum, the elemental abundances, and the ionization parameter U : where Q(H) is the number of hydrogen ionizing photons ( =13.6 eV) emitted per second by the central source:  U characterizes the ionization balance within the cloud, since Q(H)/r 2 is proportional to the number of ionizations occurring per unit area, while n e is proportional to the recombination rate.  To first order, AGN spectra all look alike, i.e. they have the same ionization parameter and electron density (typical values are: Q(H) ~ 10 54 h 0 -2 photons s -1 ; n e ~ 10 11 cm -3 ; U ~ 0.1). Therefore, we expect

62. BLR Scaling with Luminosity  QSOs (Kaspi et al. 2000)  Seyfert 1s (Wandel, Peterson, Malkan 1999)  Narrow-line AGNs  NGC 4051 (NLS1) r(H  )  L 0.6±0.1  This is close to what we observe! For the 37 AGNs which have been reverberation mapped, the BLR radius, measured from the H  time lag, correlates (although with large scatter) with the continuum luminosity.

63. Suggested Readings  Review: Peterson, B.M. 2001, “Variability of Active Galactic Nuclei”, in The Starburst-AGN Connection, World Scientific (astro-ph/0109495).  Criticism: Krolik 2001, ApJ, 551, 72