kcorr: k and D Corrections

In asgr/ProSpect: Professional Spectral Analysis Package

k and D Corrections

Description

Functions to compute consistently defined k (spectral shift) and D (dust) corrections.

Usage

kcorr(wave, lum, z, DistMod = NULL, filters = "GAMA", H0 = 67.8, OmegaM = 0.308,
  OmegaL = 1 - OmegaM, prospect = NULL)
  
kcorr_evo(wave, lum, z = 10^seq(-1,1,by=0.1), DistMod = NULL, filters = 'GAMA', H0 = 67.8,
  OmegaM = 0.308, OmegaL = 1 - OmegaM, prospect = NULL)
  
Vmax_hunt(wave, lum, ApMag_lim = 19.65, z_range = c(0, 10), area = 41252.96,
  filter = "r_VST", H0 = 67.8, OmegaM = 0.308, OmegaL = 1 - OmegaM, prospect = NULL)

Dcorr(wave, lum_atten, lum_unatten, filters = "GAMA", prospect = NULL)

Arguments

wave	Numeric vector; the spectral wavelength in Angstroms. For convenience in kcorr, if a two column matrix or data frame is supplied then the first column is taken to be wave and the second is taken to be lum.
lum	Numeric vector; the spectral luminosity in Lsol / Angstrom (BC03lr / BC03hr and EMILES format). This should be post all astrophysical processes (e.g. FinalLum output of ProSpectSED).
lum_atten	Numeric vector; the spectral luminosity in Lsol / Angstrom (BC03lr / BC03hr and EMILES format). This should be the stellar output post dust attenuation (no re-emission, e.g. StarsAtten output of ProSpectSED or lum_atten output of SFHfunc).
lum_unatten	Numeric vector; the spectral luminosity in Lsol / Angstrom (BC03lr / BC03hr and EMILES format). This should be the stellar output pre dust attenuation (e.g. StarsUnAtten output of ProSpectSED or lum_unatten output of SFHfunc).
z	Numeric scalar/vector; cosmological redshift. This is the redshift you wish to make the k-correction at (need not be the redshift of the actual source, but that is most often what people want to know). For kcorr this should be a scalar, for kcorr_evo this should be a vector.
ApMag_lim	Numeric scalar; the apparent magnitude limit to search for. When the ProSpect SED hits this value for the provided filter the upper limit of z_range is updated and the VMAX computed based on the combination of the lower/upper limit of z_range and the area for the specified cosmology. The default of 19.65 is the 95% completeness limit using the r_VST imaging with ProFound (GAMA DR4, Driver et al).
z_range	Numeric vector; lower and upper redshift limits to search over. The lower automatically becomes the lower limit for Vmax purpose.
area	Numeric scalar; sky area in square degrees (default is all sky).
DistMod	Numeric scalar/vector; distance modulus used where AbsMag_dust = ApMag_dust - DistMod - kcorr, and DistMod = 5log10(LumDist/Mpc) + 25 in units of mag. If provided for speed reasons (because you are repeating the same redshifts and therefore the same DistMod for a lot of sources) then it must correspond to the distance modulus of z (if not, wrong results will be returned). See below for Details. For kcorr this should be a scalar, for kcorr_evo this should be a vector.
filters	Character vector or list; names of filters to use. See filters for options. Default 'GAMA' selects GAMA filters. If not a character then this will be passed onto bandpass, and may therefore be a list of filter responses, or even better (faster) a list of filter functions.
filter	Character scalar or list; name of filter to use. See filters for options. If not a character then this will be passed onto bandpass, and may therefore be a filter response, or even better (faster) a filter functions. The default 'r_VST' is the updated GAMA ProFound selection band, where the appropriate ApMag_lim is then 19.65 (GAMA DR4, Driver et al).
H0	Numeric scalar; Hubble constant as defined at z=0 (default is H0=100 (km/s)/Mpc).
OmegaM	Numeric scalar; Omega Matter today (default is 0.3).
OmegaL	Numeric scalar; Omega Lambda today (default is for a flat Universe with OmegaL = 1-OmegaM-OmegaR = 0.7).
prospect	List; object of class ProSpectSED. This can be passed in for convenience, in which case various inputs above are extracted from the objects structure. Note if you pass this in and specify an argument, the specified argument takes precedent. This way you can easily pass in your prospect object whilst e.g. modifying the redshift z (which you might want to do to check for volume limits).

Details

Standard convenience functions for computing survey V-maxes etc.

A pure k-correction just adjusts the SED distortion effects of redshifting an object, therefore:

AbsMag_fin = ApMag_fin - DistMod - kcorr

Where in this context AbsMag_fin and ApMag_fin are the SEDs with stellar light both attenuated by dust and re-emitted by dust.

A D-correction takes the above definition of the AbsMag and removes the effect of dust attenuation, taking you all the way to the SED of the pure stellar emission without dust either attenuating or re-emitting:

AbsMag_unatten = AbsMag_atten - Dcorr

Where in this context AbsMag_unatten is the intrinsic SED of the stellar light and AbsMag_atten is the absolute magnitude with stellar light attenuated by dust (no re-emission).

This version of the D-correction can only create more flux in AbsMag_unatten compared to AbsMag_atten, i.e. it ignores the role of dust re-emission which can be significant at longer wavelengths. Note it probably does not make much sense to compute D-corrections beyond the K/W1/W2 bands (depending on the SED and dust prescription) since you are starting to become dominated by net dust re-emission not stellar attenuation and meaning of a D-correction becomes ambiguous.

Value

kcorr returns a list with:

z	Numeric scalar; the redshift used.
DistMod	Numeric scalar; the distance modulus used.
AbsMag	Numeric vector; the per filter rest frame absolute magnitude (dust attenuated, dust re-emitted).
ApMag	Numeric vector; the per filter obseved frame apparent magnitude (dust attenuated, dust re-emitted).
kcorr	Numeric vector; the implied per filter k-correction (where kcorr = ApMag - DistMod - AbsMag).

kcorr_evo returns a list with:

z	Numeric vector; the redshift used.
DistMod	Numeric vector; the distance modulus used.
AbsMag	Numeric vector; the per filter rest frame absolute magnitude (dust attenuated, dust re-emitted).
ApMag	Numeric matrix; the per filter obseved frame apparent magnitude (dust attenuated, dust re-emitted) as columns; variation with z as rows.
kcorr	Numeric matrix; the implied per filter k-correction (where kcorr = ApMag - DistMod - AbsMag) as columns; variation with z as rows

Vmax_hunt returns a list with:

z_range

Numeric vector; lower and upper redshift bounds. The lower comes from the specified input argument, the upper limit will have been updated during the internal Vmax optimisation process when calcuting at what redshift the ProSpect SED hits the ApMag_lim given the target filter

Vmax

Numeric vector; the output of cosvol computed based on the combination of the lower/upper limit of z_range and the area for the specified cosmology. This is a 3 element vector. The first element (voltot) specifies the comoving volume of the requested cone segment in Gpc^3, the second element (volmeanz) specifies the mean redshift when mass is uniformly distributed in the volume, the third element (volmedz) specifies the median redshift when mass is uniformly distributed in the volume.

Dcorr returns a list with:

AbsMag_atten	Numeric vector; the per filter rest frame absolute magnitude (dust attenuated, no dust re-emitted).
AbsMag_unatten	Numeric vector; the per filter rest frame absolute magnitude (dust unattenuated, no dust re-emitted).
Dcorr	Numeric vector; the implied per filter D-correction, where: Dcorr = AbsMag_atten - AbsMag_unatten. Should always be positive!

Note

There can be some ambiguity with k-corrections whether they do or do not fold in the 2.5log10(1 + z) effect of pure bandpass stretching. The confusion here is because imagine a source remained at the same cosmological distance but started receding at high velocity such that its spectrum became purely doppler stretched. Even if the spectrum was perfectly flat with constant flux per band you would still notice dimming because you are numerically spreading the same amount of flux over more wavelength, so the flux density has to drop. So even without having to correct for any change in SED with a function of wavelength, you will still have this band stretching to worry about. The kcorr function includes this term in it, so even a completely flat spectrum source will have a non-0 kcorr (remember simple cosmological source dimming is taken care of with the DistMod term.

Author(s)

Aaron Robotham

References

Interested users should check the book "The Structure and Evolution of Galaxies" by Steven Phillipps (Section 2.7.2).

See Also

ProSpectSED

Examples

prospect = ProSpectSED(z=0.1, filters='GAMA')

#For k-corrections we can run:

kcorr(prospect$FinalLum, z=0.1, filters=prospect$filtout)
#or for convenience
kcorr(prospect=prospect)

#For D-corrections we can run:
Dcorr(prospect$StarsAtten$wave, prospect$StarsAtten$lum, prospect$StarsUnAtten$lum,
  filters=prospect$filtout)
#or for convenience
Dcorr(prospect=prospect)
  
#If you want to know a volume limit then you often want to know z vs the apparent mag:

zvec = seq(0.05,1,by=0.05)
evodata = kcorr_evo(z=zvec, prospect=prospect)

library(magicaxis)
library(celestial)

magplot(zvec, evodata$ApMag[,'r_VST'], type='l', xlab='z', ylab='ap_r', xlim=c(0,1))
abline(h=19.8, lty=2) #the nominal GAMA limit
abline(v=0.155, lty=2)

#For GAMA we know the total survey area (293.82 sqdeg) so can compute the Vmax:

cosvol(area=293.82, zmax=0.155, zmin=0.013, H0=67.8, OmegaM=0.308)

#More accurately and easily, we can use the Vmax_hunt function:

Vmax_hunt(area=293.82, z_range=c(0.013,1), prospect=prospect)

#Note we usually apply a lower z limit too because of the large distance errors at low z.

#You can see the impact of not correctly accounting for the k-correction.
#The black dotted line is the k-correction free implied apparent mag, and the red
#shaded region shows the implied k-correction to compute a correct apparent magnitude.

DistMod = cosdistDistMod(zvec, H0=67.8, OmegaM=0.308)
lines(zvec, -19.68021 + DistMod, lty=3) #-19.68021 is the r-band absolute magnitude above
polygon(c(zvec, rev(zvec)), c(evodata$ApMag[,'r_VST'], rev(-19.68021 + DistMod)),
  col=hsv(alpha=0.2), border=NA)

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