2014A&A...572A..97R


C.D.S. - SIMBAD4 rel 1.7 - 2020.07.13CEST07:57:31

2014A&A...572A..97R - Astronomy and Astrophysics, volume 572A, 97-97 (2014/12-1)

Constraining duty cycles through a Bayesian technique.

ROMANO P., GUIDORZI C., SEGRETO A., DUCCI L. and VERCELLONE S.

Abstract (from CDS):

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 (Nsrc≥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.

Abstract Copyright:

Journal keyword(s): methods: statistical - methods: numerical - methods: observational - X-rays: binaries

VizieR on-line data: <Available at CDS (J/A+A/572/A97): R-Language, IDL, and C-language programs>

Simbad objects: 10

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Number of rows : 10

N Identifier Otype ICRS (J2000)
RA
ICRS (J2000)
DEC
Mag U Mag B Mag V Mag R Mag I Sp type #ref
1850 - 2020
#notes
1 HD 74194 HXB 08 40 47.7915105936 -45 03 30.231146034 7.05 7.77 7.55 8.70   O8.5Ib-II(f)p 178 0
2 SWIFT J1633.8-4724B HXB 16 32 37.850 -47 23 41.45           O8Iafpe 31 0
3 2MASS J16415078-4532253 HXB 16 41 50.7854893198 -45 32 25.452141297           O8.5(sg?) 92 2
4 2MASS J16463526-4507045 HXB 16 46 35.2592332854 -45 07 04.609816032   15.2       O9.5Ia 87 1
5 2MASS J16480656-4512068 HXB 16 48 06.56 -45 12 06.8           O8.5Iab 119 2
6 IGR J17354-3255 HX? 17 35 27.6078770673 -32 55 54.407937802           O9Iab 43 2
7 AX J1739.1-3020 HXB 17 39 11.5521531365 -30 20 37.783172824       13.91   O8.5Iab(f) 141 1
8 IGR J17544-2619 HXB 17 54 25.2724584579 -26 19 52.578788584   14.71 12.94 12.10 10.38 O9Ib 164 0
9 [KRL2007b] 332 HXB 18 41 00.43 -05 35 46.5           B1Ib 115 1
10 IGR J18483-0311 HXB 18 48 17.2064881183 -03 10 16.876608322 23.702 25.162 21.884 17.888 15.88 B0.5Ia 109 0

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2020.07.13-07:57:31

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