Output Analysis Molecular Ratio

Class providing models of the H\(_2\)-to-H**i** molecular ratio \(R_\mathrm{mol} = M_{\mathrm{H}_2}/M_{\mathrm{H\,I}}\) for on-the-fly output analysis—the fraction of cold interstellar gas in molecular form, which governs the H\(_2\) mass function and the molecular gas content of galaxies. Methods return both the mean ratio (as a function of ISM mass and galaxy properties) and its logarithmic scatter, allowing the molecular gas distribution to be convolved with the total ISM mass distribution when predicting H**i** and H\(_2\) mass functions.

Default implementation: outputAnalysisMolecularRatioObreschkow2009

Methods

ratio → double precision

Return the molecular ratio, \(R_\mathrm{mol}=M_\mathrm{H_2}/M_\mathrm{HI}\).

• double precision , intent(in ) :: massISM

• type (treeNode), intent(inout) :: node

ratioScatter → double precision

Return the scatter in logarithmic molecular ratio, \(\log_{10}R_\mathrm{mol}=\log_{10}(M_\mathrm{H_2}/M_\mathrm{HI})\).

• double precision , intent(in ) :: massISM

• type (treeNode), intent(inout) :: node

outputAnalysisMolecularRatioObreschkow2009

A molecular ratio class which computes the molecular ratio. The class assumes that only the total ISM mass of each galaxy is available, along with the disk radius (assuming an exponential disk). To infer the HI mass the model of Obreschkow et al. (2009) is used. Specifically, the molecular ratio, \(R_\mathrm{mol}\equiv M_\mathrm{H_2}/M_\mathrm{HI}\), is given by:

(19)\[R_\mathrm{mol} = \left( A_1 R_\mathrm{mol}^\mathrm{c\,\alpha_1} + A_2 R_\mathrm{mol}^\mathrm{c\,\alpha_2} \right)^{-1},\]

where the ratio at the disk center is given by

\[R_\mathrm{mol}^\mathrm{c} = [ K r_\mathrm{disk}^{-4} M_\mathrm{gas} (M_\mathrm{gas} + \langle f_\sigma \rangle M_\star)]^\beta.\]

Here, \(R_\mathrm{mol}\) is the mass ratio of H\(_2\) to HI, \(M_\star\) is the stellar mass of the disk, \(r_\mathrm{disk}\) is the disk exponential scale length, \(\langle f_\sigma \rangle\) is the average ratio of the vertical velocity dispersions of gas to stars, and \(K=\mathrm{G}/(8\pi P_\star)\). The HI mass is then determined from:

\[M_\mathrm{HI} = X_\mathrm{H} M_\mathrm{gas} / ( 1 + R_\mathrm{mol} ),\]

where \(X_\mathrm{H}=0.778\) is the primordial hydrogen fraction by mass. In the above \(K=\)[K], \(\langle f_\sigma \rangle=\)[fSigma], \(A_1=\)[A1], \(A_2=\)[A2], \(\alpha_1=\)[alpha1], \(\alpha_2=\)[alpha2], and \(\beta=\)[beta]. Default values for these parameters are taken from Obreschkow et al. (2009). According to Obreschkow (private communication), there remains significant scatter of \(\sigma_{R_\mathrm{mol}}=0.4\) dex between the predicted \(R_\mathrm{mol}\) from this model and that observed. This is accounted for in when constructing the mass function (see below).

(Default implementation)

Parameters

• [K] (default 11.3d0) — The parameter, \(K\) (in units of m\(^4\) kg\(^{-2}\)), appearing in the model for the H\(_2\)/HI ratio in galaxies from Obreschkow et al. (2009).

• [fSigma] (default 0.4d0) — The parameter, \(\langle f_\sigma \rangle\), appearing in the model for the H\(_2\)/HI ratio in galaxies from Obreschkow et al. (2009).

• [A1] (default 3.44d0) — The parameter, \(A_1\), appearing in the model for the H\(_2\)/HI ratio in galaxies from Obreschkow et al. (2009).

• [A2] (default 4.82d0) — The parameter, \(A_2\), appearing in the model for the H\(_2\)/HI ratio in galaxies from Obreschkow et al. (2009).

• [alpha1] (default -0.506d0) — The parameter, \(\alpha_1\), appearing in the model for the H\(_2\)/HI ratio in galaxies from Obreschkow et al. (2009).

• [alpha2] (default -1.054d0) — The parameter, \(\alpha_2\), appearing in the model for the H\(_2\)/HI ratio in galaxies from Obreschkow et al. (2009).

• [beta] (default 0.8d0) — The parameter, \(\beta\), appearing in the model for the H\(_2\)/HI ratio in galaxies from Obreschkow et al. (2009).

• [scatter] (default 0.4d0) — The scatter (in dex) in the molecular ratio \(\log_{10}R_\mathrm{mol}\) of Obreschkow et al. (2009) compared to observational data.