Correcting the z~8 Galaxy Luminosity Function
for Gravitational Lensing Magnification Bias
Charlotte Mason *, Tommaso Treu , Kasper B. Schmidt , Thomas Collett , Michele Trenti
1
1
1,2
1
3
3
University of California, Santa Barbara, 2University of California, Los Angeles, 3University of Cambridge, Institute of Astronomy, *[email protected]
Introduction
We extend the determination of the z~8 luminosity
function1 from the Brightest of Reionizing Galaxies
(BoRG) survey by estimating how magnification bias
due to both strong and weak lensing modifies the luminosity function (LF) from its intrinsic form.
The BoRG Survey
• Primary goal: photometric identification of rare
galaxies at z~8 (PI Trenti, Cycles 17+19+20)
• 74 WFC3 independent pointings: ~350 arcmin2
• Upcoming... 480 orbits in Cycle 22 (z~9, 10)
Magnification Bias
All light travelling from the distant universe is perturbed
along its path by intervening mass. This causes a distortion in
shape, and magnitude (magnified or demagnified) of distant
sources.
Observed
Unobserved
LENS
There are many more faint galaxies than bright galaxies, so in
regions around low-redshift deflectors we expect to observe an
excess of intrinsically faint high-redshift sources.
Magnification bias increases the probability that a sample of
observed high-redshift sources have been lensed.
LENS
Size ~ Brightness
Without magnification
With magnification
Modification to Observed LF
Methods
Strong Lensing
• Expand previous2 semi-analytical framework for
including magnification bias
• Evolution of deflector population is included
within the velocity dispersion function in optical
depth, we model the evolution by comparing with
the evolution of the stellar mass function to z<43
• In order to identify fields with potential strong
lens deflectors it is vital to have a good
mass-luminosity relation to find velocity
dispersions (and so Einstein radii) without
spectroscopy.
Weak Lensing
• Reconstruct lensing potentials4 of halos in large
catalogs from the Millennium Simulation
• Calculate the total magnification of a z~8 source
due to all intervening matter for 104 lines of sight
to produce magnification probability distributions
• Produce PDFs for each BoRG field by matching
via relative over-density with PDFs generated for
simulation halo data
Estimating Intrinsic LF
Faint
Bright
Probability of Multiple Images
Predictions for Future Surveys
We use a Bayesian inference method1,5 to estimate the
intrinsic form of the LF, assuming a Schechter
function.
Draft version July 15, 2014
Preprint typeset using LATEX style emulateapj v. 12/16/11
We aim to find the posterior probability distribution
for a Schechter fit, given our observed luminosities.
more of the observed
high-z sources must
have been magnified
p(|Lobs
) ~THE
p() LUMINOSITY
× p(Lobs|) FUNCTION OF BORG FIELDS DUE TO MAGNIFICATION BIAS
CORRECTIONS
TO
FROM GRAVITATIONAL LENSING
Magnification bias adds an additional likelihood
Charlotte A. Mason1
1 Department
relating true and magnified
luminosities
(which
is then
of Physics,
University
of California, Santa Barbara, CA, 93106-9530, USA
subject to measurement error and contamination). It is
Bright
included by marginalising over the magnified
luminosity of sources,
and accounting for the
systematically account for magnification bias in our es1. INTRODUCTION
8
z
>
8
LF
extrapolation
magnification of the area of each field.
timations of high-redshift luminosity functions.
BoRG Primary goal: photometric identication of rare
p(Lmag |Ltrue ) = p(Lmag |µ, Ltrue )p(µ)dµ
(1)
galaxies at z 8 ( 650Myr after Big Bang) 74 WFC3 inde
pendent pointings: 350 arcmin2, ¿400 orbits (PI Trenti,
= δ(Lmag − µLtrue )p(µ)dµ
(2)
Cycles 17+19+20) 4 lters (optical+near-IR): V, Y, J, H
4-6 hours/eld: 5 sensitivity: mlim 27 ...480 orbits in Cy1)
predict
We use the weak lensing magnification PDFs and
cle We
22 (z
9,10) the probability of a BoRG dropout being multiply-imaged to be ~2-15%, which increases as the
2
p(Amag |µ, APDFs
(3)
mag |A
true ) =magnification
true )p(µ)dµ
survey
limit
brightens.
This
is
approximately
half
the
fraction
predicted
by
previous
work
. One candidate
includep(A
strong
lensing
for
regions
2.
METHODS
5
= δ(Amag
− µAtrue
)p(µ)dµ
(4)
strongly
lensed
dropout
was
found
in
BoRG
, sobias
we do not expect to find any more.
near dropouts with potential
deflectors
present.
We extended a simple treatment of magnification
by ? which consider strong lensing by SIS deflectors.
We extend the determination of the z=8 luminosity funcWeIncomputed
optical ifdepth
forcontains
strong lensing:
this
2)
order to the
determine
a field
potential
strong lenses, we need to accurately determine the velocity
tion1 from the Brightest of Reionizing Galaxies (BoRG)
is the
probability
that we encounter
a strong
along
dispersion
of candidate
lenses. This
needs lens
to be
done via magnitude estimates.
survey by estimating how magnification bias due to both
a randomly selected line-of-sight. The probability of a
strong and weak lensing modifies the LF from its intrinsic
1. Schmidt, K. B., Treu, T., Trenti, M., et al. 2014, ApJ, 786, 57
given high-redshift source having been strongly lensed
form.
3)
The
z
8
LF
appears
significantly
modified
for
very
bright
galaxies
M
<
-22.
Though
current
surveys
have
not
2. Wyithe, J., Yan, H., Windhorst, R. R., & Mao, S. 2011, Nature,
~
is given by Bτm , where B, the magnification bias is the
Luminosity Function Number density of galaxies as a
2
469, 181
observe
such
rare,
bright
galaxies,
future
wide
field
surveys
will
probe
this
region.
For
surveys
>100
deg
, e.g.
ratio
of
the
number
of
sources
we
observe
in
a
flux
limited
function of luminosity at a given redshift Well described
3. Muzzin, A., Marchesini, D., Stefanon, M., et al. 2013, ApJ, 777,
WISH,
Euclid,
will find low
many
more bright
z~8 have
candidates and the observed LF will be dominated by
sample
where
intrinsically
luminosity
sources
at18low redshift by a Schechter function but it is unclear
been
magnified into
theWe
sample,
to the
number
of~8sources
magnification
bias.
predict
almost
all
z
sources
in
Euclid
will
have
been
strongly
lensed.
The
framework
what
form
the
LF
takes
at
high
redshift
and
how
its
pa4. Collett, T. E., Marshall, P. J., Auger, M. W., et al. 2013,
that
would beinobserved
in the
absence
offor
magnification.
rameters
evolve
Accurate
measurements
of
the
LF
help
developed
this
work
will
be
vital
determining the intrinsic LF of high-z sources found in such surveys.
MNRAS, 432, 679
The instrinsic luminosity function, Ψ(L) is modified in
investigate
theX.,evolving
galaxy
with
5.toKelly,
B. C., Fan,
& Vestergaard,
M.population
2008, ApJ, 682,
874redthe following way by magnification:
and construct
a timelime
of reionization.
6.shift
Barone-Nugent,
R., Wyithe,
J., Trenti,
M., et al. 2013,
4) We are in the process
of re-estimating
the z ~ 8 LF
Schechter
function parameters, including the magnification
∞
Magnification
Bias All
eprint
arXiv:1303.6109,
000 light travelling from the distant
1
(1
− τm
L
)
Lexpect the effect 1todP
PDFs
for
each
field,
and
be
smaller
than
the
uncertainties
in
the
previous
estimate
.
Ψ
Ψmod (L) =
+τm
Ψ
dµ
along its
path
by2012,
intervening
7.universe
Bradley, is
L.,perturbed
Trenti, M., Oesch,
P. A.,
et al.
ApJ, 760,mass.
108
µ dµ
µ
µdemag
µdemag
0
8.This
Bouwens,
R. aJ.;distortion
Illingworth,in
G.shape,
D.; Oesch,
A., et al. 2014, (or
causes
andP.magnification
(5)
eprint arXiv:1403.4295
demagnification)
of flux from distant sources. In highwhere µdemag = (1 − µmult τm )/(1 − τm ), with µmult redshift surveys it is expected that some of the more
Conclusions
References