cosvar {celestial} R Documentation

## 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')

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

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

`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)
```

[Package celestial version 1.4.6 Index]