Ամսագրի կամ հրապարակման վերնագիր:

Բյուրականի աստղադիտարանի հաղորդումներ: Երևանի աստղադիտարանի բյուլետեն = Сообщения Бюраканской обсерватории. Бюллетень ереванской Астрономической обсерватории = Contributions from the Burakan observatory. Bulletin of the Erevan astronomical observatory

Հրապարակման ամսաթիւ:

2026

Հատոր:

73

Համար:

1

ISSN:

2579-2276

Ծածկոյթ:

39-58

Ամփոփում:

The revised and substantially extended pipeline/code for recovering the flare-rate distribution φ(ν) of a population of randomly flaring objects is presented. The capabilities of existing methods have been significantly expanded, and new ones have been added. Specifically, the new code allows (i) the use of the χ2 test to significantly improve the estimation of the number of unknown (undiscovered) flare stars n0, (ii) a refinement of the moment fit via a maximum likelihood estimate of a truncated Poisson distribution and a comparison of Pearson’s types based on AIC/BIC metrics, (iii) an analysis of the temporal evolution of φ(ν) to account for accumulated observations, (iv) the application of modern numerical calculation methods, and (v) the use of numerical simulation to work with both synthetic and real observational data. Finally, two methods for recovering the flare-rate distribution φ(ν) of a stellar population are considered. The first method is the inverse-Laplace formulation from Ambartsumian (1978), applied to the discovery curve of first-flare events. The second is the method of moments (MoM, Akopian, 2003), improved and extended here to the full Pearson family of probability distributions. A comparative analysis of these methods is also presented. In the second part of the study, the code was used to determine the distribution of flare rate among flare stars within the Kepler telescope’s field of view. Typically, both methods yield identical results for synthetic data. However, when applied to a sample of flare stars from the Kepler field of view, their results diverge. The MoM yields a Pearson Type III distribution, or gamma distribution, with a negative bias in the minimum flare frequency, which is physically impossible. In contrast, Ambartsumian’s approach yields a Type III distribution, which is physically plausible, with ν0 > 0. To identify the cause of the discrepancies, regardless of the specific form of the Pearson distribution, a numerical inverse Laplace transform was applied using modern algorithms. The inverse function m1(t)/m1(0), where m1(t) is the frequency of the first flare, was in this case represented and approximated by its purely observational realization n1(t)/n(t), where n1(t) is the number of stars that have survived exactly one flare by time t, and n(t) is the cumulative number of flares. This approach does not require knowledge of Ntot and provides the most reliable of the available cross-checks for reconstruction using the inverse Laplace transform. The nature of these discrepancies reveals the structure of the underlying distribution: a smooth density curve with a peak shifted towards values of ν ∼ 2 × 10−3 d−1, with a long tail in the region of high ν values.

Ձեւաչափ:

pdf

Նոյնացուցիչ:

oai:arar.sci.am:439336

Գլխաւոր նշումը:

Communications of the Byurakan Astrophysical Observatory (ComBAO) is a peer-reviewed scientific journal, which publishes research in observational and theoretical astronomy/astrophysics and presents recent advances in these fields. It is being published by the NAS RA V. Ambartsumian Byurakan Astrophysical Observatory (BAO) in English in electronic form. The journal publishes original papers, review papers, brief reports, book reviews, special communications, observational and theoretical results in various fields of astronomy and related sciences, and some editorial notes, including anniversaries and obituaries. Under the heading “Legacy”, the renewed magazine will republish some old articles of high value in English. The heading “Guest articles” will bring to the attention of readers the articles of researchers who are not employees of BAO. ComBAO was founded in 1946 and regularly published in 1946-1990. However, the publication was interrupted because of the economic situation after the disintegration of the Soviet Union in 1991.

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