cosvar {celestial}

Driver & Robotham (2010) cosmic variance calculator

Description

The main cosmic variance calculator function taken from Driver & Robotham (2010). cosvarcar is an interface to the Cartesian coordinate version, whilst cosvarsph is a utility interface to give approximate cosmic variance for astronomy survey regions (usually defined by RA, Dec and redshift limits).

Usage

cosvarcar(aside = 50, bside = 50, cside = 50, regions = 1)
cosvarsph(long = c(129, 141), lat = c(-2, 3), zmax = 1, zmin = 0, regions = 1,
inunit='deg', sep=":")
cosvararea(area=60, zmax=1, zmin=0, regions=1, inunit='deg2')

Arguments

aside

The aside (shortest projected side) of the Cartesian box, must be defined using 737 cosmology.

bside

The bside (longest projects side) of the Cartesian box, must be defined using 737 cosmology.

cside

The cside (radial side) of the Cartesian box, must be defined using 737 cosmology.

regions

How many well separated regions of this size will there be? The geometry provided is just for a single region, i.e. we reduce the single region CV by 1/sqrt(regions).

long

Upper and lower longitude (RA) limits of interest in units of inunit. If of length 1 then the number specified is assumed to be the upper limit and the lower limit is set to 0.

lat

Upper and lower latitude (Dec) limits of interest in units of inunit. If of length 1 then the number specified is assumed to be the upper limit and the lower limit is set to 0.

zmax

Maximum redshift of comoving cone.

zmin

Minimum redshift of comoving cone.

inunit

cosvarsph	The units of angular coordinate provided for long and lat (see skyarea).
cosvararea	The units of angular area provided (see cosvol).

sep

When inunit='sex', sep defines the type of separator used for the HMS and DMS strings (i.e. H:M:S and D:M:S would be sep=':', which is the default). See hms2deg and dms2deg for more details.

area

Sky area in units of innunit (default is square degrees)

Details

These functions use the empircally motivated cosmic variance percentage formula provided in Driver & Robotham (2010) Eqn 4.

cosvarsph is a 'best effort' approximation of the comoving box subtended by the specified spherical coordinates using the following conversions:

CoDistLow = cosdistCoDist(z=zmin,H0=70,OmegaM=0.3)

CoDistHigh = cosdistCoDist(z=zmax,H0=70,OmegaM=0.3)

cside=CoDistHigh-CoDistLow

area=skyarea(long = long, lat = lat, inunit = inunit, outunit='deg2')[1]

volume=cosvol(area=area, zmax = zmax, zmin=zmin, H0 = 70, OmegaM = 0.3, inunit='deg2')[1]

aside=cos(mean(lat)*pi/180)*(abs(diff(long))/360)*(CoDistLow+cside/2)

bside=(abs(diff(long))/180)*(CoDistLow+cside/2)

scale=sqrt(volume*1e9/(aside*bside*cside))

aside=aside*scale

bside=bside*scale

return(cosvarcar(aside=aside, bside=bside, cside=cside, subsets=subsets))

cosvararea is a simplifed version of cosvarsph, where the assumption is that aside=bside (so the aspect ratio on the sky is 1:1).

Value

The output is the approximate percentage cosmic (or sample) variance that is expected for the volume specified.

Note

Many people get upset at the term 'cosmic variance' and prefer 'sample variance'. Whilst I am sympathetic to the argument, more astronomers are familiar with the former term.

These cosmic variance estimates are defined using SDSS at z~0.1, caveats abound at higher redshifts, but these numbers should serve as a reasonably conservative (i.e. pessimistic) upper limit.

Author(s)

Aaron Robotham and Simon Driver

References

Driver S.P. & Robotham A.S.G., 2010, MNRAS, 407, 2131

See Also

cosvol, skyarea

Examples

#Approximate CV of the GAMA equatorial regions:
cosvarsph(long=12, lat=5, zmax=0.5)*1/sqrt(3)
#Or using the GAMA sexigesimal coordinates (should be the same):
cosvarsph(long = c('11:36:0','12:24:0'), lat = c('-2:0:0','3:0:0'), zmax=0.5,
inunit='sex')*1/sqrt(3)
#Approximate CV of the SDSS:
cosvarsph(long=150, lat=100, zmax=0.3)