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100644 index 0000000..660ec3d --- /dev/null +++ b/press/report/report.tex @@ -0,0 +1,320 @@ +% mnras_template.tex +% +% LaTeX template for creating an MNRAS paper +% +% v3.0 released 14 May 2015 +% (version numbers match those of mnras.cls) +% +% Copyright (C) Royal Astronomical Society 2015 +% Authors: +% Keith T. Smith (Royal Astronomical Society) + +% Change log +% +% v3.0 May 2015 +% Renamed to match the new package name +% Version number matches mnras.cls +% A few minor tweaks to wording +% v1.0 September 2013 +% Beta testing only - never publicly released +% First version: a simple (ish) template for creating an MNRAS paper + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Basic setup. Most papers should leave these options alone. +\documentclass[a4paper,fleqn,usenatbib]{article} + +% MNRAS is set in Times font. If you don't have this installed (most LaTeX +% installations will be fine) or prefer the old Computer Modern fonts, comment +% out the following line +\usepackage{newtxtext,newtxmath} +% Depending on your LaTeX fonts installation, you might get better results +% with one of these: +%\usepackage{mathptmx} +%\usepackage{txfonts} + +% Use vector fonts, so it zooms properly in on-screen viewing software +% Don't change these lines unless you know what you are doing +\usepackage[T1]{fontenc} +\usepackage{ae,aecompl} + + +%%%%% AUTHORS - PLACE YOUR OWN PACKAGES HERE %%%%% + +% Only include extra packages if you really need them. Common packages are: +\usepackage{graphicx} % Including figure files +\usepackage{amsmath} % Advanced maths commands +\usepackage{amssymb} % Extra maths symbols + +\begin{document} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +%%%%% AUTHORS - PLACE YOUR OWN COMMANDS HERE %%%%% + +% Please keep new commands to a minimum, and use \newcommand not \def to avoid +% overwriting existing commands. Example: +%\newcommand{\pcm}{\,cm$^{-2}$} % per cm-squared + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +%%%%%%%%%%%%%%%%%%% TITLE PAGE %%%%%%%%%%%%%%%%%%% + +% Title of the paper, and the short title which is used in the headers. +% Keep the title short and informative. +\title[Optical Reverberation with Max Likelihood; NGC 5548]{Optical +Reverberation Mapping of NGC 5548 with Maximum Likelihood} + +% The list of authors, and the short list which is used in the headers. +% If you need two or more lines of authors, add an extra line using \newauthor +\author[Ulrich et al.]{ +Otho A. Ulrich,$^{2}$\thanks{E-mail: otho.a.ulrich@wmich.edu} +Edward M. Cackett,$^{1}$ +\\ +% List of institutions +$^{1}$Department of Physics and Astronomy, Wayne State University, 666 W. +Hancock St., Detroit, MI 48201, USA\\ +$^{2}$Department of Physics, Western Michigan University, Kalamazoo, MI +49008-5252, USA\\ +} + +% These dates will be filled out by the publisher +%\date{Accepted XXX. Received YYY; in original form ZZZ} +\date{August 8, 2016} + +% Enter the current year, for the copyright statements etc. +% \pubyear{2016} + +% Don't change these lines +\label{firstpage} +%\pagerange{\pageref{firstpage}--\pageref{lastpage}} +\maketitle + +% Abstract of the paper +\begin{abstract} +Power spectral densities and time delays of 19 wavelength bands are recovered +as part of a reverberation mapping of NGC 5548. The latest time-variable light +curves are made available in STORM III by \cite{2016ApJ...821...56F}. The +uneven distribution of flux data in those curves necessitates the use of a +maximum likelihood method in conjunction with Fourier transformations to +produce the frequency-dependent values of interest. Variability in the +emissions is confirmed in the power spectral densities, and the time delays +show the expected frequency dependence. The time delays also appear to have +wavelength dependence. There are issues computing accurate error estimates for +both distributions that remain as yet unresolved. The transfer function should +be recoverable once those and any additional computational issues are +resolved. +\end{abstract} + +% Select between one and six entries from the list of approved keywords. +% Don't make up new ones. +\begin{keywords} +keyword1 -- keyword2 -- keyword3 +\end{keywords} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +%%%%%%%%%%%%%%%%% BODY OF PAPER %%%%%%%%%%%%%%%%%% + +\section{Introduction} +The local Type-I Seyfert galaxy NGC 5548, while perhaps the best-studied +active galaxy, remains an object of intense interest and study to modern +astronomy. An extensive observational campaign has been carried out on this +object, producing the most complete set of time-dependent light curves yet +collected from an active galactic nucleus (AGN). The physics underlying the +nature of these light curves is not completely understood, and so remains a +topic of debate and great interest. + + \subsection{Reverberation Mapping} + A primary model of AGN suggests that an accretion disk is incident upon a + central super-massive black hole (SMBH). Electromagnetic emission emergent + from the accreting gases close to the SMBH is reprocessed by the + surrounding gas clouds, resulting in observed response delays between + emission peaks that are dependent on the geometry of the system. The + impulse response encodes this geometry, and astronomers have combined + models for the orbiting gas velocities and ionization states with these + observed time delays to calculate it for some known systems. This + technique has become a standard for calculating the black hole mass of + AGN, and is well-described by \cite{2007MNRAS.380..669C} and + \cite{2014A&ARv..22...72U}. It continues to be refined, and may also + become a tool to measure the black hole spin of these systems + \citep{2016arXiv160606736K}. + + (Probably would be good to put a picture here describing simple + reverberation.) + + Many reverberation mapping techniques involve time-domain analyses, such + as cross-correlation. Time-domain techniques have limitations: + cross-correlation, for instance, provides only the average time delay + between two light curves; they also require data that is evenly-sampled + across the time domain. X-ray reverberation mapping in particular has + developed a body of techniques based on frequency-domain techniques, + primarily Fourier analysis; these techniques still require evenly-sampled + data and have been enabled by the relatively good data coverage in X-ray + bands. They provide the astronomer with more detailed information about + the variability and response delay within the system compared to + time-domain techniques. + + The power spectral density (PSD) as a function of temporal frequency for a + given emission band can be produced using Fourier transforms, providing a + measure of the time-scale of variability in that band. Given two bands, + typically a reference or "driving" band and a delayed or "response" band, + a cross spectrum can also be constructed. From the complex + argument of the cross-correlation function, one can derive the + frequency-dependent time delay between those bands; an important step + toward + constituting the transfer function of a system. Very good explanations of + these techniques and the associated mathematics are available from + \cite{2014A&ARv..22...72U}. + + A top-hat function provides a simple model of the impulse response of a + delayed light curve. A fast Fourier transform method of this impulse + response provides the time delay spectrum as a function of temporal + frequency. This simple model provides a guideline for how the computed + time delays are expected to be distributed as a function of temporal + frequency. + + + (Side-by-side graphic of top-hat impulse response function and FFT of + top-hat giving time delays.) + + \subsection{Unevenly-Spaced Data} + + Some X-ray datasets contain gaps due to orbital mechanics, which motivated + the work in \cite{2013ApJ...777...24Z}, where a maximum likelihood method + is used to perform Fourier 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{2016arXiv160606736K}. Until now, reverberation mapping in the + optical bands has been limited to time-domain techniques. Many datasets + available for these bands have uneven sampling across the time domain, + however, and so do not lend themselves well to time-domain or traditional + frequency-domain analyses. The maximum likelihood method is well-suited + to extracting useful information from the data available in those + datasets. + + + +\section{Analysis} +The 1367\AA$ $ light curve, obtained from observations made with the Hubble +Space Telescope, is chosen as the reference curve. The power spectral +densities and time delays as a function of temporal frequency are computed for +each band in the dataset -- 18 bands not including the reference band. + +The light curves analysed here are unevenly distributed along the time axis, +which suggests that the maximum likelihood method developed by +\cite{2013ApJ...777...24Z} is a reasonable candidate for producing the PSD and +time delays in the frequency domain. The latest version (CHECK THIS) of the +C++ program psdlag associated with that work is used to directly produce the +PSD and cross spectra. The time delay spectrum is produced from the cross +spectrum by dividing it by $2 \pi f$, with $f$ the mean frequency for a given +bin. + + \subsection{Dataset} + \cite{2016ApJ...821...56F} published the best dynamic data yet collected + from NGC 5548 over a 200-day (CHECK THIS) period, for 19 bands throughout + the optical and into the UV spectra. These data were collected from a + variety of observatories, including both space and ground-based + telescopes, and thus have significantly variable sampling rates. + + (Include picture of Fausnaugh data here) + + \subsection{Error Analysis} + For the presented set of resultant data, the error estimates are extracted + from the covariance matrix. This method assumes that the errors between + frequency bins are not correlated, so these values only represent a lower + limit of the true variability. Scanning the likelihood function can + provide better error estimates at the cost of computation time, as can + running Monte Carlo simulations. All of these methods are built into the + psdlag program provided by \cite{2013ApJ...777...24Z}, however, some + issues have prevented proper error analysis using the latter two methods. + This is discussed in more detail in section \ref{results}. + +\section{Results} +\label{results} + + An atlas of the power spectral densities as functions + of temporal frequency for all 18 delayed bands is provided in this section. + One is also provided of the time delay spectra for each band. The reference + band PSD is also provided separately. Errors presented in these atlases + are obtained from the covariance matrix. + + (Atlas of PSD) + + (Atlas of Time Delays) + + \subsection{Dubious Error Computations} + The errors obtained from the covariance matrix are only a lower estimate + of the true error. An error analysis by scanning the likelihood function + was attempted, but dubious values led to their exclusion from these results. + In the case of + + (Example of bad LF error) + + Monte Carlo simulations were also attempted as a way of estimating the + variability of the resultant values. Many errors obtained from this method + were much larger than the expected accurate values. Therefore, this analysis + was also excluded. + + (Example of bad MC error) + + +\section{Discussion} +Frequency-dependent power spectral densities confirm time-dependent variability +in the emission strengths for each band. This behaviour is expected for +any active galactic nucleus and has been long-confirmed in NGC 5548, so +it comes as no surprise to find those results here. + +Analysis of the top-hat impulse response model predicted frequency-dependent +time delays, which have been recovered from the light curves in this analysis. +Furthermore, the distribution of time delays indicates a wavelength-dependent +nature. This warrants further study and analysis. + +(Maybe a graph comparing the top-hat time delays to one band's time delays.) + +The analyses performed on these data have elucidated clear trends in the PSD +and time delays. With reverberation mapping, the goal is to recover the transfer +function, which encodes the geometry of the system. Recovering the time delays +is a significant step toward that goal. + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +%%%%%%%%%%%%%%%%%%%% REFERENCES %%%%%%%%%%%%%%%%%% + +% The best way to enter references is to use BibTeX: + +\bibliographystyle{mnras} +\bibliography{wsu_reu} % if your bibtex file is called example.bib + + +% Alternatively you could enter them by hand, like this: +% This method is tedious and prone to error if you have lots of references +% \begin{thebibliography}{99} +% \bibitem[\protect\citeauthoryear{Author}{2012}]{Author2012} +% Author A.~N., 2013, Journal of Improbable Astronomy, 1, 1 +% \bibitem[\protect\citeauthoryear{Others}{2013}]{Others2013} +% Others S., 2012, Journal of Interesting Stuff, 17, 198 +% \end{thebibliography} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +%%%%%%%%%%%%%%%%% APPENDICES %%%%%%%%%%%%%%%%%%%%% + +% \appendix +% +% \section{Some extra material} +% +% If you want to present additional material which would interrupt the flow of +% the main paper, it can be placed in an Appendix which appears after the list +% of references. + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + +% Don't change these lines +\bsp % typesetting comment +\label{lastpage} +\end{document} + +% End of mnras_template.tex \ No newline at end of file