A new approach for measuring power spectra and reconstructing time series in active galactic nuclei

We provide a new approach to measure power spectra and reconstruct time series in active galactic nuclei (AGNs) based on the fact that the Fourier transform of AGN stochastic variations is a series of complex Gaussian random variables. The approach parameterizes a stochastic series in frequency domain and transforms it back to time domain to fit the observed data. The parameters and their uncertainties are derived in a Bayesian framework, which also allows us to compare the relative merits of different power spectral density models. The well-developed fast Fourier transform algorithm together with parallel computation enable an acceptable time complexity for the approach.

[1]  Eduardo Serrano,et al.  LSST: From Science Drivers to Reference Design and Anticipated Data Products , 2008, The Astrophysical Journal.

[2]  S. Kozłowski.  A Method to Measure the Unbiased Decorrelation Timescale of the AGN Variable Signal from Structure Functions , 2016, 1701.00005.

[3]  S. Kozłowski,et al.  Limitations on the recovery of the true AGN variability parameters using Damped Random Walk modeling , 2016, 1611.08248.

[4]  Y. Xue,et al.  USING LEAKED POWER TO MEASURE INTRINSIC AGN POWER SPECTRA OF RED-NOISE TIME SERIES , 2016, 1604.07984.

[5]  Doreen Eichel,et al.  Data Analysis A Bayesian Tutorial , 2016 .

[6]  Brendon J. Brewer,et al.  Modelling reverberation mapping data – I. Improved geometric and dynamical models and comparison with cross-correlation results , 2014, 1407.2941.

[7]  Chen Hu,et al.  A BAYESIAN METHOD FOR THE INTERCALIBRATION OF SPECTRA IN REVERBERATION MAPPING , 2014, 1404.2351.

[8]  Brandon C. Kelly,et al.  FLEXIBLE AND SCALABLE METHODS FOR QUANTIFYING STOCHASTIC VARIABILITY IN THE ERA OF MASSIVE TIME-DOMAIN ASTRONOMICAL DATA SETS , 2014, 1402.5978.

[9]  L. Ho,et al.  A BAYESIAN APPROACH TO ESTIMATE THE SIZE AND STRUCTURE OF THE BROAD-LINE REGION IN ACTIVE GALACTIC NUCLEI USING REVERBERATION MAPPING DATA , 2013, 1310.3907.

[10]  S. Vaughan,et al.  X-ray variability of 104 active galactic nuclei - XMM-Newton power-spectrum density profiles , 2012, 1205.4255.

[11]  Rick Edelson,et al.  KEPLER OBSERVATIONS OF RAPID OPTICAL VARIABILITY IN ACTIVE GALACTIC NUCLEI , 2011, 1111.0672.

[12]  C. S. Kochanek,et al.  AN ALTERNATIVE APPROACH TO MEASURING REVERBERATION LAGS IN ACTIVE GALACTIC NUCLEI , 2010, 1008.0641.

[13]  Brendon J. Brewer,et al.  Diffusive nested sampling , 2009, Stat. Comput..

[14]  S. Vaughan,et al.  A Bayesian test for periodic signals in red noise , 2009, 0910.2706.

[15]  Brandon C. Kelly,et al.  ARE THE VARIATIONS IN QUASAR OPTICAL FLUX DRIVEN BY THERMAL FLUCTUATIONS? , 2009, 0903.5315.

[16]  A. J. Drake,et al.  FIRST RESULTS FROM THE CATALINA REAL-TIME TRANSIENT SURVEY , 2008, 0809.1394.

[17]  U. Southampton,et al.  Non‐linear X‐ray variability in X‐ray binaries and active galaxies , 2005, astro-ph/0502112.

[18]  Yu. F. Malkov,et al.  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 , 2002, astro-ph/0208064.

[19]  P. Uttley,et al.  Measuring the broad-band power spectra of active galactic nuclei with RXTE , 2002, astro-ph/0201134.

[20]  C. Megan Urry,et al.  VARIABILITY OF ACTIVE GALACTIC NUCLEI , 1997 .

[21]  John Skilling,et al.  Data analysis : a Bayesian tutorial , 1996 .

[22]  David B. Dunson,et al.  Bayesian Data Analysis , 2010 .

[23]  Hideyo Kunieda,et al.  The X-ray variability of NGC 6814 : power spectrum , 1992 .

[24]  Paul F. Fougere,et al.  On the accuracy of spectrum analysis of red noise processes using maximum entropy and periodogram methods: Simulation studies and application to geophysical data , 1985 .

[25]  D. B. Preston.  Spectral Analysis and Time Series , 1983 .