We have classified possible transonic solutions of galactic outflows in the gravitational potential of the dark matter halo (DMH) and super massive black hole (SMBH) under the assumptions of isothermal, spherically symmetric and steady state. It is clarified that the gravity of SMBH adds a new branch of transonic solutions with the transonic point in very close proximity to the centre in addition to the outer transonic point generated by the gravity of DMH. Because these two transonic solutions have substantially different mass fluxes and starting points, these solutions may have different influences on the evolution of galaxies and the release of metals into intergalactic space. We have applied our model to the Sombrero galaxy and obtained a new type of galactic outflow: a slowly accelerated transonic outflow through the transonic point at very distant region (≃ 126 kpc). In this galaxy, previous works reported that although the trace of the galactic outflow is observed by X-ray, the gas density distribution is consistent with the hydrostatic state. We have clarified that the slowly accelerating outflow has a gas density profile quite similar to that of the hydrostatic solution in the widely spread subsonic region. Thus, the slowly accelerating transonic solution cannot be distinguished from the hydrostatic solution in the observed region ( 25 kpc) even if slow transonic flow exists. Our model provides a new perspective of galactic outflows and is applicable even to quiescent galaxies with inactive star formation.

Polytropic transonic solutions of spherically symmetric and steady galactic winds in the gravitational potential of a dark matter halo (DMH) with a supermassive black hole (SMBH) are studied. The solutions are classified in terms of their topological features, and the gravitational potential of the SMBH adds a new branch to the transonic solutions generated by the gravity of the DMH. The topological types of the transonic solutions depend on the mass distribution, the amount of supplied energy, the polytropic index γ, and the slope α of the DMH mass distribution. When α becomes larger than a critical value α c , the transonic solution types change dramatically. Further, our model predicts that it is possible for a slowly accelerating outflow to exist, even in quiescent galaxies with small γ. This slowly accelerating outflow differs from those considered in many of the previous studies focusing on supersonic outflows in active star-forming galaxies. In addition, our model indicates that outflows in active star-forming galaxies have only one transonic point in the inner region (∼ 0.01 kpc). The locus of this transonic point does not strongly depend on γ. We apply the polytropic model incorporating mass flux supplied by stellar components to the Sombrero Galaxy, and conclude that it can reproduce the observed gas density and the temperature distribution well. This result differs significantly from the isothermal model, which requires an unrealistically large mass flux (Igarashi et al. 2014). Thus, we conclude that the polytropic model is more realistic than the isothermal model, and that the Sombrero Galaxy can have a slowly accelerating outflow.

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Abstract. Galactic winds are widely recognized as important ingredients in galaxy evolution, and they impact the chemical enrichment of galaxies and the intergalactic medium. We investigate the acceleration process of isothermal, spherically symmetric steady galactic outflows in an appropriate galactic gravitational potential applying the transonic analysis which is the well-known approach for the solar wind. The results show that the transonic solutions of the galactic winds critically depend upon the mass distribution in a galaxy such as the dark matter halo (DMH) and the central super massive black hole (SMBH). We discover the existence of two types of transonic solutions in the gravity from the combination of DMH and SMBH. The first one is accelerated near the SMBH which is similar to the Parker solution, and the other is slowly accelerated over the entire region of DMH. These two transonic solutions have different mass fluxes and starting points. Therefore, they have different influences to the chemical evolution of galaxies and intergalactic space. We have found that the mass fluxes of two transonic solutions are considerably different by several orders of magnitude in spite of the same mass distribution. This result indicates that mass flux is very sensitive not only to the mass distribution but also to the chosen transonic solution.

We study fundamental properties of transonic galactic outflows in the gravitational potential of a cold dark matter halo (DMH) with a central super-massive black hole (SMBH) assuming an isothermal, steady and spherically symmetric state. Transonic solutions of galactic outflows are classified according to their topological features. As result, we find two types of transonic solutions distinguished by a magnitude relationship between the gravity of DMH and that of SMBH. The loci of transonic points for two types are different; one transonic point is formed at a central region (< 0.01kpc) and another is at a very distant region (> 100kpc). Also, mass fluxes and outflow velocities are different for two solutions. Thus, these solutions may differently influence the evolution of galaxies and the release of metals into the intergalactic space.Furthermore, we apply our model to the Sombrero galaxy. In this galaxy, the wide-spread hot gas is detected as the trace of galactic outflows while the star-formation rate is low, and the observed gas density distribution is similar to the hydrostatic state (Li et al. 2011). To solve this discrepancy, we propose a solution that this galaxy has a slowly accelerating outflow; the transonic point forms in a very distant region (~ 120 kpc) and the wide subsonic region spreads across the stellar distribution. Thus, the gas density distribution in the observed region is similar to the hydrostatic state. Such slowly accelerating outflows are different from high-velocity outflows conventionally studied (Igarashi et al. 2014).However, this isothermal model requires an unrealistically large mass flux. Then, we apply the polytropic model to this galaxy incorporating mass flux supplied by stellar components. We find that it can reproduce the observed gas density and the temperature distributions with the realistic mass flux. Thus, our polytropic model successfully demonstrates the existence of the slowly accelerating outflow in the Sombrero galaxy (Igarashi et al. 2015).