Star Formation Rates in Disk Galaxies and Circumnuclear Starbursts from Cloud Collisions
by Jonathan C. Tan
Astrophysical Journal, 536, 173
ABSTRACT:
We invoke star formation triggered by cloud-cloud collisions to
explain global star formation rates of disk galaxies and circumnuclear
starbursts. Previous theories based on the growth rate of
gravitational perturbations ignore the dynamically important presence
of magnetic fields. Theories based on triggering by spiral density
waves fail to explain star formation in systems without such
waves. Furthermore, observations suggest gas and stellar disk
instabilities are decoupled. Following Gammie, Ostriker \& Jog (1991),
the cloud collision rate is set by the shear velocity of encounters
with initial impact parameters of a few tidal radii, due to
differential rotation in the disk. This, together with the effective
confinement of cloud orbits to a two dimensional plane, enhances the
collision rate above that for particles in a three dimensional box. We
predict $\Sigma_{SFR}(R)\propto \Sigma_{gas} \Omega (1-0.7
\beta)$. For constant circular velocity ($\beta = 0$), this is in
agreement with recent observations (Kennicutt 1998). We predict a
B-band Tully-Fisher relation: $L_{B}\propto v_{circ}^{7/3}$, also
consistent with observations. As additional tests, we predict enhanced
star formation in regions with relatively high shear rates, and lower
star formation efficiencies in clouds of higher mass.
DATA FOR FIGURES:
The data for figures (1) and (2) are from Kennicutt (1998).
Here are the figures from the paper and some of the associated data:
| figure1.ps |
Classical Schmidt Law : Sigma_{SFR}\propto (Sigma_{gas})^1.40.
|
| figure2.ps |
Modified Schmidt Law : Sigma_{SFR}\propto Sigma_{gas} Omega.
|
Figure 3 - Star formation efficiency, $\epsilon$, versus cloud mass,
$M_c$. (a) {\it Top:} Full sample of 39 clouds associated with 83 HII
regions. The cross shows typical errors of 0.3 in ${\rm log_{10}}\: M_c$ and
0.4 in ${\rm log_{10}}\: \epsilon$. The {\it diagonal dashed} line shows the
efficiency a cloud would have if associated with an HII region of
luminosity $L_{min}=400\:{\rm Jy\:kpc^{2}}$. The data are incomplete
below this line. The {\it vertical dashed} line shows the molecular cloud
survey completeness boundary at $M_c=4\times 10^{5}\:{\rm M_{\odot}}$
(Williams \& McKee 1997). (b) {\it Middle:} Complete sample of 19
clouds associated with individual HII regions, each with
$L_{rad}>L_{min}$. The completeness boundary is again shown by the
{\it diagonal dashed} line. The adopted value of $\epsilon_{max}=0.2$ is
shown by the {\it horizontal dashed} line. The best linear fit to
this data in logarithmic space is shown by the {\it long dashed line}. {\it Solid} lines show various model predictions: A - Collision induced star
formation; B - Stochastic star formation (Williams \& McKee 1997); C -
Stochastic star formation with $\epsilon_{max}(M)={\rm constant}$; D -
Uniform distribution of $\epsilon$ in logarithmic space. (c) {\it
Bottom:} 95\% Confidence intervals on the best linear fit ({\it long dashed}
line) to the data in logarithmic space are shown by the {\it dotted} lines:
1 - limit for the existing 19 data points, with errors shown by cross
in (a); 2 - limit for hypothetical data set of 190 clouds with the
same distribution as the existing 19; 3 - limit for these 190 clouds
with typical errors half of those shown by cross in (a). Note,
although these limits are based on the (poor) assumption of a normal
distribution of the data about the best fit line, and are only limits
on linear fits (hence the deviation at low $M_c$), this figure still illustrates that with ten times more
data and with errors reduced by a factor of two, one can hope to
distinguish between the different models ({\it solid} lines, as in (b)).
