Constraining cluster abundances using weak

lensing

Håkon DahleInstitute of Theoretical Astrophysics, University of

Oslo

Cluster abundances

Cluster mass function n(>M, z) The number density of clusters above a certain

mass threshold is sensitive to: m - The average mass density of the universe 8 - The rms of density fluctuations (using a

spherical tophat filter of radius 8h-1 Mpc)

m- neutrino mass w - equation of state parameter of dark energy (e.g. cosmological constant: w = -1) Complementary to CMB, SN Ia

Dark energywith w=-1

No dark energy

Evolution of the cluster population (from simulations) (Borgani et al. 2003)

Time

Requirements for “precision cosmology”

1.Precise mass measurements/ calibration of mass-observable relation

2.Well-understood selection criteria (survey volume, mass limit)

A new approach to an old problem…

• Most previous studies use the X-ray temperature function (XTF) or the X-ray Luminosity function (XLF) to constrain n(>M)

• This requires good knowledge of the M-Tx or M-Lx relation (and the scatter around these!!)

• Calibrate M-Tx using lensing masses ?

• Here (for the first time!) we derive n(>M) from lensing directly (i.e., not via XLF or XTF)

• X-ray data only enter through the cluster selection

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 > 1.2x1045 h50-2

erg/s, corresponds to M180 > 7.5x1014 h-1 Msun

• Complete, volume-limited sub-sample of 36 (e)BCS clusters (0.l5<z<0.3, > 0o, |b| > 20o )

Weak lensing cluster survey

2.56m NOT + UH2.2m

M180 estimate from lensing

Observable: reduced shear gT = Taveraged in radial bins

Fit to NFW profile with concentration parameter predicted by Bullock et al. (2001) M180c

Significant extrapolation is required for ~2/3 of the clusters (those not observed with UH8k camera)

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:

< Mobs/Mtrue > = 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~1.0x1014 h-1 Msunto the mass uncertainty

Lx cutoff + scatter soft mass cutoff.Probablility of including cluster of mass M180c ?

Observed cumulative mass function

Strong

Incompleteness

M-Lx normalization and scatter

Weak lensing masses for 50 clusters; Lx from RASS (Solid: fixed slope; dashed: arbitrary slope)

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 (=0.75):

Luminosity cutoff limit LX > 1.2x1045 h50-2 erg/scorresponds to mass cutoff

Procedure: Account for selection effects: - BCS/eBCS completeness estimate

- Probability of including a cluster of intrinsic mass M180c Only used clusters well above mass cutoff ( M180c > 1015 h-1 Msun )

Account for observed uncertainties: - Convolve theoretical mass function with set of observed uncertainties in M180c Contribution to these from 2D projection effects should be better understood w.r.t. bias and scatter

Include errors from cosmic variance

Fit to theoretical/simulated mass function (Sheth & Tormen 1999; Warren et al. 2005)

m-8 from lensing-based cluster mass function

WMAP + SDSS WMAP

(soliddashFrom fit to mass function predicted from simulations by Warren et al.

(2005)

m

Summary - First cluster mass function directly from weak lensing

- Avoids the problem with M-Tx calibration

- We find 8(m=0.3) = (0.78+/-0.05)

Future: 1. Combination with similar cluster sample at higher z (e.g. MACS) evolution of mass fn. constrains w 2. More clusters with wide-field data (reduces M180 uncertainty by ~2) 3. Lensing measurements of SZ clusters (from Planck etc.)