Previous studies of fueling black holes in galactic nuclei have argued (on scales ${\sim}0.01{-}1000\,$pc) accretion is dynamical with inflow rates $\dot{M}\sim \eta \, M_{\rm gas}/t_{\rm dyn}$ in terms of gas mass Mgas, dynamical time tdyn, and some η. But these models generally neglected expulsion of gas by stellar feedback, or considered extremely high densities where expulsion is inefficient. Studies of star formation, however, have shown on sub-kpc scales the expulsion efficiency fwind = Mejected/Mtotal scales with the gravitational acceleration as $(1-f_{\rm wind})/f_{\rm wind}\sim \bar{a}_{\rm grav}/\langle \dot{p}/m_{\ast }\rangle \sim \Sigma _{\rm eff}/\Sigma _{\rm crit}$ where $\bar{a}_{\rm grav}\equiv G\, M_{\rm tot}(\lt r)/r^{2}$ and $\langle \dot{p}/m_{\ast }\rangle$ is the momentum injection rate from young stars. Adopting this as the simplest correction for stellar feedback, $\eta \rightarrow \eta \, (1-f_{\rm wind})$, we show this provides a more accurate description of simulations with stellar feedback at low densities. This has immediate consequences, predicting the slope and normalization of the MBH − σ and MBH − Mbulge relation, LAGN −SFR relations, and explanations for outliers in compact Es. Most strikingly, because star formation simulations show expulsion is efficient (fwind ∼ 1) below total-mass surface density $M_{\rm tot}/\pi \, r^{2}\lt \Sigma _{\rm crit}\sim 3\times 10^{9}\, \mathrm{M}_{\odot }\, {\rm kpc^{-2}}$ (where $\Sigma _{\rm crit}=\langle \dot{p}/m_{\ast }\rangle /(\pi \, G)$), BH mass is predicted to specifically trace host galaxy properties above a critical surface brightness Σcrit (B-band $\mu _{\rm B}^{\rm crit}\sim 19\, {\rm mag\, arcsec^{-2}}$). This naturally explains why BH masses preferentially reflect bulge properties or central surface densities (e.g. $\Sigma _{1\, {\rm kpc}}$), not ‘total’ galaxy properties.
The analytic galactic wind model derived by Chevalier and Clegg in 1985 (CC85) assumes uniform energy and mass-injection within the starburst galaxy nucleus. However, the structure of nuclear star clusters, bulges, and star-forming knots are non-uniform. We generalize to cases with spherically-symmetric energy/mass injection that scale as r−Δ within the starburst volume R, providing solutions for Δ = 0, 1/2, 1, 3/2, and 2. In marked contrast with the CC85 model (Δ = 0), which predicts zero velocity at the centre, for a singular isothermal sphere profile (Δ = 2), we find that the flow maintains a constant Mach number of $\mathcal {M}=\sqrt{3/5} \simeq 0.77$ throughout the volume. The fast interior flow can be written as $v_{r \lt R} = (\dot{E}_T/3\dot{M}_T)^{1/2} \simeq 0.41 \, v_\infty$, where v∞ is the asymptotic velocity, and $\dot{E}_T$ and $\dot{M}_T$ are the total energy and mass injection rates. For $v_\infty \simeq 2000 \, \mathrm{km \, s^{-1}}$, $v_{r\lt R} \simeq 820 \, \mathrm{km\, s^{-1}}$ throughout the wind-driving region. The temperature and density profiles of the non-uniform models may be important for interpreting spatially-resolved maps of starburst nuclei. We compute velocity resolved spectra to contrast the Δ = 0 (CC85) and Δ = 2 models. Next generation X-ray space telescopes such as XRISM may assess these kinematic predictions.
more » « less- NSF-PAR ID:
- 10381289
- Publisher / Repository:
- Oxford University Press
- Date Published:
- Journal Name:
- Monthly Notices of the Royal Astronomical Society: Letters
- Volume:
- 518
- Issue:
- 1
- ISSN:
- 1745-3925
- Format(s):
- Medium: X Size: p. L87-L91
- Size(s):
- ["p. L87-L91"]
- Sponsoring Org:
- National Science Foundation
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