.. _gas:

The Gas Supply
==============

.. _gas_ifr_sfr_eff:

Inflows, Star Formation, and Efficiency
---------------------------------------
Like the :ref:`enrichment equation <enr_eq>`, the time derivative of the mass
of the gas in the interstellar medium (ISM) :math:`M_\text{g}` is a simple sum
of source and sink terms. For an infall rate (IFR) :math:`\dot{M}_\text{in}`,
star formation rate (SFR) :math:`\dot{M}_\star`, and outflow rate (OFR)
:math:`\dot{M}_\text{out}`:

.. math:: \dot{M}_g = \dot{M}_\text{in} - \dot{M}_\star - \dot{M}_\text{out} +
	\dot{M}_\text{r}

where :math:`\dot{M}_\text{r}` is the rate of recycling from stars producing
remnants and return gas to the ISM at their birth metallicity. Because VICE is
implemented with a Forward Euler solution, this equation is evaluated via:

.. math:: \Delta M_g \approx \dot{M}_g\Delta t =
	\dot{M}_\text{in}\Delta t - \dot{M}_\star \Delta t - \dot{M}_\text{out}
	\Delta t + \dot{M}_\text{r}\Delta t

By construction, VICE operates such that the user specifies either an infall
history (:math:`\dot{M}_\text{in}` in :math:`M_\odot yr^{-1}` as a function of
time), a star formation history (:math:`\dot{M}_\star` in :math:`M_\odot
yr^{-1}` as a function of time), or the gas history (:math:`M_\text{g}` in
:math:`M_\odot` as a function of time). The user also specifies a star
formation efficiency timescale [1]_:

.. math:: \tau_\star \equiv \frac{M_g}{\dot{M}_\star}

Users may specify an arbitrary function of time in Gyr to describe
:math:`\tau_\star`, whose units are assumed to be Gyr. With one of either
:math:`\dot{M}_\text{in}`, :math:`\dot{M}_\star`, or :math:`M_\text{g}`
specified by the user, :math:`\tau_\star`,  and the implementation of
:math:`\dot{M}_\text{out}` and :math:`\dot{M}_\text{r}` discussed in this
section, the solutions to :math:`\dot{M}_\text{in}`, :math:`\dot{M}_\star`,
and :math:`M_g` as functions of time are unique.

VICE also allows users to adopt a formulation of :math:`\tau_\star` that
depends on the gas supply; this is an application of the Kennicutt-Schmidt
relation to the single-zone approximation. This is implemented as a power-law:

.. math:: \tau_\star^{-1} = \tau_{\star,\text{spec}}^{-1}
	\left(\frac{M_g}{M_{g,\text{Schmidt}}}\right)^\alpha

where :math:`M_{g,\text{Schmidt}}` is a normalizing gas supply and
:math:`\tau_{\star,\text{spec}}` is the user-specified :math:`\tau_\star`.
The ``singlezone`` object will employ this scaling when the attribute
``schmidt = True``.

Users may also allow :math:`\tau_\star` to vary with the gas supply in a
customized way by specifying a function which accepts a second parameter in
addition to time in Gyr. In infall and gas modes, VICE will interpret the
second parameter as the gas mass in :math:`M_\odot`; in star formation mode,
VICE will interpret it as the star formation rate in :math:`M_\odot/yr`.
While such an approach also allows the single power-law solution, such a model
has a well-defined solution implemented in VICE's C library, allowing them to
not suffer from a decrease in computational speed.

Relevant Source Code:

	- ``vice/src/singlezone/ism.c``

.. [1] In the interstellar medium literature, this quantity is often referred
	to as the "depletion time" due to star formation. In the chemical
	evolution literature, it quantifies the fractional rate at which gas
	forms stars, and is thus often refered to in terms of star formation
	efficiency. We retain this nomenclature here.

.. _gas_outflows:

.. include:: outflows.rst

.. _gas_recycling:

.. include:: recycling.rst