.. _physics-outputAnalysisMolecularRatio:

Output Analysis Molecular Ratio
===============================

Class providing models of the H\ :math:`_2`-to-H**i** molecular ratio :math:`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\ :math:`_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\ :math:`_2` mass functions.

**Default implementation:** ``outputAnalysisMolecularRatioObreschkow2009``

Methods
-------

``ratio`` → ``double precision``
   Return the molecular ratio, :math:`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, :math:`\log_{10}R_\mathrm{mol}=\log_{10}(M_\mathrm{H_2}/M_\mathrm{HI})`.

   * ``double precision , intent(in ) :: massISM``

   * ``type (treeNode), intent(inout) :: node``

.. _physics-outputAnalysisMolecularRatioObreschkow2009:

``outputAnalysisMolecularRatioObreschkow2009``
----------------------------------------------

A molecular ratio class which computes the molecular ratio. The class assumes that only the total :term:`ISM` mass of each galaxy is available, along with the disk radius (assuming an exponential disk). To infer the HI mass the model of :cite:t:`obreschkow_simulation_2009` is used. Specifically, the molecular ratio, :math:`R_\mathrm{mol}\equiv M_\mathrm{H_2}/M_\mathrm{HI}`, is given by:

.. math::
   :label: eq-HIMassSystematic

   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

.. math::

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

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

.. math::

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

where :math:`X_\mathrm{H}=0.778` is the primordial hydrogen fraction by mass. In the above :math:`K=`\ ``[K]``, :math:`\langle f_\sigma \rangle=`\ ``[fSigma]``, :math:`A_1=`\ ``[A1]``, :math:`A_2=`\ ``[A2]``, :math:`\alpha_1=`\ ``[alpha1]``, :math:`\alpha_2=`\ ``[alpha2]``, and :math:`\beta=`\ ``[beta]``. Default values for these parameters are taken from :cite:t:`obreschkow_simulation_2009`. According to Obreschkow (private communication), there remains significant scatter of :math:`\sigma_{R_\mathrm{mol}}=0.4` dex between the predicted :math:`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, :math:`K` (in units of m\ :math:`^4` kg\ :math:`^{-2}`), appearing in the model for the H\ :math:`_2`/HI ratio in galaxies from :cite:t:`obreschkow_simulation_2009`.
* ``[fSigma]`` (default ``0.4d0``) — The parameter, :math:`\langle f_\sigma \rangle`, appearing in the model for the H\ :math:`_2`/HI ratio in galaxies from :cite:t:`obreschkow_simulation_2009`.
* ``[A1]`` (default ``3.44d0``) — The parameter, :math:`A_1`, appearing in the model for the H\ :math:`_2`/HI ratio in galaxies from :cite:t:`obreschkow_simulation_2009`.
* ``[A2]`` (default ``4.82d0``) — The parameter, :math:`A_2`, appearing in the model for the H\ :math:`_2`/HI ratio in galaxies from :cite:t:`obreschkow_simulation_2009`.
* ``[alpha1]`` (default ``-0.506d0``) — The parameter, :math:`\alpha_1`, appearing in the model for the H\ :math:`_2`/HI ratio in galaxies from :cite:t:`obreschkow_simulation_2009`.
* ``[alpha2]`` (default ``-1.054d0``) — The parameter, :math:`\alpha_2`, appearing in the model for the H\ :math:`_2`/HI ratio in galaxies from :cite:t:`obreschkow_simulation_2009`.
* ``[beta]`` (default ``0.8d0``) — The parameter, :math:`\beta`, appearing in the model for the H\ :math:`_2`/HI ratio in galaxies from :cite:t:`obreschkow_simulation_2009`.
* ``[scatter]`` (default ``0.4d0``) — The scatter (in dex) in the molecular ratio :math:`\log_{10}R_\mathrm{mol}` of :cite:t:`obreschkow_simulation_2009` compared to observational data.