Е-Публикации
Технически университет - София

Abstract: We set ourselves the goal of obtaining the equations which govern the evolution of the mass density profile of a dense irrotational molecular cloud. We base our study on the notion of "ensemble of molecular clouds", introduced in our previous work. We model the studied clouds making use of the "ensemble abstract representative member"- a spherically symmetric and isotropic cloud. This cloud is isothermal and radially accreting matter from its surroundings. Starting from the equations of hydrodynamics applied to a self-gravitating isothermal spherical gas cloud, we obtain a system of two first-order nonlinear partial differential equations, which govern the evolution of two unknown fields: the exponent of density profile and the accretion velocity. Under the assumption of steady state flow, we get approximate solutions, using the method of leading order terms. Far from the cloud's center we obtain density profile =ℓ-2, and the accretion velocity is constant, while near to the center we have =ℓ-3/2 and va ℓ-1/2. Through our dynamical equations, the obtained solutions coincide completely with the solutions found by using the equation of energy conservation of a fluid element (in our previous work). Also, combining the equations of energy balance for a fluid element, we arrive at the conclusion that the cloud's layers, far from the center, are in a stable dynamical state if the accretion velocity flow is sub- or trans-sonic, otherwise they are marginally stable (moderately supersonic flow) or unstable (supersonic flow). Both solutions are consistent only if the accretion flow is subsonic, and hence the outer layers are stable. Finally, under the assumption that both the accretion velocity and density scale with ℓ and their power-law exponents are position-independent, we show that the density scaling exponent far away from the center is p=2 and this value is an attractor. Hence, this value should be observable in dense molecular clouds.

References

1. B. Elmegreen and J. Scalo, Annu. Rev. Astron. Astrophys. 42, 211 (2004) 0066-4146 10.1146/annurev.astro.41.011802.094859.
2. P. Hennebelle and E. Falgarone, Astron. Astrophys. Rev. 20, 55 (2012) 0935-4956 10.1007/s00159-012-0055-y.
3. R. S. Klessen and S. C. O. Glover, Star Formation in Galaxy Evolution: Connecting Numerical Models to Reality, Saas-Fee Advanced Course, Vol. 43 (Springer-Verlag Berlin Heidelberg, 2016), p. 85.
4. K. M. Ferriere, Rev. Mod. Phys. 73, 1031 (2001) 0034-6861 10.1103/RevModPhys.73.1031.
5. P. Wang, Z.-Y. Li, T. Abel, and F. Nakamura, Astrophys. J. 709, 27 (2010) 0004-637X 10.1088/0004-637X/709/1/27.
6. C. Federrath, Mon. Not. R. Astron. Soc. 450, 4035 (2015) 1365-2966 10.1093/mnras/stv941.
7. S. S. Mathew and C. Federrath, Mon. Not. R. Astron. Soc. 507, 2448 (2021) 0035-8711 10.1093/mnras/stab2338.
8. M. Lombardi, J. Alves, and C. Lada, Astron. Astrophys. 519, L7 (2010) 0004-6361 10.1051/0004-6361/201015282.
9. E. Vázquez-Semadeni, Astrophys. J. 423, 681 (1994) 0004-637X 10.1086/173847.
10. P. Padoan, M. Juvela, A. Kritsuk, and M. Norman, Astrophys. J. 653, L125 (2006) 0004-637X 10.1086/510620.
11. C. Federrath, J. Roman-Duval, R. S. Klessen, W. Schmidt, and M.-M. Mac Low, Astron. Astrophys. 512, A81 (2010) 0004-6361 10.1051/0004-6361/200912437.
12. F. Molina, S. C. O. Glover, C. Federrath, and R. S. Klessen, Mon. Not. R. Astron. Soc. 423, 2680 (2012) 0035-8711 10.1111/j.1365-2966.2012.21075.x.
13. R. S. Klessen, Astrophys. J. 535, 869 (2000) 0004-637X 10.1086/308854.
14. A. Kritsuk, M. Norman, and R. Wagner, Astrophys. J. 727, L20 (2011) 2041-8205 10.1088/2041-8205/727/1/L20.
15. P. Girichidis, L. Konstandin, A. Whitworth, and R. S. Klessen, Astrophys. J. 781, 91 (2014) 0004-637X 10.1088/0004-637X/781/2/91.
16. T. V. Veltchev, P. Girichidis, S. Donkov, N. Schneider, O. Stanchev, L. Marinkova, D. Seifried, and R. S. Klessen, Mon. Not. R. Astron. Soc. 489, 788 (2019) 0035-8711 10.1093/mnras/stz2151.
17. S. Khullar, C. Federrath, M. R. Krumholz, and C. D. Matzner, Mon. Not. R. Astron. Soc. 507, 4335 (2021) 0035-8711 10.1093/mnras/stab1914.
18. M. Einasto, P. Tenjes, M. Gramann, H. Lietzen, R. Kipper, L. J. Liivamägi, E. Tempel, S. Sankhyayan, and J. Einasto, Astron. Astrophys. 666, A52 (2022) 10.1051/0004-6361/202142938.
19. G.-X. Li, Mon. Not. R. Astron. Soc. 477, 4951 (2018) 0035-8711 10.1093/mnras/sty657.
20. S. Donkov and I. Zh. Stefanov, Mon. Not. R. Astron. Soc. 485, 3224 (2019) 0035-8711 10.1093/mnras/stz636.
21. E. Vázquez-Semadeni, A. Palau, J. Ballesteros-Paredes, G. Gómez, and M. Zamora-Aviles, Mon. Not. R. Astron. Soc. 490, 3061 (2019) 0035-8711 10.1093/mnras/stz2736.
22. S. Donkov, I. Zh. Stefanov, T. V. Veltchev, and R. S. Klessen, Mon. Not. R. Astron. Soc. 527, 2790 (2024) 0035-8711 10.1093/mnras/stad3372.
23. C. Federrath and R. S. Klessen, Astrophys. J. 763, 51 (2013) 0004-637X 10.1088/0004-637X/763/1/51.
24. S. Donkov, T. V. Veltchev, and R. S. Klessen, Mon. Not. R. Astron. Soc. 466, 914 (2017) 0035-8711 10.1093/mnras/stw3147.
25. R. Larson, Mon. Not. R. Astron. Soc. 145, 271 (1969) 0035-8711 10.1093/mnras/145.3.271.
26. M. V. Penston, Mon. Not. R. Astron. Soc. 145, 457 (1969) 0035-8711 10.1093/mnras/145.4.457.
27. F. H. Shu, Astrophys. J. 214, 488 (1977) 0004-637X 10.1086/155274.
28. C. Hunter, Astrophys. J. 218, 834 (1977) 0004-637X 10.1086/155739.
29. A. Whitworth and D. Summers, Mon. Not. R. Astron. Soc. 214, 1 (1985) 0035-8711 10.1093/mnras/214.1.1.
30. M.-M. Mac Low and R. S. Klessen, Rev. Mod. Phys. 76, 125 (2004) 0034-6861 10.1103/RevModPhys.76.125.
31. R. Naranjo-Romero, E. Vázquez-Semadeni, and R. M. Loughnane, Astrophys. J. 814, 48 (2015) 1538-4357 10.1088/0004-637X/814/1/48.
32. S. Donkov and I. Zh. Stefanov, Mon. Not. R. Astron. Soc. 474, 5588 (2018) 0035-8711 10.1093/mnras/stx3116.
33. S. Donkov, I. Zh. Stefanov, T. V. Veltchev, and R. S. Klessen, Mon. Not. R. Astron. Soc. 516, 5726 (2022) 0035-8711 10.1093/mnras/stac2660.
34. E. Jaupart and G. Chabrier, Astrophys. J. Lett. 903, L2 (2020) 2041-8205 10.3847/2041-8213/abbda8.
35. G. Gómez, E. Vázquez-Semadeni, and A. Palau, Mon. Not. R. Astron. Soc. 502, 4963 (2021) 0035-8711 10.1093/mnras/stab394.
36. K. E. Mueller, Y. L. Shirley, N. J. Evans II, and H. R. Jacobson, Astrophys. J. Suppl. Ser. 143, 469 (2002) 0067-0049 10.1086/342881.
37. N. J. Evans II, L. E. Allen, G. A. Blake, A. C. A. Boogert, T. Bourke, P. M. Harvey, J. E. Kessler, D. W. Koerner, C. W. Lee, L. G. Mundy, P. C. Myers, D. L. Padgett, K. Pontoppidan, A. I. Sargent, K. R. Stapelfeldt, E. F. van Dishoeck, C. H. Young, and K. E. Young, in SFChem: Chemistry as a Diagnostic of Star Formation, edited by L. C. Curry and M. Fich (Publications of the Astronomical Society of the Pacific, 2003), Vol. 115, pp. 965-980.
38. F. Wyrowski, R. Gusten, K. M. Menten, H. Wiesemeyer, and B. Klein, Astron. Astrophys. 542, L15 (2012) 0004-6361 10.1051/0004-6361/201218927.
39. F. Wyrowski, R. Güsten, K. M. Menten, H. Wiesemeyer, T. Csengeri, S. Heyminck, B. Klein, C. König, and J. S. Urquhart, Astron. Astrophys. 585, A149 (2016) 0004-6361 10.1051/0004-6361/201526361.
40. A. Palau et al., Astrophys. J. 785, 42 (2014) 0004-637X 10.1088/0004-637X/785/1/42.
41. T. Csengeri et al., Astron. Astrophys. 600, L10 (2017) 0004-6361 10.1051/0004-6361/201629754.
42. C.-P. Zhang and G.-X. Li, Mon. Not. R. Astron. Soc. 469, 2286 (2017) 0035-8711 10.1093/mnras/stx954.
43. W. B. Bonnor, Mon. Not. R. Astron. Soc. 116, 351 (1956) 0035-8711 10.1093/mnras/116.3.351.
44. R. Ebert, Z. Astrophys. 42, 263 (1957).
45. A. Zhivkov, Differential Equations Problems, Demokratichni tradicii (Demetra, Sofia, 1999).
46. K. F. Riley, M. P. Hobson, and S. J. Bence, Mathematical Methods for Physics and Engineering (Cambrige University Press, Cambridge, New York, 2006).
47. J. Ballesteros-Paredes et al., Space Sci. Rev. 216, 76 (2020) 0038-6308 10.1007/s11214-020-00698-3.
48. L. Linke, P. A. Burger, S. Heydenreich, L. Porth, and P. Schneider, Astron. Astrophys. 681, A33 (2024) 0004-6361 10.1051/0004-6361/202346225.

Issue

Copyright American Physical Society