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).
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')The output is the approximate percentage cosmic (or sample) variance that is expected for the volume specified.
The aside (shortest projected side) of the Cartesian box, must be defined using 737 cosmology.
The bside (longest projects side) of the Cartesian box, must be defined using 737 cosmology.
The cside (radial side) of the Cartesian box, must be defined using 737 cosmology.
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).
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.
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.
Maximum redshift of comoving cone.
Minimum redshift of comoving cone.
| cosvarsph | The units of angular coordinate provided for long and lat (see skyarea). |
| cosvararea | The units of angular area provided (see cosvol). |
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.
Sky area in units of innunit (default is square degrees)
Aaron Robotham and Simon Driver
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).
Driver S.P. & Robotham A.S.G., 2010, MNRAS, 407, 2131
cosvol, skyarea
#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)
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