astro (version 1.2)

schechter: The Schechter Function

Description

This function calculates the single or double Schechter function, most usually associated with the luminosity function.

Usage

schechter(x, knee, slope, norm, bw = 0.1, mag = FALSE, log = FALSE, ...)

Arguments

x

input values

knee

the knees(s) of the Schechter function (L_star/M_star)

slope

the slope(s) of the Schechter function (alpha)

norm

the normalisation(s) of the Schechter function (phi_star)

bw

integration bin width sizes

mag

are the input data magnitudes?

log

are the input data logged?

...

additional arguments to be passed to 'integrate'

Value

A vector of length equal to the length of data representing the number density *per dex* at each input data point. Note: to convert the final number densities into their original bin-width (e.g., per 0.5 dex) multiply the output of this function by the bin-width.

References

Blanton M. R., Lupton R. H., Schlegel D. J., Strauss M. A., Brinkmann J., Fukugita M., Loveday J., 2005, ApJ, 631, 208

Driver S. P., Popescu C. C., Tuffs R. J., Graham A. W., Liske J., Baldry I., 2008, ApJ, 678, L101

Baldry I. K. Driver S. P., Loveday J., et al., 2012, MNRAS, 421, 621

See Also

The astronomy package: astro.

Examples

#
#
# Driver et al. 2008, Figure 2 (magnitude)
#
#

# setup input magnitudes
mag = seq(-24,-17,len=100)

# calculate number densities
num = schechter(mag, bw = 0.5, mag = TRUE, log = FALSE, knee = -21.32, 
slope = -1.32, norm = 4.8E-3)

# plot
aplot(mag, log10(0.5*num), las=1, ylim=c(-6,-2), type="l", xaxs="i", yaxs="i", 
nxmin=1, xlab="Magnitude / mag", 
ylab=bquote(paste("log ", phi, " [ 0.5mag ]", " "^-1)), 
main="Driver et al. 2008, Figure 2")
label("bottomright", lab=bquote(paste("M* = -21.32     ", 
alpha, " = -1.32     ", phi, "* = 4.8x", 10^{-3})), inset=0.1)

#
#
# Baldry et al. 2012, Figure 13 (stellar mass)
#
#

# setup input masses
mass = seq(7,11.6,len=100)

# calculate number densities
num = schechter(mass, bw = 0.1, mag = FALSE, log = TRUE, knee = 10.66, 
slope = c(-0.35,-1.47), norm = c(3.96E-3,0.79E-3))

# plot
aplot(log10(mass), num, las=1, ylim=c(1e-5,2e-1), type="l", log="y", xaxs="i", 
yaxs="i", xlab="log (M / Msun)", 
ylab=bquote(paste("number density (", dex^{-1}, " ", , Mpc^{-3}, ")")), 
yformat="p", main="Baldry et al. 2012, Figure 13")
label("bottomleft", 
lab=bquote(paste("log M* = 10.66   ", alpha[1], " = -0.35   ", 
phi, "*", ""[1], " = 3.96x", 10^{-3}, "   ", alpha[2], " = -1.47   ", 
phi, "*", ""[2], " = 0.79x", 10^{-3})), inset=0.1)