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−644.31±0.57 2.94 ±0.13 – 0.40 ±0.07 1
Note. —aExtrapolated to r2500using the best-fit relation between YSZD2
A(350kpc) and YSZD2
A(r2500) for eight clusters in common
between B08 and M09.
Note. — Redshift zand velocity dispersion σpare computed for galaxies defined as members using the causti cs. Masses M100,vand
M100,care evaluated using the virial mass profile and caustic mass p rofile respectively.
Note. — REFERENCES: SZE data are from (1) Bonamente et al. 2008 and (2) Marrone et al. 2009.
Our shallow slopes may also arise in part from the fact
that our sample, which has been assembled from the lit-
erature and whose selection function is difficult to deter-
mine, is likely to be biased against clusters with small
mass and low SZE signal. Larger samples should deter-
mine whether unknown observational biases or issues in
the physical understanding of the relation account for
this discrepancy.
4.DISCUSSION
Thestrongcorrelationbetweenmassesfromgalaxydy-
namics and SZE signals indicates that the SZE is a rea-
sonableproxyforcluster mass. B08compareSZEsignals
toX-rayobservables,inparticularthetemperature TXof
the intracluster medium and YX=MgasTX, whereMgas
isthemassoftheICM(seealsoPlagge et al.2010). Both
of these quantities are measured within r500, a signifi-
cantly smaller radius than r100where we measure virial
mass. M09 compare SZE signals to masses estimated
from gravitational lensing measurements. The lensing
masses are measured within a radius of 350 kpc. For the
clusters studied here, this radius is smaller than r2500
and much smaller than r100. Numerical simulations indi-
cate that the scatter in masses measured within an over-
densityδdecreases as δdecreases (White 2002), largely
because variations in cluster cores are averaged out at
larger radii. Thus, the dynamical measurement reaching
to larger radius may provide a more robust indication
of the relationship between the SZE measurements and
cluster mass.
TheYSZD2
A−Mlensdata presented in M09 show a
weakercorrelationthanouropticaldynamicalproperties.
A Spearman test rejects the hypothesis of uncorrelated
data for the M09 data at only the 94.8% confidence level,
compared to the 98.4-99.8% confidence levels for our op-
tical dynamical properties. One possibility is that Mlensis more strongly affected by substructure in cluster cores
and by line-of-sight structures than are the virial masses
and velocity dispersions we derive.
Few measurements of SZE at large radii ( > r500) are
currently available. Hopefully, future SZ data will allow
a comparisonbetween virialmass and YSZwithin similar
apertures.
5.CONCLUSIONS
Our first direct comparison of virial masses, velocity
dispersions, and SZ measurements for a sizable clus-
ter sample demonstrates a strong correlation between
these observables (98.4-99.8% confidence). The SZE sig-
nal increases with cluster mass. However, the slopes of
both the YSZ−σrelation ( YSZ∝σ2.94±0.74
p) and the
YSZ−M100relation ( YSZ∝M1.11±0.16
100) are significantly
shallower(giventheformaluncertainties)thantheslopes
predictedbynumericalsimulations(4.76and1.60respec-
tively).
This result may be partly explained by a bias against
less massive clusters that could artificially flatten our
measured slopes. Unfortunately, the selection function
of our sample is unknown and we are unable to quan-
tify the size of this effect. More importantly, our sample
indicates that the relation between SZE and virial mass
estimates (or velocity dispersion) has a non-negligible in-
trinsicscatter. Acomplete, representativeclustersample
is required to robustly determine the size of this scatter,
its origin, and its possible effect on the SZE as a mass
proxy.
Curiously, YSZis more strongly correlated with both
σpandM100than with Mlens(M09). Comparison of
lensingmassesandclustervelocitydispersions(andvirial
masses)forlarger,complete, objectivelyselected samples
of clusters may resolve these differences.
Thefull HeCS sampleof53clusterswill providealargeHectospec Virial Masses and SZE 5
Fig. 2.— Integrated S-Z Compton parameter YSZD2
Aversus dynamical properties for 15 clusters from HeCS. Left panels: SZE data
versus virial mass M100estimated from the virial mass profile (top) and the caustic m ass profile (bottom). Solid and open points indicate
SZ measurements from B08 and M09 respectively. The dashed li ne shows the slope of the scaling predicted from numerical si mulations:
YSZ∝M1.6(Motl et al. 2005), while the solid line shows the ordinary le ast-squares bisector. Arrows show the aperture correction s to
the SZE measurements (see text). Right panels: SZE data versus projected velocity dispersions measured fo r galaxies inside the caustics
and (top) inside r100,cestimated from the caustic mass profile and (bottom) inside t he Abell radius 2.14 Mpc. The dashed line shows the
scaling predicted from simulations: YSZ∝M1.6(Motl et al. 2005) and σ∝M0.33(Evrard et al. 2008). The solid line shows the ordinary
least-squares bisector. Data points and arrows are defined a s in the left panels.
sample of clusters with robustly measured velocity dis-
persions and virial masses as a partial foundation for
these comparisons.
We thank Stefano Andreon for fruitful discussions
about fitting scaling relations with measurement errorsand intrinsic scatter in both quantities. AD gratefully
acknowledges partial support from INFN grant PD51.
We thank Susan Tokarz for reducing the spectroscopic
data and Perry Berlind and Mike Calkins for assisting
with the observations.
Facilities: MMT (Hectospec)
REFERENCES