Abstract
In this paper, we have investigated the effects of galactic cosmic rays (CRs) and finite electrical resistivity on the linear gravitational instability of magnetized viscoelastic fluid considering the physical conditions of molecular cloud clumps. The generalized hydrodynamic (GH) fluid model has been formulated, accounting for the effects of galactic CRs in terms of the cosmic ray (CR) pressure and CR diffusion coefficient along the direction of the magnetic field. The non-ideal magnetohydrodynamic (MHD) effects are considered in the generalized Ohm’s law. The modified dispersion relations are derived using the normal mode analysis under hydrodynamic (weakly coupled) and kinetic (strongly coupled) limits and discussed for both transverse and longitudinal modes of wave propagation. The modified Jeans instability criteria are obtained for various cases, and it is found that the values of the critical Jeans wavenumber are modified due to the presence of viscoelastic and CR pressure effects. Further, the presence of CR pressure and gas pressure supports gravity; hence it decreases the growth rate of the Jeans instability. In addition to CR pressure, the viscoelastic effects also suppress the growth rate of the Jeans instability, while CR diffusion coefficient enhances the growth rate. In the transverse mode, no effect of CR diffusion is observed while the Ohmic diffusion coefficient enhances the growth rate in a similar way as the CR diffusion coefficient does in the longitudinal mode. The outcomes of the present work shall be helpful in understanding the impact of CRs and Ohmic diffusion on the gravitational collapse in the viscoelastic region of molecular cloud clumps.
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References
Bergin, E.A., Tafalla, M.: Annu. Rev. Astron. Astrophys. 45, 339 (2007)
Bittencourt, J.A.: Fundamentals of Plasma Physics. Springer, New York (2004)
Boro, P., Prajapati, R.P.: Mon. Not. R. Astron. Soc. 522(2), 1752 (2023)
Butsky, I.S., Fielding, D.B., Hayward, C.C., Hummels, C.B., Quinn, T.R., Werk, J.K.: Astrophys. J. 903(2), 77 (2020)
Byleveld, S., Melrose, D., Cram, L.: Publ. Astron. Soc. Aust. 10(3), 218 (1993)
Caselli, P., Walmsley, C.M., Terzieva, R., Herbst, E.: Astrophys. J. 499(1), 234 (1998)
Cesarsky, C., Volk, H.: Astron. Astrophys. 70, 367 (1978)
Chakrabarti, N.: Phys. Lett. A 389, 127084 (2021)
Chandrasekhar, S.: Hydrodynamic and Hydromagnetic Stability. Oxford University Press, London (1961)
Dasgupta, S., Karmakar, P.K.: Astrophys. Space Sci. 364, 1 (2019)
Dhiman, J.S., Mahajan, M.: J. Astrophys. Astron. 44(1), 8 (2023)
Dhiman, J.S., Sharma, R.: Phys. Scr. 89(12), 125001 (2014)
Dhiman, J.S., Sharma, R.: J. Astrophys. Astron. 38, 1 (2017)
Dolai, B., Prajapati, R.P.: Phys. Plasmas 24(11), 112101 (2017)
Dolai, B., Prajapati, R.: Phys. Lett. A 384(25), 126462 (2020)
Drury, L., Voelk, J.: Astrophys. J. 248, 344 (1981)
Elmegreen, B.G.: Astrophys. J. 344, 306 (1989)
Guillemin, E.A.: The Mathematics of Circuit Analysis. Wiley, New York (1949)
Hennebelle, P., Inutsuka, S-i.: Front. Astron. Space Sci. 6, 5 (2019)
Ichimaru, S.: Rev. Mod. Phys. 54(4), 1017 (1982)
Jain, S., Sharma, P., Kaothekar, S., Chhajlani, R.: Astrophys. J. 829(2), 122 (2016)
Janaki, M., Chakrabarti, N., Banerjee, D.: Phys. Plasmas 18(1), 012901 (2011)
Jeans, J.H.: Philos. Trans. R. Soc. Lond. Ser. A 199, 1 (1902)
Kalita, D., Karmakar, P.K.: Phys. Plasmas 27(2), 022902 (2020)
Kaothekar, S., Soni, G.D., Prajapati, R., Chhajlani, R.K.: Astrophys. Space Sci. 361, 1 (2016)
Karmakar, P.K., Kalita, D.: Astrophys. Space Sci. 363, 1 (2018)
Kaw, P., Sen, A.: Phys. Plasmas 5(10), 3552 (1998)
Kempski, P., Quataert, E., Squire, J.: Mon. Not. R. Astron. Soc. 493(4), 5323 (2020)
Kuwabara, T., Ko, C.-M.: Astrophys. J. 636(1), 290 (2006)
Kuwabara, T., Ko, C.-M.: Astrophys. J. 899(1), 72 (2020)
Kuznetsov, V., Ptuskin, V.: Astrophys. Space Sci. 94, 5 (1983)
Leite, N., Evoli, C., D’Angelo, M., Ciardi, B., Sigl, G., Ferrara, A.: Mon. Not. R. Astron. Soc. 469(1), 416 (2017)
Lipari, P.: C. R. Phys. 15(4), 357 (2014)
Marcowith, A., Van Marle, A., Plotnikov, I.: Phys. Plasmas 28(8), 080601 (2021)
Morfill, G.E., Ivlev, A.V.: Rev. Mod. Phys. 81(4), 1353 (2009)
Mouschovias, T.C., Ciolek, G.E., Morton, S.A.: Mon. Not. R. Astron. Soc. 415(2), 1751 (2011)
Murillo, M.S.: Phys. Plasmas 11(5), 2964 (2004)
Naddaf, M.H., Czerny, B.: Astron. Astrophys. 663, 77 (2022)
Padovani, M., Galli, D., Glassgold, A.E.: Astron. Astrophys. 501(2), 619 (2009)
Padovani, M., Ivlev, A.V., Galli, D., Offner, S.S., Indriolo, N., Rodgers-Lee, D., Marcowith, A., Girichidis, P., Bykov, A.M., Kruijssen, J.D.: Space Sci. Rev. 216(2), 29 (2020)
Pinto, C., Galli, D., Bacciotti, F.: Astron. Astrophys. 484(1), 1 (2008)
Prajapati, R.P.: Mon. Not. R. Astron. Soc. 510(2), 2127 (2022)
Prajapati, R.P., Chhajlani, R.K.: Astrophys. Space Sci. 344, 371 (2013)
Prajapati, R., Chhajlani, R.: Astrophys. Space Sci. 350, 637 (2014)
Prajapati, R.P., Shailesh, I.: J. Astrophys. Astron. 43, 33 (2022)
Prajapati, R., Pensia, R., Kaothekar, S., Chhajlani, R.: Astrophys. Space Sci. 327, 139 (2010)
Ptuskin, V., Zirakashvili, V., Seo, E.-S.: Astrophys. J. 718(1), 31 (2010)
Rosenberg, M., Shukla, P.: Phys. Scr. 83(1), 015503 (2011)
Ryu, D., Kim, J., Hong, S.S., Jones, T.W.: Astrophys. J. 589(1), 338 (2003)
Schuppan, F., Becker, J.K., Black, J.H., Casanova, S.: Astron. Astrophys. 541, 126 (2012)
Shadmehri, M.: Mon. Not. R. Astron. Soc. 397(3), 1521 (2009)
Shaikh, S., Khan, A., Bhatia, P.K.: Z. Naturforsch. A 61, 275 (2006)
Sharma, R., Bhardwaj, S., Dhiman, J.S.: Astrophys. Space Sci. 365, 1 (2020)
Tasker, E.J., Tan, J.C.: Astrophys. J. 700, 358 (2009)
Thompson, T.A.: Astrophys. J. 684, 212 (2008)
Tsiklauri, D.: Astrophys. J. 507, 226 (1998)
Vranjes, J., Cadez, V.: Astrophys. Space Sci. 164, 329 (1990)
Williams, J.P., Bergin, E.A., Caselli, P., Myers, P.C., Plume, R.: Astrophys. J. 503(2), 689 (1998)
Xu, S., Lazarian, A.: Astrophys. J. 927(1), 94 (2022)
Yang, R-z., Li, G.-X., Wilhelmi, E.d.O., Cui, Y.-D., Liu, B., Aharonian, F.: Nature Astron. 1 (2023)
Acknowledgements
The authors thank the learned reviewers for their useful comments and insightful suggestions, which helped us in the improvement of the manuscript. We also thank Ram Prasad Prajapati, JNU, New Delhi for helpful discussions on this paper.
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Dhiman, J.S., Mahajan, M. Effects of galactic cosmic rays and finite electrical resistivity on the Jeans instability in magnetized viscoelastic fluid. Astrophys Space Sci 368, 41 (2023). https://doi.org/10.1007/s10509-023-04199-x
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DOI: https://doi.org/10.1007/s10509-023-04199-x