massfuncs: Useful Star Formation Functions
In asgr/ProSpect: Professional Spectral Analysis Package
massfunc R Documentation
Useful Star 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
massfunc_const(age, mSFR = 1, magemax = 13.8)
massfunc_p2(age, m1 = 1, m2 = m1, m1age = 0, m2age = magemax, magemax = 13.8)
massfunc_p3(age, m1 = 1, m2 = m1, m3 = m2, m1age = 1e-4, m2age = 7, m3age = 13,
magemax = 13.8)
massfunc_p3_burst(age, mburst = 0, m1 = 1, m2 = m1, m3 = m2, m1age = 1e-4, m2age = 7,
m3age = 13, mburstage = 0.1, magemax = 13.8)
massfunc_p4(age, m1 = 1, m2 = m1, m3 = m2, m4 = m3, m1age = 1e-4, m2age = 2,
m3age = 9, m4age = 13, magemax = 13.8)
massfunc_p6(age, m1 = 1, m2 = m1, m3 = m2, m4 = m3, m5 = m4, m6 = m5, m1age = 1e-4,
m2age = 0.1, m3age = 1, m4age = 5, m5age = 9, m6age = 13, magemax = 13.8)
massfunc_b5(age, m1 = 1, m2 = m1, m3 = m2, m4 = m3, m5 = m4, m1age = 0, m2age = 0.1,
m3age = 1, m4age = 5, m5age = 9, m6age = 13, magemax = 13.8)
massfunc_exp(age, mSFR = 10, mtau = 1, mpivot = magemax, magemax = 13.8)
massfunc_exp_burst(age, mburst = 0, mSFR = 10, mtau = 1, mpivot = magemax,
mburstage = 0.1, magemax = 13.8)
massfunc_snorm(age, mSFR = 10, mpeak = 10, mperiod = 1, mskew = 0.5, magemax = 13.8)
massfunc_snorm_burst(age, mburst = 0, mSFR = 10, mpeak = 10, mperiod = 1, mskew = 0.5,
mburstage = 0.1, magemax = 13.8)
massfunc_snorm_trunc(age, mSFR = 10, mpeak = 10, mperiod = 1, mskew = 0.5, magemax = 13.8,
mtrunc = 2)
massfunc_snorm_burst_trunc(age, mburst = 0, mSFR = 10, mpeak = 10, mperiod = 1,
mskew = 0.5, mburstage = 0.1, magemax = 13.8, mtrunc = 2)
massfunc_dtau(age, mSFR = 10, mpeak = 10, mtau = 2, magemax = 13.8)
Arguments
age
Numeric vector; age in lookback time where 0 means now (yr).
mSFR
Numeric scalar; SFR scaling (Msol/yr). For most functions this ends up being the peak SFR [massfunc_const / massfunc_exp / massfunc_exp_burst / massfunc_snorm / massfunc_snorm_burst / massfunc_dtau].
mburst
Numeric scalar; SFR of a recent Age < mburstage yr burst (Msol/yr) [massfunc_p3_burst / massfunc_exp_burst / massfunc_snorm_burst].
mburstage
Numeric scalar; max age of recent SFR burst [massfunc_p3_burst / massfunc_exp_burst].
m1
Numeric scalar; SFR at 1st node (Msol/yr) [massfunc_p2 / massfunc_p3 / massfunc_p3_burst / massfunc_p4 / massfunc_p6].
m2
Numeric scalar; SFR at 2nd node (Msol/yr) [massfunc_p2 / massfunc_p3 / massfunc_p3_burst / massfunc_p4 / massfunc_p6].
m3
Numeric scalar; SFR at 3rd node (Msol/yr) [massfunc_p3 / massfunc_p3_burst / massfunc_p6 / massfunc_p4].
m4
Numeric scalar; SFR at 4th node (Msol/yr) [massfunc_p6 / massfunc_p4].
m5
Numeric scalar; SFR at 5th node (Msol/yr) [massfunc_p6].
m6
Numeric scalar; SFR at 6th node (Msol/yr) [massfunc_p6].
m1age
Numeric scalar; age at 1st node (Gyr) [massfunc_p2 / massfunc_p3 / massfunc_p3_burst / massfunc_p4 / massfunc_p6].
m2age
Numeric scalar; age at 2nd node (Gyr) [massfunc_p2 / massfunc_p3 / massfunc_p3_burst / massfunc_p4 / massfunc_p6].
m3age
Numeric scalar; age at 3rd node (Gyr) [ massfunc_p3 / massfunc_p3_burst / massfunc_p6 / massfunc_p4].
m4age
Numeric scalar; age at 4th node (Gyr) [massfunc_p6 / massfunc_p4].
m5age
Numeric scalar; age at 5th node (Gyr) [massfunc_p6].
m6age
Numeric scalar; age at 6th node (Gyr) [massfunc_p6].
mtau
Numeric scalar; exponential decline parameter tau [massfunc_exp / massfunc_exp_burst / massfunc_dtau].
mpivot
Numeric scalar; exponential pivot age where SFR passes though mSFR (Gyr) [massfunc_exp / massfunc_exp_burst].
mpeak
Numeric scalar; location of peak SFR (Gyr) [massfunc_snorm / massfunc_snorm_burst / massfunc_dtau].
mperiod
Numeric scalar; time period of the star formation, the standard deviation of the Normal when mskew=0 (Gyr) [massfunc_snorm / massfunc_snorm_burst].
mskew
Numeric scalar; the skew of the star formation history, 0 means perfectly Normal, -ve means long tail to old ages, +ve means long tail to young ages [massfunc_snorm / massfunc_snorm_burst].
magemax
Numeric scalar; max age allowed, SFR is set to 0 beyond this value (Gyr) [all]. In the case of massfunc_dtau the star formation truncation is scaled such that it is exactly 0 at magemax and grows from this point up to its peak value.
mtrunc
Numeric scalar; controls truncation between mpeak and magemax. For massfunc_snorm_trunc and massfunc_snorm_burst_trunc, 0 means no extra truncation, 1 is about half truncated and 2 is softly but fairly fully truncated. Larger values will be sharper.
Details
Below are the brief functional forms.
massfunc_const produces constant star formation until a certain age:
SFR = ifelse(age < magemax, mSFR, 0)
massfunc_p2 produces linearly varying star formation between 2 age nodes:
SFR = m1 + ((m2-m1)/(m2age-m1age))*(age-m1age) [also 0 outside of m1age / m2age / magemax]
massfunc_p3 produces a smooth spline star formation that passes through 3 age nodes:
SFR = splinefun(c(m1age,m2age,m3age),c(m1,m2,m3),method='monoH.FC')(age) [also 0 above magemax]
massfunc_p3_burst produces a smooth spline star formation that passes through 3 age nodes and has a recent burst:
SFR = splinefun(c(m1age,m2age,m3age),c(m1,m2,m3),method='monoH.FC')(age) [also 0 above magemax]
SFR[age<mburstage] = SFR[age<mburstage] + mburst
massfunc_p4 produces a smooth spline star formation that passes through 6 age nodes:
SFR = splinefun(log10(c(m1age,m2age,m3age,m4age)), c(m1,m2,m3,m4), method='monoH.FC')(log10(age) [also 0 above magemax]
massfunc_p6 produces a smooth spline star formation that passes through 6 age nodes:
SFR = splinefun(log10(c(m1age,m2age,m3age,m4age,m5age,m6age)), c(m1,m2,m3,m4,m5,m6), method='monoH.FC')(log10(age) [also 0 above magemax]
massfunc_b5 produces a series of constant periods of star formation (defined by the age limits), creating a stepwise SFH (sometimes called 'non-parametric' even though it is parameteric).
massfunc_exp produces exponentially declining star formation from a certain age:
SFR = mSFR*exp(-mtau*((mpivot-age)/mpivot)) [also 0 above magemax]
massfunc_exp_burst produces exponentially declining star formation from a certain age and has a recent burst:
SFR = mSFR*exp(-mtau*((mpivot-age)/mpivot)) [also 0 above magemax]
SFR[age<mburstage] = SFR[age<mburstage] + mburst
massfunc_snorm produces a rising and falling skewed Normal star formation that looks a bit like the CSFH (can be perfectly Normal if mskew=0):
SFR = mSFR*dnorm(((age-mpeak)/mperiod)*(exp(mskew))^asinh((age-mpeak)/mperiod))*sqrt(2*pi) [also 0 above magemax]
massfunc_snorm_burst produces a rising and falling skewed Normal star formation that looks a bit like the CSFH (can be perfectly Normal if mskew=0) and has a recent burst:
SFR = mSFR*dnorm(((age-mpeak)/mperiod)*(exp(mskew))^asinh((age-mpeak)/mperiod))*sqrt(2*pi) [also 0 above magemax]
SFR[age<mburstage] = SFR[age<mburstage] + mburst
massfunc_snorm_trunc produces a rising and falling skewed Normal star formation that looks a bit like the CSFH (can be perfectly Normal if mskew=0). The truncation means it can be forced to have very low SFR in the early Universe:
SFR = mSFR*dnorm(((age-mpeak)/mperiod)*(exp(mskew))^asinh((age-mpeak)/mperiod))*sqrt(2*pi) [also 0 above magemax]
timetrunc = abs(magemax - mpeak)
SFR = SFR * (1 - pnorm(age, mean = mpeak + timetrunc/mtrunc, sd = timetrunc/(2*mtrunc)))
massfunc_snorm_burst_trunc produces a rising and falling skewed Normal star formation that looks a bit like the CSFH (can be perfectly Normal if mskew=0) and has a recent burst. The truncation means it can be forced to have very low SFR in the early Universe:
SFR = mSFR*dnorm(((age-mpeak)/mperiod)*(exp(mskew))^asinh((age-mpeak)/mperiod))*sqrt(2*pi) [also 0 above magemax]
SFR[age<mburstage] = SFR[age<mburstage] + mburst
timetrunc = abs(magemax - mpeak)
SFR = SFR * (1 - pnorm(age, mean = mpeak + timetrunc/mtrunc, sd = timetrunc/(2*mtrunc)))
massfunc_dtau produces a delayed tau rising and falling star formation that looks a bit like the CSFH. It is a modified version of the typical delayed tau SFH, where it is possible to specify the exact age the star formation starts growing from via the magemax parameter. If magemax = mpeak + mtau then the function reverts exactly to the standard delated tau model:
mtrunc = mtau / (magemax - mpeak)
x[age<=mpeak] = (mtau + mpeak - age[age<=mpeak]) / mtau
x[age>mpeak] = ((mtau/mtrunc) + mpeak - age[age>mpeak]) / (mtau/mtrunc)
SFR = x * exp(-x)
SFR = (mSFR/exp(-1)) * SFR
Value
In all cases the output is the star formation rate (Msol/yr) at a given age in years.
Author(s)
Aaron Robotham
See Also
SFHfunc, ProSpectSED, Zfunc
Examples
curve(massfunc_const, 0, 14e9, xlab='Age/yr', ylab='SFR / Msol/yr')
curve(massfunc_p2, 0, 14e9, xlab='Age/yr', ylab='SFR / Msol/yr')
curve(massfunc_p3, 0, 14e9, xlab='Age/yr', ylab='SFR / Msol/yr')
curve(massfunc_p3_burst, 0, 14e9, xlab='Age/yr', ylab='SFR / Msol/yr')
curve(massfunc_p4, 0, 14e9, xlab='Age/yr', ylab='SFR / Msol/yr')
curve(massfunc_p6, 0, 14e9, xlab='Age/yr', ylab='SFR / Msol/yr')
curve(massfunc_exp, 0, 14e9, xlab='Age/yr', ylab='SFR / Msol/yr')
curve(massfunc_exp_burst, 0, 14e9, xlab='Age/yr', ylab='SFR / Msol/yr')
curve(massfunc_snorm, 0, 14e9, xlab='Age/yr', ylab='SFR / Msol/yr')
curve(massfunc_snorm_burst, 0, 14e9, xlab='Age/yr', ylab='SFR / Msol/yr')
curve(massfunc_snorm_trunc, 0, 14e9, xlab='Age/yr', ylab='SFR / Msol/yr')
curve(massfunc_snorm_burst_trunc, 0, 14e9, xlab='Age/yr', ylab='SFR / Msol/yr')
curve(massfunc_dtau, 0, 14e9, xlab='Age/yr', ylab='SFR / Msol/yr')
asgr/ProSpect documentation built on Feb. 21, 2025, 1:43 a.m.
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| massfunc | R Documentation |
Useful Star 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
massfunc_const(age, mSFR = 1, magemax = 13.8)
massfunc_p2(age, m1 = 1, m2 = m1, m1age = 0, m2age = magemax, magemax = 13.8)
massfunc_p3(age, m1 = 1, m2 = m1, m3 = m2, m1age = 1e-4, m2age = 7, m3age = 13,
magemax = 13.8)
massfunc_p3_burst(age, mburst = 0, m1 = 1, m2 = m1, m3 = m2, m1age = 1e-4, m2age = 7,
m3age = 13, mburstage = 0.1, magemax = 13.8)
massfunc_p4(age, m1 = 1, m2 = m1, m3 = m2, m4 = m3, m1age = 1e-4, m2age = 2,
m3age = 9, m4age = 13, magemax = 13.8)
massfunc_p6(age, m1 = 1, m2 = m1, m3 = m2, m4 = m3, m5 = m4, m6 = m5, m1age = 1e-4,
m2age = 0.1, m3age = 1, m4age = 5, m5age = 9, m6age = 13, magemax = 13.8)
massfunc_b5(age, m1 = 1, m2 = m1, m3 = m2, m4 = m3, m5 = m4, m1age = 0, m2age = 0.1,
m3age = 1, m4age = 5, m5age = 9, m6age = 13, magemax = 13.8)
massfunc_exp(age, mSFR = 10, mtau = 1, mpivot = magemax, magemax = 13.8)
massfunc_exp_burst(age, mburst = 0, mSFR = 10, mtau = 1, mpivot = magemax,
mburstage = 0.1, magemax = 13.8)
massfunc_snorm(age, mSFR = 10, mpeak = 10, mperiod = 1, mskew = 0.5, magemax = 13.8)
massfunc_snorm_burst(age, mburst = 0, mSFR = 10, mpeak = 10, mperiod = 1, mskew = 0.5,
mburstage = 0.1, magemax = 13.8)
massfunc_snorm_trunc(age, mSFR = 10, mpeak = 10, mperiod = 1, mskew = 0.5, magemax = 13.8,
mtrunc = 2)
massfunc_snorm_burst_trunc(age, mburst = 0, mSFR = 10, mpeak = 10, mperiod = 1,
mskew = 0.5, mburstage = 0.1, magemax = 13.8, mtrunc = 2)
massfunc_dtau(age, mSFR = 10, mpeak = 10, mtau = 2, magemax = 13.8)
Arguments
age |
Numeric vector; age in lookback time where 0 means now (yr). |
mSFR |
Numeric scalar; SFR scaling (Msol/yr). For most functions this ends up being the peak SFR [ |
mburst |
Numeric scalar; SFR of a recent Age < mburstage yr burst (Msol/yr) [ |
mburstage |
Numeric scalar; max age of recent SFR burst [ |
m1 |
Numeric scalar; SFR at 1st node (Msol/yr) [ |
m2 |
Numeric scalar; SFR at 2nd node (Msol/yr) [ |
m3 |
Numeric scalar; SFR at 3rd node (Msol/yr) [ |
m4 |
Numeric scalar; SFR at 4th node (Msol/yr) [ |
m5 |
Numeric scalar; SFR at 5th node (Msol/yr) [ |
m6 |
Numeric scalar; SFR at 6th node (Msol/yr) [ |
m1age |
Numeric scalar; age at 1st node (Gyr) [ |
m2age |
Numeric scalar; age at 2nd node (Gyr) [ |
m3age |
Numeric scalar; age at 3rd node (Gyr) [ |
m4age |
Numeric scalar; age at 4th node (Gyr) [ |
m5age |
Numeric scalar; age at 5th node (Gyr) [ |
m6age |
Numeric scalar; age at 6th node (Gyr) [ |
mtau |
Numeric scalar; exponential decline parameter tau [ |
mpivot |
Numeric scalar; exponential pivot age where SFR passes though mSFR (Gyr) [ |
mpeak |
Numeric scalar; location of peak SFR (Gyr) [ |
mperiod |
Numeric scalar; time period of the star formation, the standard deviation of the Normal when mskew=0 (Gyr) [ |
mskew |
Numeric scalar; the skew of the star formation history, 0 means perfectly Normal, -ve means long tail to old ages, +ve means long tail to young ages [ |
magemax |
Numeric scalar; max age allowed, SFR is set to 0 beyond this value (Gyr) [all]. In the case of |
mtrunc |
Numeric scalar; controls truncation between mpeak and magemax. For |
Details
Below are the brief functional forms.
massfunc_const produces constant star formation until a certain age:
SFR = ifelse(age < magemax, mSFR, 0)
massfunc_p2 produces linearly varying star formation between 2 age nodes:
SFR = m1 + ((m2-m1)/(m2age-m1age))*(age-m1age) [also 0 outside of m1age / m2age / magemax]
massfunc_p3 produces a smooth spline star formation that passes through 3 age nodes:
SFR = splinefun(c(m1age,m2age,m3age),c(m1,m2,m3),method='monoH.FC')(age) [also 0 above magemax]
massfunc_p3_burst produces a smooth spline star formation that passes through 3 age nodes and has a recent burst:
SFR = splinefun(c(m1age,m2age,m3age),c(m1,m2,m3),method='monoH.FC')(age) [also 0 above magemax] SFR[age<mburstage] = SFR[age<mburstage] + mburst
massfunc_p4 produces a smooth spline star formation that passes through 6 age nodes:
SFR = splinefun(log10(c(m1age,m2age,m3age,m4age)), c(m1,m2,m3,m4), method='monoH.FC')(log10(age) [also 0 above magemax]
massfunc_p6 produces a smooth spline star formation that passes through 6 age nodes:
SFR = splinefun(log10(c(m1age,m2age,m3age,m4age,m5age,m6age)), c(m1,m2,m3,m4,m5,m6), method='monoH.FC')(log10(age) [also 0 above magemax]
massfunc_b5 produces a series of constant periods of star formation (defined by the age limits), creating a stepwise SFH (sometimes called 'non-parametric' even though it is parameteric).
massfunc_exp produces exponentially declining star formation from a certain age:
SFR = mSFR*exp(-mtau*((mpivot-age)/mpivot)) [also 0 above magemax]
massfunc_exp_burst produces exponentially declining star formation from a certain age and has a recent burst:
SFR = mSFR*exp(-mtau*((mpivot-age)/mpivot)) [also 0 above magemax] SFR[age<mburstage] = SFR[age<mburstage] + mburst
massfunc_snorm produces a rising and falling skewed Normal star formation that looks a bit like the CSFH (can be perfectly Normal if mskew=0):
SFR = mSFR*dnorm(((age-mpeak)/mperiod)*(exp(mskew))^asinh((age-mpeak)/mperiod))*sqrt(2*pi) [also 0 above magemax]
massfunc_snorm_burst produces a rising and falling skewed Normal star formation that looks a bit like the CSFH (can be perfectly Normal if mskew=0) and has a recent burst:
SFR = mSFR*dnorm(((age-mpeak)/mperiod)*(exp(mskew))^asinh((age-mpeak)/mperiod))*sqrt(2*pi) [also 0 above magemax] SFR[age<mburstage] = SFR[age<mburstage] + mburst
massfunc_snorm_trunc produces a rising and falling skewed Normal star formation that looks a bit like the CSFH (can be perfectly Normal if mskew=0). The truncation means it can be forced to have very low SFR in the early Universe:
SFR = mSFR*dnorm(((age-mpeak)/mperiod)*(exp(mskew))^asinh((age-mpeak)/mperiod))*sqrt(2*pi) [also 0 above magemax] timetrunc = abs(magemax - mpeak) SFR = SFR * (1 - pnorm(age, mean = mpeak + timetrunc/mtrunc, sd = timetrunc/(2*mtrunc)))
massfunc_snorm_burst_trunc produces a rising and falling skewed Normal star formation that looks a bit like the CSFH (can be perfectly Normal if mskew=0) and has a recent burst. The truncation means it can be forced to have very low SFR in the early Universe:
SFR = mSFR*dnorm(((age-mpeak)/mperiod)*(exp(mskew))^asinh((age-mpeak)/mperiod))*sqrt(2*pi) [also 0 above magemax] SFR[age<mburstage] = SFR[age<mburstage] + mburst timetrunc = abs(magemax - mpeak) SFR = SFR * (1 - pnorm(age, mean = mpeak + timetrunc/mtrunc, sd = timetrunc/(2*mtrunc)))
massfunc_dtau produces a delayed tau rising and falling star formation that looks a bit like the CSFH. It is a modified version of the typical delayed tau SFH, where it is possible to specify the exact age the star formation starts growing from via the magemax parameter. If magemax = mpeak + mtau then the function reverts exactly to the standard delated tau model:
mtrunc = mtau / (magemax - mpeak) x[age<=mpeak] = (mtau + mpeak - age[age<=mpeak]) / mtau x[age>mpeak] = ((mtau/mtrunc) + mpeak - age[age>mpeak]) / (mtau/mtrunc) SFR = x * exp(-x) SFR = (mSFR/exp(-1)) * SFR
Value
In all cases the output is the star formation rate (Msol/yr) at a given age in years.
Author(s)
Aaron Robotham
See Also
SFHfunc, ProSpectSED, Zfunc
Examples
curve(massfunc_const, 0, 14e9, xlab='Age/yr', ylab='SFR / Msol/yr')
curve(massfunc_p2, 0, 14e9, xlab='Age/yr', ylab='SFR / Msol/yr')
curve(massfunc_p3, 0, 14e9, xlab='Age/yr', ylab='SFR / Msol/yr')
curve(massfunc_p3_burst, 0, 14e9, xlab='Age/yr', ylab='SFR / Msol/yr')
curve(massfunc_p4, 0, 14e9, xlab='Age/yr', ylab='SFR / Msol/yr')
curve(massfunc_p6, 0, 14e9, xlab='Age/yr', ylab='SFR / Msol/yr')
curve(massfunc_exp, 0, 14e9, xlab='Age/yr', ylab='SFR / Msol/yr')
curve(massfunc_exp_burst, 0, 14e9, xlab='Age/yr', ylab='SFR / Msol/yr')
curve(massfunc_snorm, 0, 14e9, xlab='Age/yr', ylab='SFR / Msol/yr')
curve(massfunc_snorm_burst, 0, 14e9, xlab='Age/yr', ylab='SFR / Msol/yr')
curve(massfunc_snorm_trunc, 0, 14e9, xlab='Age/yr', ylab='SFR / Msol/yr')
curve(massfunc_snorm_burst_trunc, 0, 14e9, xlab='Age/yr', ylab='SFR / Msol/yr')
curve(massfunc_dtau, 0, 14e9, xlab='Age/yr', ylab='SFR / Msol/yr')
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