vice.cumulative_return_fraction

Calculate the cumulative return fraction for a single stellar population at a given age. This quantity represents the fraction of the stellar population’s mass that is returned to the interstellar medium as gas at the birst metallicity of the stars.

Signature: vice.cumulative_return_fraction(age, IMF = “kroupa”, m_upper = 100, m_lower = 0.08, postMS = 0.1)

Parameters

agereal number

The age of the stellar population in Gyr.

IMFstr [case-insensitive] or <function> [default“kroupa”]

The assumed stellar initial mass function (IMF). Strings denote built-in IMFs. Functions must accept only one numerical parameter and will be interpreted as a custom, arbitrary stellar IMF.

Recognized built-in IMFs:

Note

Functions do not need to be normalized. VICE will take care of this automatically.

m_upperreal number [default100]

The upper mass limit on star formation in solar masses.

m_lowerreal number [default0.08]

The lower mass limit on star formation in solar masses.

postMSreal number [default0.1]

The ratio of a star’s post main sequence lifetime to its main sequence lifetime.

New in version 1.1.0: Prior to version 1.1.0, VICE approximated postMS = 0.

Returns

crfreal number

The value of the cumulative return fraction for a stellar population at the specified age under the specified parameters.

Notes

Note

VICE operates under the approximation that stars have a mass-luminosity relationship given by:

\[L \sim M^{4.5}\]

leading to a mass-lifetime relation that is also a power law, given by:

\[\tau \sim M/L \sim M^{-3.5}\]

Note

VICE implements the remnant mass model of Kalirai et al. (2008) [3], assuming that stars above 8 \(M_\odot\) leave behind remnants of 1.44 \(M_\odot\), while stars below 8 \(M_\odot\) leave behind remnants of \(0.394M_\odot + 0.109M\).

Raises

  • TypeError

    • age is not a real number

    • IMF is neither a string nor a function

    • m_upper is not a real number

    • m_lower is not a real number

    • postMS is not a real number

  • ValueError

    • age < 0

    • built-in IMF is not recognized

    • m_upper <= 0

    • m_lower <= 0

    • m_lower >= m_upper

    • postMS < 0 or > 1

Example Code

>>> vice.cumulative_return_fraction(1)
        0.3560160079575864
>>> vice.cumulative_return_fraction(2)
        0.38056657042902253
>>> vice.cumulative_return_fraction(3)
        0.394760119115021