the complete universe
TRANSCRIPT
The Complete Universe
Known Issues in Observational Cosmology
Completeness
Selection EffectsGalaxy Evolution
Systematicsk - correction
The probability that a galaxy of a given apparent magnitude is observable.
m
The Origianl ROBUST Test of Completeness
From Rauzy (2001):
The luminosity function does not depend on the 3D redshift space position i.e it is Universal
Assumptions
The variables (Absolute Magnitude) & (Distance Modulus) are separable
MZ
The (M,Z) distribution is described by a sharp apparent magnitude limit, mlim
The Original ROBUST Test of Completeness
1 ( , ) ( ) ( )dP m z z f M dzdMAψ ρ=
Selection effects
Spatial distribution
Luminosity Function
( ) ( ) ( ) ( , )corr corrZ m M z k z e z A l bµ= − = + + +
Corrected distance modulus:
Probability density:
The Original ROBUST Test of Completeness
cut in apparent magnitude, mlim
Defining the Random Variable, ζThe Original ROBUST Test of Completeness
ζ =
F( M )F( M lim (Z ))
, F( M ) = f ( M )dM−∞
M
∫
ζ i =
F( Mi )F( M lim (Zi ))
=ri
ni +1
unbiased estimate of ζ
Tc = ζ i −
12
#
$%
&
'( Vi
i=1
Ngal
∑#
$%
&
'(
i=1
Ngal
∑12
The quantity, is defined as cT
m*
P(Tc ) > −3 : 99.38% P(Tc ) > −2 : 97.72%
P(Tc ) > −1 : 84.13%
Millennium Galaxy Catalogue
m* > mlim
Applying the Statistic cT
Applying the Statistic cT
What happens if there is an imposed bright limit?
The Improved ROBUST method (Johnston et. al. 2007) Re-defining the Random Variable ζ
lim
lim lim
( ) ( ( ))( ( )) ( ( ))
b
f b
F M F M ZF M Z F M Z
ζ−
=−
Tc = ζ i −
12
#
$%
&
'( Vi
i=1
Ngal
∑#
$%
&
'(
i=1
Ngal
∑12
The quantity, is defined as cT
Applying the modified ROBUST Method
Original Method Generalised Method
The 2dF Survey
2dF - including a bright limit
SDSS (Early Types) - (Bernardi et. al. 2003)
Improved Method of Using ROBUST MAXV VDefining the Random Variable τ
( ) ( ( ))( ( )) ( ( ))
low
upp low
H Z H Z M MH Z M H Z M M
δτ
δ− −
=− −
Tv = τ i −
12
#
$%
&
'( Vi
i=1
Ngal
∑#
$%
&
'(
i=1
Ngal
∑12
and Tc TV