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ABSTRACT It has been established for decades that rotation curves deviate from the Newtonian gravity expectation given baryons alone below a characteristic acceleration scale $$g_{\dagger }\sim 10^{-8}\, \rm {cm\, s^{-2}}$$, a scale promoted to a new fundamental constant in MOND. In recent years, theoretical and observational studies have shown that the star formation efficiency (SFE) of dense gas scales with surface density, SFE ∼ Σ/Σcrit with $$\Sigma _{\rm crit} \sim \langle \dot{p}/m_{\ast }\rangle /(\pi \, G)\sim 1000\, \rm {M_{\odot }\, pc^{-2}}$$ (where $$\langle \dot{p}/m_{\ast }\rangle$$ is the momentum flux output by stellar feedback per unit stellar mass in a young stellar population). We argue that the SFE, more generally, should scale with the local gravitational acceleration, i.e. that SFE $${\sim}g_{\rm tot}/g_{\rm crit}\equiv (G\, M_{\rm tot}/R^{2}) / \langle \dot{p}/m_{\ast }\rangle$$, where Mtot is the total gravitating mass and $$g_{\rm crit}=\langle \dot{p}/m_{\ast }\rangle = \pi \, G\, \Sigma _{\rm crit} \approx 10^{-8}\, \rm {cm\, s^{-2}} \approx \mathit{ g}_{\dagger }$$. Hence, the observed g† may correspond to the characteristic acceleration scale above which stellar feedback cannot prevent efficient star formation, and baryons will eventually come to dominate. We further show how this may give rise to the observed acceleration scaling $$g_{\rm obs}\sim (g_{\rm baryon}\, g_{\dagger })^{1/2}$$ (where gbaryon is the acceleration due to baryons alone) and flat rotation curves. The derived characteristic acceleration g† can be expressed in terms of fundamental constants (gravitational constant, proton mass, and Thomson cross-section): $$g_{\dagger }\sim 0.1\, G\, m_{\mathrm{ p}}/\sigma _{\rm T}$$.
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Why do black holes trace bulges (& central surface densities), instead of galaxies as a whole?
ABSTRACT 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.
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- PAR ID:
- 10361033
- Publisher / Repository:
- Oxford University Press
- Date Published:
- Journal Name:
- Monthly Notices of the Royal Astronomical Society
- Volume:
- 510
- Issue:
- 1
- ISSN:
- 0035-8711
- Page Range / eLocation ID:
- p. 630-638
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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