Supernovae and AGN Driven Galactic Outflows

We present analytical solutions for winds from galaxies with a Navarro-Frank-White (NFW) dark matter halo. We consider winds driven by energy and mass injection from multiple supernovae (SNe), as well as momentum injection due to radiation from a central black hole. We find that the wind dynamics depends on three velocity scales: (1) v_\star ∼ (\dot{E} / 2 \dot{M})^{1/2} describes the effect of starburst activity, with \dot{E} and \dot{M} as energy and mass injection rate in a central region of radius R; (2) v _• ~ (GM _•/2R)^1/2 for the effect of a central black hole of mass M _• on gas at distance R; and (3) v_{s} =(GM_h / 2 {C}r_s)^{1/2}, which is closely related to the circular speed (v_c ) for an NFW halo, where r_s is the halo scale radius and {C} is a function of the halo concentration parameter. Our generalized formalism, in which we treat both energy and momentum injection from starbursts and radiation from the central active galactic nucleus (AGN), allows us to estimate the wind terminal speed to be (4v ² _sstarf + 6(Γ - 1)v _• ² - 4v ² _s )^1/2, where Γ is the ratio of force due to radiation pressure to gravity of the central black hole. Our dynamical model also predicts the following: (1) winds from quiescent star-forming galaxies cannot escape from 10^11.5 M _⊙ <= M_h <= 10^12.5 M _⊙ galaxies; (2) circumgalactic gas at large distances from galaxies should be present for galaxies in this mass range; (3) for an escaping wind, the wind speed in low- to intermediate-mass galaxies is ~400-1000 km s^-1, consistent with observed X-ray temperatures; and (4) winds from massive galaxies with AGNs at Eddington limit have speeds >~ 1000 km s^-1. We also find that the ratio [2v ² _sstarf - (1 - Γ)v _• ²]/v ² _c dictates the amount of gas lost through winds. Used in conjunction with an appropriate relation between M _• and M_h and an appropriate opacity of dust grains in infrared (K band), this ratio has the attractive property of being minimum at a certain halo mass scale (M_h ~ 10¹²-10^12.5 M _⊙) that signifies the crossover of AGN domination in outflow properties from starburst activity at lower masses. We find that stellar mass for massive galaxies scales as M _sstarfvpropM ^0.26 _h , and for low-mass galaxies, M _sstarfvpropM ^5/3 _h .