Cosmology functions

Description

Package contains functions for computation of distances and luminosities in a flat cosmology.

Details

Author(s)

A. Harris

Maintainer: <harris@astro.umd.edu>

References

"Distance Measures in Cosmology," D.W. Hogg (2000), arXiv:astro-ph/9905116; "Warm Molecular Gas in the Pirmeval Galaxy 10214+4724", P.M. Solomon, D. Downes, and S.J.E. Radford (1992), Ap.J. 398, L29; "First-year WMAP observations...", Spergel et al., ApJS 148:175 (2003). "Submillimetre and far-infrared spectral energy distributions of galaxies...", A.W. Blain, V.E. Barnard \& S.C. Chapman 2003, MNRAS 338, 733.

Examples

D.L(z=2.3)

Angular diameter distance

Description

Function computes angular diameter distance

Usage

D.A(z, omega.m = 0.27, omega.lambda = 0.73, H.0 = 71)

Arguments

Value

Angular distance in Mpc

Note

For flat universe, omega.k = 0.

Author(s)

A. Harris

References

Hogg (2000), arXiv:astro-ph/9905116, equation (18)

Examples

D.A(2.3)

z <- seq(0.1, 5, 0.1)
d <- D.A(z)
plot(z, d/max(d), t='l', xlab='z', ylab='Normalized D.A')

Luminosity distance

Description

Function computes luminosity distance in a flat cosmology.

Usage

D.L(z, omega.m = 0.27, omega.lambda = 0.73, H.0 = 71)

Arguments

Value

Luminosity distance in Mpc

Author(s)

A. Harris

References

Hogg (2000), arXiv:astro-ph/9905116, equation (21)

Examples

D.L(2.3)

Comoving distance

Description

Function computes comoving distance in a flat cosmology.

Usage

D.M(z, omega.m = 0.27, omega.lambda = 0.73, H.0 = 71)

Arguments

Value

Comoving distance in Mpc

Note

For flat universe, omega.k = 0, so transverse and line-of-sight comoving distances are equal.

Author(s)

A. Harris

References

Hogg (2000), arXiv:astro-ph/9905116, equations (16) and (15)

Examples

D.M(2.3)

Line luminosity, L'

Description

Compute L' line luminosity

Usage

Lprime(intInt, z, f.rest = 115.27, omega.m = 0.27, omega.lambda = 0.73, H.0 = 71)

Arguments

Value

Rest-frame line luminosity in K km/s pc^-2.

Note

For flat universe, omega.k = 0. Useful for empirical mass estimates. L' is proportional to the brightness temperature of the transition.

Author(s)

A. Harris

References

Solomon, Downes & Radford (1992), ApJ 398, L29, equation (3)

See Also

lineLum, mass.CO

Examples

snu <- 1.e-3 # 1 mJy peak
wid <- 400   # 400 km/s wide
intInt <- 1.06*snu*wid  # Gaussian line
z <- 2.3
Lprime(intInt, z)

Differential comoving volume

Description

Function computes differential comoving volume in a flat cosmology.

Usage

dComovVol(z, omega.m = 0.27, omega.lambda = 0.73, H.0 = 71)

Arguments

Value

Differential comoving volume in Mpc^3

Author(s)

A. Harris

References

Hogg (2000), arXiv:astro-ph/9905116, equation (28)

Examples

dComovVol(2.3)

Flux dimming factor

Description

Function computes flux dimming factor in a flat cosmology.

Usage

dimmingFactor(z, omega.m = 0.27, omega.lambda = 0.73, H.0 = 71)

Arguments

Value

Flux dimming factor, unnormalied. Mathematically, it is (1+z)/D.L^2. This is the factor that scales luminosity densitiy in the observed frame to flux density in the observed frame.

Author(s)

A. Harris

References

Hogg (2000), arXiv:astro-ph/9905116: section 7, part of equation (22)

See Also

D.L

Examples

z <- seq(0.1, 5, 0.1)
df <- dimmingFactor(z)
plot(z, df/max(df), t='l', xlab='z', ylab='Normalized dimming factor')

Line luminosity

Description

Compute rest-frame line luminosity.

Usage

lineLum(intInt, z, f.rest = 115.27, omega.m = 0.27, omega.lambda = 0.73, H.0 = 71)

Arguments

Value

Rest-frame line luminosity in solar luminosities.

Note

For flat universe, omega.k = 0.

Author(s)

A. Harris

References

Solomon, Downes & Radford (1992), ApJ 398, L29, equation (1)

See Also

Lprime

Examples

snu <- 1.e-3 # 1 mJy peak
wid <- 400   # 400 km/s wide
intInt <- 1.06*snu*wid  # Gaussian line
z <- 2.3
lineLum(intInt, z)

Cosmic lookback time

Description

Compute cosmic lookback time given z and cosmological parameters

Usage

lookbackTime(z, omega.m = 0.27, omega.lambda = 0.73, H.0 = 71)

Arguments

Details

Defaults for omega.m, omega.lambda, and omega.m, are from WMAP cosmology; omega.k (curvature term) is computed from relationship between omegas in flat cosmology (omega.k = 0).

Value

Lookback time in Gyr.

Author(s)

A. Harris

References

"Principles of Physical Cosmology," P.J. Peebles, Princeton c. 1993, (5.63); "Distance Measures in Cosmology," Hogg (2000), arXiv:astro-ph/9905116, equation (30); "First-year WMAP observations...", Spergel et al., ApJS 148:175 (2003)

Examples

# lookback time for z = 2
lookbackTime(2)
# Inverse problem, age of Earth (4.6 Gyr) example:
uniroot(function(x) lookbackTime(x) - 4.6, c(0,2))$root

Molecular mass

Description

Compute molecular mass (default CO J = 1-0) from L' and empirical conversion factor.

Usage

mass.CO(intInt, z, alpha = 0.8, f.rest = 115.27, omega.m = 0.27,
omega.lambda = 0.73, H.0 = 71)

Arguments

Details

alpha is an empirical mass conversion factor. The exact value is a topic of considerable debate. For CO, see Solomon and Vanden Bout (2005), also Tacconi et al. (2008) for reviews.

Value

Gas mass in solar masses.

Author(s)

A. Harris

References

Solomon, Downes & Radford (1992), ApJ 398, L29, equations (3) and (4); Solomon & Vanden Bout (2005) ARA&A 43, 677; Tacconi et al. (2008) ApJ 680, 246.

See Also

Lprime

Examples

snu <- 1.e-3 # 1 mJy peak
wid <- 400   # 400 km/s wide
intInt <- 1.06*snu*wid  # Gaussian line
z <- 2.3
mass.CO(intInt, z)

Optically-thin SED fit

Description

Function takes Herschel-SPIRE photometry and fits optically-thin greybody function for a single-component temperature and galaxy luminosity. Function generates nsamp realizations of observed flux densities with standard deviations for error analysis.

Usage

sedFitThin(s, e = s*0.2, z = 2.5, nsamp = 100, alpha = 2, beta = 1.5,
wl= c(250, 350, 500), sc.start = 1.e-6, T.start = 50)

Arguments

Details

Conversion from observed to rest frame is from equation (24) in Hogg 2000. Dust temperature and 8-1000 micron luminosity derivation is described in Blain, Barnard & Chapman 2003. Galaxy SEDs typically fall off more slowly than greybody on the Wien side; see plot generated by examples below to visualize power-law extension suggested by Blain et al. 2003.

Value

List of class sedfit with elements:

Note

Fit will sometimes crash on numerical derivative and throw an error. In this case the routine will halt without producing results. The more usual lack of convergence is reported as a warning, and the corresponding results will be NA in the output matrix.

Author(s)

A. Harris

References

Hogg 2000, astro-ph 9905116v4; Blain, Barnard & Chapman 2003, MNRAS 338, 733.

Examples

s <- c(0.242, 0.293, 0.231)
e <- c(0.037, 0.045, 0.036)
z <- 2.41
beta <- 1.5
alpha <- 2
X <- sedFitThin(s=s, e=e, z=z, alpha=alpha, beta=beta, nsamp=100)
str(X)

## Make a plot
# greybody in blue, power-law extension in red dashed line
# functions
# optically thin greybody
otGreybody <- function(nu, T, beta, sc=1) {
                       # nu in GHz, T in K, beta and sc unitless
                       sc*nu^(3+beta)/(exp(0.04801449*nu/T) - 1)
              }
# high frequency tail
hfTail <- function(nu, alpha) nu^-alpha
#
# setups for 8-1000 microns:
nu.low <- 3e5/1000
nu.high <- 3e5/8
l.nue <- s*X$scaleFactor
#
# greybody
nue.sweep <- seq(nu.low, nu.high, len=350)
pred <- otGreybody(nue.sweep, X$results[1,1], beta=beta,
                   X$results[1,4])
ylim <- range(pred, l.nue)
par(fig=c(0,1,0.2,1), mgp=c(1.8, 0.6, 0))
plot(3e5/nue.sweep, pred, t='l', ylim=ylim, log='xy', col=4,
     xlab='Rest frame wavelength [microns]',
     ylab=expression(paste('Luminosity density [ ', L[sun],
                           ' ', Hz^-1, ']')))
# power law
nue.sweep <- seq(X$results[1,5], nu.high, len=100)
val.t <- otGreybody(nu=X$results[1,5], T=X$results[1,1], beta=beta,
     sc=X$results[1,4])
lines(3e5/nue.sweep, val.t*hfTail(nue.sweep/X$results[1,5], alpha=alpha),
      col=2, lwd=1, lty=2)
# data
wl <- c(250, 350, 500)
nue <- 3e5/wl*(1+z)
points(3e5/nue, l.nue, pch=16, col=3)