Zfuncs: Useful Metallicity Formation Functions

In asgr/ProSpect: Professional Spectral Analysis Package

Useful Metallicity Formation Functions

Description

These functions can all be passed into SFHfunc and ProSpectSED. They should be a good starting point for people interested in constructing their own.

Usage

Zfunc_p2(age, Z1 = 0.02, Z2 = Z1, Z1age = 0, Z2age = Zagemax, Zagemax = 13.8, ...)
Zfunc_massmap_lin(age, Zstart = 1e-4, Zfinal = 0.02, Zagemax = 13.8, massfunc, ...)
Zfunc_massmap_box(age, Zstart = 1e-4, Zfinal = 0.02, yield = 0.03, Zagemax = 13.8,
massfunc, ...)

Arguments

age	Numeric vector; age in lookback time where 0 means now (yr).
Z1	Numeric scalar; Z at 1st node (Msol/yr) [Zfunc_p2].
Z2	Numeric scalar; Z at 2nd node (Msol/yr) [Zfunc_p2].
Z1age	Numeric scalar; age at 1st node (Gyr) [Zfunc_p2].
Z2age	Numeric scalar; age at 2nd node (Gyr) [Zfunc_p2].
Zagemax	Numeric scalar; max age allowed, Z is set to 1e-04 beyond this value (Gyr) [all].
Zstart	Numeric scalar; Z at the start of star formation (Msol/yr) [Zfunc_massmap].
Zfinal	Numeric scalar; Z at the end of star formation (Msol/yr) [Zfunc_massmap].
yield	The yield for the closed box model, where Zfinal = Zstart - (yield x ln(gasfrac_final)).
massfunc	Function; mass function to have metallicity mapped back against [Zfunc_massmap], see massfunc.
...	All further arguments are passed directly into massfunc, so by this mechanism you can set function specific arguments that control the star formation history etc [Zfunc_massmap].

Details

Below are the brief functional forms.

Zfunc_p2 produces linearly varying star formation between 2 age nodes:

Z = Z1 + ((Z2-Z1)/(Z2age-Z1age))*(age-Z1age) [also 1e-4 outside of Z1age / Z2age / Zagemax]

Zfunc_massmap_lin linearly maps the fraction of mass formed for the given SFH against the target start (Zstart) and finish (Zfinal) metallicity. Basically this means if you double you fractional mass you will also roughly double the metallicity you form stars with (assuming you start at close to 0 metallicity, which is the default). In detail Zgas = Zstart + (Zfinal - Zstart) x starfrac (where starfrac is the fraction of final stars formed at a given time, i.e. 1 today and 0 at the Big Bang by construction).

Zfunc_massmap_box maps the fraction of mass formed to Z using Z = Zstart - (yield x ln(gasfrac)). The lowest value for the gas fraction is derived using Zfinal = Zstart - (yield x ln(gasfrac_final)), i.e. gasfrac_final = exp(-(Zfinal - Zstart)/yield). Then Zfinal = Zstart - (yield x ln((1 - starfrac) x gasfrac_final)) (where starfrac is the fraction of final stars formed at a given time, i.e. 1 today and 0 at the Big Bang by construction). Interestingly, if we use this mapping then we naturally predict a gas fraction for the galaxy today!

Value

In all cases the output is the metallicity (Z = 1 - (X + Y), where X is the mass fraction in H and Y is the mass fraction in He) at a given age in years (where 0.02 is solar).

Author(s)

Aaron Robotham

See Also

SFHfunc, ProSpectSED, massfunc

Examples

curve(Zfunc_p2(age=x, Z1=0.03, Z2=0.01), 0, 13.8e9, xlab='Age/yr', ylab='Z',
ylim=c(0,0.03))
curve(Zfunc_massmap_lin(age=x, Zstart=0.01, Zfinal=0.03, massfunc=massfunc_snorm),
add=TRUE, col='red')
curve(Zfunc_massmap_box(age=x, Zstart=0.01, Zfinal=0.03, massfunc=massfunc_snorm),
add=TRUE, col='blue')

asgr/ProSpect documentation built on Feb. 21, 2025, 1:43 a.m.