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Lane-Emden equation with inertial force and general polytropic dynamic model for molecular cloud cores
Li, DaLei1,2; Lou, Yu-Qing3,4,5; Esimbek, Jarken1,6
2018
Source PublicationMONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY
ISSN0035-8711
Volume473Issue:2Pages:2441-2464
Corresponding AuthorLou, Yu-Qing(louyq@mail.tsinghua.edu.cn)
AbstractWe study self-similar hydrodynamics of spherical symmetry using a general polytropic ( GP) equation of state and derive the GP dynamic Lane-Emden equation ( LEE) with a radial inertial force. In reference to Lou & Cao, we solve the GP dynamic LEE for both polytropic index gamma = 1 + 1/n and the isothermal case n -> +infinity; our formalism is more general than the conventional polytropic model with n = 3 or gamma = 4/3 of Goldreich & Weber. For proper boundary conditions, we obtain an exact constant solution for arbitrary n and analytic variable solutions for n = 0 and n = 1, respectively. Series expansion solutions are derived near the origin with the explicit recursion formulae for the series coefficients for both the GP and isothermal cases. By extensive numerical explorations, we find that there is no zero density at a finite radius for n >= 5. For 0 <= n < 5, we adjust the inertial force parameter c and find the range of c > 0 for monotonically decreasing density from the origin and vanishing at a finite radius for c being less than a critical value C-cr. As astrophysical applications, we invoke our solutions of the GP dynamic LEE with central finite boundary conditions to fit the molecular cloud core Barnard 68 in contrast to the static isothermal Bonnor-Ebert sphere by Alves et al. Our GP dynamic model fits appear to be sensibly consistent with several more observations and diagnostics for density, temperature and gas pressure profiles.
Keywordhydrodynamics planets and satellites: gaseous planets brown dwarfs stars: formation stars: protostars ISM: clouds
DOI10.1093/mnras/stx1925
WOS KeywordGRAVITATING GASEOUS SPHERES ; SELF-SIMILAR SOLUTIONS ; FIELD EXTINCTION MAPS ; ENVELOPE EXPANSION ; STAR-FORMATION ; STELLAR CORES ; SERIES SOLUTIONS ; SPIRAL GALAXIES ; BARNARD 68 ; COLLAPSES
Indexed BySCI
Language英语
WOS Research AreaAstronomy & Astrophysics
WOS SubjectAstronomy & Astrophysics
WOS IDWOS:000423731200072
PublisherOXFORD UNIV PRESS
Citation statistics
Cited Times:1[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://libir.pmo.ac.cn/handle/332002/22206
Collection中国科学院紫金山天文台
Corresponding AuthorLou, Yu-Qing
Affiliation1.Chinese Acad Sci, Xinjiang Astron Observ, Urumqi 830011, Peoples R China
2.Univ Chinese Acad Sci, Beijing 100080, Peoples R China
3.Tsinghua Univ, Dept Phys, Beijing 100084, Peoples R China
4.Tsinghua Univ, Tsinghua Ctr Astrophys THCA, Beijing 100084, Peoples R China
5.Tsinghua Univ, Joint Res Ctr Astrophys, Tsinghua Natl Astron Observ China, Beijing 100084, Peoples R China
6.Chinese Acad Sci, Key Lab Radio Astron, Urumqi 830011, Peoples R China
Recommended Citation
GB/T 7714
Li, DaLei,Lou, Yu-Qing,Esimbek, Jarken. Lane-Emden equation with inertial force and general polytropic dynamic model for molecular cloud cores[J]. MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY,2018,473(2):2441-2464.
APA Li, DaLei,Lou, Yu-Qing,&Esimbek, Jarken.(2018).Lane-Emden equation with inertial force and general polytropic dynamic model for molecular cloud cores.MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY,473(2),2441-2464.
MLA Li, DaLei,et al."Lane-Emden equation with inertial force and general polytropic dynamic model for molecular cloud cores".MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY 473.2(2018):2441-2464.
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