We have derived the quasar luminosity function assuming that the quasar
activity is driven by a thermal-viscous unstable accretion disk around a
supermassive black hole. The instabilities produce ...large amplitude, long-term
variability of a single source. We take a light curve of a single source and
calculate the luminosity function, from the function of time it spends at each
luminosity. Convolving this with an assumed mass distribution we fit well the
observed optical luminosity function of quasars at four redshifts. As a result
we obtain the evolution of the mass distribution between redshifts 2.5 and 0.5.
The maximum of the active black hole mass function moves towards lower mass by
a factor ~10 at the low redshift. The number of high mass sources declines
rapidly, and so low mass sources become dominant at lower redshift. The main
conclusions are following: 1) The quasar long-term variability due to the disk
thermal-viscous instabilities provides a natural explanation for the observed
quasar luminosity function. 2) The peak of the mass function evolves towards
lower black hole masses at lower redshifts by a factor ~10. 3) High mass
sources die subsequently when redshift gets smaller. 4) The number of high mass
sources declines rapidly, and so low mass sources become dominant at lower
redshift. 5) The periodic outbursts of activity appear as long as the matter is
supplied to the accretion disk. 6) Since the time-averaged accretion rate is
low, the remnant sources (or sources in the low activity phase) do not grow to
very massive black holes. 7) A continuous fuel supply at a relatively low
accretion rate (~0.01 - 0.1 \dot M_{Edd}$) for each single source is required
over the lifetime of the entire quasar population.
A common problem in astrophysics is determining how bright a source could be and still not be detected. Despite the simplicity with which the problem can be stated, the solution involves complex ...statistical issues that require careful analysis. In contrast to the confidence bound, this concept has never been formally analyzed, leading to a great variety of often ad hoc solutions. Here we formulate and describe the problem in a self-consistent manner. Detection significance is usually defined by the acceptable proportion of false positives (the TypeI error), and we invoke the complementary concept of false negatives (the TypeII error), based on the statistical power of a test, to compute an upper limit to the detectable source intensity. To determine the minimum intensity that a source must have for it to be detected, we first define a detection threshold, and then compute the probabilities of detecting sources of various intensities at the given threshold. The intensity that corresponds to the specified TypeII error probability defines that minimum intensity, and is identified as the upper limit. Thus, an upper limit is a characteristic of the detection procedure rather than the strength of any particular source and should not be confused with confidence intervals or other estimates of source intensity. This is particularly important given the large number of catalogs that are being generated from increasingly sensitive surveys. We discuss the differences between these upper limits and confidence bounds. Both measures are useful quantities that should be reported in order to extract the most science from catalogs, though they answer different statistical questions: an upper bound describes an inference range on the source intensity, while an upper limit calibrates the detection process. We provide a recipe for computing upper limits that applies to all detection algorithms.
We associate the existence of short-lived compact radio sources with the intermittent activity of the central engine caused by a radiation pressure instability within an accretion disk. Such objects ...may constitute a numerous sub-class of Giga-Hertz Peaked Spectrum sources, in accordance with the population studies of radio-loud active galaxies, as well as detailed investigations of their radio morphologies. We perform the model computations assuming the viscosity parametrization as proportional to a geometrical mean of the total and gas pressure. The implied timescales are consistent with the observed ages of the sources. The duration of an active phase for a moderate accretion rate is short enough (< 10^3-10^4 years) that the ejecta are confined within the host galaxy and thus these sources cannot evolve into large size radio galaxies unless they are close to the Eddington limit.
We present {\it Chandra} X-ray Observatory observations of Giga-Hertz Peaked Spectrum (GPS) and Compact Steep Spectrum (CSS) radio sources. The {\it Chandra} sample contains 13 quasars and 3 galaxies ...with measured 2-10 keV X-ray luminosity within \(10^{42} - 10^{46}\) erg s\(^{-1}\). We detect all of the sources, five of which are observed in X-ray for the first time. We study the X-ray spectral properties of the sample. The measured absorption columns in the quasars are different than those in the galaxies in the sense that the quasars show no absorption (with limits \(\sim 10^{21} \rm cm^{-2}\)) while the galaxies have large absorption columns (\(> 10^{22} \rm cm^{-2}\)) consistent with previous findings. The median photon index of the sources with high S/N is \(\Gamma=1.84 \pm0.24\) and it is larger than the typical index of radio loud quasars. The arcsec resolution of {\it Chandra} telescope allows us to investigate X-ray extended emission, and look for diffuse components and X-ray jets. We found X-ray jets in two quasars (PKS 1127-145, B2 0738+32), an X-ray cluster surrounding a CSS quasar (z=1.1, 3C 186), detected a possible binary structure in 0941-080 galaxy and an extended diffuse emission in galaxy PKS B2 1345+12. We discuss our results in the context of X-ray emission processes and radio source evolution. We conclude that the X-ray emission in these sources is most likely unrelated to a relativistic jet, while the sources' radio-loudness may suggest a high radiative efficiency of the jet power in these sources.
In this work we use a sample of 318 radio-quiet quasars (RQQ) to investigate the dependence of the ratio of optical/UV flux to X-ray flux, alpha_ox, and the X-ray photon index, Gamma_X, on black hole ...mass, UV luminosity relative to Eddington, and X-ray luminosity relative to Eddington. Our sample is drawn from the SDSS, with X-ray data from ROSAT and Chandra, and optical data mostly from the SDSS; 153 of these sources have estimates of Gamma_X from Chandra. We estimate M_BH using standard estimates derived from the Hbeta, Mg II, and C IV broad emission lines. Our sample spans a broad range in black hole mass (10^6 < M_BH / M_Sun < 10^10) and redshift (z < 4.8). We find that alpha_ox increases with increasing M_BH and L_UV / L_Edd, and decreases with increasing L_X / L_Edd. In addition, we confirm the correlation seen in previous studies between Gamma_X and M_BH and both L_UV / L_Edd and L_X / L_Edd; however, we also find evidence that the dependence of Gamma_X of these quantities is not monotonic, changing sign at M_BH ~ 3 x 10^8 M_Sun. We argue that the alpha_ox correlations imply that the fraction of bolometric luminosity emitted by the accretion disk, as compared to the corona, increases with increasing accretion rate relative to Eddington. In addition, we argue that the Gamma_X trends are caused by a dependence of X-ray spectral index on accretion rate. We discuss our results within the context of accretion models with comptonizing corona, and discuss the implications of the alpha_ox correlations for quasar feedback. To date, this is the largest study of the dependence of RQQ X-ray parameters on black hole mass and related quantities, and the first to attempt to correct for the large statistical uncertainty in the broad line mass estimates.
The time dependent evolution of the accretion disk around black hole is
computed. The classical description of the $\alpha$-viscosity is adopted so the
evolution is driven by the instability ...operating in the innermost
radiation-pressure dominated part of the accretion disk. We assume that the
optically thick disk always extends down to the marginally stable orbit so it
is never evacuated completely. We include the effect of the advection, coronal
dissipation and vertical outflow. We show that the presence of the corona
and/or the outflow reduce the amplitude of the outburst. If only about half of
the energy is dissipated in the disk (with the other half dissipated in the
corona and carried away by the outflow) the outburst amplitude and duration are
consistent with observations of the microquasar GRS 1915+105. Viscous evolution
explains in a natural way the lack of direct transitions from the state C to
the state B in color-color diagram of this source. Further reduction of the
fraction of energy dissipated in the optically thick disk switches off the
outbursts which may explain why they are not seen in all high accretion rate
sources being in the Very High State.
Data analysis Smith, Randall K.; Arnaud, Keith A.; Siemiginowska, Aneta
Handbook of X-ray Astronomy,
09/2011
Book Chapter
IntroductionThis chapter describes some of the data-analysis methods used by X-ray astrophysicists. Any data analysis must begin with careful consideration of the physics underlying the emission ...before starting to progress through a series of software tools and scripts. After confirming that existing observations could (at least potentially) answer the question at hand, the first step is to determine what observations of the desired source(s) exist. Recent observations are often the best starting point, but even old data are better than nothing. Once some usable data are available the analysis, either spectral, imaging, timing, or some combination of the three, can proceed.Low-resolution spectral analysisGeneral commentsMost recent and current X-ray observations are performed using detectors which provide imaging combined with relatively low spectral resolution. Early missions such as the Einstein Observatory or ROSAT used X-ray mirrors with good imaging capability combined with microchannel plates or position-sensitive proportional counters that had limited spectral sensitivity, typically R ≡ E/ΔE ∼ 1-10. More recent missions, starting with ASCA, and current missions, such as Chandra and XMM–Newton, use X-ray-sensitive CCDs. These tend to have somewhat higher backgrounds, small pixels, and substantially better spectral resolution, R ≡ E/ΔE ∼ 10-50, than proportional counters. For comparison, the standard “UBVRI” optical filter system is equivalent to R ∼ 4.
While considerable advance has been made to account for statistical uncertainties in astronomical analyses, systematic instrumental uncertainties have been generally ignored. This can be crucial to a ...proper interpretation of analysis results because instrumental calibration uncertainty is a form of systematic uncertainty. Ignoring it can underestimate error bars and introduce bias into the fitted values of model parameters. Accounting for such uncertainties currently requires extensive case-specific simulations if using existing analysis packages. Here we present general statistical methods that incorporate calibration uncertainties into spectral analysis of high-energy data. We first present a method based on multiple imputation that can be applied with any fitting method, but is necessarily approximate. We then describe a more exact Bayesian approach that works in conjunction with a Markov chain Monte Carlo based fitting. We explore methods for improving computational efficiency, and in particular detail a method of summarizing calibration uncertainties with a principal component analysis of samples of plausible calibration files. This method is implemented using recently codified Chandra effective area uncertainties for low-resolution spectral analysis and is verified using both simulated and actual Chandra data. Our procedure for incorporating effective area uncertainty is easily generalized to other types of calibration uncertainties.
The ever-increasing quality and complexity of astronomical data underscores
the need for new and powerful data analysis applications. This need has led to
the development of Sherpa, a modeling and ...fitting program in the CIAO software
package that enables the analysis of multi-dimensional, multi-wavelength data.
In this paper, we present an overview of Sherpa's features, which include:
support for a wide variety of input and output data formats, including the new
Model Descriptor List (MDL) format; a model language which permits the
construction of arbitrarily complex model expressions, including ones
representing instrument characteristics; a wide variety of fit statistics and
methods of optimization, model comparison, and parameter estimation;
multi-dimensional visualization, provided by ChIPS; and new interactive
analysis capabilities provided by embedding the S-Lang interpreted scripting
language. We conclude by showing example Sherpa analysis sessions.
We have derived the quasar luminosity function assuming that the quasar activity is driven by a thermal-viscous unstable accretion disk around a supermassive black hole. The instabilities produce ...large amplitude, long-term variability of a single source. We take a light curve of a single source and calculate the luminosity function, from the function of time it spends at each luminosity. Convolving this with an assumed mass distribution we fit well the observed optical luminosity function of quasars at four redshifts. As a result we obtain the evolution of the mass distribution between redshifts 2.5 and 0.5. The maximum of the active black hole mass function moves towards lower mass by a factor ~10 at the low redshift. The number of high mass sources declines rapidly, and so low mass sources become dominant at lower redshift. The main conclusions are following: 1) The quasar long-term variability due to the disk thermal-viscous instabilities provides a natural explanation for the observed quasar luminosity function. 2) The peak of the mass function evolves towards lower black hole masses at lower redshifts by a factor ~10. 3) High mass sources die subsequently when redshift gets smaller. 4) The number of high mass sources declines rapidly, and so low mass sources become dominant at lower redshift. 5) The periodic outbursts of activity appear as long as the matter is supplied to the accretion disk. 6) Since the time-averaged accretion rate is low, the remnant sources (or sources in the low activity phase) do not grow to very massive black holes. 7) A continuous fuel supply at a relatively low accretion rate (~0.01 - 0.1 \dot M_{Edd}$) for each single source is required over the lifetime of the entire quasar population.
