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Drinking tea with a fork:
Techniques for
Photometric redshift surveys
• Motivation
– Some galaxy scaling relations and clustering
from spectroscopic data at low-z
– How much of this can be done with photo-z
datasets (DES, PanStarrs, LSST)
• Methods for noisy distance estimates
– Typically at higher-z
– Also apply to ‘local’ surveys where peculiar
velocities contaminate distance estimate
– Or to stellar distances from color-magnitude
relation
Scaling
relations
Slope,
amplitude,
curvature
→
nature,
formation
history
Bernardi et al. 2011
Bernardi et al. 2011
Mark Correlations
• Weight galaxies when measuring clustering
signal; divide by unweighted counts
• WW(r)/DD(r) means no need for random catalog
• Error scales as scatter in weights times scatter in
pair counts (Sheth et al. 2005)
– If scatter in weights small, can do better than typical
cosmic variance estimate
– Basis for recent excitement about constraining
primordial non-Gaussianity from LSS
Close pairs
(~ galaxies
in clusters)
more
luminous,
older than
average
Sheth, Jimenez, Panter, Heavens 2006
SDSS/MOPED
+
Mark correlation analysis
Predicts inversion of SFR-density
relation at z >1 (if densest regions
today were densest in the past)
• Radius of circle
represents total
mass in stars
formed, in units
of average
stellar mass
formed at same
redshift
• Star formation
only in less
dense regions at
low z?
Sheth, Jimenez, Panter, Heavens 2006
Sheth, Jimenez, Panter, Heavens 2006
A Nonlinear and Biased View
• Observations of galaxy clustering on large
scales are expected to provide information
about cosmology (because clustering on
large scales is still in the ‘linear’ regime)
• Observations of small scale galaxy
clustering provide a nonlinear, biased view
of the dark matter density field, but they do
contain a wealth of information about
galaxy formation
How much of this information
can be got from a photometric
redshift survey?
- Cosmology mainly wants dN/dz
- Galaxy formation wants p(L,R,…|z)
- Both want clustering: accurate distances
A fool in a hurry
drinks tea with a fork
Techniques for
Photometric redshift surveys
‘Representative’ spectra required
to calibrate mags →z mapping
• Typically
zphot(mags)
• So can get
p(zphot|z) or
p(z|zphot)
• More
generally,
can get
p(z|mags)
One mouse dropping
ruins the whole pudding
Catastrophic failures: dN/dz
Deconvolution:
dN/dzphot = ∫dz dN/dz p(zphot|z)
Convolution:
dN/dz = ∫dzphot dN/dzphot p(z|zphot)
or, more generally,
dN/dz = ∫dm dN/dm p(z|m)
Deconvolve
(Sheth 2007
uses
Lucy 1974)
distorted
fixed
In SDSS
If <z|z> = z
then <z|z> ≠ z
Rossi et al. 2009
Sheth & Rossi 2010
All crows in the world
are black
Deconvolution
Convolution
For luminosity function in
magnitude limited survey,
remember that
N(Mphot) = ∫dM N(M) p(Mphot|M)
where
N(M) = Vmax(M) f(M)
(De)convolve to get N(M) …
… then divide by Vmax(M)
<M|M> = M
so
<M|M> ≠ M
Deconvolve
Convolve
Riding a mule
while looking for a horse
Convolution/deconvolution/
Maximum-likelihood
(Sheth 2007; Christlein et al. 2010)/
Weights (Lima et al. 2008; Cunha et al. 2009)
Biased
scaling
relations
can be
fixed
similarly
Biased because same
distance error affects
both observables
True, intrinsic
Similarly for size - L relation
If a single family member eats,
the whole family
will not feel hungry
Cross-correlations:
MgII systems and z~0.7 LF in SDSS
N.B. <zspec> ~ 0.1
Churchill et al. 2005
Knowledge of ra, dec, zMgII
+ correlation length only few Mpc
+ sufficiently deep photometry
= estimate of z~0.7 LF
(Caler et al. 2010)
1880 absorbers in DR3
from Procter et al (2006)
•Assume all galaxies in same
field as absorber have zabs
•Wrong for all objects except
those at zabs
•Do same for random position
•Subtract counts
50 kpc
500 kpc
100 kpc
900 kpc
50 kpc
500 kpc
900 kpc
To hit a dog
with a meat-bun
Only small fraction of absorbers
(~400/1900) are in SDSS imaging
See Zibetti et al. (2007) for more about SDSS
MgII absorbers
Accounting for
magnitude limit
gives z~0.7
galaxy
luminosity
function
EW < 1.3 A
More
weak
50
kpc
500
kpc
More
strong
Another view of measurement
• 1880 fields each ~ p(3 arcmin)2
• So LF estimate from total area ~ 10 degrees2
• Comparable to COMBO-17; final data release
even larger; can even do evolution
• Summing over L gives ~ dN/dz from cross
correlation/background subtraction, so this is
yet another photo-z method
A person is blessed once,
But his troubles
never come alone
dN/dz estimate depends on how
correlated objects in photo-sample are
with those in spectroscopic sample:
in general, this ‘bias’ unknown
In principle,
progress from combining all
previous methods.
Especially if spectra taken to
calibrate photo-z’s cover same
survey area (…unlikely!)
Water can float a boat
But it can sink it too
Will calibration spectra themselves
provide higher S/N measurement of
galaxy scaling relations?
Summary
• Many complementary methods allow robust
checks of derived scaling relations
– Honest reporting of photo-z errors crucial
• Cross-correlating photo/spectro samples useful
– SDSS-BOSS LRGs with SDSS photometry
– SDSS photometric QSOs with spectroscopic QSO
sample (= faint end of QSO LF)
– Better if spectra throughout survey volume
• Deep photometry around absorption line
systems interesting even if absorbers not seen
Ongoing ...
• How to measure mark correlations in
(magnitude limited) photo-z surveys
– Worry about color-selected next
– Correlated errors in L,R,color as well as pair
separation
The
Danaids:
Fetching
water with a
sieve
The standard lore
Massive halos form later (hierarchical
clustering)
Mass function ‘top-heavy’ in dense regions:
n(m|d) = [1+b(m)d] n(m)
Massive halos cluster more strongly than
lower mass halos (halo bias):
xhh(r|m) = b2(m) xdm(r)
Dense regions host massive halos
30% least dense
• Environment is
number of
neighbours within
8Mpc
30% densest
Aside:
Poisson cluster
models
(thermodynamic,
Neg. Binomial)
quite accurate,
N.B. Counts are in
cells centered on
particles
• Assume
cosmology →
halo profiles,
halo abundance,
halo clustering
• Calibrate g(m) by
matching ngal and
ξgal(r) of full
sample
• Make mock
catalog assuming
same g(m) for all
environments
• Measure clustering
in sub-samples
defined similarly
to SDSS
M
r<−19.5
SDSS
Abbas & Sheth 2007
• Galaxy
distribution
remembers
that, in
Gaussian
random
fields, high
peaks and
low troughs
cluster
similarly
s8
• Environment
= neighbours
within 8 Mpc
• Clustering
stronger in
dense regions
• Dependence
on density
NOT
monotonic in
less dense
regions!
• Same seen in
mock catalogs
 Choice of scale not important
 Mass function ‘top-heavy’ in dense
regions
 Massive halos have larger radii
(halos have same density whatever
their mass)
 Gaussian initial conditions?
 Void galaxies, though low mass,
should be strongly clustered
SDSS
 Little room for additional (e.g.
assembly bias) environmental effects
• Environment
= neighbours
within 8 Mpc
• Clustering
stronger in
dense regions
• Dependence
on density
NOT
monotonic in
less dense
regions!
• Same seen in
mock catalogs;
little room for
extra effects
SDSS
Abbas & Sheth 2007
The Halo
Mass
Function
No evolution in
abundance of
~1012 Msun/h
halos from z=2
to present