vice.toolkit.J21_sf_law

The default star formation law of the milkyway object. This is a callable object, accepting simulation time and either star formation rate or gas supply as second arguments. By default, it implements the star formation law adopted in Johnson et al. (2021) [1].

Signature: vice.toolkit.J21_sf_law(area, **kwargs)

New in version 1.2.0.

Warning

In a milkyway object, every zone has an instance of this class as its tau_star attribute. Any modifications to the attributes of this class should be made for every zone; if this is not ensured, the star formation law will not be consistent across all zones.

Parameters

areareal number

The value of the attribute area. See below.

**kwargsvarying types

Other attributes can have their values set via keyword. See below.

Attributes

areareal number

The surface area in \(kpc^2\) of the corresponding annulus in a milkyway model.

present_day_molecularreal number [default2.0]

The depletion time of molecular gas at the present day in Gyr. Positive definite.

molecular_indexreal number [default0.5]

The power-law index on the time-dependence.

Sigma_g1real number [default5.0e+06]

The smaller of the two surface densities of gas at which there is a break in the Kennicutt-Schmidt relation. Assumes units of \(M_\odot kpc^{-2}\).

Sigma_g2real number [default2.0e+07]

The larger of the two surface densities of gas at which there is a break in the Kennicutt-Schmidt relation. Assumes units of \(M_\odot kpc^{-2}\).

index1real number [default1.7]

The index of the power-law at gas surface densities below Sigma_g1.

index2real number [default3.6]

The index of the power-law at gas surface densities between Sigma_g1 and Sigma_g2, above which it is assumed to be linear.

modestr [“sfr”, “ifr”, or “gas”] [default“ifr”]

The mode of the milkyway object.

Calling

Calling this object will calculate the star formation efficiency timescale \(\tau_\star\) according to the parameters of the star formation law entered as attributes of this object. As in the singlezone object, this timescale is the gas supply per unit star formation in Gyr.

Parameters:

  • timereal number

    Simulation time in Gyr. Postive definite.

  • arg2real number

    Either the gas supply in \(M_\odot\) or the star formation rate in \(M_\odot Gyr^{-1}\). Will be called by VICE directly. With the attribute area, the surface density of the corresponding quantity is known. Positive definite.

Returns:

  • tau_starreal number

    The star formation efficiency timescale given that simulation time and star formation rate/gas supply, in Gyr (as necessary).

See also

vice.milkyway

Notes

This object encodes the parameters of the desired Kennicutt-Schmidt relation into the milkyway object. This is the relationship relating the surface densities of star formation \(\dot{\Sigma}_\star\) and gas \(\Sigma_\text{gas}\).

This object implements a star formation law in the milkyway object defined according to:

\[\dot{\Sigma}_\star \sim \Sigma_\text{gas}^N\]

The value of the power-law index \(N\) has two breaks, at \(\Sigma_{\text{gas},1}\) and \(\Sigma_{\text{gas},2}\).

\[\begin{split}N = 1.0\ (\Sigma_\text{gas} \geq \Sigma_{\text{gas},2}) \\ N = \gamma_2\ (\Sigma_{\text{gas},1} \leq \Sigma_\text{gas} \leq \Sigma_{\text{gas},2}) \\ N = \gamma_1\ (\Sigma_\text{gas} \leq \Sigma_{\text{gas},1})\end{split}\]

The values \(\gamma_1\) and \(\gamma_2\) correspond to the attributes index1 and index2, respectively. As their names would suggest, \(\Sigma_{\text{gas},1}\) and \(\Sigma_{\text{gas},2}\) correspond to Sigma_g1 and Sigma_g2.

The depletion time of molecular gas due to star formation \(\tau_\text{mol}\) is defined according to the following scaling:

\[\tau_\text{mol} = \tau_{\text{mol},0} \left(t/t_0\right)^\beta\]

where \(t_0\) is the age of the universe today, \(t\) is the age of the universe at some simulation time, and \(\tau_{\text{mol},0}\) is \(\tau_\text{mol}\) at the present day. Because the milkyway model only supports lookback times up to 13.2 Gyr, the relation between age of the universe and simulation time is a simple linear translation:

\[t = t_\text{sim} + 0.5\ \text{Gyr}\]

with the assumption that \(t_0\) = 13.7 Gyr is the age of the universe at the present day.