During discussion we discussed the dominant errors in observational measurements of cluster masses via weak lensing.
Anja pointed out that the dominant source of uncertainty is shape noise (estimated via bootstrapping background galaxies); with increasing cluster redshift, the second big source of error are uncertainties in redshift distribution of background sources. Tommaso added that also dilution by cluster / foreground galaxies needs to be taken into account.

No tests have been done on mocks derived from cosmological simulations thus far for the techniques treating separation of background galaxies and cluster members (or foregrounds) - the corrections are based on assumptions.

Andrey brought up the possible bias for disturbed clusters due to the presence of second peak that is not modeled as part of lensing analysis. Such peak can cancel out some of the shear, which (if not taken into account) leads to underestimate of shear and derived lensing mass (Meneghetti et al. 2010). This may well be the source of offset between disturbed'' and undisturbed'' clusters in X-ray-weak lensing mass scaling relations found in recent studies (e.g., Okabe et al. 2010). Becker & Kravtsov (2011) show that fitting NFW may be biased if the fit is done on data with low background counts, which forces extension of fit out to scales beyond Rvir. A more accurate cluster profile at large scales may reduce/eliminate this bias. Although such profiles have been calibrated in cosmological simulations (e.g., Prada et al. 2006; Tavio et al. 2008, Oguri et al. 2011), the difficulty is that typical WL data cannot reliably fit more than one parameter for each cluster right now.

Andrey also brought up effect of covariance between X-ray observables, such as Mgas and weak lensing mass Mwl. If r500 is derived from Mwl and used to measure Mgas(<r500), this introduces a correlation into errors of Mgas and Mwl. The error on Mgas due to error in Mwl is
sigma_Mgas=alpha_M/3 * sigma_Mwl, where alpha_M is the local logarithmic slope of the gas density profile around r500: Mgas(r)=Mgas,500(r/r500)^alpha_M. For massive clusters alpha_M~1-1.3. This covariance between sigma_Mgas and sigma_Mwl reduces apparent scatter in the Mgas-Mwl correlation by a factor of (1-alpha_M/3)~0.55-0.65, which may explain why scatter in this relation was found to be small relative to Yx-Mwl, and Tx-Mwl relations (e.g., Okabe et al. 2010). Note that it is not sufficient to take into account errors on Mwl due only to shot noise, errors due to triaxiality and correlated large-scale structures (sigma_Mwl/Mwl~0.16-0.18; see Becker & Kravtsov 2011), need to be taken into account as well in evaluation of this covariance.

Note that a similar covariance is introduced into Tx-Mwl relation. Moreover, if Tx (measured say within 0.15-1r500) falls with increasing r500, then corresponding alpha_T<0 and such covariance would increase the apparent scatter in the Tx-Mwl relation, compared to the true scatter.

Similar covariances influence scatter in the Yx-Mwl relation, but effect for this relation is smaller because both Mgas and Tx enter relation in power 3/5=0.6.

Anja presented a wish list to theorists to address with cosmological simulations. This (incomplete) list is presented below.
Andrey wanted to add that observers should bug their theorist friends (busy pursuing more fun things) to address these or even dig into simulations themselves with help from theorist friends.

Main motivation: weak lensing calibration of X-ray/SZ/optical mass proxies

Triaxiality and line-of-sight projections can bias individual cluster
masses (e.g. Clowe et al. 2004, Meneghetti et al. 2010), so the key
question is whether the ensemble average is unbiased. Becker & Kravtsov (2011) show that when fitting a spherical NFW model to a
large number of halos in N-body simulations, the average mass is
unbiased, as long as the profile is fit only within ~R_vir. This goes
a long way in answering the key question with "yes", and so my
wishlist mainly addresses some details:

DM only simulations:

Are there `better' lensing mass estimators than sperical NFW?
Henk Hoekstra's method(s)? Aperture mass?

Choice of radius within which to measure the mass:
We argued that determining r_Delta from the lensing profile
artificially decreases the intrinsic scatter in the M_true - M_lens
relation (see above), since M_gas rises more steeply with radius than M_total.
For measuring the true scatter, the mass should therefore be fit
within a radius given by a low-scatter baryonic mass proxy, or
a fixed metric aperture.
I still wonder whether determining r_Delta from lensing biases the
M_lens vs. M_true relation? My oversimplified picture here is that
the mass of clusters elongated along the sight is overestimated by a
larger amount than the underestimate for clusters elongated in the
plane of the sky. Because the latter are more common, the bias
cancels out on average, if measured within an independent
radius. When measuring r_Delta from lensing, however, the radius is
also overestimated for clusters elongated along the LOS, and thus
the mass is overestimated even more. This could lead at least to
anisotropic scatter; I'm not sure whether it can lead to a bias, as
well.

Weak lensing alone is generally too noisy to reliably measure more
than one parameter. The concentration, or c-M relation, is therefore
often fixed. Does the mass remain unbiased?
More generally, how well can lensing recover the 3D c-M relation in
the presence of triaxiality and correlated structure? (The influence
of uncorrelated structure is discussed in Hoekstra et al. 2011b.)

DM+baryon simulations:

Choice of centroid:
What's the best center for X-ray / SZ / optical / lensing mass
measurements? X-ray luminosity peak / centroid? BCG?
Stellar-mass-weighted centroid?
This would require `realistic' BCGs (with realistic offsets from the
lowest point in the potential) and cool cores...

Selection biases:
DM-only simuls select on `true' DM mass, but cluster surveys
have large scatter in mass-observable relation. Can this bias
the average mass? What role do the details of baryon physics
play in this?
(For the strong lensing equivalent, see Meneghetti et al. 2011b.)

Cluster STEP (Shear TEsting Program):
This is being done by the DES collaboration; I hope they will
open it to non-DES groups, too!

Shear measurement bias for cluster-like shear

Red sequence cut method: uncertainty and variation in <D_LS/D_S>,
dilution by cluster members

Photo-z's: realistic p(z) + outliers; role of prior

Weak lensing masses Discussion31 March, 2011During discussion we discussed the dominant errors in observational measurements of cluster masses via weak lensing.

Anja pointed out that the dominant source of uncertainty is shape noise (estimated via bootstrapping background galaxies); with increasing cluster redshift, the second big source of error are uncertainties in redshift distribution of background sources. Tommaso added that also dilution by cluster / foreground galaxies needs to be taken into account.

No tests have been done on mocks derived from cosmological simulations thus far for the techniques treating separation of background galaxies and cluster members (or foregrounds) - the corrections are based on assumptions.

Andrey brought up the possible bias for disturbed clusters due to the presence of second peak that is not modeled as part of lensing analysis. Such peak can cancel out some of the shear, which (if not taken into account) leads to underestimate of shear and derived lensing mass (Meneghetti et al. 2010). This may well be the source of offset between disturbed'' and undisturbed'' clusters in X-ray-weak lensing mass scaling relations found in recent studies (e.g., Okabe et al. 2010).

Becker & Kravtsov (2011) show that fitting NFW may be biased if the fit is done on data with low background counts, which forces extension of fit out to scales beyond Rvir. A more accurate cluster profile at large scales may reduce/eliminate this bias. Although such profiles have been calibrated in cosmological simulations (e.g., Prada et al. 2006; Tavio et al. 2008, Oguri et al. 2011), the difficulty is that typical WL data cannot reliably fit more than one parameter for each cluster right now.

Andrey also brought up effect of covariance between X-ray observables, such as Mgas and weak lensing mass Mwl. If r500 is derived from Mwl and used to measure Mgas(<r500), this introduces a correlation into errors of Mgas and Mwl. The error on Mgas due to error in Mwl is

sigma_Mgas=alpha_M/3 * sigma_Mwl, where alpha_M is the local logarithmic slope of the gas density profile around r500: Mgas(r)=Mgas,500(r/r500)^alpha_M. For massive clusters alpha_M~1-1.3. This covariance between sigma_Mgas and sigma_Mwl reduces apparent scatter in the Mgas-Mwl correlation by a factor of (1-alpha_M/3)~0.55-0.65, which may explain why scatter in this relation was found to be small relative to Yx-Mwl, and Tx-Mwl relations (e.g., Okabe et al. 2010). Note that it is not sufficient to take into account errors on Mwl due only to shot noise, errors due to triaxiality and correlated large-scale structures (sigma_Mwl/Mwl~0.16-0.18; see Becker & Kravtsov 2011), need to be taken into account as well in evaluation of this covariance.

Note that a similar covariance is introduced into Tx-Mwl relation. Moreover, if Tx (measured say within 0.15-1r500) falls with increasing r500, then corresponding alpha_T<0 and such covariance would increase the apparent scatter in the Tx-Mwl relation, compared to the true scatter.

Similar covariances influence scatter in the Yx-Mwl relation, but effect for this relation is smaller because both Mgas and Tx enter relation in power 3/5=0.6.

Anja presented a wish list to theorists to address with cosmological simulations. This (incomplete) list is presented below.

Andrey wanted to add that observers should bug their theorist friends (busy pursuing more fun things) to address these or even dig into simulations themselves with help from theorist friends.

Main motivation: weak lensing calibration of X-ray/SZ/optical mass proxies

Triaxiality and line-of-sight projections can bias individual cluster

masses (e.g. Clowe et al. 2004, Meneghetti et al. 2010), so the key

question is whether the ensemble average is unbiased. Becker &

Kravtsov (2011) show that when fitting a spherical NFW model to a

large number of halos in N-body simulations, the average mass is

unbiased, as long as the profile is fit only within ~R_vir. This goes

a long way in answering the key question with "yes", and so my

wishlist mainly addresses some details:

DM only simulations:

Henk Hoekstra's method(s)? Aperture mass?

We argued that determining r_Delta from the lensing profile

artificially decreases the intrinsic scatter in the M_true - M_lens

relation (see above), since M_gas rises more steeply with radius than M_total.

For measuring the true scatter, the mass should therefore be fit

within a radius given by a low-scatter baryonic mass proxy, or

a fixed metric aperture.

I still wonder whether determining r_Delta from lensing biases the

M_lens vs. M_true relation? My oversimplified picture here is that

the mass of clusters elongated along the sight is overestimated by a

larger amount than the underestimate for clusters elongated in the

plane of the sky. Because the latter are more common, the bias

cancels out on average, if measured within an independent

radius. When measuring r_Delta from lensing, however, the radius is

also overestimated for clusters elongated along the LOS, and thus

the mass is overestimated even more. This could lead at least to

anisotropic scatter; I'm not sure whether it can lead to a bias, as

well.

than one parameter. The concentration, or c-M relation, is therefore

often fixed. Does the mass remain unbiased?

More generally, how well can lensing recover the 3D c-M relation in

the presence of triaxiality and correlated structure? (The influence

of uncorrelated structure is discussed in Hoekstra et al. 2011b.)

DM+baryon simulations:

What's the best center for X-ray / SZ / optical / lensing mass

measurements? X-ray luminosity peak / centroid? BCG?

Stellar-mass-weighted centroid?

This would require `realistic' BCGs (with realistic offsets from the

lowest point in the potential) and cool cores...

DM-only simuls select on `true' DM mass, but cluster surveys

have large scatter in mass-observable relation. Can this bias

the average mass? What role do the details of baryon physics

play in this?

(For the strong lensing equivalent, see Meneghetti et al. 2011b.)

Cluster STEP (Shear TEsting Program):

This is being done by the DES collaboration; I hope they will

open it to non-DES groups, too!

dilution by cluster members

(started 4/3/11 by Anja; + edited by Andrey)