alx-ai/arxiv_papers · Datasets at Hugging Face

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the Hectospec instrument (Fabricant et al. 2005) on the
MMT 6.5m telescope. Hectospec provides simultaneous
spectroscopy of up to 300 objects across a diameter of
1◦. This telescope and instrument combination is ideal
for studying the virial regions and outskirts of clusters
at these redshifts. We use the red sequence to preselect
likely cluster members as primary targets, and we ﬁll
ﬁbers with bluer targets (Rines et al. in prep. describes
the details of target selection). We eliminate all targets
withexistingSDSSspectroscopyfromourtargetlistsbut
include these in our ﬁnal redshift catalogs.
Ofthe15clustersstudiedhere,onewasobservedwitha
single Hectospec pointing and the remaining 14 were ob-
served with two pointings. Using multiple pointings and
incorporatingSDSS redshifts of brighterobjectsmitigate
ﬁber collision issues. Because the galaxy targets are rel-
atively bright ( r≤20.8), the spectra were obtained with
relativelyshortexposuretimes of3x600sto 4x900sunder
a variety of observing conditions.
Figure 1 shows the redshifts of galaxies versus their
projected clustrocentric radii for the 15 clusters stud-
ied here. The infall patterns are clearly present in all
clusters. We use the caustic technique (Diaferio 1999)
to determine cluster membership. Brieﬂy, the caustic
technique uses a redshift-radius diagram to isolate clus-
ter members in phase space by using an adaptive ker-
nel estimator to smooth out the galaxies in phase space,
and then determining the edges of this distribution (see
Diaferio 2009, for a recent review). This technique has
been successfully applied to optical studies of X-ray clus-
ters, and yields cluster mass estimates in agreement
with estimatesfromX-rayobservationsandgravitational
lensing (e.g., Rines et al. 2003; Biviano & Girardi 2003;
Diaferio et al. 2005; Rines & Diaferio 2006; Rines et al.
2007, and references therein).
We apply the prescription of Danese et al. (1980) to
determine the mean redshift cz⊙and projected velocity
dispersion σpof each cluster from all galaxies within the
caustics. We calculate σpusing only the cluster members
projected within r100estimated from the caustic mass
proﬁle.
2.2.SZE Measurements
The SZE detections are primarily from
Bonamente et al. (2008, hereafter B08), supplemented
by three measurements from Marrone et al. (2009,
hereafter M09). Most of the SZ data were obtained with
the OVRO/BIMA arrays; the additional clusters from
M09 were observed with the Sunyaev-Zel’dovich Array
(SZA; e.g., Muchovej et al. 2007).
Numerical simulations indicate that the integrated
Compton y-parameter YSZhas smaller scatter than the
peak y-decrement ypeak(Motl et al. 2005), so B08 and
M09 report only YSZ. Although ypeakshould be nearly
independent of redshift, YSZdepends on the angular size
of the cluster. The quantity YSZD2
Aremoves this depen-
dence. Thus, we compare our dynamical mass estimates
to this quantity rather than ypeakorYSZ. Table 1 sum-
marizes the SZ data and optical spectroscopy.
It is also critical to determine the radius within whichYSZis determined. B08 use r2500, the radius that en-
closes an average density of 2500 times the critical den-
sity at the cluster’s redshift; r2500has physical values of
300-700kpc forthe massiveclustersstudied by B08(470-
670kpcforthesubsamplestudiedhere). M09useaphys-
ical radius of 350 kpc because this radius best matches
their lensing data.
To use both sets of data, we must estimate the con-
version between YSZ(r2500) measured within r2500and
YSZ(r= 350 kpc) measured within the smaller radius
r=350 kpc. There are 8 clusters analyzed in both B08
and M09 (5 of which are in HeCS). We perform a least-
squaresﬁt to YSZ(r2500)−YSZ(r= 350kpc) to determine
an approximate aperture correction for the M09 clusters.
We list both quantities in Table 1.
3.RESULTS
We examine two issues: (1) the strength of the corre-
lation between SZE signal and the dynamical mass and
(2) the slope of the relationship between them. Figure 2
shows the YSZ−σprelation. Here, we compute σpfor all
galaxies inside both the caustics and the radius r100,cde-
ﬁned by the caustic mass proﬁle [ rδis the radius within
which the enclosed density is δtimes the critical density
ρc(z)].
Because we make the ﬁrst comparison of dynami-
cal properties and SZE signals, we ﬁrst conﬁrm that
these two variables are well correlated. A nonparametric
Spearman rank-sum test (one-tailed) rejects the hypoth-
esis of uncorrelated data at the 98.4% conﬁdence level.
The strong correlation in the data suggests that both σp
andYSZD2
Aincrease with increasing cluster mass.
Hydrodynamic numerical simulations indicate that
YSZ(integrated to r500) scales with cluster mass as
YSZ∝Mα
500, whereα=1.60 with radiative cooling and
star formation, and 1.61 for simulations with radiative
cooling, star formation, and AGN feedback ( α=1.70 for
non-radiative simulations, Motl et al. 2005). Combin-
ing this result with the virial scaling relation of dark
matter particles, σp∝M0.336±0.003

the Hectospec instrument (Fabricant et al. 2005) on the

MMT 6.5m telescope. Hectospec provides simultaneous

spectroscopy of up to 300 objects across a diameter of

1◦. This telescope and instrument combination is ideal

for studying the virial regions and outskirts of clusters

at these redshifts. We use the red sequence to preselect

likely cluster members as primary targets, and we ﬁll

ﬁbers with bluer targets (Rines et al. in prep. describes

the details of target selection). We eliminate all targets

withexistingSDSSspectroscopyfromourtargetlistsbut

include these in our ﬁnal redshift catalogs.

Ofthe15clustersstudiedhere,onewasobservedwitha

single Hectospec pointing and the remaining 14 were ob-

served with two pointings. Using multiple pointings and

incorporatingSDSS redshifts of brighterobjectsmitigate

ﬁber collision issues. Because the galaxy targets are rel-

atively bright ( r≤20.8), the spectra were obtained with

relativelyshortexposuretimes of3x600sto 4x900sunder

a variety of observing conditions.

Figure 1 shows the redshifts of galaxies versus their

projected clustrocentric radii for the 15 clusters stud-

ied here. The infall patterns are clearly present in all

clusters. We use the caustic technique (Diaferio 1999)

to determine cluster membership. Brieﬂy, the caustic

technique uses a redshift-radius diagram to isolate clus-

ter members in phase space by using an adaptive ker-

nel estimator to smooth out the galaxies in phase space,

and then determining the edges of this distribution (see

Diaferio 2009, for a recent review). This technique has

been successfully applied to optical studies of X-ray clus-

ters, and yields cluster mass estimates in agreement

with estimatesfromX-rayobservationsandgravitational

lensing (e.g., Rines et al. 2003; Biviano & Girardi 2003;

Diaferio et al. 2005; Rines & Diaferio 2006; Rines et al.

2007, and references therein).

We apply the prescription of Danese et al. (1980) to

determine the mean redshift cz⊙and projected velocity

dispersion σpof each cluster from all galaxies within the

caustics. We calculate σpusing only the cluster members

projected within r100estimated from the caustic mass

proﬁle.

2.2.SZE Measurements

The SZE detections are primarily from

Bonamente et al. (2008, hereafter B08), supplemented

by three measurements from Marrone et al. (2009,

hereafter M09). Most of the SZ data were obtained with

the OVRO/BIMA arrays; the additional clusters from

M09 were observed with the Sunyaev-Zel’dovich Array

(SZA; e.g., Muchovej et al. 2007).

Numerical simulations indicate that the integrated

Compton y-parameter YSZhas smaller scatter than the

peak y-decrement ypeak(Motl et al. 2005), so B08 and

M09 report only YSZ. Although ypeakshould be nearly

independent of redshift, YSZdepends on the angular size

of the cluster. The quantity YSZD2

Aremoves this depen-

dence. Thus, we compare our dynamical mass estimates

to this quantity rather than ypeakorYSZ. Table 1 sum-

marizes the SZ data and optical spectroscopy.

It is also critical to determine the radius within whichYSZis determined. B08 use r2500, the radius that en-

closes an average density of 2500 times the critical den-

sity at the cluster’s redshift; r2500has physical values of

300-700kpc forthe massiveclustersstudied by B08(470-

670kpcforthesubsamplestudiedhere). M09useaphys-

ical radius of 350 kpc because this radius best matches

their lensing data.

To use both sets of data, we must estimate the con-

version between YSZ(r2500) measured within r2500and

YSZ(r= 350 kpc) measured within the smaller radius

r=350 kpc. There are 8 clusters analyzed in both B08

and M09 (5 of which are in HeCS). We perform a least-

squaresﬁt to YSZ(r2500)−YSZ(r= 350kpc) to determine

an approximate aperture correction for the M09 clusters.

We list both quantities in Table 1.

3.RESULTS

We examine two issues: (1) the strength of the corre-

lation between SZE signal and the dynamical mass and

(2) the slope of the relationship between them. Figure 2

shows the YSZ−σprelation. Here, we compute σpfor all

galaxies inside both the caustics and the radius r100,cde-

ﬁned by the caustic mass proﬁle [ rδis the radius within

which the enclosed density is δtimes the critical density

ρc(z)].

Because we make the ﬁrst comparison of dynami-

cal properties and SZE signals, we ﬁrst conﬁrm that

these two variables are well correlated. A nonparametric

Spearman rank-sum test (one-tailed) rejects the hypoth-

esis of uncorrelated data at the 98.4% conﬁdence level.

The strong correlation in the data suggests that both σp

andYSZD2

Aincrease with increasing cluster mass.

Hydrodynamic numerical simulations indicate that

YSZ(integrated to r500) scales with cluster mass as

YSZ∝Mα

500, whereα=1.60 with radiative cooling and

star formation, and 1.61 for simulations with radiative

cooling, star formation, and AGN feedback ( α=1.70 for

non-radiative simulations, Motl et al. 2005). Combin-

ing this result with the virial scaling relation of dark

matter particles, σp∝M0.336±0.003