We model the conservation of energy in the framework of the thin layer approximation for two types of interstellar medium (ISM). In particular, we analyse an ISM in the presence of self-gravity and a Gaussian ISM which produces an asymmetry in the advancing shell. The astrophysical targets to be simulated are the Fermi bubbles, the local bubble, and the W4 super-bubble. The theory of images is applied to a piriform curve, which allows deriving some analytical formulae for the observed intensity in the case of an optically thin medium.
References
[1]
Heiles, C. (1979) H I Shells and Supershells. Astrophysical Journal, 229, 533-537. https://doi.org/10.1086/156986
[2]
Cash, W., Charles, P., Bowyer, S., Walter, F., Garmire, G. and Riegler, G. (1980) The X-Ray Superbubble in Cygnus. The Astrophysical Journal, 238, L71-L76. https://doi.org/10.1086/183261
[3]
Heiles, C. (1984) HI Shells, Supershells, Shell-Like Objects, and ‘‘Worms’’. The Astrophysical Journal Supplement Series, 55, 585-595. https://doi.org/10.1086/190970
[4]
Tenorio-Tagle, G. and Bodenheimer, P. (1988) Large-Scale Expanding Superstructures in Galaxies. Annual Review of Astronomy and Astrophysics, 26, 145-197. https://doi.org/10.1146/annurev.aa.26.090188.001045
[5]
McCray, R.A. (1987) Coronal Interstellar Gas and Supernova Remnants. In: Dalgarno A. and Layzer, D., Eds., Spectroscopy of Astrophysical Plasmas, Cambridge University Press, Cambridge, 255-278. https://doi.org/10.1017/CBO9780511564659.011
[6]
McCray, R. and Kafatos, M. (1987) Supershells and Propagating Star Formation. The Astrophysical Journal, 317, 190. https://doi.org/10.1086/165267
[7]
MacLow, M.M. and McCray, R. (1988) Superbubbles in Disk Galaxies. The Astrophysical Journal, 324, 776. https://doi.org/10.1086/165936
[8]
Igumenshchev, I.V., Shustov, B.M. and Tutukov, A.V. (1990) Dynamics of Supershells—Blow-Out. Astronomy and Astrophysics, 234, 396-402.
[9]
Basu, S., Johnstone, D. and Martin, P.G. (1999) Dynamical Evolution and Ionization Structure of an Expanding Superbubble: Application to W4. The Astrophysical Journal, 516, 843. https://doi.org/10.1086/307125
[10]
Kompaneyets, A.S. (1960) A Point Explosion in an Inhomogeneous Atmosphere. Doklady Physics, 5, 46.
[11]
Olano, C.A. (2009) The Propagation of the Shock Wave from a Strong Explosion in a Plane-Parallel Stratified Medium: The Kompaneets Approximation. Astronomy and Astrophysics, 506, 1215-1228. https://doi.org/10.1051/0004-6361/200912602
[12]
Pon, A., Johnstone, D., Bally, J. and Heiles, C. (2014) Kompaneets Model Fitting of the Orion-Eridanus Superbubble. Monthly Notices of the Royal Astronomical Society, 444, 3657-3669. https://doi.org/10.1093/mnras/stu1704
[13]
Pon, A., Ochsendorf, B.B., Alves, J., Bally, J., Basu, S. and Tielens, A.G.G.M. (2016) Kompaneets Model Fitting of the Orion-Eridanus Superbubble. II. Thinking Outside of Barnard’s Loop. The Astrophysical Journal, 827, 42. https://doi.org/10.3847/0004-637X/827/1/42
[14]
MacLow, M.M., McCray, R. and Norman, M.L. (1989) Superbubble Blowout Dynamics. The Astrophysical Journal, 337, 141. https://doi.org/10.1086/167094
[15]
Melioli, C., Brighenti, F., D’Ercole, A. and de Gouveia Dal Pino, E.M. (2009) Hydrodynamical Simulations of Galactic Fountains—II. Evolution of Multiple Fountains. Monthly Notices of the Royal Astronomical Society, 399, 1089-1105. https://doi.org/10.1111/j.1365-2966.2009.14725.x
[16]
Soler, J.D., Bracco, A. and Pon, A. (2018) The Magnetic Environment of the Orion-Eridanus Superbubble as Revealed by Planck. Astrophysics of Galaxies, 609, L3. https://doi.org/10.1051/0004-6361/201732203
[17]
Tomisaka, K. (1992) The Evolution of a Magnetized Superbubble. Publications of the Astronomical Society of Japan, 44, 177-191.
[18]
Rafikov, R.R. and Kulsrud, R.M. (2000) Magnetic Flux Expulsion in Powerful Superbubble Explosions and the α-Ω Dynamo. Monthly Notices of the Royal Astronomical Society, 314, 839-848. https://doi.org/10.1046/j.1365-8711.2000.03408.x
[19]
Bisnovatyi-Kogan, G.S. and Silich, S.A. (1995) Shock-Wave Propagation in the Nonuniform Interstellar Medium. Reviews of Modern Physics, 67, 661. https://doi.org/10.1103/RevModPhys.67.661
[20]
Dickey, J.M. and Lockman, F.J. (1990) H I in the Galaxy. Annual Review of Astronomy and Astrophysics, 28, 215-259. https://doi.org/10.1146/annurev.aa.28.090190.001243
[21]
Lockman, F.J. (1984) The H I Halo in the Inner Galaxy. Astrophysical Journal, 283, 90-97. https://doi.org/10.1086/162277
[22]
Tenenbaum, M. and Pollard, H. (1963) Ordinary Differential Equations: An Elementary Textbook for Students of Mathematics, Engineering, and the Sciences. Dover, New York.
[23]
Ince, E.L. (2012) Ordinary Differential Equations. Dover, New York.
[24]
Spitzer, Jr. L. (1942) The Dynamics of the Interstellar Medium. III. Galactic Distribution. Astrophysical Journal, 95, 329. https://doi.org/10.1086/144407
[25]
Rohlfs, K. (1977) Lectures on Density Wave Theory Vol. 69 of Lecture Notes in Physics. Springer-Verlag, Berlin.
[26]
Bertin, G. (2000) Dynamics of Galaxies. Cambridge University Press, Cambridge.
[27]
Padmanabhan, P. (2002) Theoretical Astrophysics. Vol. III: Galaxies and Cosmology. Cambridge University Press, Cambridge.
[28]
Olver, F.W.J., Lozier, D.W., Boisvert, R.F. and Clark, C.W. (2010) NIST Handbook of Mathematical Functions. Cambridge University Press, Cambridge.
[29]
Zaninetti, L. (2020) On the Shape of the Local Bubble. International Journal of Astronomy and Astrophysics, 10, 11-27. https://doi.org/10.4236/ijaa.2020.101002
[30]
Zaninetti, L. (2018) The Fermi Bubbles as a Superbubble. International Journal of Astronomy and Astrophysics, 8, 200-217. https://doi.org/10.4236/ijaa.2018.82015
[31]
Normandeau, M. and Basu, S. (1999) Observations and Modeling of the Disk-Halo Interaction in Our Galaxy. In: Taylor, A.R., Landecker, T.L. and Joncas, G., Eds., New Perspectives on the Interstellar Medium Vol. 168 of Astronomical Society of the Pacific Conference Series, Astron. Soc. Pac., San Francisco, 287.
[32]
Normandeau, M. (2000) The W4 Chimney/Superbubble. In: Alloin, D., Olsen, K. and Galaz, G., Eds., Stars, Gas and Dust in Galaxies: Exploring the Links Vol. 221 of Astronomical Society of the Pacific Conference Series, Astron. Soc. Pac., San Francisco, 41.
[33]
West, J.L., English, J., Normandeau, M. and Landecker, T.L. (2007) The Fragmenting Superbubble Associated with the H II Region W4. The Astrophysical Journal, 656, 914. https://doi.org/10.1086/510609
[34]
Gao, X.Y., Reich, W., Reich, P., Han, J.L. and Kothes, R. (2015) Magnetic Fields of the W4 Superbubble. Astronomy & Astrophysics, 578, Article ID: A24.
[35]
Baumgartner, V. and Breitschwerdt, D. (2013) Superbubble Evolution in Disk Galaxies. I. Study of Blow-Out by Analytical Models Astronomy & Astrophysics, 557, Article ID: A14.
[36]
Megeath, S.T., Townsley, L.K., Oey, M.S. and Tieftrunk, A.R. (2008) Low and High Mass Star Formation in the W3, W4, and W5 Regions. In: Reipurth, B., Ed., Handbook of Star Forming Regions, Chapter 9, Astronomical Society of the Pacific, 264-295.
[37]
Lawrence, J.D. (2013) A Catalog of Special Plane Curves. Dove, New York.
