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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 |
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