978 research outputs found
Mass Functions of Supermassive Black Holes Across Cosmic Time
The black hole mass function of supermassive black holes describes the
evolution of the distribution of black hole mass. It is one of the primary
empirical tools available for mapping the growth of supermassive black holes
and for constraining theoretical models of their evolution. In this review we
discuss methods for estimating the black hole mass function, including their
advantages and disadvantages. We also review the results of using these methods
for estimating the mass function of both active and inactive black holes. In
addition, we review current theoretical models for the growth of supermassive
black holes that predict the black hole mass function. We conclude with a
discussion of directions for future research which will lead to improvement in
both empirical and theoretical determinations of the mass function of
supermassive black holes.Comment: 40 pages, 7 figures, review paper accepted for the Advances in
Astronomy Special Issue "Seeking for the Leading Actor on the Cosmic Stage:
Galaxies versus Supermassive Black Holes
Some Aspects of Measurement Error in Linear Regression of Astronomical Data
I describe a Bayesian method to account for measurement errors in linear
regression of astronomical data. The method allows for heteroscedastic and
possibly correlated measurement errors, and intrinsic scatter in the regression
relationship. The method is based on deriving a likelihood function for the
measured data, and I focus on the case when the intrinsic distribution of the
independent variables can be approximated using a mixture of Gaussians. I
generalize the method to incorporate multiple independent variables,
non-detections, and selection effects (e.g., Malmquist bias). A Gibbs sampler
is described for simulating random draws from the probability distribution of
the parameters, given the observed data. I use simulation to compare the method
with other common estimators. The simulations illustrate that the Gaussian
mixture model outperforms other common estimators and can effectively give
constraints on the regression parameters, even when the measurement errors
dominate the observed scatter, source detection fraction is low, or the
intrinsic distribution of the independent variables is not a mixture of
Gaussians. I conclude by using this method to fit the X-ray spectral slope as a
function of Eddington ratio using a sample of 39 z < 0.8 radio-quiet quasars. I
confirm the correlation seen by other authors between the radio-quiet quasar
X-ray spectral slope and the Eddington ratio, where the X-ray spectral slope
softens as the Eddington ratio increases.Comment: 39 pages, 11 figures, 1 table, accepted by ApJ. IDL routines
(linmix_err.pro) for performing the Markov Chain Monte Carlo are available at
the IDL astronomy user's library, http://idlastro.gsfc.nasa.gov/homepage.htm
The Cross-Wavelet Transform and Analysis of Quasiperiodic Behavior in the Pearson-Readhead VLBI Survey Sources
We introduce an algorithm for applying a cross-wavelet transform to analysis
of quasiperiodic variations in a time-series, and introduce significance tests
for the technique. We apply a continuous wavelet transform and the
cross-wavelet algorithm to the Pearson-Readhead VLBI survey sources using data
obtained from the University of Michigan 26-m parabloid at observing
frequencies of 14.5, 8.0, and 4.8 GHz. Thirty of the sixty-two sources were
chosen to have sufficient data for analysis, having at least 100 data points
for a given time-series. Of these thirty sources, a little more than half
exhibited evidence for quasiperiodic behavior in at least one observing
frequency, with a mean characteristic period of 2.4 yr and standard deviation
of 1.3 yr. We find that out of the thirty sources, there were about four time
scales for every ten time series, and about half of those sources showing
quasiperiodic behavior repeated the behavior in at least one other observing
frequency.Comment: Revised version, accepted by ApJ. 17 pages, 13 figures, color figures
included as gifs, seperate from the text. The addition of statistical
significance tests has resulted in modifying the technique and results, but
the broad conclusion remain the same. A high resolution version may be found
at http://www.astro.lsa.umich.edu/obs/radiotel/prcwdata.htm
Dust SEDs in the era of Herschel and Planck: a Hierarchical Bayesian fitting technique
We present a hierarchical Bayesian method for fitting infrared spectral
energy distributions (SEDs) of dust emission to observed fluxes. Under the
standard assumption of optically thin single temperature (T) sources the dust
SED as represented by a power--law modified black body is subject to a strong
degeneracy between T and the spectral index beta. The traditional
non-hierarchical approaches, typically based on chi-square minimization, are
severely limited by this degeneracy, as it produces an artificial
anti-correlation between T and beta even with modest levels of observational
noise. The hierarchical Bayesian method rigorously and self-consistently treats
measurement uncertainties, including calibration and noise, resulting in more
precise SED fits. As a result, the Bayesian fits do not produce any spurious
anti-correlations between the SED parameters due to measurement uncertainty. We
demonstrate that the Bayesian method is substantially more accurate than the
chi-square fit in recovering the SED parameters, as well as the correlations
between them. As an illustration, we apply our method to Herschel and sub
millimeter ground-based observations of the star-forming Bok globule CB244.
This source is a small, nearby molecular cloud containing a single low-mass
protostar and a starless core. We find that T and beta are weakly positively
correlated -- in contradiction with the chi-square fits, which indicate a
T-beta anti-correlation from the same data-set. Additionally, in comparison to
the chi-square fits the Bayesian SED parameter estimates exhibit a reduced
range in values.Comment: 20 pages, 9 figures, ApJ format, revised version matches ApJ-accepted
versio
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