Weak lensing measurement of the cluster mass function from weak lensing Hkon Dahle OsloLAM

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Weak lensing measurement of the cluster mass
function from weak lensingHåkon
Dahle(Oslo/LAM)

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Cluster abundances

• Cluster mass function n(gtM, z)
• The number density of clusters above a certain
  mass threshold is sensitive to Wm, s8,
  Mn??w,..
• Complementary to CMB, SN Ia, cosmic shear

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Motivation

• Current studies commonly use the X-ray
  temperature function (XTF) or the X-ray
  luminosity function (XLF) to constrain MF
• Normalization (and scatter!) of M-Tx or M-Lx
  relation needs to be determined
• Recent efforts to calibrate M-Tx via lensing
• (G. Smith et al. 2005, Pedersen Dahle 2006,
  Bardeau et al. 2007)
• Here (for the first time!) we derive MF from
  lensing directly (i.e., not via XLF or XTF)
• X-ray data only enter through the cluster sample
  selection. Massive clusters (Bigger is better)
  

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Weak lensing survey of X-ray
luminous clusters

• Initial data set 38 clusters Dahle et al. 2002
  
• Current data set 53 clusters
• From RASS-based samples of X-ray luminous
  clusters Ebeling et al. 1996,1998,2000
  Boehringer et al. 2000 Briel Henry 1993
• LX gt 1.2x1045 h50-2 erg/s, corresponds to M180 gt
  7.5x1014 h-1 Msun
• Complete, volume-limited sub-sample of 35 (e)BCS
  clusters (0.l5ltzlt0.3, d gt 0o, b gt 20o )

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Weak lensing survey of X-ray
luminous clusters

• NOT and UH 2.24m VI-band imaging
• 2k CCDs (f.o.v.1 h-1 Mpc) or UH8K mosaic
  (f.o.v.3 h-1 Mpc)
• Seeing ltFWHMgt 0.81 (I-band)
  0.89 (V-band)
• Exposure times 1.5h (2k CCDs) or 3.5h (UH8k)
• Faint galaxy samples 21 lt I lt 24.5 , 22 lt V lt
  25.5

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Weak lensing cluster survey UH2.2m 2.56m NOT
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M180 estimate from lensing

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Observed mass profile(average of 6 z0.3
clusters with wide-field UH8K data)
Dahle, Hannestad Sommer-Larsen (2003)
NFW
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Scatter in concentration parameterX-ray based
mass profiles of nearby relaxed clusters
Pratt et al (2005)
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Projection effects
Effect of correlated structures Metzler, White
Loken (2001) estimate Mobs/Mtrue dispersion of
0.26 about the mean, tail towards high
Mobs/Mtrue Clowe, De Lucia King (2004) find no
net bias lt Mobs/Mtrue gt 1, when fitting the
radial shear profile out to the virial radius

Effect of uncorrelated structures Foreground
and background structures do not produce a net
bias, but add 1x1014 h-1 Msunto the mass
uncertainty
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Contamination by cluster galaxies
Dash Average of 5 clusters at z0.23
Solid Average of 6 clusters at z0.30
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Uncertainties

• Projection effects (correlated uncorrelated
  structures)
  sproj 0.26
• Deviations from mean contamination correction
  (richness variations)
  srich 0.12 (8k) /
  0.20 (2k)
• Scatter around mean value of cvir
  sc 0.10 (8k)
  / 0.18 (2k)
• Typical lensing mass measurement uncertainties
  
• slens 0.25 (8k) / 0.5 (2k)

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Observed cumulative mass function
Strong Incompleteness
Lx cutoff scatter g soft mass
cutoff. Probablility of including cluster of mass
M180c ?
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M-Lx normalization and scatter

Weak lensing masses for 50 clusters Lx values
from RASS (Solid fixed slope dashed
arbitrary slope)
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The mass-luminosity relationship evolution
parameter Best fit slope and normalization
from 50 clusters with weak lensing masses

Best fit normalization when fixing slope to
theoretical value (a0.75)
Luminosity cutoff limit LX gt 1.2x1045 h50-2 erg/s
corresponds to mass cutoff
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Probability of including a cluster of true mass
M180c PdML is assumed to be lognormal,
with a measured dispersion of slogM 0.178
Prediction of observed mass fn


P(dM180c) is a probability distribution with a
width given by the error in observed mass. The
average is taken over the ensemble of observed
errors
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Procedure

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Wm-s8 from lensing-based cluster mass function
(thick 1s , thin 2s)

s8(Wm0.3) 0.??/-0.05
Dahle (2006, ApJ, 653, 954), fit to theoretical
mass function of Sheth Tormen (1999)
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Comparison of to cluster (CMF) constraints to
constraints from other data sets

SDSS seems discrepant (could be problem with how
it is included in standard parameter estimation
codes, not the data themselves)
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Effect of neutrinos (red curves)
CMB power spectrum
Matter power spectrum
(thick 1s , thin 2s)

Full line ?m 0.25, ?? 0.05, h0.735 Dashed
line ?m 0.50, ?? 0.1, h0.3675
Kristiansen, Elgarøy Dahle, astro-ph/0611761
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A robust, bias-free upper limit on M?

• ??????????????????????????????????h2 M? / 93.14
  eV
• Power spectrum of CMB temperature fluctuations
  breaks parameter degeneracies for ???, but CMB
  alone cannot constrain M??to better than 1.7 eV
• When adding LSS structure data, galaxy bias comes
  into play (as a function of scale, galaxy color,
  luminosity)
• Weak lensing mass measurements are free of such
  assumptions, WLCMB both based on well-understood
  physics
• Gives robust upper limit M? lt 1.43 eV

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Neutrino mass (upper limits) from various
astrophysical data sets, adding one set at a time
(thick 1s , thin 2s)

Kristiansen, Elgarøy Dahle, astro-ph/0611761
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Is Dark Matter Stable?

• With
• Signe Riemer-Sørensen, Steen Hansen Kristian
  Pedersen (DARK)
• Riemer-Sørensen et al., astro-ph/0610034
• plus
• Konstantin Zioutas (CERN)
• Anastasios Liolios (U. Thessaloniki)
• Riemer-Sørensen et al., astro-ph/0703342

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Sterile neutrinos as Warm Dark Matter

• Sterile neutrinos will only interact with
  non-neutrinos through gravity
• From minimal extension (standard model 3
  sterile neutrinos) of standard model of particle
  physics, nMSM
• - can provide solution to baryon asymmetry
  problem (Asaka Shaposhnikov 2005)
• - can explain masses of active neutrinos
  (Asaka et al. 2005)
• - possible solution to CDM problems (?) on
  small scales
• - compatible with early star formation
• - can provide extra kick to pulsars
• - falsifiable!
• ns -gt na g
• Decay of keV particles -gt narrow X-ray line
  emission, E ms/2
• Idea of Steen Hansenet al. 2002 Look for dark
  blobs with low baryon content

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Abell 520 (z0.20)
(2.24m University of Hawaii Telescope 4.5h
(I-band) 1.5h (V-band)
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X-ray emission (diffuse blue) and lensing mass
(green contours) in Abell 520
Mass of the DM blob region determined from weak
grav.lensing MDM 6.71013 MO.
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Upper limit on the decay rate of sterile
neutrinos Gg lt 8pFDL2/Mfov
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Robust constraints in parameter space
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PQ and KK axions

• Standard Axions (Peccei-Quinn)
• rest mass mPQ 10-6 - 10-2 eV/c2
• lifetime much longer than the age of the Universe

Kaluza-Klein Axions predicted by theories of
extra-dimensions excited KK states an mass
larger than PQ mass. Spectrum with a mass
spacing 1/R. lifetime
axion-photon coupling constant can be the same
for both types ga?? ?
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CAST
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The X-ray emission spectra

• Black triangles
• the spectrum of the reference region
• Black, solid line
• the fitted basis model (reduced ?2 1).
• Red squares
• the spectrum of the blob region

Upper limits on the luminosity Abell 520 L
0.2x1044 erg/sec Bullet Cl L 1.4x1044 erg/sec
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Lifetime lower limits
?ssuming that all of the dark matter is made up
of one single candidate with a two-photon decay,
the strongest constraint comes from Abell 520
(upper limit on the luminosity L 0.2x1044
ergs/sec, mass of DM blob region MDM 6.71013
MO).

• Lower limit on the lifetime
• t 1024 sec
• corresponding to g a?? 10-15 GeV-1
• for a mean axion rest mass of 5 keV

For the two clusters t 1023 - 1024 sec
If KK-axions is only a fraction Xa of the dark
matter in clusters, the lifetime constraint
relaxes to lower values.
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Summary