vestifmИзвестия Национальной академии наук Беларуси. Серия физико-математических наукProceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series1561-24302524-2415The Republican Unitary Enterprise Publishing House "Belaruskaya Navuka"10.29235/1561-2430-2023-59-2-136-146vestifm-713Research ArticleФИЗИКАPHYSICSЗалежнасць спектраў гама-ўсплёскаў ад пачатковага размеркавання энергіі ў абалонцы, якая ультрарэлятывісцкі пашыраеццаDependence of the spectra of gamma-ray bursts on the initial energy distribution in the ultrarelativistically expanding shellhttps://orcid.org/0000-0001-7802-0691СіўцоўI. А.SiutsouI. A.

Сіўцоў Іван Аляксандравіч – кандыдат фізіка-матэматычных навук, старшы інжынер-праграміст

Плошча каралевы Вільгельміны 1-40601, Амстэрдам

 

Ivan А. Siutsou – Ph. D. (Physics and Mathematics), Senior Software Engineer

Koningin Wilhelminaplein 1-40601, Amsterdam

siu@tut.byКургузаваА. Э.KurhuzavaA. E.

Кургузава Аксана Эдуардаўна – аспірант, малодшы навуковы супрацоўнік

пр. Незалежнасці, 68-2, 220072, Мінск

Aksana Е. Kurhuzava – Postgraduate Student, JuniorResearcher

68-2, Nezalezhnasci Ave., 220072, Minsk

kuppory@gmail.comStream HPC B.V.Stream HPC B.V.Інстытут фізікі імя Б. І. Сцяпанава Нацыянальнай акадэміі навук БеларусіCFIA of B. I. Stepanov Institute of Physics of the National Academy of Sciences of Belarus202306072023592136146Copyright © Сіўцоў I.А., Кургузава А.Э., 20232023Сіўцоў I.А., Кургузава А.Э.Siutsou I.A., Kurhuzava A.E.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://vestifm.belnauka.by/jour/article/view/713

Пачатковы этап гама-ўсплёску можна апісаць дыфузіяй выпраменьвання ў абалонцы, якая ультрарэлятывісцкі пашыраецца. Разгледжаны выпадак, калі пачатковае размеркаванне энергіі ў абалонцы залежыць ад глыбіні па лінейным законе. Пры гэтым ад нахілу функцыі пачатковага размеркавання энергіі залежаць эфектыўная тэмпература і імгненны спектр гама-ўсплёску ў пачатковы момант часу, а таксама інтэграваны па часе спектр на высокіх частотах. Таксама была даследавана залежнасць выгляду імгненнага спектра гама-ўсплёска ад часу прыбыцця: пры яго павелічэнні максімум патоку назіраецца на меншай частаце незалежна ад пачатковага размеркавання энергіі ў абалонцы; пры значэннях часу прыбыцця большых за 1 с імгненны спектр не залежыць ад пачатковага размеркавання энергіі ў абалонцы. Нахіл ступеннай часткі інтэграванага па часе спектра на больш нізкіх частотах аднолькавы для любога пачатковага размеркавання энергіі ў абалонцы і складае 1,98; на больш высокіх частотах становіцца больш крутым з павелічэннем нахілу функцыі, якая адпавядае размеркаванню энергіі ў абалонцы ў пачатковы момант часу, і мае значэнні ад –2,38 да –13,73. Гэта дазваляе патлумачыць з дапамогай нашай мадэлі вялікую колькасць гама-ўсплёскаў, якія маюць тыповы спектр Банда. 

The initial stage of a gamma-ray burst can be described by the diffusion of radiation in the shell which is ultrarelativistically widening. We have herein considered the case when the initial energy distribution in the shell depends on the depth according to a linear law. At the same time, the slope of the initial energy distribution function determines the effective temperature and the instantaneous spectrum of the gamma-ray burst at the initial time moment, as well as the time-integrated spectrum at high frequencies. Moreover, we investigated the dependence of the instantaneous spectrum of the gamma-ray burst on the time of arrival: if it increases, the flux maximum is observed for a smaller frequency independently of the initial energy distribution in the shell. It the time of arrival is larger than 1 s, the instantaneous spectrum is independent of the initial energy distribution in the shell. The slope of the power-law part of the time-integrated spectrum at lower frequencies is the same for any initial energy distribution in the shell and it is equal to 1.98; at higher frequencies, it becomes steeper with increasing the slope of the function corresponding to the energy distribution in the shell at the initial instant of time, and it has values between –2.38 and –13.73.This allows us to explain with the help of our model a large number of gamma-ray bursts that have a typical Band spectrum.

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The authors declare that there are no conflicts of interest present.