Measurement of Black Hole Masses in Active Galactic Nuclei

Home , Galactic astronomy, Velocity dispersion

DISSERTATION

Presented in Partial Fulﬁllment of the Requirements for

the Degree Doctor of Philosophy in the

Graduate School of The Ohio State University

Christopher A. Onken

*****

The Ohio State University

2005

Dissertation Committee: Approved by

Professor Bradley M. Peterson, Adviser

Professor Richard W. Pogge Adviser Astronomy Graduate Program Professor Smita Mathur ABSTRACT

We investigate the calibration and application of reverberation mapping techniques for determining black hole (BH) masses in active galactic nuclei (AGNs).

We present revised BH mass determinations for several AGNs based on the use of updated methodologies with archival data, demonstrating signiﬁcant reductions in the sizes of the BH mass uncertainties. Moreover, the study of the Seyfert 1 galaxy,

NGC 3783, shows that the gas in the broad-line region of this AGN obeys the virial theorem.

We use measurements of stellar velocity dispersions, σ∗, in AGNs and the assumption that AGNs follow the same relation between BH mass and σ∗ as quiescent galaxies to provide the ﬁrst empirical calibration for reverberation-based

BH masses. We also attempt to determine an independent calibration of these masses by studying the reverberation-mapped AGN, NGC 4151, with ground- and space-based observations, and by trying to constrain the BH mass through modeling of the galaxy’s stellar dynamics.

We estimate the BH masses and bolometric luminosities in 400 AGNs ∼ selected from the multi-wavelength AGN and Galaxy Evolution Survey (AGES),

ii where the BH masses are calculated from scaling relationships that have grown out of reverberation mapping. We ﬁnd the distribution of Eddington ratios at ﬁxed luminosity to be sharply peaked around a value of 1/3, with a dispersion of just

0.3 dex. The distribution of Eddington ratios at ﬁxed mass looks to be similarly narrow, and we are able to conﬁrm a drop in the underlying distribution at low

Eddington ratios for certain combinations of redshift and BH mass—all previous studies in these redshift mass bins are aﬀected by selection eﬀects at low Eddington − ratio (as are the AGES data in lower mass or higher redshift bins). The dominance of AGN accretion at rates relatively close to the Eddington limit has important implications for the growth of BHs and the joint evolution of BHs and their host galaxies.

iii Dedicated to all the helping hands along the way...

the ones who guided and the ones who pushed.

iv ACKNOWLEDGMENTS

Innumerable people deserve to be acknowledged for their inﬂuence, personal and professional, on the incredible experience I have had. Thank you to my adviser,

Brad Peterson, for taking a fellow Minnesotan under your wing and showing me how to work as an astronomer. Thanks to Rick Pogge for your willingness to share your time and encyclopedic knowledge of topics astrophysical and otherwise. Thank you to all of the Astronomy Department faculty members, postdocs, and staﬀ at The

Ohio State University–I’ve pestered every one of you with questions at some time over the last ﬁve years and you have all been willing to stop whatever you were doing and provide me with answers. To the OSU faculty with whom I’ve been fortunate enough work directly (in chronological order: Darren DePoy, Don Terndrup, Brad,

Jordi Miralda-Escud´e, Smita Mathur, Rick, Chris Kochanek, Andy Gould, and

David Weinberg), I thank you for fostering my development as a scientist. And to the postdocs who have given me so much guidance, Marianne Vestergaard and

Matthias Dietrich, thank you for your help.

To my fellow OSU grad students, I am grateful to call all of you my friends.

The space it would take to explain your importance to my time in Columbus would

v double the size of this document. Let me simply say that you are a magniﬁcent bunch of people, and I look forward to seeing all of you again.

Prior to my arrival in Columbus, I benefited from the advice and instruction offered by several people. I am indebted to Evan Skillman, who kindly took the time to answer question after question in Intro Astronomy and in the years that followed; and to Ted Bowell, Bruce Koehn, and Brian Skiff, who gave me my first taste of observing; and to David Alves and Howard Bond, who sparked continuing research interests that are beyond the scope of this dissertation; and to John Dickey, who both demonstrated how to be an effective teacher and patiently advised me on my senior thesis; and to Terry Jones, who first suggested applying to OSU for grad school.

Finally, I am pleased to be able to acknowledge the role of my wonderful family.

Without your love, interest, and support, I never would have come so far. Thank you.

vi VITA

August 14, 1978 ...... Born – Springﬁeld, IL, USA

2000 ...... B.S., Physics (magna cum laude), University of Minnesota

2000 ...... B.S., Astrophysics (summa cum laude), University of Minnesota

2000 – 2005 ...... Graduate Teaching and Research Associate, The Ohio State University

2003 ...... M.S., The Ohio State University

PUBLICATIONS

Research Publications

1. H. E. Bond, D. R. Alves, and C. Onken, “CCD Photometry of the Globular Cluster NGC 5986 and Its Post-Asymptotic Giant Branch and RR Lyrae Stars”, AJ, 121, 318, (2001).

2. C. A. Onken, and B. M. Peterson, “The Mass of the Central Black Hole in the Seyfert Galaxy NGC 3783”, ApJ, 572, 746, (2002).

3. B. M. Peterson, et al. (41 authors, incl. C. A. Onken), “Steps toward Determination of the Size and Structure of the Broad-Line Region in Active Galactic Nuclei. XVI. A 13 Year Study of Spectral Variability in NGC 5548”, ApJ, 581, 197, (2002).

vii 4. C. A. Onken, B. M. Peterson, M. Dietrich, A. Robinson, and I. M. Salamanca, “Black Hole Masses in Three Seyfert Galaxies”, ApJ, 585, 121, (2003).

5. C. A. Onken, and J. Miralda-Escud´e, “History of Hydrogen Reionization in the Cold Dark Matter Model”, ApJ, 610, 1, (2004).

6. B. M. Peterson et al. (12 authors, incl. C. A. Onken), “Central Masses and Broad-Line Region Sizes of Active Galactic Nuclei. II. A Homogeneous Analysis of a Large Reverberation-Mapping Database”, ApJ, 613, 682, (2004).

7. C. A. Onken, L. Ferrarese, D. Merritt, B. M. Peterson, R. W. Pogge, M. Vestergaard, and A. Wandel, “Supermassive Black Holes in Active Galactic Nuclei. II. Calibration of the Black Hole Mass-Velocity Dispersion Relationship for Active Galactic Nuclei”, ApJ, 615, 645, (2004).

FIELDS OF STUDY

Major Field: Astronomy

viii Table of Contents

Abstract ...... ii

Dedication ...... iv

Acknowledgments ...... v

Vita ...... vii

List of Tables ...... xii

List of Figures ...... xiv

Chapter 1 Introduction 1

1.1 Active Galactic Nuclei ...... 1

1.2 Reverberation Mapping ...... 3

1.2.1 Time Delay ...... 4

1.2.2 Velocity Width ...... 9

1.2.3 BH Mass ...... 10

1.3 Stellar Dynamical BH Masses ...... 11

1.4 Scaling Relations ...... 14

1.5 Focus of This Study ...... 16

1.6 Published Work ...... 18

Chapter 2 Reverberation Mapping of NGC 3783 23

ix 2.1 Introduction ...... 23

2.2 Data ...... 24

2.2.1 UV Data ...... 24

2.2.2 Optical Data ...... 26

2.3 Methods and Techniques ...... 28

2.3.1 Spectral Analysis ...... 28

2.3.2 Light Curve Analysis ...... 29

2.4 Results ...... 30

2.4.1 Line widths ...... 30

2.4.2 Time delays ...... 30

2.5 Discussion ...... 33

Chapter 3 Additional Reverberation Mapping Studies 70

3.1 Introduction ...... 70

3.2 Observations and Data Reduction ...... 71

3.2.1 NGC 3227 ...... 72

3.2.2 NGC 3516 ...... 73

3.2.3 NGC 4593 ...... 74

3.3 Analysis ...... 75

3.4 Mass Calculations ...... 76

3.4.1 NGC 3227 ...... 77

3.4.2 NGC 3516 ...... 77

3.4.3 NGC 4593 ...... 78

3.5 The BH Mass—Stellar Velocity Dispersion Relationship ...... 78

x 3.6 Conclusion ...... 80

Chapter 4 The Black Hole Mass Stellar Velocity Dispersion Relation − for AGNs 89

4.1 Introduction ...... 89

4.2 Observations and Data Reduction ...... 91

4.2.1 Data Reduction and Analysis ...... 93

4.3 Results and Discussion ...... 94

4.3.1 Measuring Velocity Dispersions ...... 94

4.3.2 Measuring Virial Products ...... 95

4.3.3 The BH Mass–Velocity Dispersion Relation ...... 96

4.3.4 BLR Models ...... 100

4.3.5 Gravitational Redshifts ...... 101

4.3.6 Velocity Dispersion Versus FWHM([O III]λ5007 A)˚ ...... 103

4.4 Conclusion ...... 104

Chapter 5 Stellar Dynamics of NGC 4151 113

5.1 Introduction ...... 113

5.2 Stellar Dynamics Overview ...... 115

5.3 Imaging ...... 117

5.3.1 ACS/HRC ...... 118

5.3.2 MDM ...... 118

5.4 Spectroscopy ...... 119

5.4.1 HST/STIS ToO ...... 120

5.4.2 Ground-based ...... 122

xi 5.5 Analysis & Results ...... 125

5.5.1 Surface Brightness Proﬁle Modeling ...... 125

5.5.2 Gauss-Hermite Parameter Estimation ...... 129

5.5.3 Orbit Modeling ...... 131

5.6 Discussion ...... 133

Chapter 6 Black Hole Masses and Eddington Ratios at 0.3 < z < 4 156

6.1 Introduction ...... 156

6.2 Data ...... 158

6.2.1 Completeness ...... 160

6.3 Analysis ...... 162

6.3.1 Line Width ...... 163

6.3.2 Continuum Luminosity ...... 166

6.3.3 Calibrating the Mg IIRelation ...... 167

6.3.4 Bolometric Luminosity Calculation ...... 168

6.4 Results ...... 169

6.4.1 Luminosity-Redshift Bins ...... 171

6.4.2 Mass-Redshift Bins ...... 175

6.5 Discussion ...... 179

Chapter 7 Conclusion 197

7.1 Future Work ...... 200

Bibliography 202

xii List of Tables

2.1 NGC 3783 Continuum and Emission Line Wavelength Limits . . . . . 42

2.2 NGC 3783 UV Continuum Flux Data ...... 43

2.3 NGC 3783 UV Emission Line Flux Data ...... 51

2.4 NGC 3783 UV Velocity Data ...... 64

2.5 NGC 3783 Optical Flux Data ...... 65

2.6 NGC 3783 Sampling Statistics ...... 68

2.7 NGC 3783 Cross-Correlation Results ...... 69

3.1 Sampling Statistics ...... 85

3.2 Cross-Correlation Results ...... 86

3.3 Velocity Width Results ...... 87

3.4 Reverberation Masses ...... 88

4.1 Observing Log ...... 109

4.2 Velocity Dispersion Measurements ...... 110

4.3 MBH σ∗ Data ...... 111 −

4.4 MBH σ∗ Fitting Results ...... 112 − 5.1 GALFIT Results for MDM Image of NGC 4151 ...... 153

5.2 GALFIT Results for ACS Image of NGC 4151 ...... 154

5.3 MGE Results for Combined Imaging Data of NGC 4151 ...... 155

xiii 6.1 Gaussian Parameters of Data and Fits to Data ...... 196

xiv List of Figures

1.1 AGN structure diagram...... 20

1.2 Ellipsoidal light echo...... 21

1.3 Velocity width vs. time delay...... 22

2.1 NGC 3783 mean and rms UV spectra...... 36

2.2 NGC 3783 mean and rms optical spectra...... 37

2.3 NGC 3783 UV and optical light curves...... 38

2.4 Time lag versus centroid threshold for NGC 3783...... 39

2.5 Light curve cross-correlation for NGC 3783...... 40

2.6 Line width versus time lag for NGC 3783...... 41

3.1 Mean and rms Hα spectra...... 81

3.2 Mean and rms Hβ spectra...... 82

3.3 Light curve cross-correlation...... 83

3.4 Black hole mass versus stellar velocity dispersion...... 84

4.1 Stellar absorption line spectra...... 106

4.2 Virial product versus stellar velocity dispersion...... 107

4.3 Stellar velocity dispersion versus O III line width...... 108

5.1 ACS image of NGC 4151 ...... 135

5.2 MDM image of NGC 4151 ...... 136

xv 5.3 Radial color proﬁle in NGC 4151 ...... 137

5.4 Optical light curve of NGC 4151 ...... 138

5.5 STIS spectrum of NGC 4151 ...... 139

5.6 Residual MDM image of NGC 4151 ...... 140

5.7 Residual ACS image of NGC 4151 ...... 141

5.8 MGE ﬁt to ACS image ...... 142

5.9 MGE ﬁt to MDM image ...... 143

5.10 Example pPXF ﬁt to MMT data ...... 144

5.11 Example pPXF ﬁt to KPNO data ...... 145

5.12 GH parameter ﬁts to MMT spectra ...... 146

5.13 GH parameter ﬁts to KPNO spectra ...... 147

5.14 Orbit model results with BH ...... 148

5.15 Orbit model results with BH (cont.) ...... 149

5.16 Orbit model results with BH (cont.) ...... 150

5.17 Orbit model results with BH (cont.) ...... 151

5.18 Orbit model results with BH (cont.) ...... 152

6.1 AGES-I completeness ...... 184

6.2 Method of FWHM measurement ...... 185

6.3 Examples of AGES-I spectra ...... 186

6.4 Recalibration of Mg II scaling relation ...... 187

6.5 Dependence of BH masses on Mg II FWHM ...... 188

6.6 AGN luminosity versus redshift ...... 189

6.7 BH mass versus AGN luminosity ...... 190

xvi 6.8 Eddington ratio distribution in redshift-luminosity bins ...... 191

6.9 BH mass versus AGN luminosity for rejected objects ...... 192

6.10 Eddington ratio distribution in redshift-mass bins ...... 193

6.11 Eddington ratio distributions not biased by selection eﬀects ...... 194

6.12 Eddington ratio distributions accounting for removed objects . . . . . 195

xvii Chapter 1

Introduction

The last ﬁve years have seen rapid advancement in our understanding of the role that supermassive black holes (BHs) play in the evolution of galaxies. Part of this progress has come from increased conﬁdence in the techniques for measuring

BH masses, and part has arisen from the discovery of new correlations between

BH masses and properties of their host galaxies. Some of these developments have regarded quiescent, or inactive, BHs, and some have come from the study of active galactic nuclei (AGNs; 1.1). §

This dissertation employs several techniques used for measuring BH masses, examining the calibration of such methods and using them to provide BH mass estimates for a large survey of AGNs.

1.1. Active Galactic Nuclei

The observational characteristics of AGNs in the UV and optical bands can be summarized as follows (although certain exceptions exist to many of these generalizations). In imaging data, AGNs (as the moniker suggests) appear as bright,

1 unresolved point-sources at the centers of galaxies. The luminosity of the AGN places it into one of two categories: quasar (brighter: MB < 21.5 mag; rarer in the − local universe) or Seyfert galaxy (fainter: MB > 21.5 mag; more common locally). − Spectroscopically, AGNs are further divided into two classes: Types 1 and 2. Type 1

AGNs typically show broad emission lines of highly ionized atomic species, narrower emission lines (sometimes of the same species as the broad lines, but also of lower ionization atoms), a power-law continuum slope, and, in some cases, absorption features at velocities indicative of fast-moving gas. Type 2 AGNs show only the narrow emission lines and typically a weaker continuum. Nearby galaxies that host

AGNs oﬀer us the best opportunity to study these systems in detail, but often prove to be exceedingly complicated in their structure and kinematics.

The standard model for AGNs consists of a central, supermassive BH (with a

6−10 mass of 10 M¯) surrounded by highly ionized gas, some of which is accreting ∼ onto the BH (and thereby powering the system), and some of which is being driven away from the BH in a wind or outﬂow (by radiative, electromagnetic, or kinetic processes). A recent incarnation of such a model is diagrammed in Figure 1.1.

These kinds of models have come to be favored over earlier versions (in which the broad-line region (BLR) was made up of many small clouds) because they provide a simpler explanation for a variety of AGN phenomena (as suggested by the number of labels in Fig. 1.1) and because very high spectral resolution has yet to see the broad emission lines break into clumps of material with discrete velocities,

2 as one would expect for “clouds” of any appreciable size. The smoothness of the emission lines is easier to understand in a disk-wind model.

Whatever the precise geometry and kinematic structure of the BLR, the gas close enough to the BH to produce the emission lines of highly ionized species is strongly inﬂuenced by the gravity of the BH. This was demonstrated most convincingly with the advent of reverberation mapping.

1.2. Reverberation Mapping

The fundamental idea of reverberation mapping is that by watching a light echo propagate through an AGN, you can learn about the spatial and kinematic distribution of the BLR gas (Blandford & McKee 1982; Peterson 2001). In the simplest case, one can imagine a rapid burst of ionizing photons being emitted from very close to the BH (something akin to a ﬂashbulb going oﬀ), and as these photons expand outward in a shell, they encounter ions of the BLR and increase the strength of their emission lines. After the shell of photons has passed, the emission lines return to their prior state (determined by the steady-state ionization conditions of the BLR).

Because the BLR is not yet spatially resolved with interferometric techniques, reverberation mapping is currently a spectroscopic method. As such, the main properties measured by such studies are the light-travel-time (i.e. the distance)

3 between the BH and the BLR (determined from the time delay between variations in the ionizing continuum and the emission line response), and the velocity of the gas in the BLR (determined by the width of the emission line). The key elements of these measurements are described below.

1.2.1. Time Delay

While the light echo propagates through the BLR in a radial direction and impinges on all gas at a given distance, R, from the BH at the same, unless the

BLR takes the form of a perfectly face-on thin disk, the 3-D geometry of the system will spread out the emission line response from a given R over a time span of up to

2R/c, where c is the speed of light. Moreover, because the emission line arises from a range in radius, the line strength at a given time will be the sum of the gas response at each point that intersects the expanding ellipsoid that characterizes the material illuminated at a ﬁxed value of the time delay (cross-sections of such ellipsoids are shown in Fig. 1.2).

Formally, the responses of the emission line to the continuum changes are determined by the product of the ionizing continuum light curve and the “transfer function” that describes the gas kinematic and spatial distribution:

∞ L(t) = Ψ(τ)C(t τ)dτ, (1.1) Z0 − 4 where L(t) is the emission line ﬂux as a function of time t, Ψ is the transfer function,

C(t τ) is the continuum ﬂux at a point in time that is τ earlier than t. The transfer − function is also a function of line-of-sight velocity, but the quality of data needed to perform velocity-resolved reverberation mapping (dubbed “2-D reverberation mapping”) requires observational resources of a level only practical for a dedicated instrument (e.g., Kronos; Peterson et al. 2004b).

Reverberation mapping campaigns can be rather demanding of observational resources. To accurately resolve the timing of the BLR response to continuum

ﬂuctuations, the sampling interval between observations must be much shorter than the delay time and the duration should exceed the time delay by more than a factor of two. Beyond these requirements, AGN variability is irregular, often entering relatively stable states of signiﬁcant length. A strong event (either rising or falling) in the continuum light curve is essential for measuring an accurate time delay—without an extremely long campaign, a bit of luck is crucial.

In practice, almost all reverberation mapping data has been insuﬃcient to constrain the transfer function, and reverberation analysis has instead relied on cross-correlation techniques. The light curves are measured for the emission line and the continuum region (measured over some line-free wavelength range) and then cross-correlated with one of two methods: the interpolated cross-correlation function

(ICCF), or the discrete correlation function (DCF).

5 The ICCF method uses linear interpolation between points in the light curve to allow calculation of the cross-correlation coeﬃcient at any amount of time delay between the continuum light curve and the emission line response (Gaskell

& Peterson 1987; White & Peterson 1994). The typical implementation of this technique (1) shifts one dataset; (2a) interpolates between points of the shifted light curve; (3a) calculates the correlation coefficient; (2b) interpolates between the points in the other light curve; (3b) calculates the correlation coefficient; (4) takes the mean of the two cross-correlation coefficients.

Alternatively, the DCF (Edelson & Krolik 1988) uses an unmodified version of one light curve and the mean flux value of data within a bin centered on whatever time delay is being considered. The bin width can be modified for a given dataset to balance between resolving the time delay and providing enough data points per bin. A variant of this technique, the Z-Transformed DCF (ZDCF; Alexander 1997), adapts the bin size to produce the desired number of points in each bin. However,

Gaskell (1994) notes that the DCF also relies on interpolation, but does so in the correlation function, rather than the original time series.

Both methods operate by calculating the correlation coeﬃcient, r:

(x x¯)(y y¯) r = i − i − (1.2) (xP x¯)2 (y y¯)2 i − i − ³qP ´ ³qP ´ 6 where (xi, yi) is the ith flux value pair (i.e., a flux point in one light curve and the corresponding interpolated or binned flux value), and x¯ and y¯ are the mean fluxes in the x and y light curves.

Once the ICCF or DCF has been computed for a range of time delay values, the task remains of identifying the best estimate of the “true” time delay. One approach is to simply take the peak, τp, the time delay value with the highest value of the cross-correlation coeﬃcient. While the determination of this quantity from the data is unambiguous, it can be extremely sensitive to small changes in the data. A preferable method is to measure the centroid of the correlation function,

τc. One virtue of using the centroid is that it is more clearly related to the transfer function: in the limit of inﬁnite-duration light curves, the centroid of the correlation function is equal to the centroid of the transfer function. In practice, the centroid is calculated based only on values above some threshold, typically 80% of the peak r value. Koratkar & Gaskell (1991a) show how the choice of this threshold value can impact the calculated centroid.

To assess the uncertainties in the time lags, we used the Monte Carlo method described by Peterson et al. (1998). This technique for model-independent error estimation consists of two components, each testing for a separate contribution to the cross-correlation uncertainty. To account for the uncertainty in an individual

ﬂux measurement, each data point in the light curve is altered by a random Gaussian deviation that corresponds to the ﬂux error. The result of many such realizations,

7 referred to as “ﬂux randomization” (FR), should yield average values equal to the original data with standard deviations given by the original uncertainties.

Secondly, the effects of non-uniform temporal sampling of the AGN fluctuations are investigated with “random subset selection” (RSS). Given a sample of N observations, N data points are randomly chosen from the set (ignoring whether they have been chosen previously). While DCF (and ZDCF) analyses can weight multiply-selected data, the ICCF does not consider the flux uncertainties and simply excludes the redundant data points. Ignoring these data reduces the set by N/e ∼ on average and so should yield a wider range of peak lags from the ICCF. Repeated

Monte Carlo realizations (typically at least 103, combining the FR/RSS methods for each calculation) are used to create a cross-correlation peak distribution (CCPD;

Maoz & Netzer 1989), which provides an empirical measurement of the uncertainties for both τc and τp, based on the τ values which encompass 68% of the realizations.

For well-sampled light curves, the ICCF is generally in good agreement with the results from the DCF and usually has much smaller uncertainties in the time lag, although it is more susceptible to producing spurious correlations (White &

Peterson 1994; Litchﬁeld et al. 1995).

8 1.2.2. Velocity Width

The other quantity used in reverberation mapping is the width of the variable emission lines, V . Many early reverberation mapping efforts calculated V from a mean spectrum created from the entire dataset (typically having a very high signal-to-noise ratio, S/N). However, a better way to isolate the BLR gas that is giving rise to the time delay measurement is to construct the rms spectrum. The rms spectrum will remove any constant spectral features, e.g., narrow emission lines arising from much larger distances from the BH (and so varying over much slower time scales), and host galaxy contribution. The advantage of only measuring the variable part of the spectrum comes at the cost of a lower S/N spectrum from which to measure V . Previous work examining the difference between using the mean and rms spectra have not produced significantly different results (e.g., Kaspi et al. 2000), but in principle the rms spectrum should better trace the gas with which we are concerned.

The most common measurement of V is the full-width-at-half-maximum

(FWHM), which, for a Gaussian emission line shape, is equal to 2.35σG, where σG is the dispersion of the Gaussian. Recently, Peterson et al. (2004a) advocated the use of σline, the line dispersion, deﬁned as:

2 2 2 λ F (λ)dλ λF (λ)dλ σline = , (1.3) R F (λ)dλ − "R F (λ)dλ # R R 9 where λ is the wavelength, F (λ) is the line flux at λ, and the integrals extend over the wavelength range of the line. Measurements of σline are preferable to the FWHM because they are well-defined for any line profile and are less sensitive to features near the line center (e.g., residual narrow-line components).

1.2.3. BH Mass

The virial theorem predicts a relationship between time delay and velocity width of a form, τ V −2. For objects in which multiple emission lines have been ∝ reverberation mapped, the data are in excellent agreement with the virial expectation

(Fig. 1.3). The time delay and the velocity width can be used to estimate the BH mass via the following relationship:

c τV 2 M = f , (1.4) BH G where c is the speed of light, G is Newton’s constant, and f is a factor that accounts for the geometry and detailed kinematics of the BLR gas. The quantity (c τV 2/G) is called the virial product, and is equal to the BH mass to within the factor f. The close ﬁt to a virial relationship among the diﬀerent emission lines of a given object in Figure 1.3 means that the lines give a consistent value of the virial product.

The value of the scale factor f has not been well constrained. The most commonly used value has been 0.75 (Netzer 1990), which comes from assuming that

10 the velocity distribution in the BLR is isotropic and that the circular velocity at the radius given by τ is equal to half of the FWHM. A few authors have pursued other estimates of f (e.g., McLure & Dunlop 2001; Wu & Han 2001; McLure & Dunlop

2002), but these rely on modeling with some severe assumptions. Chapter 4 provides the ﬁrst empirical calibration of the average value of f that is independent of any

BLR modeling.

1.3. Stellar Dynamical BH Masses

In a few dozen quiescent galaxies, the technique of stellar dynamics has been used to estimate BH masses. The general principles of this method will be described here, leaving a more detailed treatment for Chapter 5.

In contrast to the approach used to measure the mass of the BH at the center of the Milky Way, the motions of individual stars cannot be observed in galaxies beyond the Local Group. Instead, the gravitational inﬂuence of the BH must be discerned from the collective distribution of orbital motions for all stars within the observed region of the galaxy (where the observed region is commonly deﬁned by the slit width of a long-slit spectroscopic observation and the spatial extraction window of the spectrum). Moreover, because the velocity information is coming from the

Fizeau shift (the photon equivalent of a sound wave’s Doppler shift; Fizeau 1848), only the component of the velocity along the line of sight is measurable. These shifts

11 are determined with stellar absorption lines arising in the atmospheres of red giant stars (spectral classes G and K). The lines are intrinsically much narrower than the observed proﬁles in the centers of galaxies, so the broadening is taken to be a measure of the distribution of velocities among the diﬀerent stars. The line-of-sight velocity distribution (LOSVD) is a composite, weighted by luminosity and line strength, of all stars within the observed window. Studies of stellar dynamics use the detailed shape of the LOSVD as a constraint for modeling the mass of the central

BH.

The ﬁrst step in the modeling process is to build a picture of the mass distribution of the stars in the galaxy. Images of the galaxy are used to estimate the total light being emitted by the stars. One then assumes (often based on the observed colors of the stars) a value for the mass-to-light ratio (M/L), and this provides a 2-D map of the stellar mass distribution. The 2-D mass distribution is then deprojected into a 3-D mass proﬁle based on assumptions about the intrinsic shape and orientation of the galaxy.

An integral of motion is any function of a particle’s 3-D position and 3-D velocity that is constant along a given orbit. Orbits in galactic gravitational potentials are often deﬁned by three integrals of motion: the energy of the orbit, the vertical angular momentum of the orbit, and a third quantity that has no simple form but can implemented numerically (see, e.g., Ollongren 1962; Richstone 1982;

Famaey et al. 2002). Applying the technique of orbit superposition (Schwarzschild

12 1979; Cretton et al. 1999), within the 3-D mass distribution for the galaxy, one selects a series of regularly spaced positions and values for the parameters defining the integrals of motion. Test particles are placed at these positions in phase space and followed for several hundred orbits through the potential. This is done for thousands of different orbits. A spatial grid is overlaid on the galaxy and the amount of time an orbit spends inside each box of the grid and its line-of-sight velocity within the box are tabulated. The linear combination of orbits that provides the best fit to the observed LOSVD is then determined.

To the original mass model, one can add the gravity of a central BH with a given mass and then recalculate the orbits and the best ﬁt to the observations. The relative quality of the ﬁts from one BH mass to the next provides an estimate of the most likely value of the BH mass and its uncertainty.

Recently, Silge et al. (2005) made an estimate for the BH mass in the Seyfert 2 galaxy, Centaurus A (NGC 5128)—the ﬁrst stellar dynamic BH measurement in an

AGN. This measurement was made possible by the combination of a large telescope

(the Gemini-South 8 m), sensitive near-infrared instruments (to penetrate the broad swath of obscuring material in front of the nucleus of Cen A), and the modern computing resources required for the timely integration of 10,000 orbits for each of many tens of parameter sets. This measurement is important because it provides a needed (although strongly model-dependent) point of comparison with estimates of the BH mass from gas dynamics (Marconi et al. 2001; H¨aring-Neumayer et al. 2005;

13 Marconi et al. 2005). What is still missing, however, is a direct point of comparison between stellar dynamics and reverberation mapping. In Chapter 5, we seek to address this missing link.

1.4. Scaling Relations

The remarkable success of the reverberation mapping approach (e.g., Chap. 2) implies that most of the flux in each emission line is coming from a narrow spatial extent, which is able to reverberate quite coherently. The locally optimally emitting cloud model (Baldwin et al. 1995) provides an explanation for this fact, even if cloud-based models have fallen out of favor. Baldwin et al. (1995) show that the maximum flux from a given emission line is produced from a relatively small range in the combination of gas density and ionizing photon density. While AGN conditions may span a large range in, say, ionizing luminosity (both on an object-by-object basis, and as a function of distance), the region of parameter space that can give rise to a strong emission line at any particular luminosity remains tightly confined.

Hence, most of the ﬂux of a given line arises from a small radial span in the BLR, and reverberates in a coherent manner.

That the emission lines are dominated by the small regions where they are most favorably formed explains the incredible similarity among AGN spectra across

14 a wide range of luminosity and redshift, and also oﬀers the possibility of exploiting this fact in the vast number of AGNs which have not been reverberation mapped.

In addition to the tight relationship between time delay and line width described above and illustrated in Chapter 2, reverberation mapping discovered a strong correlation between the radius (i.e. time delay) and the continuum luminosity.

The radius-luminosity (R L) relationship has been established using the optical − continuum at 5100 A˚ and the Hβ emission line (Kaspi et al. 1996, 2000, 2005), and deviates in a slight, but statistically significant way from the na¨ıve prediction of photoionization modeling that R L0.5. This difference may be caused by the ∝ non-linear relationship between the ionizing luminosity in the UV and the optical continuum luminosity. In the local AGN, NGC 5548, Peterson et al. (2002) find that the optical luminosity is proportional to L0.56, which then leads to an R L UV − UV relationship that agrees with the expectations from simple photoionization. Another possibility is that host galaxies have contaminated the optical luminosity estimates of these AGNs and have skewed the observed R L relation away from its true − nature (M. Bentz et al., in preparation).

The existence of the R L relationship means that a measurement of the − continuum luminosity from a single spectrum allows one to estimate the characteristic radius of the emission line gas. Coupled with a single-epoch measurement of the line width, this yields an estimate of the BH mass. To allow BH mass measurements at higher redshifts, these scaling relations have been extended to emission lines at

15 shorter rest wavelengths: Mg II λ2800 (McLure & Jarvis 2002) and C IV λ1549

(Vestergaard 2002). However, it should be noted that the new relationships rely exclusively on intercalibration with the Hβ relation, and are not established independently by reverberation mapping of Mg II or C IV. Several C IV reverberation studies have been conducted, which typically give virial products consistent with those from Hβ (see Peterson et al. 2004a). However, reverberation results for

Mg II have only been published for two objects (NGC 3783: Reichert et al. 1994;

NGC 5548: Clavel et al. 1991, Dietrich & Kollatschny 1995), and these give rather uncertain and somewhat conﬂicting indications as to where Mg II arises in the BLR.

Although subject to greater uncertainties than full reverberation mapping studies, the BH masses produced by these scaling relationships provide an opportunity to estimate the distribution of BH masses for AGNs observed in large spectroscopic surveys (i.e., the Sloan Digital Sky Survey (SDSS; McLure & Dunlop

2004; M. Vestergaard, in preparation), the Two-Degree Field QSO Redshift survey

(2QZ; Corbett et al. 2003), and the AGN and Galaxy Evolution Survey (AGES;

Chap. 6)).

1.5. Focus of This Study

This dissertation examines the key steps in the process of measuring BH masses in AGNs via reverberation mapping and tries to calibrate those masses through two

16 independent means. Reverberation-derived scaling relations are then used to study the population of AGNs at z = 0.5 4. −

In Chapter 2, we present our reverberation mapping analysis of a nearby AGN,

NGC 3783, in which we revise the estimate of its BH mass and dramatically reduce the uncertainty in the mass.

Following similar procedures for three AGNs with lower quality data, we show in Chapter 3 that these objects also beneﬁt from the improved reverberation mapping techniques developed since the data were originally obtained.

Chapter 4 exploits the tight correlation between the stellar velocity dispersions of galaxies and their BH masses to provide the ﬁrst empirical calibration of reverberation-based masses.

An independent test of this calibration is studied in Chapter 5, in which we attempt to measure the BH mass in NGC 4151, a reverberation-mapped AGN, via modeling of stellar dynamics near the BH.

In Chapter 6, scaling relationships established from reverberation mapping results are applied to over 400 AGNs from the AGN and Galaxy Evolution Survey

(AGES), and point to a very narrow distribution of Eddington ratios among AGNs.

This result suggests that BHs tend to be “on” as AGNs, or “oﬀ” as quiescent galaxies with a very sharp (i.e., quick) transition between the two states.

17 Chapter 7 addresses the implications of all of these results and notes a few avenues of future work that would build upon these studies and further test the conclusions we have drawn.

1.6. Published Work

Chapter 2 has been published as Christopher A. Onken, and Bradley M.

Peterson, “The Mass of the Central Black Hole in the Seyfert Galaxy NGC 3783”,

2002, The Astrophysical Journal, 572, 746.

Chapter 3 has been published as C. A. Onken, B. M. Peterson, M. Dietrich,

A. Robinson, and I. M. Salamanca, “Black Hole Masses in Three Seyfert Galaxies”,

2003, The Astrophysical Journal, 585, 121.

Chapter 4 has been published as Christopher A. Onken, Laura Ferrarese, David

Merritt, Bradley M. Peterson, Richard W. Pogge, Marianne Vestergaard, and Amri

Wandel, “Supermassive Black Holes in Active Galactic Nuclei. II. Calibration of the

Black Hole Mass-Velocity Dispersion Relationship for Active Galactic Nuclei”, 2004,

The Astrophysical Journal, 615, 645.

Chapter 6 will be published as Juna A. Kollmeier, Christopher A. Onken,

Christopher S. Kochanek, Andrew Gould, David H. Weinberg, Matthias Dietrich,

Richard Cool, Arjun Dey, Daniel J. Eisenstein, Buell T. Jannuzi, Emeric Le Floc’h,

18 and Daniel Stern, “Black Hole Masses and Eddington Ratios at 0.3 < z < 4”, 2005,

The Astrophysical Journal, submitted.

The previously published works have been formatted to better conform to

Graduate School rules, and edited to improve continuity and clarity.

19 20

Fig. 1.1.— Cartoon of AGN structure from Elvis (2000). To observer

0.01r/c

0.5r/c

2r/c r/c 1.5r/c

Fig. 1.2.— Cross-sections of reverberating light echo. As time advances, the signal reaching the observer from radiation emitted near the BH is deﬁned by the surface of an expanding ellipsoid with foci at the BH and the observer, and a semi-major axis equal to (0.5d + 2ct), where d is the distance between the BH and the observer, c is the speed of light, and t is the time elapsed since the radiation reached the observer directly. From Peterson (2001).

21 1016 cm 1017 cm 30,000

3C 390.3

10,000 ) 1 − s m k ( M H W F V 3000 NGC 5548 NGC 7469

1000 1 10 100 Lag (days)

Fig. 1.3.— Log V as a function of log τ for three AGNs in which multiple emission lines have been reverberation mapped. The virial theorem predicts a relationship with a slope of 2. The solid lines show the best fits to the data from each object with fixed − slope equal to the virial value. Dotted lines show the best fits with unconstrained slopes (which are consistent with the virial expectation in all three cases). From

Peterson (2001). 22 Chapter 2

Reverberation Mapping of NGC 3783

2.1. Introduction

As the AGN community’s experience with RM campaigns and datasets increased, the techniques of RM analysis were revised and improved. While the treatment of new data made use of these advances, there were a number of existing datasets to which the updated approaches had not yet been applied. We returned to some of these archival data and reﬁned the BH mass measurements for four AGNs

(described here and in Chapter 3).

This chapter details our analysis of the Seyfert 1 galaxy, NGC 3783, and the extensive optical and UV datasets that were obtained from a mixture of space- and ground-based observatories. We describe these data in 2.2, the details of our § analysis techniques in 2.3, our results in 2.4, and their implications in 2.5. § § § 23 2.2. Data

Our study of NGC 3783 combined optical and UV observations from a monitoring campaign carried out in 1991-1992 by the International AGN Watch consortium. The initial results of the seven-month program were published by

Reichert et al. (1994), Stirpe et al. (1994), and Alloin et al. (1995).

2.2.1. UV Data

The IUE observations of NGC 3783 were conducted in 69 separate epochs, with two sampling rates. The ﬁrst interval (of 45 epochs) had an average spacing of 4.0 days, while the ﬁnal 24 epochs observed the AGN with an average spacing of 2.0 days. A more complete description of the UV observing program is provided by

Reichert et al. (1994).

In addition to the original IUE Spectral Image Processing System (IUESIPS),

Reichert et al. (1994) used a Gaussian extraction method (GEX; see Clavel et al. 1991) to obtain the spectra of NGC 3783. After the original data had been taken, a new standard processing pipeline was introduced. The main advantages of the New Spectral Image Processing System (NEWSIPS; Nichols et al. 1993) with respect to the older IUESIPS are the improved photometric accuracy and higher S/N of the spectra; these characteristics have been achieved by introducing a new method of raw data science registration (which both reduces the ﬁxed

24 pattern noise in the images and improves the photometric corrections), a weighted slit extraction method, and re-derived absolute ﬂux calibrations. NEWSIPS also includes corrections for non-linearity that might have aﬀected previous studies.

Overall, NEWSIPS-processed spectra show average S/N increases of 10–50% over

IUESIPS data (Nichols & Linsky 1996).

We retrieved the NEWSIPS-extracted short wavelength prime camera (SWP;

Harris & Sonneborn 1987) spectra from the IUE Final Archive1. While Reichert et al. (1994) analyzed data from both the SWP and long wavelength prime cameras, we have limited our study to observations made with the SWP instrument, which has a wavelength range of 1150–1975 A˚ in the low-dispersion mode (Newmark et al. 1992).

Each spectrum was examined and several types of problems led to spectra being removed from further consideration: (1) low S/N (determined by inspection, but corresponding roughly to a continuum S/N limit of 10); (2) unusual spectral features (possibly due to grazing cosmic-ray impacts); (3) short exposure times

(when longer-exposure data were available from the same epoch and the line flux data were discrepant). Some anomalous features were checked against the GEX frames, from which cosmic ray impacts were carefully removed. Problems with the spectra were ignored in cases where they occurred in spectral regions outside those used in computing line and continuum fluxes. Continuum and emission line flux values were measured using the wavelengths limits listed in Table 3.

1http://ines.laeff.esa.es/ines/

25 The emission line fluxes were measured after the continuum was defined by a linear fit through four spectral regions (1340–1370 A,˚ 1440–1480 A,˚ 1710–1730 A,˚ and 1840–1860 A).˚ An alternate fit through the first three of these regions produced consistent results. Wavelength-specific problems in two cases (SWP 45150, SWP

45206) led us to substitute the alternate continuum ﬁt for these spectra.

We have estimated the ﬂux uncertainties by considering instances in which multiple independent exposures were obtained at the same epoch (i.e., a single pointing toward the target). Flux ratios between pairs of points within each epoch were calculated and the standard deviation of the ﬂux ratios was taken as the fractional uncertainty for all observations. This analysis was conducted independently for each emission line and continuum band. As noted above, however, highly discrepant data were removed prior to this analysis. In spite of our use of an edited dataset, the large number of data pairs contributing to our error estimate

(about 35) justiﬁes our continued use of these values in the analysis. The ﬁnal UV dataset is given in Table 2.2 for the continuum measurements and in Table 2.3 for the emission lines.

2.2.2. Optical Data

Ground-based optical spectroscopy was conducted over the same time period as the IUE observations. The optical data analyzed here were retrieved from

26 the AGN Watch website2, and details of the observations are described by Stirpe et al. (1994). We have limited our investigation to the data gathered at the

Cerro Tololo Inter-American Observatory (CTIO) 1.0 m telescope to ensure the most homogeneous dataset possible for the cross-correlation analysis and for the construction of the mean and rms spectra. Spectra that were excessively noisy or contained other anomalies were discarded from consideration, leaving 37 CTIO observations for further analysis.

Narrow spectral lines are assumed not to vary over the timescales these data are probing. Thus the individual spectra were scaled to a constant ﬂux by using the spectral scaling technique of van Groningen & Wanders (1992). This method computes a smooth scaling function between the input spectrum and a reference (the mean spectrum in this case, shown in Figure 2.2) over a speciﬁed wavelength range.

We scaled over the spectral region 4972–5150 A˚ in order to span the redshifted

[O III] λλ4959, 5007 emission lines and a suitable amount of continuum. We found that two iterations were required for full convergence. This reduced the fractional rms scatter in the [O III] λ5007 light curve (measured between 5028 and 5090 A)˚ to less than 2.5%. Additional iterations failed to produce any light curves with smaller scatter. The mean [O III] λ5007 ﬂux was normalized to 8.44 10−13 erg s−1 cm−2, × the value derived by the careful analysis of Stirpe et al. (1994).

2http://www.astronomy.ohio-state.edu/~agnwatch/

27 Following the calibration of the spectra, the Hβ line was measured between

4830 and 4985 A˚ (with the continuum set by a linear ﬁt between 4800–4820 A˚ and

5130–5150 A).˚ The flux uncertainties were measured in the same way as for the UV data ( 2.2.1), and the results are given in Table 2.5. Due to the smaller optical § dataset, the flux errors for Hβ and the 5150 A˚ continuum rely on only seven data pairs. To be cautious, we have been more conservative in our estimation of the optical flux uncertainties.

2.3. Methods and Techniques

2.3.1. Spectral Analysis

For the reverberation masses calculated here, we measure the line width V as the full width at half maximum (FWHM) of each emission line, and assume f = 0.75 to maintain consistency with previous work (e.g., Wandel et al. 1999; Kaspi et al.

2000).

An rms spectrum was created from the data to isolate the varying parts of the emission lines and it was from this spectrum that the primary FWHM values for the emission lines were measured. The FWHM data were constructed by considering the extreme flux values within the continuum regions, fitting two continuum slopes (to the highest flux levels and lowest flux levels), and averaging the measures of FWHM

28 derived from the two continuum determinations. Finally, the data were converted to their rest-frame widths using z = 0.009730 0.000007 (Theureau et al. 1998). §

2.3.2. Light Curve Analysis

Applying the techniques described by Peterson et al. (1998) and in Chapter 1, we generated cross-correlation functions (CCFs) relating the various emission line light curves to the 1355 A˚ continuum ﬂux. We report both peak (τp) and centroid

(τc) cross-correlation lags. However, the reader should be warned that “lags” in the text will hereafter refer to centroids, unless otherwise noted, and that such lags do not represent a simple phase shift between the light curves.

As Koratkar & Gaskell (1991a) noted for NGC 3783 (and other reverberation- mapped AGNs), the choice of what threshold to use for the centroid calculation can significantly affect the resulting time lag. Figure 2.4 shows that some lines tend toward larger lags and others toward smaller values as the centroid becomes increasingly dominated by the peak value. For the ICCF, we experimented with different interpolation lengths and different thresholds for the calculation of the lag centroid. Our subsequent analysis uses an interpolation unit of 0.1 days in both light curves (interpolating one dataset at a time, with the resulting lags averaged) and a centroid threshold of 80% of the peak correlation coefficient. In addition to the ICCF, we calculated the DCF for each continuum band and emission line. The

29 uncertainties in the time lag calculations were calculated with the FR/RSS methods described in Chapter 1.

2.4. Results

2.4.1. Line widths

We have measured Vrest from both the mean and rms UV spectra (Figure 2.1) and report the results in Table 3. Geocoronal Lyα emission blended into the Lyα spectral region precludes a FWHM measurement for this line and thus also prevents

Lyα contribution to the mass determination, but cross-correlation analysis is still feasible by excluding the contaminated portion of the spectrum (see Table 3).

The same method for measuring Vrest was also applied to the optical data and yielded values of (2.91 0.19) 103 km s−1 for the rms spectrum and (2.65 0.02) 103 § × § × km s−1 for the mean optical spectrum.

2.4.2. Time delays

Figure 2.3 shows the light curves for each of the UV and optical emission lines and continuum bands.

30 In Table 3 we compare the sampling characteristics of our data with the previously published light curves. When we bin the data in each epoch, the variability parameters of the old and new UV datasets appear nearly identical. The

“excess variance”, Fvar, represents the mean fractional variation of each dataset

(see Rodr´igues-Pascual et al. 1997); Rmax is the ratio of maximum to minimum

ﬂux levels. The updated optical dataset is much more sparse than the previously published data because of our desire for the most homogeneous dataset possible.

Emission Lines

The light curves for each emission line (He II λ1640 + O III] λ1663, Si IV λ1400

+ O IV] λ1402, Lyα, C IV λ1549, Si III] λ1892 + C III] λ1909, and Hβ) were run through the ICCF, DCF, and FR/RSS programs, using the 1355 A˚ continuum data as the “driving” light curve. The CCFs and CCPDs are shown for each emission line in the panels of Figure 2.5. The CCPDs are shown to give a graphical indication of the empirical uncertainties and are scaled to the maximum value in each panel.

Each of the emission lines was very well correlated with the continuum ﬂux.

The poorest correlation with the continuum was found for Si III] λ1892 + C III]

λ1909, which was found to have a peak ICCF value of rmax=0.354 (i.e., a probability of arising from an uncorrelated parent population of roughly < 0.001) and we limited the range of computation for this line to 16 days to avoid aliasing. Table 3 § summarizes the previous data and our new results.

31 Our results for the UV emission lines are generally in agreement with those of Reichert et al. (1994). It should be noted, however, that the peak and centroid lags calculated by Reichert et al. (1994) and Stirpe et al. (1994) used the 1460 A˚ continuum as the driving light curve. The results quoted here are consistent with those derived from the recalibrated data with the continuum centered at 1460 A˚ rather than at 1355 A.˚ Because of the large uncertainties assigned to previous lag values, most of our NEWSIPS lags are within 1-σ of the old data. The exceptions are Si III] λ1892 + C III] λ1909, for which the IUESIPS-based data failed to produce any lag at all, and Hβ. The GEX extraction method yielded a peak lag for Si III]

λ1892 + C III] λ1909 similar to what we found, but a centroid lag approximately

2-σ larger than the current result. Our centroid lag for Hβ was only slightly more than 1-σ greater than the previous value.

The signiﬁcant discrepancy between our Hβ results and those of Wandel et al.

+3.6 (1999, 4.5−3.1 days) arises from the double-peaked nature of the CCF. The centroid lag calculated for the 5150 A˚ continuum-Hβ CCF is based on fewer points than the

1355 A˚ continuum-Hβ lag, and gives precedence to the peak at smaller lags. We have greater conﬁdence in the results that use the UV continuum data, and those results closely match the UV-Hβ correlation found by Stirpe et al. (1994).

32 Continuum

Strong evidence for wavelength-dependent continuum lags has been found for only two AGNs (NGC 7469 and Akn 564), but appears to be consistent with simple accretion disk models that predict τ λ4/3 (see Wanders et al. 1997; Collier et ∝ al. 1998, 2001). However, Korista & Goad (2001) note that diﬀuse emission from broad-line clouds can produce a similar wavelength dependence, so the origin of this phenomenon is not clear.

The large uncertainties still present in the NEWSIPS continuum lags prevent us from reasonably testing the τ–λ relationship because the continuum-continuum time lags we ﬁnd are not statistically signiﬁcant (see Table 3).

2.5. Discussion

As the tabular data indicate, the expected pattern of more highly ionized lines having smaller time lags (i.e., originating closer to the ionization source) is reconﬁrmed by our analysis.

rest Figure 2.6 plots Vrest(rms) versus τc for the ﬁve emission lines we measured.

The virial assumption predicts a slope of 0.5 (in log-log space). Deviation from − this relationship would contradict our model, but agreement with the predicted

33 slope cannot rule out other dynamical possibilities (see Krolik 2001, and references therein).

The statistical problem of ﬁtting to intrinsically scattered data with heteroscedastic errors has been addressed with computational methods by Akritas

& Bershady (1996). However, our data has the additional difficulty of asymmetric errors in the lags. To account for the asymmetric time lag uncertainties we first used the larger of the two lag errors and then assessed in which direction the data points differed from the regression. We recalculated the fit using the errors toward the previous regression and confirmed that those were the appropriate choices in the final

ﬁt. The slope of the V (rms) τ rest relation derived by the regression software3 was rest − c 0.450 0.070, consistent with our expectations for a virial relationship (irrespective − § of the speciﬁc multiplicative factor relating the line widths and FWHM values).

Hence, we ﬁxed the slope at 0.5 and calculated the mass independently for each − emission line, applying our previously stated assumption of isotropic BLR gas motion and inserting the appropriate rest-frame values into the following equation:

3 c τ V 2 M = . (2.1) 4 G

Weighting the data by the uncertainty in the direction of the mean (since the lag

6 errors are still asymmetric) yields an average BH mass of (8.7 1.1) 10 M¯. § ×

3available at http://www.astro.wisc.edu/ mab/archive/stats/stats.html ∼ 34 Previous work with IUE archival data having much poorer temporal resolution measured a much larger C IV λ1549 time lag and derived a mass of 7.3+3.5 107 −3.6 ×

M¯ (Koratkar & Gaskell 1991a,b). Wandel et al. (1999) calculated the Hβ lag with respect to the 5100 A˚ continuum from the light curves of Stirpe et al. (1994) and

+1.1 7 then used the rms velocity width to estimate a mass of 1.1 10 M¯. Applying −1.0 × +4.7 6 this method to our version of the optical data yields a BH mass of 6.2 10 M¯, −6.1 × within the 1-σ error bars for our mass measurement with the full dataset. Fromerth

& Melia (2000) employed a diﬀerent means of measuring the velocity dispersion

+0.8 7 from the data of Reichert et al. (1994) and derived masses of 1.6 10 M¯ and −0.4 × +0.8 7 1.3 10 M¯ from Lyα and C IV λ1549, respectively. Various disk accretion −0.5 × 7 models predicting a BH mass in the range of 2.0–7.0 10 M¯ were cited by Alloin × et al. (1995). However, they note the simple nature of these spatially thin, optically thick disk models and the potential for a large discrepancy from the true BH mass.

The dramatic reduction in the relative mass error for NGC 3783 demonstrates the value of both a homogeneous dataset and the improved analysis techniques. The revised results for NGC 3783 comprised one of just four AGNs at the time in which several lines yielded consistent answers for the BH mass, providing increased support for the idea that reverberation mapping is indeed probing the gravity of the BH and is not subject to excessive statistical uncertainties.

35 Fig. 2.1.— Top: rms UV spectrum. Bottom: Mean UV spectrum. Wavelengths delineated above the spectrum indicate emission-line ranges; those below the spectrum mark ranges of continuum ﬂux measurement.

36 Fig. 2.2.— Top: rms optical spectrum. Bottom: Mean optical spectrum. Wavelength indications as in Fig. 1.

37 Fig. 2.3.— UV and optical light curves: (a) 1355 A˚ continuum, (b) 1460 A˚ continuum,

Si IV λ1400 + O IV] λ1402, (g) Lyα, (h) C IV λ1549, (i) Si III] λ1892 + C III] λ1909, and (j) Hβ. Continuum ﬂuxes are in units of 10−15 ergs cm−2 s−1 A˚−1. Emission line

ﬂuxes are given in units of 10−13 ergs cm−2 s−1. 38 Fig. 2.4.— Rest-frame centroid time lag versus threshold level for centroid determination (as a fraction of the peak correlation coeﬃcient). The data plotted are for He II λ1640 + O III] λ1663 (solid), Si IV λ1400 + O IV] λ1402 (short dashed),

Lyα (dotted), C IV λ1549 (long dashed), Si III] λ1892 + C III] λ1909 (dot-short dashed), and Hβ (dot-long dashed).

39 Fig. 2.5.— Results of cross-correlation of the 1355 A˚ continuum with (a) itself; (b)

1460 A˚ continuum; (c) 1835 A˚ continuum; (d) 5150 A˚ continuum; (e) He II λ1640

+ O III] λ1663; (f) Si IV λ1400 + O IV] λ1402; (g) Lyα; (h) C IV λ1549; (i) Si III]

λ1892 + C III] λ1909; (j) Hβ. The solid lines show the ICCFs, the data points are the DCFs, and the dashed lines represent the CCPDs. Note that the y-axis scale for the CCPDs is the fraction of MC realizations producing a centroid of that lag value and is scaled to the maximum in each panel.

40 Fig. 2.6.— Rest-frame velocity FWHM versus rest-frame centroid time lag for the

five emission lines we have measured. The dashed line is the best fit to the data; the solid line is the best fit with fixed slope of -0.5.

41 Table 2.1. NGC 3783 Continuum and Emission Line Wavelength Limits

Line/Band Wavelength Range (A)˚

1355 A˚ continuum 1340–1370 1460 A˚ continuum 1445–1475 1835 A˚ continuum 1820–1850 5150 A˚ continuum 5140–5160 Lyα 1225–1280 Si IV λ1400 + O IV] λ1402 1355–1460 C IV λ1549 1460–1624 He II λ1640 + O III] λ1663 1624–1710 Si III] λ1892 + C III] λ1909 1890–1948 Hβ 4830–4985

42 Table 2.2:: NGC 3783 UV Continuum Flux Data

Image Julian Date

Name (2,440,000+) F(λ1355) F(λ1460) F(λ1835)

SWP 43438 8611.948 60.811 2.432 57.899 2.142 52.244 1.776 § § § SWP 43439 8612.031 57.353 2.294 57.395 2.124 50.582 1.720 § § § SWP 43472 8615.949 51.984 2.079 50.204 1.858 47.259 1.607 § § § SWP 43473 8616.029 51.979 2.079 45.407 1.680 45.024 1.531 § § § SWP 43485 8618.118 47.391 1.896 47.043 1.741 44.713 1.520 § § § SWP 43539 8624.202 60.846 2.434 58.123 2.151 48.605 1.653 § § § SWP 43540 8624.294 61.371 2.455 58.173 2.152 50.031 1.701 § § § SWP 43541 8624.385 58.033 2.321 59.779 2.212 48.735 1.657 § § § SWP 43557 8628.595 46.814 1.873 47.146 1.744 40.850 1.389 § § § SWP 43587 8631.680 36.975 1.479 43.277 1.601 37.136 1.263 § § § SWP 43588 8631.765 41.661 1.666 42.163 1.560 35.594 1.210 § § § SWP 43636 8635.688 45.680 1.827 49.405 1.828 39.628 1.347 § § § SWP 43676 8639.862 53.819 2.153 52.490 1.942 45.264 1.539 § § § Continued on next page...

43 Table 2.2 – Continued

Image Julian Date

Name (2,440,000+) F(λ1355) F(λ1460) F(λ1835)

SWP 43716 8643.948 53.593 2.144 56.866 2.104 47.434 1.613 § § § SWP 43871 8649.367 56.758 2.270 55.327 2.047 48.963 1.665 § § § SWP 43872 8649.454 55.680 2.227 52.634 1.947 46.580 1.584 § § § SWP 43894 8651.756 49.667 1.987 48.990 1.813 43.264 1.471 § § § SWP 43895 8651.855 48.352 1.934 52.337 1.936 41.435 1.409 § § § SWP 43921 8656.130 61.961 2.478 62.436 2.310 53.664 1.825 § § § SWP 43945 8660.040 64.188 2.568 67.311 2.491 51.531 1.752 § § § SWP 43946 8660.121 63.656 2.546 63.607 2.353 52.300 1.778 § § § SWP 43962 8664.048 43.983 1.759 43.716 1.617 40.467 1.376 § § § SWP 43995 8668.022 32.648 1.306 30.813 1.140 31.508 1.071 § § § SWP 43996 8668.115 31.491 1.260 32.760 1.212 32.328 1.099 § § § SWP 44020 8672.106 40.887 1.635 44.671 1.653 38.755 1.318 § § § SWP 44048 8676.272 44.897 1.796 49.399 1.828 44.148 1.501 § § § SWP 44072 8680.310 50.035 2.001 49.829 1.844 42.224 1.436 § § § Continued on next page...

44 Table 2.2 – Continued

Image Julian Date

Name (2,440,000+) F(λ1355) F(λ1460) F(λ1835)

SWP 44099 8684.199 49.072 1.963 38.191 1.413 33.057 1.124 § § § SWP 44100 8684.275 36.331 1.453 39.336 1.455 32.631 1.109 § § § SWP 44126 8688.228 33.912 1.356 27.773 1.028 30.118 1.024 § § § SWP 44149 8692.216 28.542 1.142 30.410 1.125 28.579 0.972 § § § SWP 44176 8695.910 27.667 1.107 29.197 1.080 26.109 0.888 § § § SWP 44189 8699.713 28.465 1.139 27.397 1.014 29.131 0.990 § § § SWP 44208 8703.723 27.708 1.108 24.374 0.902 26.402 0.898 § § § SWP 44237 8707.871 25.508 1.020 33.736 1.248 31.970 1.087 § § § SWP 44267 8711.731 32.335 1.293 45.001 1.665 39.240 1.334 § § § SWP 44307 8715.612 44.933 1.797 49.245 1.822 45.781 1.557 § § § SWP 44349 8719.932 46.150 1.846 55.077 2.038 47.230 1.606 § § § SWP 44350 8720.020 56.100 2.244 54.303 2.009 46.392 1.577 § § § SWP 44381 8724.004 50.768 2.031 44.383 1.642 42.641 1.450 § § § SWP 44408 8727.967 49.801 1.992 44.960 1.664 41.495 1.411 § § § Continued on next page...

45 Table 2.2 – Continued

Image Julian Date

Name (2,440,000+) F(λ1355) F(λ1460) F(λ1835)

SWP 44409 8728.068 42.096 1.684 43.414 1.606 38.242 1.300 § § § SWP 44410 8728.168 45.123 1.805 43.196 1.598 40.839 1.389 § § § SWP 44434 8731.946 43.086 1.723 49.410 1.828 46.087 1.567 § § § SWP 44435 8732.205 49.680 1.987 48.115 1.780 43.598 1.482 § § § SWP 44461 8735.946 48.231 1.929 39.557 1.464 38.632 1.313 § § § SWP 44486 8739.990 41.475 1.659 35.484 1.313 35.752 1.216 § § § SWP 44492 8744.129 37.318 1.493 47.640 1.763 40.569 1.379 § § § SWP 44581 8747.874 44.276 1.771 45.235 1.674 41.850 1.423 § § § SWP 44627 8751.845 45.411 1.816 55.741 2.062 47.994 1.632 § § § SWP 44628 8751.950 51.002 2.040 53.867 1.993 48.992 1.666 § § § SWP 44629 8752.056 53.204 2.128 54.219 2.006 47.375 1.611 § § § SWP 44659 8755.872 52.803 2.112 46.318 1.714 45.237 1.538 § § § SWP 44660 8755.949 47.175 1.887 44.828 1.659 40.003 1.360 § § § SWP 44682 8759.702 47.448 1.898 51.934 1.922 48.939 1.664 § § § Continued on next page...

46 Table 2.2 – Continued

Image Julian Date

Name (2,440,000+) F(λ1355) F(λ1460) F(λ1835)

SWP 44731 8763.559 52.863 2.115 44.915 1.662 42.596 1.448 § § § SWP 44760 8767.535 47.646 1.906 45.992 1.702 41.306 1.404 § § § SWP 44803 8771.689 47.353 1.894 47.380 1.753 41.833 1.422 § § § SWP 44804 8771.772 52.010 2.080 46.543 1.722 42.305 1.438 § § § SWP 44830 8775.633 46.666 1.867 44.004 1.628 38.184 1.298 § § § SWP 44873 8779.607 54.715 2.189 54.094 2.001 53.352 1.814 § § § SWP 44907 8783.948 56.424 2.257 54.764 2.026 49.191 1.672 § § § SWP 44918 8785.949 57.362 2.294 55.285 2.046 50.312 1.711 § § § SWP 44921 8787.786 57.131 2.285 57.471 2.126 49.797 1.693 § § § SWP 44922 8787.864 56.597 2.264 59.267 2.193 46.567 1.583 § § § SWP 44935 8790.113 54.404 2.176 60.190 2.227 50.947 1.732 § § § SWP 44949 8791.769 60.256 2.410 55.655 2.059 49.797 1.693 § § § SWP 44950 8791.857 70.247 2.810 55.465 2.052 55.578 1.890 § § § SWP 44964 8793.963 57.656 2.306 56.226 2.080 48.742 1.657 § § § Continued on next page...

47 Table 2.2 – Continued

Image Julian Date

Name (2,440,000+) F(λ1355) F(λ1460) F(λ1835)

SWP 44974 8795.768 56.318 2.253 53.796 1.990 48.098 1.635 § § § SWP 44992 8797.448 54.836 2.193 53.977 1.997 46.297 1.574 § § § SWP 44993 8797.538 52.793 2.112 54.654 2.022 46.258 1.573 § § § SWP 45010 8799.460 54.291 2.172 47.346 1.752 50.123 1.704 § § § SWP 45024 8801.764 55.805 2.232 50.718 1.877 45.454 1.545 § § § SWP 45025 8801.887 49.579 1.983 54.021 1.999 43.688 1.485 § § § SWP 45026 8801.996 44.498 1.780 52.914 1.958 44.756 1.522 § § § SWP 45038 8803.458 52.139 2.086 58.489 2.164 49.668 1.689 § § § SWP 45052 8805.543 50.742 2.030 61.563 2.278 52.663 1.791 § § § SWP 45063 8807.520 51.641 2.066 59.254 2.192 50.333 1.711 § § § SWP 45064 8807.603 51.587 2.063 62.612 2.317 54.971 1.869 § § § SWP 45081 8809.509 59.759 2.390 57.843 2.140 50.158 1.705 § § § SWP 45082 8809.601 60.228 2.409 53.138 1.966 51.993 1.768 § § § SWP 45096 8811.493 63.860 2.554 55.395 2.050 49.903 1.697 § § § Continued on next page...

48 Table 2.2 – Continued

Image Julian Date

Name (2,440,000+) F(λ1355) F(λ1460) F(λ1835)

SWP 45097 8811.595 56.369 2.255 52.657 1.948 50.072 1.702 § § § SWP 45106 8813.384 51.571 2.063 54.998 2.035 47.810 1.626 § § § SWP 45118 8816.028 57.179 2.287 51.851 1.918 45.563 1.549 § § § SWP 45133 8818.024 57.305 2.292 42.796 1.583 39.882 1.356 § § § SWP 45150 8819.700 54.163 2.167 37.296 1.380 § § · · · SWP 45151 8819.800 52.810 2.112 38.618 1.429 38.881 1.322 § § § SWP 45152 8819.904 41.373 1.655 37.208 1.377 38.237 1.300 § § § SWP 45167 8821.689 39.568 1.583 45.306 1.676 44.545 1.515 § § § SWP 45168 8821.791 48.325 1.933 47.669 1.764 46.635 1.586 § § § SWP 45169 8821.892 51.088 2.044 53.395 1.976 43.804 1.489 § § § SWP 45194 8824.353 50.394 2.016 63.151 2.337 52.316 1.779 § § § SWP 45195 8824.440 61.519 2.461 60.085 2.223 51.566 1.753 § § § SWP 45206 8825.701 60.748 2.430 63.864 2.363 § § · · · SWP 45207 8825.798 66.760 2.670 62.632 2.317 53.268 1.811 § § § Continued on next page...

49 Table 2.2 – Continued

Image Julian Date

Name (2,440,000+) F(λ1355) F(λ1460) F(λ1835)

SWP 45219 8827.904 67.384 2.695 67.817 2.509 59.430 2.021 § § § SWP 45227 8829.302 69.254 2.770 59.651 2.207 56.059 1.906 § § § SWP 45237 8831.317 70.910 2.836 67.452 2.496 58.335 1.983 § § § SWP 45246 8833.326 72.855 2.914 76.033 2.813 59.754 2.032 § § §

Continuum ﬂuxes are given in units of 10−15 ergs cm−2 s−1 A˚−1.

50 Table 2.3:: NGC 3783 UV Emission Line Flux Data

Image Julian Date He II λ1640 + Si IV λ1400 + Si III λ1892 +