Abstract
The propagation of cylindrical ionizing shock waves in a self-gravitating ideal gas with axial magnetic field is investigated. The density and magnetic pressure are assumed to be varying according to power law with distance in the undisturbed medium. Approximate analytical solutions are obtained by expanding the flow variables in power series. The zeroth order and first order approximate solutions are discussed. Solutions for zeroth order approximation are constructed in analytical form. Distributions of hydrodynamical quantities for zeroth order approximation are discussed. Also, the effect of various flow parameters, namely shock Cowling number, adiabatic exponent, gravitational parameter and ambient density variation exponent are studied on the flow variables.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Balick B., Frank A. 2002, Annu. Rev. Astron. Astrophys., 40, 439
Butler D. S. 1965, J. Fluid Mech., 23, 1
Carrus P., Fox P., Hass F., Kopal Z. 1951, Astrophys. J., 113, 496
Christer A. H. 1972, Z. Angew Math. Mech., 52, 11
Chu C. K. 1964, Phys. Fluids, 7, 1349
Fiege J. D., Pudritz, R. E. 2000, Mon. Not. R. Astron. Soc., 311, 85
Greifinger C., Cole J. D. 1962, Phys. Fluids, 5, 1597
Greenspan H. P. 1962, Phys. Fluids, 5, 255
Hartmann L. 1998, Accretion Processes in Star Formation, Cambridge University Press, Cambridge
Hutchens G. J. 1995, J. Appl. Phys. 77, 2912
Inutsuka S. I., Miyama S. M. 1997, Astrophys. J., 480, 681
Inutsuka S. I., Tsuribe T. 2001, in Symposium-International Astronomical Union, Cambridge University Press, Cambridge, vol. 200, p. 391
Kelly T. J., Klein R. I., McKee C. F., Holliman J. H., Howell L. H., Jeffrey A. G., Wood D. T. 1998, Astrophys. J., 495, 821
Klein R. I., McKee C. F., Colella P. 1994, Astrophys. J., 420, 213
Lerche I. 1979, Aust. J. Phys., 32, 491
Lerche I. 1981, Aust. J. Phys., 34, 279
Lin S.-C. 1954, J. Appl. Phys., 25, 54
Nath G. 2014, J. Theor. Appl. Phys., 8, 131, https://doi.org/10.1007/s40094-014-0131-y
Nath G., Singh S. 2017, Int. J. Non Linear Mech., 88, 102
Nath G., Singh S., Srivastava P. 2018, J. Eng. Phys. Thermophys., 91, 1302
Nath G., Vishwakarma J. P., Srivastava V. K., Sinha A. K. 2013, J. Theor. Appl. Phys., 7, 15
Purohit S. C. 1974, J. Phys. Soc. Japan, 36, 288
Rangarao M. P., Ramana B. V. 1973, Int. J. Eng. Sci., 11, 337
Rybakin B. P., Betelin V. B., Dushin V. R., Mikhalchenko E. V., Moiseenko S. G., Stamov L. I., Tyurenkova V. V. 2016, Acta Astronaut., 119, 131
Sakurai A. 1953, J. Phys. Soc. Japan, 8, 662
Sakurai A. 1954, J. Phys. Soc. Japan, 9, 256
Sedov L. I. 1959, Similarity and Dimensional Methods in Mechanics, Academic Press, New York
Singh J. B., Vishwakarma P. R. 1983, Astrophys. Space Sci., 95, 99
Taylor G. 1950a, Proc. Roy. Soc. London A, 201, 159
Taylor G. 1950b, Proc. Roy. Soc. London A, 201, 175
Vishwakarma J. P., Singh A. K. 2009, J. Astrophys. Astron., 30, 53
Vishwakarma J. P., Singh M. 2012, Appl. Math., 2, 1
Vishwakarma J. P., Yadav A. K. 2003, EPJ B-Condensed Matter and Complex Systems, 34, 247
Acknowledgements
The second author, Sumeeta Singh, acknowledges DST, New Delhi, India for providing INSPIRE Fellowship, IF No. 150736, to pursue research work.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Nath, G., Singh, S. Cylindrical ionizing shock waves in a self-gravitating gas with magnetic field: Power series method. J Astrophys Astron 40, 47 (2019). https://doi.org/10.1007/s12036-019-9615-0
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s12036-019-9615-0