J/A+A/572/A97 Code to constraint duty cycles in HMXB (Romano+, 2014)
Constraining duty cycles through a Bayesian technique.
Romano P., Guidorzi C., Segreto A., Ducci L., Vercellone S.
<Astron. Astrophys. 572, A97 (2014)>
=2014A&A...572A..97R 2014A&A...572A..97R
ADC_Keywords: X-ray sources ; Binaries, X-ray ; Surveys ; Stars, supergiant
Keywords: methods: statistical - methods: numerical - methods: observational -
X-rays: binaries
Abstract:
The duty cycle (DC) of astrophysical sources is generally defined as
the fraction of time during which the sources are active. It is used
to both characterize their central engine and to plan further
observing campaigns to study them. However, DCs are generally not
provided with statistical uncertainties, since the standard approach
is to perform Monte Carlo bootstrap simulations to evaluate them,
which can be quite time consuming for a large sample of sources. As an
alternative, considerably less time-consuming approach, we derived the
theoretical expectation value for the DC and its error for sources
whose state is one of two possible, mutually exclusive states,
inactive (off) or flaring (on), as based on a finite set of
independent observational data points. Following a Bayesian approach,
we derived the analytical expression for the posterior, the conjugated
distribution adopted as prior, and the expectation value and variance.
We applied our method to the specific case of the inactivity duty
cycle (IDC) for supergiant fast X-ray transients, a subclass of
flaring high mass X-ray binaries characterized by large dynamical
ranges. We also studied IDC as a function of the number of
observations in the sample. Finally, we compare the results with the
theoretical expectations. We found excellent agreement with our
findings based on the standard bootstrap method. Our Bayesian
treatment can be applied to all sets of independent observations of
two-state sources, such as active galactic nuclei, X-ray binaries,
etc. In addition to being far less time consuming than bootstrap
methods, the additional strength of this approach becomes obvious when
considering a well-populated class of sources (N_src ≥ 50) for which
the prior can be fully characterized by fitting the distribution of
the observed DCs for all sources in the class, so that, through the
prior, one can further constrain the DC of a new source by exploiting
the information acquired on the DC distribution derived from the other
sources.
Description:
We calculate the errors on duty cycles of two-state sources using a
Bayesian technique.
Objects:
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RA (2000) DE Designation(s)
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08 40 47.83 -45 03 31.1 IGR J08408-4503 = IGR J08408-4503
16 32 37.87 -47 23 41.2 IGR J16328-4726 = IGR J16328-4726
16 41 50.65 -45 32 27.3 IGR J16418-4532 = IGR J16418-4532
16 46 35.5 -45 07 04 IGR J16465-4507 = IGR J16465-4507
16 48 06.58 -45 12 06.74 IGR J16479-4514 = IGR J16479-4514
17 35 27.59 -32 55 54.4 IGR J17354-3255 = IGR J17354-3255
17 39 11.58 -30 20 37.6 XTE J1739-302 = IGR J17391-3021
17 54 25.284 -26 19 52.62 IGR J17544-2619 = IGR J17544-2619
18 41 00.54 -05 35 46.8 AX J1841.0-0536 = IGR J18410-0535
18 48 17.2 -03 10 16.8 IGR J18483-0311 = IGR J18483-031
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File Summary:
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FileName Lrecl Records Explanations
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ReadMe 80 . This file
confintervalsbetafunction.c 90 117 C-language program
confintervalsunderRbetafunction.R 122 78 IDL program
confintervalsunder_betafunction.pro 75 115 IDL program (ISML)
confintervalsunderbetafunctionimsl.pro 77 108 R-language program
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See also:
http://www.ifc.inaf.it/sfxt : SWIFT Home Page
Acknowledgements:
Patrizia Romano, patrizia.romano(at)inaf.it
References:
Romano et al. (2014A&A...568A..55R 2014A&A...568A..55R), Soft X-ray characterisation of the
long-term properties of supergiant fast X-ray transients
Romano et al. (2011MNRAS.410.1825R 2011MNRAS.410.1825R), Two years of monitoring supergiant
fast X-ray transients with Swift
Romano et al. (2009MNRAS.399.2021R 2009MNRAS.399.2021R), Monitoring supergiant fast X-ray
transients with Swift: results from the first year
(End) Patricia Vannier [CDS] 29-Oct-2014