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\title{Optical/UV Band
Reverberation Mapping of NGC 5548 with Frequency-Resolved Techniques}
\author{Adamo}
\date{August 19, 2016}
\author{Otho A. Ulrich,$^{1,2}$ Edward M. Cackett$^{1}$\\
$^{1}$Department of Physics and Astronomy, Wayne State University\\
$^{2}$Department of Physics, Western Michigan University\\
}
\date{August 20, 2016}
\maketitle
@ -29,11 +32,11 @@ Power spectral densities and time lags of 19 wavelength bands are recovered as p
\section{Introduction}
\label{sec:intro}
Active galactic nuclei (AGN) are distant, powerfully luminous compact objects, with strongly variable spectra that have no recognized period. There is strong observational evidence that AGN influence galactic evolution through a process called AGN feedback (see \cite{2012ARA&A..50..455F} for a detailed review). Due to their immense luminosities, AGN are prime candidates for serving as standard candles to measure fundamental cosmological parameters -- well beyond the supernova horizon. The Hubble constant $H_0$ and deceleration parameter $q_0$ respectively describe the rate at which the universe is expanding and the rate at which gravity within the universe resists that expansion. \cite{1999MNRAS.302L..24C} presents a method for measuring these parameters by observing the wavelength-dependent time delays emergent from AGN systems, and this approach has been corroborated by \cite{2007MNRAS.380..669C}. Constraint of these parameters depends on properly modelling the light echo, or reverberation, effects within AGN. This work endeavors towards a better understanding of the accretion disk structure of AGN.
Active galactic nuclei (AGN) are distant, powerfully luminous compact objects, with strongly variable spectra that have no recognized period. There is strong observational evidence that AGN influence galactic evolution through a process called AGN feedback (see \cite{2012ARA&A..50..455F} for a detailed review). Due to their immense luminosities, AGN are prime candidates for serving as standard candles to measure fundamental cosmological parameters -- well beyond the supernova horizon. The Hubble constant $H_0$ and deceleration parameter $q_0$ respectively describe the rate at which the universe is expanding and the rate at which gravity within the universe resists that expansion. \cite{1999MNRAS.302L..24C} presents a method for measuring these parameters by observing the wavelength-dependent time delays emergent from AGN systems, and this approach has been corroborated by \cite{2007MNRAS.380..669C}. Constraint of these parameters depends on properly modelling the light echo, or reverberation, effects within AGN. This work endeavors toward a better understanding of the accretion disk structure of AGN.
AGN systems are complex, with the widely-accepted picture having a super-massive black hole (SMBH) at the center, surrounded by an accretion disk, a much larger broad line region, an obscuring torus, and a relativistic matter jet. In almost all cases, astronomers are unable to resolve the configurations of these systems directly, because their angular size is far too small, so the geometry must be inferred using some other method. Reverberation mapping refers to the technique of inferring the configuration of a system by analysing the observed time lags between wavelength bands and recovering the transfer function which encodes the system geometry. It uses echoes of light to map the region surrounding the SMBH, analogous to mapping the sea floor using sonar. \cite{1999MNRAS.302L..24C} and \cite{2007MNRAS.380..669C} provide methods for constraining Hubble's constant and the deceleration parameter, with increasing certainty as the size of the dataset grows. While retaining sight of that ultimate goal, this work has a less-encompassing scope. The thermal reprocessing hypothesis describes the reprocessing of high-energy electromagnetic emission by the accretion disk; it is explained in greater detail in section \ref{sec:reverbmap}. The work executed herein attempts to test that hypothesis as one step toward greater understanding of the structure of AGN.
The Type-I Seyfert galaxy NGC 5548 is one of the most studied Seyfert galaxies, and yet remains an object of intense interest. Seyfert galaxies are a subclass of AGN that are found in the local universe. The Space Telescope and Optical Reverberation Mapping Project encompasses the most in-depth study of NGC 5548 yet performed \citep{2015ApJ...806..128D} \citep{2015ApJ...806..129E} \citep{2016ApJ...821...56F}. In STORM III, \cite{2016ApJ...821...56F} published the most complete set of time-dependent light curves yet collected for this object in the optical and UV spectrum. In section \ref{sec:reverbmap}, the theory of reverberation mapping is described in more detail, including details on using frequency-domain analyses to elucidate observed time delays between the wavelength bands, and determining the geometry of the system from the observed time delays by recovering the transfer function. In section \ref{analysis}, these methods are applied to the NGC 5548 light curves published in STORM III. Finally, the results are discussed in the context of whether they support the thermal reprocessing hypothesis.
The Type-I Seyfert galaxy NGC 5548 is one of the most studied Seyfert galaxies, and yet remains an object of intense interest. Seyfert galaxies are a subclass of AGN that are found in the local universe. The Space Telescope and Optical Reverberation Mapping Project (STORM) encompasses the most in-depth study of NGC 5548 yet performed \citep{2015ApJ...806..128D} \citep{2015ApJ...806..129E} \citep{2016ApJ...821...56F}. In part III of STORM, \cite{2016ApJ...821...56F} published the most complete set of time-dependent light curves yet collected for this object in the optical and UV spectrum. In section \ref{sec:reverbmap}, the theory of reverberation mapping is described in more detail, including details on using frequency-domain analyses to elucidate observed time delays between the wavelength bands, and determining the geometry of the system from the observed time delays by recovering the transfer function. In section \ref{analysis}, these methods are applied to the NGC 5548 light curves published in STORM III. Finally, the results are discussed in the context of whether they support the thermal reprocessing hypothesis.
\section{Reverberation Mapping}
@ -46,7 +49,7 @@ Reverberation mapping has become a standard technique for calculating the black
\subsection{Continuum Reverberation}
\label{sec:cont_reverb}
The thermal reprocessing hypothesis suggests that a hot accretion disk is incident upon a central SMBH. High-energy EM emission, possibly in the form of X-rays, illuminate the disk, driving an increase in temperature in the disk that propagates at the speed of light. \cite{1999MNRAS.302L..24C} provides a model for the average expected time lag $\tau$ as a function of wavelength band $\lambda$, presented in equation \ref{eq:timelag}.
The thermal reprocessing hypothesis suggests that a hot accretion disk is incident upon a central SMBH. High-energy EM emission, possibly in the form of X-rays, illuminate the disk, driving an increase in temperature in the disk that propagates at the speed of light. \cite{1999MNRAS.302L..24C} provide a model for the average expected time lag $\tau$ as a function of wavelength band $\lambda$, presented in equation \ref{eq:timelag}.
\begin{equation}
\label{eq:timelag}
@ -134,16 +137,16 @@ Reverberation mapping has become a standard technique for calculating the black
Some X-ray datasets contain gaps due to the approximately 90-minute orbital period for satellites in low-Earth orbit, which motivated the work by \cite{2013ApJ...777...24Z}, where a maximum likelihood method is used to perform the frequency-domain analyses prepared in section \ref{sec:freq_analysis} on light curves with gaps. Since its development, this technique has found success among studies of observations captured by low-orbit X-ray telescopes that exceed the telescopes' orbital periods, such as the analysis performed by \cite{2016Natur.535..388K}. For the first time, we are applying these techniques to UV/optical data, making use of the high-quality light curves published in STORM III. If successful, they may provide new insight into the reverberations present in the accretion disk and other structures of the nucleus in NGC 5548.
\section{Analysis}
\section{Analysis of Light Curves in STORM III}
\label{analysis}
\cite{2016ApJ...821...56F} published the best dynamic data yet collected from NGC 5548 over a 260-day period, for 19 bands throughout the optical and into the UV domains. They are presented in figure \ref{fig:lightcurves}. These data were collected from a variety of observatories, including space and ground-based facilities, and thus have significantly uneven and variable sampling rates. In STORM III, a reverberation mapping analysis is performed using cross-correlation to find the average time lag for each wavelength (figure \ref{fig:cc_analysis}). These results are superposed over some possible models and while lags increase with wavelength as expected from the the accretion disk model, the amplitude of the lags is about 10 times larger than expected based on the observed flux of the source, meaning that our understanding of accretion disk structure and/or reprocessing is incomplete. More information is contained in the light curves, so a frequency-domain analysis should provide better constraints.
In part III of the Space Telescope and Optical Reverberation Mapping Project, \cite{2016ApJ...821...56F} published the best dynamic data yet collected from NGC 5548 over a 260-day period, for 19 bands throughout the optical and into the UV domains. They are presented in figure \ref{fig:lightcurves}. These data were collected from a variety of observatories, including space and ground-based facilities, and thus have significantly uneven and variable sampling rates. In STORM III, a reverberation mapping analysis is performed using cross-correlation to find the average time lag for each wavelength (figure \ref{fig:cc_analysis}). These results are superposed over some possible models and while lags increase with wavelength as expected from the the accretion disk model, the amplitude of the lags is about 10 times larger than expected based on the observed flux of the source, meaning that our understanding of accretion disk structure and/or reprocessing is incomplete. More information is contained in the light curves, so a frequency-domain analysis should provide better constraints.
The uneven sampling of these data suggest that the maximum likelihood method developed by \cite{2013ApJ...777...24Z} is a reasonable candidate for analysing them. Using the method described in section \ref{sec:uneven_data}, the power spectral densities and time lags as functions of temporal frequency are computed for each band in the dataset -- 18 bands not including the reference band. The 1367\AA$ $ light curve, obtained from observations made with the Hubble Space Telescope, is chosen as the reference curve. The power spectral density for 1367\AA$ $ is presented in figure \ref{fig:psd_1367}, giving a description of the flux variability seen in that band. Figure \ref{fig:timelag_7647} provides the time lag of variability observed at 7647\AA$ $ relative to 1367\AA$ $.
\begin{figure}
\centering
\includegraphics[width=1\linewidth]{../img/lightcurves.pdf}
\captionof{figure}{Data published by \cite{2016ApJ...821...56F} in STORM III show highly-variable light curves with significantly uneven sampling.}
\captionof{figure}{Data published by \cite{2016ApJ...821...56F} in STORM III show strongly-variable light curves with significantly uneven sampling.}
\label{fig:lightcurves}
\end{figure}