SHARC-2 350 μm Observations of Distant Submillimeter-selected Galaxies

TLDR: In this paper, the authors verified the linear radio-far-infrared correlation at redshifts of z ~ 1-3 and luminosities of 10^(11)-10^(13) L_☉, with a power-law index of 102 ± 012 and rms scatter of 012 dex However, the correlation constant q or the dust emissivity index β is lower than measured locally.

Abstract: We present 350 μm observations of 15 Chapman et al submillimeter galaxies (SMGs) with radio counterparts and optical redshifts We detect 12 and obtain sensitive upper limits for three, providing direct, precise measurements of their far-infrared luminosities and characteristic dust temperatures With these, we verify the linear radio-far-infrared correlation at redshifts of z ~ 1-3 and luminosities of 10^(11)-10^(13) L_☉, with a power-law index of 102 ± 012 and rms scatter of 012 dex However, either the correlation constant q or the dust emissivity index β is lower than measured locally The best-fitting q ≃214 is consistent with SMGs being predominantly starbust galaxies, without significant AGN contribution, at far-infrared wavelengths Gas-to-dust mass ratios are estimated at 54^(+14)_(-11)(κ_(850μm)/015 m^2 kg^(-1)), depending on the absoption efficiency κ_ν, with intrinsic dispersion ≃40% around the mean value Dust temperatures consistent with 346 ± 3 K (15/β)^(071), at z ~ 15-35, suggest that far-infrared photometric redshifts may be viable, and perhaps accurate to 10% ≲ dz/(1 + z), for up to 80% of the SMG population in this range, if the above temperature characterizes the full range of SMGs However, observed temperature evolution of T_d ∝ (1 + z) is also plausible and could result from selection effects From the observed luminosity-temperature (L-T) relation, L ∝ T^(282±029)_(obs), we derive scaling relations for dust mass versus dust temperature, and we identify expressions to interrelate the observed quantities These suggest that measurements at a single wavelength, in the far-infrared, submillimeter, or radio wave bands, might constrain dust temperatures and far-infrared luminosities for most SMGs with redshifts at z ~ 05-4

Figures

Fig. 4.—Median dust temperatures vs. redshift. Data are binned for this paper (squares), for the Chapman et al. (2005) sample (circles) with temperatures estimates incorporating the radio data, and for dusty quasars (triangles); 1 error bars were estimated from the scatter inside the bins and the uncertainties of dust temperatures where available (thick bars). Dispersion within bins are also shown (thin bars), while dotted error bars indicate measurement error for a single datum inside a bin. A Td of 35 3 Kmay be applicable for z 1:5Y3:5, which, if true, can provide photometric redshifts in that range. However, observing frame temperatures of around 10 K appear to fit the SMG data somewhat better than constant Td in the rest frame. This similarity of the SEDs in the observing frame may be due to selection effects. [See the electronic edition of the Journal for a color version of this figure.]

Fig. 9.—Relations between observed quantities. Radio and far-infrared fluxes (top), radio fluxes (middle), and far-infrared fluxes (bottom) vs. observed temperatures. Results from this paper are plotted as squares, with upper limits indicated as appropriate (arrows); Laurent et al. (2006) data are shown as circles. The model deriving from the radio-FIR correlation and the observed L-T relation is also shown (solid curve). The data show excellent agreement with predictions within the measurement uncertainties involved. A single radio or submillimeter measurement may, therefore, suffice to predict the other quantities. Thus, these relationship can offer a useful tool for all radio or submillimeter surveys. [See the electronic edition of the Journal for a color version of this figure.]

Fig. 5.—Radio to far-infrared correlation for SMGs. Galaxies observed by the authors shown with squares, data from Laurent et al. (2006) with circles; 2 upper limits are indicated when appropriate (arrows). Far-infrared luminosities were calculated exclusively based on the available submillimeter measurements, with ¼ 1:5. The best-fit model (solid line) reveals no deviation from linearity in the relationship. The deduced 2 instrinsic scatters around the model are also shown (dotted lines). [See the electronic edition of the Journal for a color version of this figure.]

Fig. 6.—Original definition of q from Helou et al. (1985) (left), and the modified, luminosity-based definition qL as a function of redshift (right); 2 upper limits are indicated as appropriate (arrows). Data from this paper are shownwith squares, while those from Laurent et al. (2006) are shown as circles. The observed SMGs seem to consistently fall below the locally observed mean of 2.34 (Yun et al. 2001) for local bright IRAS sources (solid line) whose 2 scatters are also indicated (dashed lines). The values were all derived assuming ¼ 1:5. The derived distribution mean values of the non-radio-loud subsample (q > 1) are also shown (shaded bands). [See the electronic edition of the Journal for a color version of this figure.]

TABLE 1 Summary of Observations

Fig. 7.—Likelihood contours (at 68%, 90%, and 95% confidence) for the dust emissivity and the radio to far-infrared correlation constant qL, using only the available detections (dashed curves) and all information, including nondetections (solid curves). The best-fit locii of both fits are indicated by plus signs. The more inclusive set is expected to be a more reliable indicator of SMG properties, as it is less affected by the selection biases that are introduced by requiring detections in all bands. A similar fit to Arp 220 is also indicated (black circle).

Full text

SHARC-2 350 m OBSERVATIONS OF DISTANT SUBMILLIMETER-SELECTED GALAXIES
A. Kova
´
cs,
1
S. C. Chapman,
1
C. D. Dowell,
1
A. W. Blain,
1
R. J. Ivison,
2
I. Smail,
3
and T. G. Phillips
1
Received 2006 January 26; accepted 2006 April 27
ABSTRACT
We presen t 350 m observations of 15 Chapman et al. submillimeter galaxies (SMGs) with radio counterparts
and optical redshifts. We detect 12 and obtain sensitive upper limits for three, providing direct, precise measurements of
their far-infrared luminosities and characteristic dust temperatures. With these, we verify the linear radioYfar-infrared
correlation at redshifts of z  1Y3 and luminosities of 10
11
Y10
13
L

, with a power-law index of 1 :02  0:12 and rms
scatter of 0.12 dex. However, either the correlation constant q or the dust emissivity index  is lower than measured
locally. The best-fitting q ’ 2:14 is consistent with SMGs being predominantly starbust galaxies, without significant
AGN contribution, at far-infrared wavelengths. Gas-to-dust mass ratios are estimated at 54
þ14
11

850 m
/0:15 m
2
kg
1

,
depending on the absoption efficiency 

, with intrinsic dispersion ’40% around the mean value. Dust temperatures
consistent with 34:6  3K(1:5/)
0.71
,atz  1:5Y3 :5, suggest that far-infrared photometric redshifts may be viable,
and perhaps accurate to 10% P dz/(1 þ z), for up to 80% of the SMG population in this range, if the above temperature
characterizes the full range of SMGs. However, observed temperature evolution of T
d
/ (1 þ z)isalsoplausibleand
could result from selection effects. From the observed luminosity-temperature (L-T ) relation, L / T
2:820:29
obs
,wederive
scaling relations for dust mass versus d ust temperature, and we identify expressions to interrelate the observed
quantities. These suggest that measurements at a single wavelength, in the far-infrared, submillimeter, or radio wave
bands, might constrain dust temperatures and far-infrared luminosities for most SMGs with redshifts at z  0:5Y 4.
Subject headinggs: galaxies: evolution — galaxies: high-redshift — galaxies: ISM — galaxies: pho tometry —
galaxies: starburst — infrared: galaxies — submillimeter
Online material: color figures
1. INTRODUCTION
Ever since the first submillimeter-selected galaxy (SMG) sam-
ples debuted from SCUBA 850 m surveys (Smail et al. 1997;
Barger et al. 1998; Hug hes et al. 1 998; Eales et al. 1999), the
nature of the SMG population has been the foc us o f atte ntion for
the galaxy formation community, because the 850 mselectionis
expected to pick similar sources almost independently of redshift
(z  1Y8), due to a negative K -correction t hat essentially com-
pensates for the loss of flux from increasing distance. This allows
unbiased, luminosity-selected studies of galaxy formation. The
hunger for information on these sources spurred a flurry of follow-
up studies at all wavelengths, l ong and sh ort. Sin ce then man y
of these sources have been identified at optical, UV (Borys et al.
2003; Chapman et al. 2003; Web b et al. 2003), and radio wave-
lengths (Smail et al. 20 00; Ivison et al. 2002), providing ac-
curate positions, which allowed optical redshift measurements
(Chapman et al. 2003, 2005). As a result we now know that these
massive galaxies, with redshifts distributed around z ’ 2:3, are
enshrouded with such quantities of dust that they often lie hidden
at optical wavelengths, and therefore constitute a distinct pop-
ulation from the galaxies selected by optical surveys.
More recently, longer wavelength submillimeter surveys, at
1100 and at 1200 m (Laurent et a l. 2005; Greve et al. 2004),
added to the pool of available information. However, the close
proximity of the SCUBA, Bolocam, an d M AMBO wavelengths
on the R ayleigh-Jeans side of the spectral energy distribution
(SED) does not allow for an effective constraint on the thermal
far-infrared SEDs at the relevant redshifts. Nor do the latest results
from the Spitzer Space Telescope pr ovide powerful constraints,
since at the shorter m id-infrared wavelengths the emission is
dominated by po lycyclic a romati c hydr ocarbon s (PAHs) an d a
minority popu lation of hot dust. For t hese reasons, the best
estimates o f the characteristic temperatures and the integrated
luminosities, to date, have relied on the assumption that the lo-
cal radio to far-infrared correlation (Helou et al. 1985; Condon
1992; Yun et al. 2001) can be extended into the distant uni-
verse. There are hints that this may be appropriate (Garrett 2002;
Appleton et a l . 2 00 4), but the assumption has remained largely
unchecked.
Shorter wavelength submillimeter measurements, sampling
near the rest-frame peak of the emission, are thus essential to
provide firm constraints to the far-infrared SED. Here we present
results at 350 m, using the second-generation Submillimeter
High Angular Resolution Camera (SHARC-2; Dowell et al.
2003) a t the Caltech Submillimeter Observatory (CSO). From
these we derive t he first direct measures of dust temperatures
and far-infrared luminosities for a sample of SMGs, testing t he
radio to far-infared correlation. We also attempt to constrain dust
emission properties and investigate the implications of our find-
ings for the viability of photometric redshifts based on far-infrared
and rad io measurements. F inally, we present a ra nge of useful
scaling relations that may apply to the SMG population.
2. SHARC-2 350 m OBSERVATIONS
We conducted follo w-up observa tions of SCUBA 850 m
detected sources w ith radio identifications and optical redshifts
(Chapman et al. 2003, 2005). S even of the 15 targets were hand-
picked on the basis of their p redicted bright 350 mfluxes
A
1
California Institute of Technology, Mail Code 320-47, 1200 East Cal-
ifornia Boulevard, Pasadena, CA 91125.
2
Royal Observatory, Blackford Hill, Edinburgh EH9 3HJ, UK.
3
Institute for Computational Cosmology, Durham University, South Road,
Durham DH1 3LE, UK.
592
The Astrophysical Journal, 650:592Y603, 2006 October 20
# 2006. The American Astronomical Society. All rights reserved. Printed in U.S.A.

(S
350 m
> 45 mJy from Chapman et al. 2005), while the re-
maining were selected at random to partially compensa te for
any selection bias.
The observation s were carried ou t during eight se parate ob-
serving runs between 2002 November and 2005 April, in excel-
lent weather (
225 GHz
< 0:06), reaching 1  depths of 5 Y9mJy
in 2Y 4 hr of integration in 14 small fields (’2:5 ; 1arcmin
2
)
around the targeted sources. Our scanning strategy was to mod-
ulate the telescope pointing with a small-amplitude (15
00
Y20
00
)
nonconnecting Lissajous pattern within the limits of reasonable
telescope acceleration (with typical periods of 10Y20 s). This
pattern was chosen to p rovide fast, two-dimensional, re curring
but nonclosed patterns with crossing paths—all of which are es-
sential to a llow the separation of the superposed source, atmo-
spheric, and instrumental signals. For the observations since 2003
February, w e have take n adva ntage of the CSO’s Dish Surface
Optimization System (Leong 2005) to improve beam shape s
and efficiencies, and hence sensitivities, at all elevations.
Pointing corrections were retroactively applied to the ob-
servations by a c areful fit to the pointing data taken during each
run. In addition, our preliminary source identifications re vealed
a small, albeit significant (’3
00
) systematic pointing shift in the
negative R.A. direction. All maps were realigned accordingly.
The reconstructed pointing is accurate t o 3B5 rms, in good
agreement with CSO specifications.
The data were processed using the CRUSH
4
software pack-
age, developed at Caltech (Kova
´
cs 2006), which models total
power detector signals using a n iterate d sequenc e of ma ximum
likelihood estimators. The FWHM point-spread functions of the
final maps (F ig. 1) are approximately 12
00
after optimal filtering
to search for beam-sized (’9
00
) features in order to yield maximal
signal-to-noise ratios on point sour ces. This degradation of the
imageresolutionbyapproximately
ffiffiffi
2
p
, from the nominal instru-
mental beam width of 8B5, is because the fitting for beam-sized
features is equivalent to convolving the image with the slightly
wider effective beam of around 9
00
, which accounts for the smear-
ing of the nominal beam by pointing and focus variations on the
long integrations.
Calibration was performed primarily against planets and aster-
oids, when available, or using stable galactic continuum sources
and Arp 220.
5
Trends in aperture efficiency, especially with ele-
vation, were estimated and were ta ken into account when cali-
brating our science targets. The systematic flux filtering effect
Fig. 1.—30
00
; 30
00
SHARC-2 350 m thumbnail images of the SMG s observed (sources 1Y15 in Tables 1Y3) shown in reading order (left to right, top to bottom).
Images are centered on the radio positions, and displayed on the same flux scale for comparison. The 12B4 FWHM effective beams of the optimally filtered (convolved)
images are also indicated. Sources 3, 9, a nd 10 are not detected. [See the electronic edition of the Journal for a color ver sion of this figure.]
4
See http://www.submm.caltech.edu/sharc/crush.
5
See http://www.submm.caltech.edu/sharc/analysis/calibration.htm.
SHARC-2 350 m OBSERVATIONS OF DISTANT SMGs 593

of the aggressive reduction parameters used in CRUSH to su b-
tract noise signals and reach maximal image depths, was carefully
estimated for the case of point sources, and the appropriate correc-
tions were applied to the images. The final calibration is expected
with high confidence to be more accurate than 15%, with sys-
tematic effects anticipated to be less.
The maps produced by CRUSH reveal Gaussian noise profiles
with an anticipated tail at positive fluxes. H ence, in searching
for 350 m counterparts around the published radio positions, we
calculate detection t hresholds b ased on the effective number of
beams N
beam
 1 þ A/A
beam
(Kova
´
cs 2006) inside a detection
area A in the smoothed image. A detection confidence C  1is
reached at the significan ce level S/ N, at which
1 C 
N
beam
ffiffiffiffiffiffi
2
p
Z
1
S= N
e
(1=2) x
2
dx: ð1Þ
As for the appropriate search radius, the probability that the
peak of the smoothed image falls at some radius away from the
true position is essentially the likelihood that the smoothed noise
level a t that radius is sufficient to make up for the deficit in the
underlying signal. Therefore, for the case of Gaussian noise pro-
files, we expect the detection to lie inside of a 2  noise peak, and
therefore within a maximal radius given by the condition S/ N ¼
2/½1  exp ( r
2
max
/2
2
beam
) for a Gaussian beam profile with

beam
spread at an underlying signal-to-noise ratio of S/ N. To
this we must add the appropriate pointing tolerance (at 2  level)
in quadrature, arriving at an expression for the detection radius
around the actual position as a function of detection significance,
that is,
r
2
max
¼ 4
2
pointing
 2
2
beam
ln 1 
2
S=N

: ð2Þ
Note that this expression simplifies to r
max
! 2
beam
S/ NðÞ
1/2
for the case of S/ N 3 1 and negligible 
pointing
.
The combination of S/N ¼ 2:30 and r
max
¼ 10 B4 simulta-
neously satisfy both constrain ts (eqs. [1] and [2]) at C ¼ 95%
confidence level for a 
beam
¼ 9
00
effe ctive beam and 
pointing
¼
3B5 pointing rms. Potential candidates thus identified are sub-
sequently verified to lie within the expected distance from their
respective radio positions. The resulting identifications are sum-
marized in Table 1. When counterparts were not found, the peak
measurement values inside the search area are reported.
The sources, collectively, are much smaller than the SHARC-2
beam (i.e., dT9
00
), as neither (1) fitting larger (12
00
) beams or
(2) filtering extended structures produces systematically different
fluxes for the sample as a whole. Source extents typically P30 kpc
are therefore implied. While the partial resolution of a few objects
cannot be excluded, the peak fluxes of the optimally filtered im-
ages are expected to be genera lly accurate measures of the total
integrated flux for the objects concern ed.
3. SPECTRAL ENERGY DISTRIBUTIONS OF SMGs
We fitted the SHARC-2 350 m a nd SCUBA 850 mfluxes,
combined with Bolocam 1100 m (Laurent et al. 2005) a nd
TABLE 1
Summary of Observations
ID Name
Offset
a
(J2000.0)
(arcsec) z
S(350 m)
(mJy)
S(850 m)
(mJy)
S(1100 m)
(mJy)
S(1200 m)
(mJy)
S(1.4 GHz)
(mJy)
1....................... SMM J030227.73+000653.5 +1.0, +0.8 1.408 42.2  9.8 4.4  1.3 ... ... 217  9
2....................... SMM J105207.49+571904.0 1.0, +3.7 2.689 38.0  7.2 6.2  1.6 ... (0.4  0.8) 277.8  11.9
3
b
..................... SMM J105227.77+572218.2 ... 1.956 (11.3  6.7) 7.0  2.1 5.1  1.3
b
3.1  0.7 40.4  9.4
c
4
b
..................... SMM J105230.73+572209.5 +3.3, 1.8 2.611 41.0  6.8 11.0  2.6 5.1  1.3
b
2.9  0.7 86.3  15.4
c
5....................... SMM J105238.30+572435.8 +1.4, +2.5 3.036 40.5  6.5 10.9  2.4 4.8  1.3 4.8  0.6 61.0  22.0
c
6....................... SMM J123600.15+621047.2 1.4, +2.0 1.994 22.3  6.3 7.9  2.4 ... ... 131  10.6
7....................... SMM J123606.85+621021.4 +6.7, +3.5 2.509 35.1  6.9 11.6  3.5 ... ... 74.4  4.1
8....................... SMM J131201.17+424208.1 ... 3.405 21.1  7.7 6.2  1.2 ... ... 49.1  6.0
9....................... SMM J131212.69+424422.5 +2.2, 4.2 2.805 (3.7  4.4) 5.6  1.9 ... ... 102.6  7.4
10..................... SMM J131225.73+423941.4 ... 1.554 (14.7  7.4) 4.1  1.3 ... ... 752.5  4.2
11..................... SMM J163631.47+405546.9 1.3, 4.0 2.283 38.3  5.5 6.3  1.9 ... (1.1  0.7) 99  23
12..................... SMM J163650.43+405737.5 1.0, 1.7 2.378 33.0  5.6 8.2  1.7 ... 3.1  0.7 221  16
13..................... SMM J163658.19+410523.8 +1.1, 1.2 2.454 45.2  5.3 10.7  2.0 ... 3.4  1.1 92  16
14..................... SMM J163704.34+410530.3 1.8, 4.4 0.840 21.0  4.7 11.2  1.6 ... (0.8  1.1) 45  16
15..................... SMM J163706.51+405313.8 2.3, +2.4 2.374 36.1  7.7 11.2  2.9 ... 4.2  1.1 74  23
(16).................. SMM J163639.01+405635.9 ... 1.495 ... 5.1  1.4 ... 3.4  0.7 159  27
(17)
d
................ SMM J105201.25+572445.7 ... 2.148 24.1  5.5 9.9  2.2 4.4  1.3 3.4  0.6 72.1  10.2
(18).................. SMM J105158.02+571800.2 ... 2.239 ... 7.7  1.7 ... 2.9  0.7 98.1  11.6
(19)
d,e
.............. SMM J105200.22+572420.2 ... 0.689 15.5  5.5 5.1  1.3 4.0  1.3 2.4  0.6 57.4  13.2
(20)
d
................ SMM J105227.58+572512.4 ... 2.142 44.0  16.0 4.5  1.3 4.1  1.3 2.8  0.5 39.2  11.4
c
(21)
f
................. SMM J105155.47+572312.7 ... 2.686 ... 5.7  1.7 ... 3.3  0.8 46.3  10.2
Notes.—MAMBO 1200 m fluxes are from Greve et al. (2004), upper limits (bracketed fluxes) are from T. Greve (2005, private communication), Bolocam 1100 mfluxes
are from Laurent et al. (2006), and 850 m SCUBA and 1.4 GHz fluxes are taken from Chapman et al. (2005). Biggs & Ivison (2006) provide alternative radio fluxes for many
of the listed objects. The bracketed IDs indicate sources that have not been observed by the authors within the context of this paper, but archived data are used in the analysis.
a
SHARC-2 detection offsets are with respect to the published radio positions.
b
Both of these sources are likely contributors to the observed 1100 m flux. The Bolocam data are ignored in the analysis.
c
The alternative radio fluxes from Biggs & Ivison (2006) are significantly different from or more accurate than the values listed here.
d
SHARC-2 35 0 m fluxes from Laurent et al. (200 6).
e
Chapman et al. (2005): ‘‘These SMGs have double radio identifications, one lying at the tabulated redshift and a second lying at z < 0:5.’’ The higher redshift
source is assumed to be the dominant contributor.
f
Chapman et al. (2005): ‘‘These SMGs have double radio iden tifications, both confirmed to lie at the same redshift.’’
KOVA
´
CS ET AL.594 Vol. 650

MAMBO 1200 m (Greve et al. 2004) data when available,
with single-temperature, optically thin graybody mod els of the
form S(; T ) / ()B(; T ), where () / 

is an approxi-
mation for the full emissivity term (1  exp ½(/
0
)

)for
obs
T

0
. Alternative SED models incorporating the full optical depth,
or a distribution of t emperatures and power-law Wien tails, did
not provide a better description of the data. Specifically, the
flattening of the Rayleigh-J eans slope due to optica l dept hs ap-
proaching unity is not detectable with the ’10% uncertain r el-
ative calibration of the bands, while the Wien side of the spectra
is not sampled by the observations. More complex SED mode ls,
e.g., the two-temperature mo del used by Dunne & Eales (2001 ),
were no t considered, since these require a greater number of
parameters than can be determined from the few, often just two,
photometric data points available for the typical SMG.
SED models, whether incorporating an emissivity slope, full
optical depth, or multiple temperature components, are simple
parameterizations of complex underlying spectral distributions,
produced by a range of dust properties inside the targeted galaxies.
Therefore, T and  of the model describe not the physical temper-
ature and emissivity of every single dust grain, but provide an ef-
fective characterization of dust emission in a galaxy as a whole. In
this sense, the characteristic -values, expected in the range 1Y2,
reflect both the underlying grain emissivities and a distribution
of physical temperatures within the observed objects. The derived
T-values provide an effective comparison of the characteristic dust
temperatures among objects with the same SED parameterization.
Simultaneous fitting of T and  requires at least t hree pho-
tometric data points (while many SMGs have only two), and
even when permitted these are highly correlated parameters
of the fit for the typical SMG (Fig. 2). Therefore, we initially
assume  ¼ 1:5 f or the SED fit, as it provides good char acter-
ization of actively star-forming environments, bot h in accu-
rately modeled Galactic clouds ( Dupa c et al. 2003) and galaxies
of th e local universe (Dunne & Eales 2001), and is broadly
consistent with laboratory measurements on carbite and s ilicate
grains (Agladze et al. 1996). The properties, thus derived, may
be scaled to the -values of the reader’s c hoosing, via the de-
duced spectral indices " and k listed in Tables 2 and 3, as
T
d
/ 
"
; L
FIR
/ 
k
; M
d
/ 
"(4þ)k
: ð3Þ
TABLE 2
Far-Infrared Properties of SMGs from SHARC-2 Data
ID
T
d
(K)
log L
FIR
(L

) q
L
" k
1................... 43.3  18.7 12.83  0.64 2.39  0.64 1.36 2.94
2................... 66.8  26.1 13.49  0.57 2.31  0.57 1.61 3.69
3................... 21.3  3.8 11.95  0.24 1.91  0.26 0.50 0.21
4................... 40.1  5.8 12.98  0.19 2.33  0.21 0.84 1.06
5................... 39.1  4.2 13.03  0.14 2.39  0.21 0.69 0.66
6................... 25.7  4.7 12.28  0.18 1.71  0.18 0.52 0.35
7................... 31.0  5.3 12.73  0.15 2.19  0.15 0.54 0.39
8................... 40.9  8.2 12.85  0.25 2.20  0.26 0.57 0.46
9................... 21.1  6.3 11.95  0.29 1.16  0.29 0.31 0.04
10................. 24.3  6.8 11.88  0.35 0.79  0.35 0.59 0.50
11................. 53.4  16.2 13.18  0.42 2.61  0.43 1.38 2.88
12................. 34.5  4.5 12.72  0.17 1.75  0.17 0.73 0.77
13................. 37.3  5.0 12.93  0.16 2.31  0.18 0.77 0.91
14................. 16.8  2.3 11.38  0.15 2.13  0.22 0.65 0.53
15................. 31.5  4.2 12.71  0.16 2.23  0.21 0.65 0.57
(17).............. 27.4  3.0 12.41  0.15 2.02  0.16 0.61 0.44
(19).............. 14.2  2.2 10.97  0.21 1.82  0.23 0.58 0.41
(20).............. 40.6  12.3 12.87  0.48 2.76  0.50 0.99 1.61
Notes.—A summary of the derived far-infrared properties of the observed SMGs.
All quantities were derived using an optically thin approximation with  ¼ 1:5.
Temperatures and luminosities may be scaled to other -values using the relations
of eq. (3) and the corresponding indices " and k listed here. The q
L
values derived
from the radio data of Biggs & Ivison (2006) tend to be higher by 0.06 on average.
Fig. 2.—Characteristic dust temperatur e T
d
and effective emissivity index 
are highly correlated parameters of the SED fit for the typical SMG, even when
threephotometricdatapointsallow simultaneous fitting of both T
d
and  (source 13
from Table 2, shown with solid 1, 2, and 3  contours). However, by assuming
 ¼ 1:5, we can accurately constrain luminosities (dotted contours) and tempera-
tures, which are listed in Tables 2 and 3. The derived properties may be scaled to
other -values of the reader’s preference using the relations of eq. (3) (thick solid
line). [See the electronic edition of the Journal for a color version of this figure.]
TABLE 3
Properties of SMGs Incorpor ating Radio Dat a
ID
T
d
(K)
log L
FIR
(L

)
log M
d
(M

) " k
1.................... 37.2  3.8 12.60  0.12 8.64  0.17 0.82 1.09
2.................... 60.3  6.1 13.34  0.12 8.22  0.16 0.86 1.15
3.................... 23.5  2.5 12.10  0.15 9.24  0.17 0.72 0.82
4.................... 37.1  3.4 12.86  0.11 8.91  0.14 0.77 0.89
5.................... 36.8  3.3 12.94  0.12 9.01  0.12 0.67 0.65
6.................... 38.6  7.0 12.66  0.13 8.61  0.33 0.94 1.29
7.................... 30.3  3.9 12.71  0.09 9.24  0.25 0.68 0.78
8.................... 39.8  4.5 12.81  0.12 8.69  0.19 0.71 0.93
9
a
.................. 21.1  6.3 11.95  0.29 9.36  0.48 0.31 0.04
10
a
................ 24.3  6.8 11.88  0.35 8.93  0.37 0.59 0.50
11.................. 41.5  4.4 12.82  0.13 8.60  0.16 0.80 0.99
12.................. 43.2  4.7 13.01  0.10 9.69  0.17 0.96 1.40
13.................. 34.8  3.2 12.84  0.10 9.04  0.14 0.73 0.83
14.................. 16.8  1.9 11.38  0.14 9.32  0.19 0.72 0.74
15.................. 30.7  3.2 12.68  0.12 9.18  0.16 0.70 0.75
(17)............... 28.6  2.3 12.47  0.12 9.14  0.13 0.75 0.85
(19)............... 16.4  1.7 11.17  0.13 9.17  0.16 0.81 1.02
(20)............... 28.6  3.5 12.31  0.17 8.98  0.15 0.76 1.02
Notes.— Quantities were derived similarly to Table 2, except that the radio
data are also incorporated with q
L
¼ 2:14. The estimate of the dust masses addi-
tionally assumes 
d
(850 m) ¼ 0:15 m
2
kg
1
for the dust absorbtion efficiency.
a
These SMGs are identified as being radio-loud. Therefore, the radio data
are not used in constraining the far-infrared SEDs .
SHARC-2 350 m OBSERVATIONS OF DISTANT SMGs 595No. 2, 2006

We included 15% calibration uncertainty in addition to the pub-
lished statistical uncertainties for all submillimeter data. Never-
theless the luminosities a re constrained accurately because the
SHARC-2 350 m measurement falls near the emission peak
for all of these sources (Fig. 3).
Flux boosting or Eddington bias (Coppin et al. 2005), in the
case of less significant detections, where the selection is in the sub-
millimeter, induce a small bias in the derived SEDs. As the bias
will not apply to follow-up measurements, and because the exact
quantification of the Eddington bias is nontrivial, requiring a
priori knowledge of the underlying source distributions, we left
fluxes uncorrected for its effects.
For the first time we are able to use multiband photometry to
accurately determine the characteristic dust temperatures and
far-infrared luminosities for the SMG population. Luminosities
(Tables 2 and 3) are calculated analytically from the fi tted gray-
body model S(; T ), following De Breuck et al. (2003):
L
FIR
¼4D
2
L
(4 þ )(4 þ )
kT
h

4þ
e
h=kT
 1

S(; T );
ð4Þ
where luminosity distances (D
L
) were obtained
6
for a CDM
cosmology with H
0
¼ 65 km s
1
Mpc
1
, 
M
¼ 0:3, and 

¼
0:7. The above expression provides the correc t SED integral as
long as the transition from the optically thin graybody approxi-
mation to optically thick blackbody is above the emission peak
where the contribution to the total luminosity is negligible. If
power-law Wien tails, with spectral slopes of  (Blain et al.
2003), are assumed instead, the luminosities can be scaled by a
constant 

(), which is around 1.5 for an Arp 220 type tem-
plate with  ¼ 2. More generally, in the range of   1:1Y4:0
and   0Y3, the values of  are well appro ximated (with an
rms of 5% or 0.02 dex) by the empirical formula


()  (1:44 þ 0:07)(  1:09)
0:42
:
Similar corrections may be derived for the case of increasing
optical depth, with  as a function of h
0
/kT.
Illuminated dust masses (Table 3) were also estimated from
the SED model S(; T ), using (De Breuck et al. 2003)
M
d
¼
S(; T )D
2
L
(1 þ z)
d
(
rest
)B(
rest
; T
d
)
:
Here the normalization for the absorption efficiency was assumed
to be 
850 m
¼ 0:15 m
2
kg
1
, representing the extrapolated av-
erage 125 mvalueof2:64  0:29 m
2
kg
1
(Dunne et al. 2003)
from various models by assuming  of 1.5. In comparison to the
gas masses derived from
7
CO measurements (Greve et al. 2005;
Tacconi et al. 2006), we find an average gas-to-dust ratio of
54
þ14
11

850 m
/0:15 m
2
kg
1

, resembling t he ratios seen in nu-
clear regions of local gala xies by Seaquist et al. (2004), who
assume a 
d
X
CO
product comparable to our s. The individ ual
measurements indicate an intrinsic spread of ’40% around the
mean value. The low ratios may be interpreted as an i ndication
for the relative p revalence of dust i n SMGs over the local pop-
ulation, which typically exhibit Milky WayYlike gas-to-dust ratios
around 120 (Stevens et al. 2005) or, alternatively, that absorption
in SMGs is more efficient with 
850 m
 0:33 m
2
kg
1
.
Our estimates of the dust temperatures, and hence luminos-
ities, are systematically lower, than those anticipated based on
the 850 m a nd 1.4 GHz fluxes alone by Chapman et al. (2005),
who overestimate these quantities by 13% and a factor of ’2,
respectively, when assuming the local f ar-infrared to radio cor-
relation. This discrepancy can be fully reconciled if a different
constant of correlation is assumed for SMGs ( see x 4).
We confirm that the SMG po pulation is domina ted by ex-
tremely luminous (several times 10
12
L

) systems with ’10
9
M

of heated dust, and characteristic 35 K dust temperatures typical to
actively star forming ULIRGs. As anticipated, these objects re-
semble the nearby archetypal ULIRG, Arp 220 (with T
d
 37 K,
similarly obtain ed), except that they are about 7 times m ore
luminous on average.
3.1. Cold, Quiescent SMGs?
In addition, there appear to be several cooler (T
d
P 25 K), less
luminous (10
11
Y10
12
L

) objects, albeit with comparable dust
masses (few times 10
9
M

) present in the population (sources 14
and 19, and possibly 3, 9, and 10 in Tables 2 and 3). While these
resemble the Milky Way in temperatures, and hence probably in
star fo rmation den sities, they are tens of times more luminous
than the Galaxy.
This combination of extreme dust masses yet surprisingly low
relative star formation rates, indicated by the lesser dust heating,
alludes to possibly incorrect low-redshift identifications. Should
Fig. 3.—Optically thin graybody SED models were fitted (solid lines)tothe
various availa ble observed fluxes and are transformed to the rest frames of the
galaxies for co mparison. Fits using Laurent et al. (2006) data are also sh own
(dashed lines). All the spectra peak in the neighborhood of the redshifted 350 m
point, providing testimony of the pivotal importance of the SHARC-2 data point
in constraining these models. The SEDs shown represent our best fit to the data
for sources detected by SHARC-2, use an emissivity index  ¼ 1:5, and incor-
porate radio fluxes via the far-infrared to radio correlation with q
L
¼ 2:14 with an
assumed 0.12 dex dispersion. [See the electronic edition of the Journal for a color
version of this figure.]
6
See http://www.astro.ucla.edu/wright/CosmoCalc.html.
7
The CO fluxes from Tacconi et al. (2006) were converted into gas masses
using the conversion factor X
CO
of 0:8 M

(K km s
1
pc
2
)
1
in Solomon et al.
(1997) approp riate for ULIRGs ( Downes & Solomon 1998). The results are
therefore consistent with Greve et al. (2005).
KOVA
´
CS ET AL.596 Vol. 650

Frequently asked questions

Q1. What have the authors contributed in "Sharc-2 350 m observations of distant submillimeter-selected galaxies" ?

The authors present 350 m observations of 15 Chapman et al. submillimeter galaxies ( SMGs ) with radio counterparts and optical redshifts. Dust temperatures consistent with 34:6 3 K ( 1:5/ ) 0. 71, at z 1:5Y3:5, suggest that far-infrared photometric redshifts may be viable, and perhaps accurate to 10 % P dz/ ( 1þ z ), for up to 80 % of the SMG population in this range, if the above temperature characterizes the full range of SMGs. These suggest that measurements at a single wavelength, in the far-infrared, submillimeter, or radio wave bands, might constrain dust temperatures and far-infrared luminosities for most SMGs with redshifts at z 0:5Y4. 

Q2. What are the future works in "Sharc-2 350 m observations of distant submillimeter-selected galaxies" ?

The authors would further like to express their gratitude for the generous sponsorship of the National Science Foundation in funding this research. 

Q3. How many SMGs are in the redshift range?

4. Far-infrared- and radio-based photometric redshifts might be appropriate for up to 80% of SMGs in the redshift range of z 1:5Y3:5, with a rest-frame temperature assumption of 34:6 3:0 K(1:5/ )0.71. 

Q4. How do the authors approximate the luminosity distance?

In order to facilitate the derivation of analytic solutions, the authors approximate the luminosity distance by DL D0(1þ z) , the effect of which is to simplify all redshift dependence to powers of (1þ z). 

Q5. What is the fit for the smaller set?

The smaller set, with detection requirement imposed, favors somewhat lower -values, in combination with ‘‘normal’’ qL, with the best fit located at the respective values of 0.95 and 2.27, whereas the more inclusive data set tends toward emissivity indices in line with expectations, but with qL decidedly below the mean in the local universe. 

Q6. What is the effect of the '10% uncertain relative calibration of the bands?

the flattening of the Rayleigh-Jeans slope due to optical depths approaching unity is not detectable with the ’10% uncertain relative calibration of the bands, while theWien side of the spectra is not sampled by the observations. 

Q7. What is the way to obtain a qL-value for distant SMGs?

Obtaining accurate redshifts for distant SMGs has relied on optical measurements, guided by radio or optical associations (Chapman et al. 2003, 2005). 

Q8. How is the dust temperature in SMGs compared to other stars?

Compared with low-redshift galaxies, SMGs are characterized either by low gas-to-dust ratios, around 54þ14 11( 850 m/ 0:15 m2 kg 1), indicating dust-rich environments, or by efficient dust absorption of 850 m k 0:33 m2 kg 1. 

Q9. What is the importance of a longer wavelength submillimeter survey?

Shorter wavelength submillimeter measurements, sampling near the rest-frame peak of the emission, are thus essential to provide firm constraints to the far-infrared SED. 

Q10. How is the calibration expected to be?

The final calibration is expected with high confidence to be more accurate than 15%, with systematic effects anticipated to be less. 

Q11. How do the authors determine the scaling relations between the radio and far-infrared correlations?

6. From the observed L-T relation, possibly biased by selection, and the radio to far-infrared correlation, the authors derive scaling relations among the observed quantities S1:4 GHz, S in the submillimeter or far-infrared, and the observing-frame dust temperature Tobs, applicable to the redshift range of z 0:5Y4. 

Q12. What is the simplest way to derive photometric redshifts?

Luminosity-Temperature RelationAn alternative, luminosity-based approach exploits the hypothetical relationship between dust temperatures and the luminosities that they fuel, to derive photometric redshifts by comparing the rest-frame relationship to observed temperature indicators and fluxes. 

Q13. Why did the authors try to fit a single emissivity slope for the entire sample?

the authors aimed to fit a single emissivity slope for the entire sample, hoping to provide a better constrained, ensemble-averaged, dust emissivity index. 

Q14. What is the way to derive a photometric redshift indicator?

The authors can, nevertheless, derive a true luminosity-based photometric redshift indicator in the low-redshift limit zT1, where the luminosity distance takes the asymptotic formDL ! 

Q15. What is the way to test the validity of this approach?

Only independent, and accurate, measurements of actual dust temperatures for SMGs with known redshifts can test the validity of this approach. 

Q16. How do the authors determine the photometric redshift indicator?

Assuming the exponents and scaling are properly determined, the authors may attempt to derive a photometric redshift indicator by comparing the expressions for the far-infrared luminosity from equations (4) and (8) and from the definitions in equations (6) and (7).