Initialize the distribution.

Estimate the error incurred by excluding stars above m_max.

m_max defaults to self.highMass.

imf_index is the powerlaw index of the imf at high masses.

Fraction of total carbon yield from stars of mass m, dfC/dm, i.e. the distribution of carbon production as a function of stellar mass.

This is weighted by the stellar initial mass function (IMF), so that metal_mass_dist(m) * dm is the fraction of carbon emitted by stars with masses between m and m+dm.

Note that this is normalized over the interval from self.lowMass to self.highMass.

Carbon yield from a star of mass m.

This is the total mass of carbon emitted by a single star of mass m over its lifetime.

Complementary cumulative distribution of metal yield by mass, i.e. the fraction of the total metal output produced by stars above mass m.

This is the integral of metal_mass_dist from m to highMass (or self.highMass).

Note that this is normalized over the interval from self.lowMass to self.highMass, so values may be negative above highMass and greater than one below lowMass.

kwargs get passed to utils.ccumulate, which may passes them to utils.integrate_piecewise, which may pass them to the integration routine.

See also: metal_mass_dist.

Calculate the values of a binned enrichment function.

Each returned value bdf[i] is the integral of the mass dist function from m[i-1] to m[i]. bdf[0] is the integral from self.lowMass to m[0].

Also returned are delta_m values (the width of each bin in units of mass), so the average derivative can be calculated, if desired.

Note that this is normalized over the interval from self.lowMass to self.highMass.

See also: metal_mass_CCDF

The delay CDF of metal yield as a function of stellar age.

I.e. the fraction of the total metal yield produced by stars with a lifetime of t or less.

Note that this is normalized over the interval from self.lowMass to self.highMass, so values may be negative above the lifetime corresponding to highMass and greater than one below the lowMass lifetime.

Calculated using metal_mass_CCDF and m_star.

kwargs get passed to metal_mass_CCDF.

Calculate the values of a binned delay function.

Each returned value bdf[i] is the integral of the delay function from t[i-1] to t[i]. bdf[0] is the integral from self.minTime to t[0].

Also returned are delta_t values (the width of each bin in units of time), so the average derivative can be calculated, if desired.

Note that this is normalized over the interval from self.lowMass to self.highMass.

See also: metal_time_CDF

Delay function inferred from metal_time_dist_binned.

Simply returns the bin values divided by the bin size. Note that the first bin is from self.minTime to t[0].

The initial mass function.

Note that the normalization may include stars that do not contribute to the yield of metals.