Joint PDF Model¶
Note
See Kim et al. (2020b) for details.
Cool outflow model¶
The cool outflow (\(T<2\times10^4{\rm K}\)) in the TIGRESS suite is well described by a model combining log-normal and generalized gamma distribution:
where \(A_c=(\ln 10)^2/(2\pi\sigma^2)^{1/2}=2.12/\sigma\).
At \(|z|=H\), we adopt \(v0=25\), \(c_{s,0}=6.7{\rm km/s}\), and \(\sigma=0.1\). We found the same function form with \((v0,c_{s,0})=(45,7.5)\), (45,8.5), and (60,10) works reasonably well at \(|z|=2H\), 500pc, and 1kpc.
Hot outflow model¶
The hot outflow (\(T>5\times10^5{\rm K}\)) in the TIGRESS suite is well described by a model combining two generalized gamma distributions:
where \(A_h\equiv 2(\ln 10)^2/\Gamma(1/2)=5.98\), \(v_{\mathcal{B},z}\equiv(v_{\rm out}^2+c_s^2)^{1/2}\), and \(\mathcal{M}=v_{\rm out}/c_s\).
where \(\Sigma_{\rm SFR,0}\equiv \Sigma_{\rm SFR}/(M_{\odot}{\rm kpc^{-2}yr^{-1}})\)
We adopt \(\mathcal{M}_0=0.5\) irrespective of \(z\).