# Ice emission and the redshifts of submillimeter sources

C. C. Dudley  Formerly: Naval Research Laboratory, Remote Sensing Division,
4555 Overlook Ave. SW, Washington, DC 20375-5351, USA
<EMAIL_ADDRESS>M. Imanishi11affiliation:
Department of Astronomy, School of Science, Graduate University for Advanced
Studies, Mitaka, Tokyo 181-8588 National Astronomical Observatory, Mitaka,
Tokyo 181-8588, Japan  P. R. Maloney  Center for Astrophysics and Space
Astronomy, University of Colorado, Bolder, CO 80309-0839, USA

###### Abstract

Observations at submillimeter wavelengths have revealed a population of
sources thought to be at relatively large redshifts. The position of the 850
$\mu$m passband on the Rayleigh-Jeans portion of the Planck function leads to
a maximum redshift estimate of $z\sim$4.5 since sources will not retain their
redshift independent brightness close to the peak of the Planck function and
thus drop out of surveys. Here we review evidence that ice absorption is
present in the spectra of local ultraluminous infrared galaxies which are
often taken as analogs for the 850 $\mu$m source population. We consider the
implication of this absorption for ice induced spectral structure at far
infrared wavelengths and present marginal astronomical evidence that amorphous
ice may have a feature similar to crystalline ice near 150 $\mu$m. Recent
corroborative laboratory evidence is supportive of this conclusion. It is
argued that early metal enrichment by pair instability SN may lead to a high
ice content relative to refractory dust at high redshift and a fairly robust
detection of ice emission in a $z=6.42$ quasar is presented. It is further
shown that ice emission is needed to understand the 450 $\mu$m sources
observed in the GOODS-N field. We are thus encouraged to apply far infrared
ice emission models to the available observations of HDF 850.1, the brightest
submillimeter source in the Hubble Deep Field. We suggest that a redshift as
large as 13 may need to be considered for this source, nearly a factor of
three above the usual top estimate. Inclusion of the possibility of far
infrared ice emission in the spectral energy distributions of model sources
generally broadens the range of redshifts to be considered for submillimeter
sources compared to models without ice emission.

galaxies: high redshift, formation — infrared: galaxies — galaxies:
individual: IRAS 00188-0856, IRAS 14348-1447, QSO J1148+5251, HDF 850.1

##  1 Introduction

Sources discovered in surveys undertaken using 450/850 $\mu$m SCUBA camera
mounted on the JCMT have a high number density per unit solid angle ($\sim$
104 deg-2; S${}_{850}>$ 1 mJy; Sanders 2000; Wang et al. 2004) and are thought
to trace the dust emission from sources at a range of redshifts. Sources
brighter than 1 mJy which have Arp 220-like far infrared (FIR) spectral energy
distributions (SEDs) are ultraluminous in the $h_{100}=0.71$,
$\Omega_{m}=0.27$, and $\Omega_{\Lambda}=0.73$ cosmology consistent with
cosmic microwave background (CMB) and Type 1a SNe observations (Spergel et al.
2003; Nolta et al. 2004; Riess et al. 2004) unless they are at redshifts $<$ 1
so that, thus far, submillimeter surveys do not detect “normal” galaxies at
high redshift. This should be the case even for gravitational lens
amplification up to a factor of 4 for 2 mJy limit surveys.

It is therefore a sensible approach to consider the properties of local
ultraluminous infrared galaxies (ULIRGs; Sanders & Mirabel 1996) as a guide to
understanding sources detected in submillimeter surveys with the proviso that
the high redshift universe may not conserve these properties. It has already
been noted that the number density of ULIRGs increases with redshift at a rate
much larger than can be explained using geometric considerations alone (Kim &
Sanders 1998) and deep field observations using the Hubble Space Telescope
have found quite obvious morphological evolution at higher redshifts compared
to local conditions (e.g. Brinchmann et al. 1998). While these particular
evidences of evolution as a function of redshift do not directly speak to
ULIRG SED evolution, they do suggest that this proviso cannot be lightly
discounted.

Ice is present in the dense ISM of the Galaxy. It is observed to occur above a
threshold depth of A${}_{V}\sim$ 3 within molecular clouds but is absent on
the cloud edges and in the diffuse (atomic/ionized) ISM (Whittet et al. 1988).
Because ice is not exposed to star light, far infrared (FIR) emission from ice
is not expected from quiescent clouds. The FIR emission from these ice bearing
clouds arises from the first few ice-free AV. To observe ice emission in the
Galaxy, centrally heated sources are needed. If mid-infrared (MIR) radiation
can illuminate the ice bearing grains so that they may be heated, then the FIR
emission will be dominated by ice if the ice mantles provide a moderate
fraction of the total grain volume. This FIR dominance is owing to greater FIR
opacity of ice relative to silicate or carbonaceous grains. In the models
presented by Aannestad (1975), a mantle-to-core volume ratio of 0.33 doubles
the 60 $\mu$m opacity: a 10% increase in grain radius doubles the opacity!

Protostars in the Galaxy which are centrally heated turn out to be good
sources for observing FIR ice emission (e.g. Dartois et al. 1998). And, there
is mounting evidence that a significant fraction of local ULIRGs are also
centrally heated (Dudley & Wynn-Williams 1997; Soifer et al. 2002; Imanishi &
Dudley 2000; Imanishi & Maloney 2003; Imanishi et al. 2006a; Spoon et al.
2006) so that the FIR emission is a result of MIR heating. Thus, if ice is
present in the FIR emitting regions, its effects on the FIR opacity may be
important. This situation differs from what occurs in lower luminosity
starburst galaxies where the FIR emission arises from the surfaces of
molecular clouds which are heated by optical and far UV rather than MIR light.
The interiors of the clouds, where ice presumably exists, are not strongly
heated by the mainly FIR emission arising from their surfaces.

If submillimeter galaxies are similar to ULIRGs in more than just their
luminosity, then they may also sometimes have FIR emission that is powered by
MIR light. For redshift estimation the question of the similarity between
submillimeter galaxies and local ULIRGs is as important as the differences
that distinguish ULIRGs from their lower luminosity starburst counterparts.

Attempts to estimate redshifts for the submillimeter sources based on their
radio fluxes could be guided by local ULIRG samples. For the 13 ULIRGs
brighter than 5.24 Jy at 60 $\mu$m (Soifer et al. 1987; Sanders et al. 1995)
available to the VLA, the mean logarithm of the ratio of FIR-to-20 cm radio
flux is 0.22 dex larger than $q$=2.43$\pm$0.19 (Condon et al. 1991) for
starburst galaxies when calculated using radio measurements reported by Condon
et al. (1991) and Yun et al. (2001). While the mean differs at only the
1$\sigma$ level, the dispersion of $q$ is a factor 1.6 (in dex) larger than
for the lower luminosity star forming galaxies. Using a different luminosity
binning, Helou et al. (1985) report a similar trend in increased dispersion
with increasing luminosity. The implication for redshift estimation is that
the range of likely redshifts would increase when using ULIRG properties
rather than starburst properties. And, a trend away from what is seen in local
ULIRGs, say through more powerful starbursts at earlier times, could have
complex implications for estimating redshifts of submillimeter galaxies using
radio observations.

However, broad limits on the redshift distribution derive from submillimeter
observations alone where the relative infrequency of detecting 450 $\mu$m
emission leads to (weak) lower limits on the redshifts while the detections
themselves at 850 $\mu$m lead to upper limits since, baring extraordinary
luminosities, the turnover from the Rayleigh-Jeans-like portion of the SED at
high redshift leads to source fluxes dropping below survey detection limits.

Given the large potential effect of ice on the FIR opacity of submillimeter
galaxies, we first review the evidence for the presence of ice in centrally
heated ULIRGs and estimate an expected FIR SED for a case where FIR ice
opacity can be expected to be dominant based on a rough abundance analysis. We
then search for FIR ice spectral features in the available data on ULIRGs. We
discuss why a high relative abundance of ice during the epoch of reionization
might be expected and present somewhat firmer evidence for FIR ice emission in
the $z=6.42$ source QSO J1148+5251 than can yet be demonstrated for ULIRGs. We
then take the submillimeter galaxy HDF 850.1 as an example to show how FIR ice
emission allows a very large redshift estimate.

##  2 Ice in ULIRGs

###  2.1 Absorption

Observations of strong absorption features from refractory dust in ULIRGs
trace dust that is cooler than the temperature of a blackbody emitting at the
wavelength of the feature: $\sim$ 300 K for the 10 $\mu$m silicate feature and
$\sim$ 150 K for the 20 $\mu$m silicate feature for example. Thus, 20 $\mu$m
silicate features are weak in ULIRGs compared to 10 $\mu$m features owing to
the dust radial temperature gradient. Ice absorption, on the other hand,
should only occur in the cooler outer regions of the dust envelope and so may
show the same relative feature strengths found in the laboratory unless the
absorbing covering factor is a strong function of the emitting source’s
wavelength dependent size (buried source radius $r\approx 0.8({L\over
10^{12}L_{\odot}})^{0.5}({\lambda\over 3\mu m})^{2}$ pc where T has been
eliminated between the Wein Displacement and Stefan-Boltzmann Laws, $L$ is the
portion of IR luminosity corrected for extended star formation, $\lambda$ runs
from 2 $\mu$m to the lesser of either the wavelength where the source is no
longer optically thick or the peak FIR wavelength and scattering is
neglected). MIR ice absorption is therefore consistent with a portion of the
FIR emission being powered by the MIR rather than the optical and UV portion
of the electromagnetic spectrum. However, it is necessary to be certain that
the reported absorption is indeed owing to ice. As an example, Spoon et al.
(2002) claim ice absorption in 18 galaxies based on 6 $\mu$m absorption
including IRAS 17208-0014 the third brightest ULIRG. However OH bond bending
needn’t occur in ice alone. The absence of 3 $\mu$m absorption in the spectra
of the dust continuum dominated sources Mkn 231 and IRAS 05189-2524 presented
by Spoon et al. (2002), where veiling by starlight is unimportant, suggests
that an identification of water ice may be premature for these sources and
refractory materials such as those studied by Greenberg et al. (1995) may
provide a more convincing model. An apparent 6 $\mu$m dip in the spectrum of
Mkn 231 plotted by Weedman et al. (2005) similar in amplitude to the 6.2
$\mu$m hump for which they report a measurement tends to confirm the Spoon et
al. (2002) claim of 6 $\mu$m absorption in this source. The spectrum of Arp
220 may be consistent with a contribution of 12.5 $\mu$m libration mode
absorption, supportive of the Spoon et al. (2002) identification of ice
absorption in this source but, until recently (Imanishi et al. 2006a; Risaliti
et al. 2006; Imanishi 2006), the only well confirmed case of ice absorption
among ULIRGs in their sample was that of IRAS 00188-0856 where ice absorption
at 3 $\mu$m confirms the identification (Imanishi & Maloney 2003). See
Imanishi et al. (2006b) for further well confirmed ice identifications.

To illustrate this we present Fig. 1 which employs a slightly detailed model
to explain the absorption features observed between 2.7 and 12.4 $\mu$m. The
upper panel reproduces the 3 $\mu$m spectrum reported by Imanishi & Maloney
(2003) together with an absorption model composed of amorphous ice and
refractory carbonaceous absorption applied to a power-law continuum, and
veiled by some starburst-like emission. The model is then applied in the lower
panel with some adjustment made for expected reduced refractory absorption at
longer wavelengths owing to a presumed dust temperature gradient. It has not
been possible to fit the entire 3 $\mu$m absorption without using ice. Thus,
the absorption at 6 $\mu$m also is partly attributed to water ice. With these
data, 12.5 $\mu$m water ice absorption, while included in the model, does not
seem to be required so that one may conclude that two features, and
particularly the degeneracy breaking short wavelength edge of the 3 $\mu$m
absorption contribute to the fairly robust identification of ice in IRAS
00188-0856. We note that the need for strong silicate absorption in this
source is confirmed by the clear presence of 18 $\mu$m silicate absorption
(Imanishi et al. 2006b)

Thus, ice absorption could play a significant role in ULIRGs, but the evidence
is not yet as strong as that showing that the MIR emission is often absorbed
by refractory dust. Evidence for or against FIR ice emission or absorption in
ULIRGs is in worse shape still. This is primarily owing to a lack of
observational data. In Fig. 2 we present archival ISO LWS spectra of Mkn 231
(filled diamonds) and IRAS 17208-0014 (filled circles) which show spectral
structure in the shortest wavelength detector band SW 1. This structure is
compared to the spectrum of the icy source HD 161796 (Hoogzaad et al. 2002)
transformed to absorption. For Mkn 231, as just noted, the absence of 3 $\mu$m
ice absorption would lead to somewhat strained geometric arguments to allow
acceptance of the Spoon et al. (2002) identification of the 6 $\mu$m
absorption, but once made, such arguments would likely allow absorption at
even longer wavelengths. A complex geometry has already been invoked for this
source on a smaller physical scale to explain its low X-ray flux (Maloney &
Reynolds 2000). For IRAS 17208-0014, the present spectrum would tend to
confirm the Spoon et al. (2002) identification of the 6 $\mu$m absorption as
do 3 $\mu$m spectra (Risaliti et al. 2006; Imanishi 2006). For either source,
the presence of crystalline ice implied by the possible 43 $\mu$m absorption
would imply a low cosmic ray abundance at least in the region where the
absorption is produced since ion bombardment erases crystalline structure in
cold ices (Moore & Hudson 1992). The inset in Fig. 2 shows the relationship
between the wavelength of the 43 $\mu$m peak and ice temperature measured by
Smith et al. (1994) which we have invoked to shift the ice spectrum derived
from HD 161796, an evolved ice forming star (Hoogzaad et al. 2002), beyond the
corrections made for the source redshifts to better match the spectra.
Inversion of these corrections would imply temperatures at which amorphous ice
may exist and would be preferentially formed. Constraints on cosmic ray
abundance would need account for the rate at which crystalline ice is
introduced into the absorbing region either through (substantial) changes in
luminosity of the source which may allow the annealing of amorphous ice to
crystalline ice, processing of ice by local heat sources in the region, or the
migration of crystalline ice into the region. The discovery of substantial
radial molecular gas motion in the ULIRG IRAS 08572+3915 (Geballe et al. 2006)
suggests the third possibility needs close scrutiny. Since the SW1 detector of
LWS is problematic, these sources must be independently re-observed and the
potential features confirmed before fully accepting that ice is present in
these sources.

###  2.2 Millimeter morphology

We have examined the LWS SW1 spectra of a two other ULIRGS, Arp 220 and Mkn
273, finding no feature consistent with crystalline ice absorption. In the
case of Arp 220, the FIR spectrum appears to be optically thick (González-
Alfonso et al. 2004). There is every reason to think ice should be present
owing to the source temperature, the clear presence of water vapor, as well as
supportive MIR observations already mentioned. Here, ice may help to resolve
an issue raised by Soifer et al. (1999) with regard to FIR sources that are
optically thick showing any detectable emission in the MIR owing to
overwhelmingly large implied MIR opacity. Since ice strongly enhances the FIR
opacity compared to refractory dust, a given FIR optical depth can be achieved
with less dust, up to a factor of seven in the models computed by Aannestad
(1975). This effect can make the issue raised by Soifer et al. (1999) less
troubling, though other approaches such as examining the effects of the dust
density distribution (e.g. Nenkova et al. 2002) may also need to be explored
as well. Ice may also have the effect of making millimeter continuum size
estimates smaller than what might be expected for refractory dust that is
optically thick in the FIR since the opacity of ice mantled grains is lower
than that of bare grains at millimeter wavelengths. This could yield a cuspy
morphology in the millimeter where one would usually expect a relatively more
flattened morphology owing to the cooler outer regions being relatively
brighter in the millimeter under the assumption of higher refractory dust
opacity.

###  2.3 FIR ice spectrum

The infrared laboratory spectrum of crystalline water ice has been well known
for some time (Bertie et. al 1969) and differences between the spectrum of
crystalline and amorphous ice have been exploited to aid understanding of
astronomical sources (e.g. Dartois et al. 1998). However owing to the low
thermal conductivity of amorphous ice, preparation of laboratory samples, via
vapor deposition, that are thick enough to conduct investigations at
wavelengths longer than 100 $\mu$m has been too difficult until recently. In
particular it has been unknown whether or not amorphous ice has a feature
corresponding to the broad feature centered near 150 $\mu$m identified by
Bertie et. al (1969) as a phonon mode in crystalline ice. Since nature
provides sources rich in amorphous ice, it may be that such a comparison could
be made through observations of these sources. The spectral coverage of the
ISO LWS spectrometer extended to $\sim$ 200 $\mu$m, too short to fully cover
the broad 150 $\mu$m crystalline ice feature. Comparison between the ISO LWS
data presented by Dartois et al. (1998) for RAFGL 7009S, a deeply embedded
ultracompact H II region, and the submillimeter observations provided by
McCutcheon et al. (1995) yield a modified optically thin blackbody parameter
set of T=27 K, $\beta$=2.1 (where the dust emissivity is proportional to
$\lambda^{-\beta}$) when attempting to the match data near 190 $\mu$m. The
large value of $\beta$ is suggestive of the presence of a feature similar to
that of crystalline ice in this amorphous ice dominated source. However, full
spectroscopic confirmation is needed to decide if the long wavelength
departure of the data from the model of Dartois et al. (1998) indicates the
existence of an amorphous ice feature analogous to the 150 $\mu$m crystalline
ice feature.

Laboratory work by Curtis et al. (2005) has explored the optical properties of
amorphous ice between 15 and 200 $\mu$m. There is little question that most of
the ice in the thick films used by Curtis et al. (2005) deposited at $T\leq
126$ K differs from ice deposited above this temperature since the wing of the
libration band is clearly shifted so it seems safe to conclude that amorphous
ice, clearly present in the thinner samples, is also largely present in the
thicker samples despite issues related to the low thermal conductivity of
amorphous ice which hampers the (rapid) growth of thick samples. Gerakines et
al. (2005) have also had recent success in growing thick samples of amorphous
ice using low deposition rates. Schober et al. (2000) take a different
approach: annealing samples of high density amorphous ice into the low density
amorphous ice found in space. As with the LWS spectroscopy, the new amorphous
ice optical constants (Curtis et al. 2005) do not extend to the wavelength
regime (300 $\mu$m) where crystalline ice shows absorption whose wavelength
dependence is described by $\lambda^{-4}$ (Bertie et. al 1969). Unlike natural
sources, however, where temperature and grain size effects make full spectral
coverage of a broad feature nearly absolutely necessary to ascertain its
reality, the controlled laboratory conditions allow a reasonable extrapolation
to be considered reliable. The finding of Curtis et al. (2005) that the
imaginary part of the refractive indices of amorphous and crystalline ice are
very similar between 100 and 200 $\mu$m would appear to be consistent with the
suggestion of Schober et al. (2000) that the order in amorphous ice indicated
by sharp features in inelastic X-ray scattering data may be owing to a
hydrogen network that is also present in crystalline ice. If this order is
indeed present, then a shared spectral structure for the interaction of (FIR)
photons with phonons between the two types would allow a first order
substitution of crystalline ice optical constants for the unknown values for
amorphous ice beyond 200 $\mu$m.

###  2.4 FIR ice emission

Turning to photometry, and returning to ULIRGs, if we accept the Spoon et al.
(2002) classification scheme then the spectrum of IRAS 14348-1447 as reported
by Genzel et al. (1998) or Charmandaris et al. (2002) must be considered Class
II, that is 6 $\mu$m “ice” absorption is present and partially filled in by
6.2 $\mu$m polycyclic aromatic hydrocarbon emission. This source occupies an
extreme position in the dust emissivity ($\beta$) vs. 100 $\mu$m optical depth
($\tau_{100}$) diagram given by Klaas et al. (2001) with both high
$\tau_{100}$ (5) and $\beta$ (2). Since the effects of optical depth and
emissivity are intertwined, a lower optical depth can imply a larger value of
$\beta$. For example, $\beta=2.4$ and $\tau_{100}=0.1$ does about as well as
the Klaas et al. (2001) parameters for data longward of 100 $\mu$m. However,
values of $\beta$ larger than 2 are not generally found except where ice is
thought to be present (e.g. Lis et al. 1998) or dust temperatures are lower
than found in ULIRGs (67 K for the Klaas et al. (2001) fit or 26 K at the
lower optical depth and larger $\beta$ tested here). In Fig. 3 we compare the
fit proposed for IRAS 14348-1447 by Klaas et al. (2001) with an alternative
model. The model shown by the dashed line is that of Klaas et al. (2001),
while that shown by the thick solid line is a core-mantle grain model taken
from Aannestad (1975) but modified to have amorphous ice features in the
following way: First, opacity data from Smith et al. (1994) for crystalline
ice cooled to 70 K was matched to the Aannestad (1975) curve for Vm/Vc=0.95 by
inducing a $\nu^{-1}$ dependence to approximate the Mie calculation results
along with the addition of an underlying continuum opacity. Second, amorphous
ice opacity data (Smith et al. 1994; deposited at 10 K and warmed to 70 K) was
substituted between 30 and 70 $\mu$m based on this matching after adjustment
for the differing sample thicknesses. This opacity curve was used to calculate
a model with 16 and 71 K components. If we take temperature and optical depth
as free parameters for the Klaas et al. (2001) fit (2 parameters;
normalization fixed by IRAS) and two temperatures, two optical depths, and the
relative contribution at 90 $\mu$m of these two components as 5 free
parameters for the present model then we may estimate how well the two models
represent the data if we know something about the errors in the data. The
statistical errors for the data are thought to be small but the absolute
calibration error could be large, $\sim$30%. What is important for comparing
models is the relative accuracy from filter to filter. We have thus assumed
13% errors for the ISOPHOT data to give a filter-to-filter accuracy of 20%
(Klaas et al. 2000). The fit of Klaas et al. (2001) for data longward of 20
$\mu$m is unacceptable (P($\chi^{2}$,$\nu$)=0.02) under our assumption about
the errors. A marginally acceptable fit (P($\chi^{2}$,$\nu$)=0.4) is found for
the amorphous ice model. Detailed inspection of the ice fit suggests that the
150 $\mu$m ice feature is not accounting for all of structure in the data. The
thin solid line (Vm/Vc=0.33, T=28.8 K; $\tau_{90}=0.2$ and Vm/Vc=0.95, T=80.5
K, $\tau_{90}=0.08$ crystalline ice; onion-skin model with warm, T=180 K,
refractory dust in the interior) shows that this might be possible. However,
our method of substituting amorphous for crystalline ice is unlikely to work
well for the thin mantle used here. Given the assumption regarding the data
errors made here, it is not possible to make a clear claim that ice emission
is detected in this source. Assuming larger errors could make both low free
parameter models acceptable while reducing the errors could make the simpler
ice model unacceptable while the more complex model cannot be evaluated via
reduced $\chi^{2}$. Clearly, Spitzer MIPS SED mode observations could be
definitive since the strong 70 $\mu$m curvature in the ice models cannot be
produced with standard refractory dust.

Thus, both astronomical and laboratory far infrared data leave questions about
ice unanswered. Crystalline ice has a feature near 150 $\mu$m which has yet to
be completely compared with amorphous ice. Comparison between crystalline and
amorphous ice has been made near 40 and 60 $\mu$m and they are quite distinct
whereas they are similar between 100 and 200 $\mu$m. Beyond 200 $\mu$m
questions remain which are presently answered by extrapolation of the
laboratory data and hints from the astronomical data. Substituting crystalline
ice for more common (in space) amorphous ice to consider wavelengths longer
than 100 $\mu$m could add to (systematic) uncertainties in photometric
redshift estimation that can not be well addressed without further
observations or measurements. Regardless of the remaining issues concerning
the 150 $\mu$m feature, for the main purpose of this work it is prudent to
consider the more extreme consequences of crystalline ice emission on redshift
estimation which are examined after the next section.

##  3 Ice at high redshift

###  3.1 Pair instability SNe enrichment

Just as interplanetary grains may preserve a record of the sources of ISM
enrichment occurring at what is presently observed to be $z=0.43$, the solid
phase of the ISM at high redshift may also record the conditions of the
earliest enrichment. Particularly for sources that contribute to the
reionization of the universe ($7<z<14$; Spergel et al. 2006), scenarios which
attribute substantial enrichment to pair instability SNe early on may leave a
mark on the solid phase of the ISM which could linger through some subsequent
processing. A chief attribute of pair instability SN enrichment is an early
high abundance of oxygen relative to other metals that usually deplete to the
the solid phase of the ISM.

For example, a 186 M⊙ progenitor yields number abundance ratios of
O:Si:C:S:Mg:56Ni = 126:29:15:10:8:1 (Heger & Woosley 2002) which, after
formation of CO (29 O removed), olivine (16 O and 4 Si removed), silica (50 O
removed), and SO2 (20 O removed), leaves 9% of the oxygen available to form OH
and H2O. For a 100 M⊙ progenitor, O:C:Mg=48:9:1 with little Si, S or 56Ni
leaving 80% of the oxygen available to combine with hydrogen assuming the
refractory solid state is MgO. In the absence of 56Ni, the formation of solids
should be enhanced since it may commence at a higher density in the SNR. These
estimates for the available oxygen are essentially lower limits, more complete
treatments which consider the possibility that the ejecta are unmixed (Nozawa
et al. 2003; Schneider et al. 2004; allowing the formation of graphite for
example) would leave an even larger fraction of oxygen available. Thus, we
might expect grains with large mantle-to-core volume ratios to result from a
period of pair instability SN enrichment. The continued presence of these ice
grains would depend on the rate of reprocessing of this initial solid phase in
the ISM.

###  3.2 Ice emission in a high redshift quasar

The Gunn-Peterson trough in QSO J1148+5251 ($z=6.42$; Bertoldi et al. 2003b)
suggests that this source may be participating in the last phases of
reionization (Fan et al. 2003). That the quasar exists indicates that the
source has been contributing to reionization for some time and we may take the
beginning of reionization as an estimate of it’s age ($\sim$500 Myr) which
gives a high average accretion rate for a blackhole mass of $3\times 10^{9}$
M⊙ (Willot et al. 2003). Thus, it seems plausible that pair instability SN
enriched material with a high ice content is being supplied toward the center
of this activity as the blackhole and presumably its stellar system grow in
mass. On the other hand, ice also forms in the more evolved ISM of the Galaxy
so an indication of the presence of ice needn’t be fully attributed to ice
rich regions that might be formed by pair instability SNe.

Fig. 4 shows an indication that the rest frame FIR emission from QSO
J1148+5251 is better explained by ice than refractory dust emission. Three
models are compared to photometric observations: 1) a refractory model (dashed
line T=55 K; $\tau_{60}=0.3$; $\beta=2$) is similar to that given by Beelen et
al. (2006), 2) a simple ice model (dot-dashed line; T=43 K; $\tau_{60}=0.4$,
Vm/Vc=5.6 amorphous), and 3) a more complex ice model described below (solid
line).

In Fig. 4, it is not possible to formally access the goodness of fit through a
reduced $\chi_{\nu}^{2}$ calculation even for the refractory dust model
(dashed line) since the number of free parameters (normalization, temperature,
optical depth, and opacity index) is the same as the number of points to be
fit. If one were to assume $\beta=2$ owing to insufficient time since the
first enrichment to produce large grains then $\chi_{\nu}^{2}=10.7$ which
strongly rules out (P($\chi,\nu$)=0.001) this model. That the fit is done by
eye probably does not affect this assessment but a failure to account for
systematic errors could since different groups give 850 $\mu$m photometric
estimates using the same data that vary by as much as the refractory dust
model differs from the present data. By selecting a particular mantle-to-core
volume ratio (5.6) we may comparably provide a single degree of freedom and
obtain $\chi_{\nu}^{2}=3.9$ (dot-dashed line) which would indicate that the
model is not fully ruled out by the data (P($\chi,\nu$)=0.05) and is an
improvement on the refractory dust model, again with the proviso that we have
only considered statistical errors. More elaborate (multi-temperature)
refractory dust or ice mantled grain models can fit the detections essentially
perfectly and are useful to calculate as they can indicate what further
observations would be decisive. The solid line in Fig. 4 is such a model where
T=71 K; $\tau_{60}=0.4$ ice-mantled dust is obscured by T=24 K;
$\tau_{60}=0.4$ ice-mantled dust. A similar model using $\beta=2$ refractory
dust (not plotted; T=300 K; $\tau_{60}=0.1$ is obscured by T=18 K;
$\tau_{60}=1$ dust) exceeds the plotted 400 $\mu$m upper limit (arrow in Fig.
4; 0.39 mJy 3$\sigma$; Bertoldi et al. 2003a) by a factor of 1.9 and is
unphysical in a number of ways including that the cool component is cooler
than the CMB at $z=6.42$. The ice models distinguish themselves from the
plotted refractory dust model by being fainter by at least a factor of 4 at
rest wavelength 400 $\mu$m (3 mm observed frame). The present upper limit does
not distinguish these cases. Such a measurement should be possible using
CARMA. Determining the composition of the emitting material can also affect
estimates of the dust mass and thus estimates of the amount of past enrichment
(and star formation) in the QSO J1148+5251 system. For the present ice model,
7 times as much refractory dust would be needed to produce the same FIR
opacity so that a lower level of total enrichment might be accommodated.

Finally, at high redshift, where theory suggests that we might most anticipate
it owing to expectations about early ISM enrichment, we find evidence for FIR
ice emission which, while still debatable, seems moderately persuasive and
which can be relatively easily checked with further observations using
existing telescopes. Now we may turn to our main theme. We have employed
amorphous ice to consider IRAS 14348-1447 and QSO J1148+5251, but now we
consider crystalline ice both because its effect on redshift estimation is the
most dramatic and because ice may form at fairly warm temperatures in the SNRs
associated with pair instability SNe.

###  3.3 Ice emission in 450 $\mu$m submillimeter sources

A set of sources that could be at high redshift and which demonstrate the
effects of ice are reported by Pope et al. (2005). They are detected at 450
$\mu$m but not at 850 $\mu$m. We consider the 7 sources tabulated by Pope et
al. (2005) and two sources from the original list of Borys et al. (2003) which
were recovered above 3.5 $\sigma$ by Pope et al. (2005). These have drawn our
attention because the reported 850 $\mu$m upper limits indicate large values
of $\beta$ (Borys et al. 2004; based on original list). Large values of
$\beta$ can indicate the presence of ice emission. If we generate 3$\sigma$
lower limits to the 450-to-850 $\mu$m flux density ratios using the 450 $\mu$m
measurements less 3/$\sqrt{(}2)\times\sigma_{450}$ together with
3/$\sqrt{(}2)\times\sigma_{850}$ 850 $\mu$m upper limits then the lowest lower
limit is 8.7 and is only one of two that can be consistent with $\beta<2$
dust. This method of calculating limits can be more conservative than
calculating the ratio of the 450 measurement to the 850 $\mu$m 3$\sigma$ upper
limit (giving 13.4 in this case) but its extension to 2$\sigma$ should be
viewed with caution since detections at the 2.9 $\sigma$ level are customarily
reported as 3$\sigma$ limits. In such situations, when data with comparable
signal-to-noise ratios become available, the “2$\sigma$ extension” may be
violated much more frequently than the name implies if many of these near
misses lurk in the original data. However, Pope et al. (2005) report no
detection from applying the method of Caillault & Helfand (1985) (stacking) to
the 850 $\mu$m data at the positions of the 450 $\mu$m sources they detect
above 3.5$\sigma$. In five cases where upper limits are calculated below we
substitute the ratio of the 450 $\mu$m 3$\sigma$ upper limit-to-the 850
measurement when it gives a more conservative value.

In Fig. 5 we plot, as a function of redshift, the 450-to-850 $\mu$m flux
density ratio calculated for a series of SEDs. The dashed line is for a model
with T=60 K, $\beta$=2, and $\tau_{90}$=2. On this line are plotted at $z=0.9$
and $z=0.5$ the 3$\sigma$ lower limits (filled circle and diamond) for SMM
J123603+620942 and J123631+620657. The arrows in the figure extend to the
2$\sigma$ lower limits. In these cases the argument given by Borys et al.
(2003) for $z<1$ may be applied directly, though tenuously, at the 3$\sigma$
level with no assumptions about ice but this is not the case for the 7
remaining lower limits. There may be some difficulty however accommodating
these two sources at these low redshifts unless sources with 0.2–2 Jy level
flux densities are present at 70 $\mu$m while Frayer et al. (2006) find about
four $\sim 30$ mJy sources at 70 $\mu$m in this region and we are unaware of
any IRAS sources in this field. At these low redshifts, it is a losing
proposition to attempt to increase the dust temperature to increase the
redshift to avoid the 70 $\mu$m constraint in an effort to avoid requiring ice
emission. When ice is invoked, then these and the remaining lower limits may
all be accommodated but the range of consistent redshifts expands. The
remaining curves in Fig. 5 correspond to increasing ice temperature. The dot-
dashed curve uses an SED similar to that shown in Fig. 1 (T=30 K), the triple-
dot-dashed curve has T=50 K as in Fig. 7., and the solid curve has T=150 K;
$\tau_{90}=0.04$ and Vm/Vc=5.6 for all ice models. For the solid curve,
ambiguity between amorphous and crystalline ice is physically resolved in
favor of crystalline ice. The SMM J123603+620942 and J123631+620657 limits are
replotted on the solid curve giving a redshift limit $z<10.2$. This limit is
little changed if the maximum possible ice temperature (170 K) is used. All
the 3$\sigma$ limits can be accommodated at $z=9.5$ but only SMM
J123603+620942 and J123631+620657 can also be accommodated there at the
2$\sigma$ level. SMM J123657+622033 (filled square) shows this clearly where
it is plotted at $z=9.6$. The 2$\sigma$ level for SMM J133747+621600 (filled
clover leaf) also constrains the ice temperature to be T$\gtrapprox$40 K. It
is plotted on the T=30 K curve at $z=1.9$. The remaining sources other than
SMM J123727+621042 are plotted with redshift upper limits well within the
epoch of reionization. However, as with sources plotted on the T = 30 K curve,
the 2$\sigma$ limits cannot be accommodated for $z\gtrapprox 2.5$. That 7 of 9
of the 450 $\mu$m sources in the GOODS-N field require ice to explain the 850
$\mu$m non-detections without recourse to any other constraint suggests
strongly that the possible effects of ice emission must be considered when
interpreting submillimeter observations. Ice dramatically changes redshift
limits: by a factor of 20 for SMM 123631+620657.

From the other direction, for the sources with 850 $\mu$m detections and 450
$\mu$m upper limits that also have estimated redshifts (Borys et al. 2004) we
may also begin to constrain the presence of ice. 14 upper limits are plotted
in Fig. 5 as open circles for sources where a redshift estimate is given. The
open diamonds are also upper limits plotted (but without arrows to avoid
crowding) at the lower limits to their redshift given by Borys et al. (2004).
For redshift estimates with $z<3$ the upper limits are constraining on the
likelihood that optically thin ice contributes to the FIR opacity: at the
2$\sigma$ level (arrow heads) little T$>$30 K optically thin ice seems to be
needed. At the 3$\sigma$ level 4 of 11 sources could be consistent with a
contribution of optically thin ice emission to the source SEDs. One source
with a redshift lower limit ($z>2.7$; SMM J123652+621225) needs to be
optically thick and cool (T $\sim$40 K) or at a higher redshift as already
noted by Borys et al. (2004). The remaining sources with with redshift
estimates above 3 or redshift lower limits are not constraining on the
presence of ice. The present considerations suggest that the 450 and ($z<3$)
850 $\mu$m detected sources differ physically in that the former have
optically thin ice emission that dominates their FIR opacity while the latter
may be optically thick at 850/(1+$z$) $\mu$m or that refractory dust dominates
their FIR opacity or both. The average 450-to-850 $\mu$m ratio for the 850
$\mu$m source calculated from the stacked 450 $\mu$m and the average of the
850 $\mu$m flux densities reported by Pope et al. (2005) is 0.5 which we have
plotted as a small open square at $z=4.25$. The plotted redshift would be
consistent with T=30 optically thick material or T=20 optically thin ice or
$\beta=2$ dust. If it is true that 850 $\mu$m sources are on average fainter
at 450 $\mu$m than at 850 $\mu$m then it seems at though many of the 850
$\mu$m sources must lie at $z>4$ and ice may be needed to make them detectable
at 850 $\mu$m with ULIRG luminosities (see end of Sec. 4.2). We do worry,
however, that the stacked 450 $\mu$m flux is underestimated owing to the
smaller 450 $\mu$m beam or that the data were normalized prior to stacking
making the reported units ambiguous. QSO J1148-5251 is also plotted (small
filled circle). As discussed above, it seems to require ice emission.

Just as detected 850 $\mu$m sources must be at least ultraluminous, so also
must the detected 450 $\mu$m sources be hyperluminous (L$>10^{13}$ L⊙). In
Fig. 6 we plot the models shown in Fig. 5 giving their 450 $\mu$m brightness
as a function of redshift under the following assumptions about luminosity:
The models for refractory dust, and ice at T=30 and 50 K are ten times more
luminous than ULIRG IRAS 00188-0856 (Fig. 1), the model for T=150 K ice is 10
times more luminous still, and we have also plotted the complex amorphous ice
model for QSO J1148+5251 at it’s observed luminosity (short dashed line and
filled circle; $\sim 10^{13}$ L⊙; Beelen et al. 2006). The brightnesses of the
450 $\mu$m sources given by Pope et al. (2005) lie in the range 77-to-291 mJy
so that the plotted models would need to be scaled up by a factor of a few to
cover this range fully unless the sources are at $z<0.2$. For example, one of
the brighter sources (SMM J123631+620657; 263 mJy) would have a luminosity of
6$\times 10^{14}$ L⊙ for the T = 150 K ice model if located at $z=9.5$, a
factor of three higher than the most luminous hyperluminous source listed by
Verma et al. (2002). It’s luminosity would be 10 times lower for the T = 30 K
ice model located at $z=2$, near the middle of the distribution of
luminosities in their list. From Fig. 5 we estimate that the 450 $\mu$m
sources would populate the redshift ranges 1–3 and 5–10, with the latter range
having a larger comoving volume by a factor of 1.7. If ice is only important
close to reionization so that the sources were all at 9.2$<z<10.2$ (see solid
line in Fig. 6) then the luminosities require about a tenth of the stellar
mass of M87 per source to be involved in star formation. The space density
would be 2.5$\times 10^{-5}$ Mpc-3, comparable to the local density of
clusters of galaxies (Bahcall et al. 2003) and the luminosity density would be
$\sim 5\times 10^{9}$ L⊙/Mpc3 (comoving), about a factor of 100 higher than
the local FIR value (Saunders et al. 1990). This would then imply a minimum of
103 recombinations per proton if the 450 $\mu$m luminosity traces a factor of
ten smaller ionizing luminosity: about 102 more recombinations than for the
lifetime of a typical H II region which seems too high for reionization unless
dust competes efficiently for reionizing photons.

On the other hand, there are six 850 $\mu$m sources with flux densities above
20 mJy listed by Pope et al. (2005) which could be close to hyperluminous (see
Fig. 7) so that we need only postulate a similar population which is (thus
far) invisible a 850 $\mu$m owing to the effects of ice and thus expect to
find these sources at a range of redshifts.

There is very clear evidence of ice rather than dust providing the FIR opacity
in 7 of the 9 450 $\mu$m sources considered here. But, the redshifts may or
may not be high and additional photometry is needed to constrain the
redshifts.

##  4 HDF 850.1 and ice

###  4.1 $z=5$

The search for counterparts at other wavelengths to the brightest 850 $\mu$m
source in the Hubble Deep Field has been arduous but Dunlop et al. (2004) make
a convincing case for detections in the radio and near infrared (NIR) and
summarize submillimeter observations. Modeling (Aretxaga et al. 2003) of these
observations leads them to conclude that the redshift of HDF 850.1 lies in the
range 4.1$\pm$0.5. Since the SED of a high $q$ ULIRG (IRAS 08572+3915) is
included in the 20 templates in the model input, the effects of the change in
the radio-FIR relation for ULIRGs compared to lower luminosity galaxies noted
in the introduction should be partly represented in their estimate. Similarly,
the suggestion of ice emission in the SED of IRAS 14348-1447 (Fig. 3) could
also influence the estimate if the photometric data were used directly rather
than fitted with a modified blackbody. In general, reliance on modified
blackbodies will give lower estimated redshifts for cooler sources when more
than one point on the Rayleigh-Jeans curve is available, as is the case for
HDF 850.1, but the addition of an ice emission feature can increase the
estimated redshift even for a cool source.

As one example, the bow-tie shown in Fig. 1 on the FIR continuum corresponds
to the range of redshift one would calculate for HDF 850.1 based on two
estimates of its 850 $\mu$m flux density (Dunlop et al. 2004; Wang et al.
2004) and the 1.3 mm flux density reported by Downes et al. (1999). That is
5.4 $<z<$5.6. It should be noted, even before describing the model upon which
this is based, that a detailed comparison between the SED shown in Fig. 1 and
the optical and NIR limits and detections for HDF 850.1 is not possible owing
to insufficient wavelength coverage for IRAS 00188-0856. See Dunlop et al.
(2004) fig. 6 for a comparison with data from two ULIRGs and a luminous
infrared galaxy calculated for a range of redshifts. However, the effects of
far infrared ice emission can be demonstrated with this example. The model,
the short-dashed line in the lower panel of Fig. 1, is based on curves given
by Aannestad (1975) which are the results of calculations of the optical
properties of ice mantled crystalline silicate grains. And, it is crystalline
water ice in the mantles. We chose the mantle-to-core volume ratio = 5.6 curve
to most closely match the ratio of 3 $\mu$m ice to silicate optical depth used
in the model shown by the solid lines in Fig. 1. For a number of reasons this
choice is probably not fully constrained by this ratio: the optical depth to
which the silicate absorption is sensitive may be larger than for ice; an odd
shift in the wavelength of the silicate feature may indicate a pyroxene
composition with a different feature-to-continuum optical depth ratio than
usual; the crystalline silicate in the Aannestad (1975) calculation is
somewhat dissimilar to astrophysical silicate models. However the first two
effects may be compensating so that as a rough abundance analysis, the
expectation that ice would dominate the FIR opacity in this source seems well
founded. This condition, and the need for the ice emission to be moderately
optically thin are really the only two requirements for ice to strongly affect
redshift estimation. The optical depth of the model of far infrared emission
shown in the lower panel of Fig. 1 is set to correspond to the 3 $\mu$m ice
optical depth used in models shown by the solid line in the upper panel (where
ice and refractory material contribute equally to the absorption optical depth
at 3.1 $\mu$m). The temperature of the far infrared emission model is set to
roughly reproduce the IRAS 60 and 100 $\mu$m measurements. This temperature
also accentuates the effects of the broad 150 $\mu$m feature over which the
HDF 850.1 data are displayed. The range of redshifts needed to place HDF 850.1
on this model falls outside of the range estimated by Dunlop et al. (2004) and
gives a first indication that the effects of ice on photometric redshift
estimation (as opposed to just limits) can be significant.

###  4.2 $z=13$

As noted in the introduction, using local ULIRGs to understand submillimeter
sources is a sensible approach if their properties are not strongly affected
by cosmic evolution. However, at higher redshift, this proviso seems fairly
likely to break down. Many local ULIRGs appear to be produced in the mergers
of gas rich spiral galaxies and it has been argued (Mihos & Hernquist 1996)
that the dynamical stability provided by bulges may preserve gas reservoirs
for the final merger stages associated with some ULIRGs. Owing to the finite
lifetime of the universe, there are earlier periods when the precursor systems
may not resemble present day precursors in their dynamical state or star-to-
gas mass ratio. It is not at all clear that seed SMBHs (Osterbrock 1993) would
be present at sufficient mass to allow accretion to be an energetically
important or dominant power source as suspected for local ULIRGs (e.g.
Imanishi et al. 2006a). Thus, in what follows we assume star formation as the
main power source at higher redshift. A sketch of how crystalline ice might
exist in a primordial galaxy environment is also given to explore the
plausibility of a very large effect of ice on redshift estimation. It is to be
noted that giving up a central power source such as would be provided by an
AGN would usually mean that ice mantled grains would contribute little to the
FIR emission since most of the energy that powers FIR emission would be
absorbed in reactive photodissociation regions (PDRs) rather than in molecular
clouds where ice is thought to exist unless an improbable scenario involving
an overabundance of protostars such as that proposed by Roussel et al. (2003)
but previously discounted by Dudley & Wynn-Williams (1997) is invoked. Below
we argue for such an overabundance.

In Fig. 7 we show the observations of HDF 850.1 at $z=12.6$ This is 18
confidence intervals beyond the Dunlop et al. (2004) estimate. So far as we
can tell, neither the new $Z$ band upper limit reported here, nor the released
Spitzer IRAC and MIPS GOODS images (Dickinson et al. 2006) rule out either the
model shown in Fig. 7 or the analysis of Dunlop et al. (2004) so long as a
reddish ULIRG (see Dudley (1999) for a discussion of 12-to-60 $\mu$m flux
density ratios in ULIRGs) is used as a basis for the Dunlop et al. (2004)
analysis. Dunlop et al. (2004) argue that the lensing source (solid diamonds
in Fig. 7) is evolved, in which case much of the tentative observed frame 24
$\mu$m flux density could be owing to HDF 850.1 but little of the 8 $\mu$m
flux density. At $z=4.1$, Mkn 231 and 273 could be too blue to account for
this level of emission whereas Arp 220 or IRAS 17208-0014 would not violate
this datum if treated as an upper limit. On the other hand, at $z=1.1$ the
chances of finding a younger elliptical galaxy to act as a lens are increased
so that some or all of the observed 24 $\mu$m flux density could be owing to
the lensing galaxy. This would still not rule out the Dunlop et al. (2004)
redshift estimate for HDF 850.1 but would accommodate the present estimate
under the assumption of the plotted starburst model. The shaded region in Fig.
7 shows a possible range for the spectral shape of the lens source emission.
The source labeled 1b in fig. 8 of Wang et al. (2004) may also contribute to
the 24 $\mu$m emission though only slightly to the IRAC data. If it is similar
to NGC 253, and at a redshift of $z_{\rm ph}=1.76$ (Fernández-Soto et al.
1999) then up to $\sim$30% of the 24 $\mu$m flux density might be attributed
to this source but again negligibly at 850 $\mu$m.

The model for HDF 850.1 shown in Fig. 7 (thick gray line) is similar to that
shown in Fig. 1 in that it has the same mantle-to-core volume ratio and
optical depth however the temperature is higher as it must be owing to the
higher CMB temperature at $z=12.6$. Whereas in Fig. 1, the 150 $\mu$m ice
feature spectral structure influences the redshift placement of the HDF 850.1
data, in Fig. 7, shorter wavelength spectral structure also owing to ice is
influential. Interestingly, assuming that there is a foreground neutral
intergalactic medium as a result of incomplete reionization (Spergel et al.
2006), one would expect Gunn-Peterson saturation or a Ly$\alpha$ blackout to
occur in the $H$ band for $z=12.6$ the shortest wavelength band for which HDF
850.1 is detected. This is represented by the change from black to gray in the
thin line using a Heaviside function as multiplier. Here the thin line is a
young starburst spectrum generated using Starburst99 (Leitherer et al. 1999).
It is notable that taking the onset in redshift of the Gunn-Peterson trough to
be $\sim$6 (Fan et al. 2004) absorption at the Lyman limit at $z<12.6$ easily
overlaps Ly$\alpha$ absorption between $z=6$ and $z=9.2$. One expects pretty
thorough opacity shortward of Ly$\alpha$.

While the choices of parameters of the starburst model are meant only to be
suggestive, for the model shown in Fig. 7, the free-free emission expected
based on the rate of production of ionizing photons would explain about 20% of
the observed radio emission (following Scoville et al. 1991) while retaining
the starburst model as it is and correcting for sufficient extinction to
account for the model infrared emission would over produce the radio emission
so that a lower contribution of stars which produce ionizing photons to the
observed frame $K$’ band flux might provide a more likely scenario.
Alternatively, invoking a chemical trigger for star formation discussed below,
it is conceivable that an object could be caught in a phase when a sufficient
number of stars are in an ultracompact H II region configuration that, given a
sufficiently high ionization parameter, higher than usually required if the
gas-to-dust mass ratio is high owing to low enrichment, free-free emission
would be suppressed (e.g. Bottorff et al. 1998).

As noted in the introduction, sources at high redshift should eventually drop
out of 850 $\mu$m surveys. In Fig. 8 we plot, for the same far infrared
luminosity, the expected 850 $\mu$m brightness as a function of redshift for
an Arp 220-like SED and the two distributions shown in Figs. 1 and 7\. The 30
K model is truncated at $z=11$ since the cosmic background radiation
temperature exceeds the model temperature above this redshift. As can be seen,
the models with ice select for high redshift sources assuming such sources
exist. For the 30 K model the brightest (non-local) source would be found near
a redshift of 5 and for the 50 K model near a redshift of 13. Should ice play
the role proposed here in a moderate fraction of the detected 850 $\mu$m
sources, it would be of little surprise that the brightest source in the HDF
(850.1) would be among them.

###  4.3 Why star formation?

Our choice of presenting a model that uses star formation as a power source
may seem strange given that PDRs would be inefficient at producing ice
emission which we require to allow, for example, HDF 850.1 to be detected at
$z=13$. One phase of star formation that does allow MIR radiation to heat ice
is the protostar phase. This phase is brief compared to O star life times and
thus would not typically be expected to provide the dominant source of FIR
radiation in a galaxy. Protogalaxies, however, are by definition required to
be young, so that while the argument concerning the relative brevity of the
protostar phase cannot be ignored, it may be overcome if the star formation
rate is increasing rapidly with time. And, it is just such sources that one
might expect to be observed as they populate the top of the infrared
luminosity function since they would be the most efficient at converting
radiation to FIR wavelengths.

A rapidly increasing star formation rate might be expected in a situation
where the gas cooling efficiency is increasing owing to ongoing initial
enrichment. A positive feedback can lead to an exponentially increasing system
response. The number at the right hand of Fig. 8 shows the 850 brightness (in
mJy) of the three SED shapes considered here if we adopt the lensing
amplification proposed by Dunlop et al. (2004) for HDF 850.1 for a source with
the FIR luminosity of IRAS 00188-0856. The increase in luminosity required to
match the Hughes et al. (1998) estimate for HDF 850.1 would be a factor of 2.3
for the dashed curve taken at a redshift of 13\. This would then correspond to
$\sim 4\times 10^{12}$ L⊙ (e.g. Fig. 7) or 107 O stars and 1.5$\times 10^{11}$
G0 stars for a Salpeter initial mass function (m-2.35), or roughly a galaxy’s
worth of star formation. This then would be the limit for the continued
exponential increase in the star formation rate: the amount of available
enrichable gas. Night et al. (2005) find 4 objects with $10^{11}$ M⊙ in stars
at $z=6$ in their largest cosmological simulation (142 Mpc; large enough to
contain $\sim$1 ULIRG at $z=0$). Thus, there is some suggestion that
relatively massive objects (or perhaps regions that will become objects) are
forming their stars a few dynamical timescales earlier than this.
Notwithstanding the existence of QSO J1148+5251 and other high redshift
quasars, it seems to us that there is a need to account for massive sources at
intermediate redshift which last formed stars near $z=13$ (Stockton et al.
2004; Jimenez 2000) as well as the apparent monotonic increase in the comoving
rate of gamma-ray bursts out to $z=7$ (Le & Dermer 2007).

However, in the low-to-moderate redshift universe, we would usually take ice
emission as an indication of a buried compact power source at least at ULIRG
luminosities, and, should blackhole growth commonly reach $\sim 10^{7}$ M⊙ by
$z=13$, as must happen at least occasionally given the existence of QSO
J1148+5251, then our low-to-moderate redshift explanation could also apply
during reionization.

##  5 Summary and prospects

Far infrared ice emission may be crucially important to understanding the far
infrared emission of sources at high redshift and may strongly affect the
range of redshifts estimated for submillimeter sources, even placing them at
reionization redshifts. Observations of infrared ice emission are definitive
in Galactic protostars and the winds of evolved stars but are scant and not
fully persuasive for the local analogs of the submillimeter sources, the
ULIRGs. This, despite mounting evidence that ice is involved in absorbing much
of the energy that is finally emitted in the far infrared in a substantial
fraction of ULIRGs.

We find stronger indications that ice emission is important at high redshift.
The data for QSO J1148+5251 as well as the 450 $\mu$m sources cataloged by
Pope et al. (2005) are both strongly suggestive. We feel that further
investigation along these lines could be quite fruitful.

We’ve considered two models where the presence of far-infrared emission
features owing to ice in the SED of HDF 850.1 would place it at redshifts
larger than the range estimated without ice by Dunlop et al. (2004). In the
first, the use of crystalline ice at 150 $\mu$m as a substitute for amorphous
ice is probably justified, subject to further laboratory investigations of
amorphous ice. In the second, consideration of a first chemical enrichment
mechanism suggests that crystalline ice could be present at early times while
energetic and timescale considerations may be compatible with protostars in
protogalaxies producing the sort of features we consider here. In the second
model, a Lyman $\alpha$ blackout would be consistent with the NIR photometry
for HDF 850.1. However, we do not prefer this model and its higher redshift
over the redshift range estimated by Dunlop et al. (2004) or $z\sim 5.5$ from
our first model. What we find to be important is that far infrared ice
emission could have such a dramatic effect on the estimated redshift. It
should be noted that redshifts estimated from the radio-FIR relation could
also turn out to be lower when ice emission is invoked since a large
submillimeter-to-radio flux density ratio is easier to produce with high
$\beta$ at some redshifts. So, the main conclusion of this work is that ice
broadens the range of redshifts to be considered for a given submillimeter
source and that ice is quite likely to be important at high redshift.

Some astronomical observations which could aid progress on open issues are:

  * •

Continuum observations at 3 mm of QSO J1148+5251 may confirm ice emission in
this source.

  * •

The Atacama Large Millimeter Array may be able to isolate the transition from
dust to free-free/synchrotron emission for sources of this type and allow more
reliable redshift estimates.

  * •

Investigating the role of ice emission locally could be taken up using SOFIA
or Spitzer.

  * •

Very low resolution H-band spectroscopy might test the possibility of a Lyman
$\alpha$ blackout for HDF 850.1.

  * •

Molecular studies which target H2O and OH maser emission may give definite
redshifts using a new generation of radio telescope arrays even if the
continuum is below detection limits.

Colleagues have commented helpfully at various stages of this work. Some are:
S. Chubb, E. Dwek, J. Fischer, P. Gerakines, A. Li, M. Moore, L. J. Rickard,
E. Shettle, and H. Smith and an anonymous referee. Research in infrared
astronomy and particularly the astrophysics of celestial backgrounds at the
Naval Research Laboratory is supported by the Office of Naval Research (USA).
This publication makes use of data products from the Two Micron All Sky
Survey, which is a joint project of the University of Massachusetts and the
Infrared Processing and Analysis Center/California Institute of Technology,
funded by the National Aeronautics and Space Administration and the National
Science Foundation. Use is also made of the USNOFS Image and Catalog Archive
operated by the United States Naval Observatory, the archive of results from
the ESA sponsored Infrared Space Observatory mission, the NASA/IPAC
Extragalactic Database operated by JPL and Caltech, and data from the GOODS
project from NASA’s Spitzer and Hubble Space Telescopes.

## References

  * Aannestad (1975) Aannestad, P. A. 1975, ApJ, 200, 30
  * Aretxaga et al. (2003) Aretxaga I., Hughes D. H., Chapin E. L., Gaztanaga E., Dunlop J. S., 2003, MNRAS, 342, 759
  * Athey et al. (2002) Athey, A., Bregman, J., Bregman, J., Temi, P., 2002, ApJ, 571, 272
  * Bahcall et al. (2003) Bahcall, N., et al., 2003, ApJS, 148, 243
  * Beelen et al. (2006) Beelen, A., Cox, P., Benford, D. J., Dowell, C. D., Kovács, A., Bertoldi, F., Omont, A., Carilli, C. L., 2006, ApJ, 642, 694
  * Bertie et. al (1969) Bertie, J. E., Labbé, H. J. & Whalley, E. 1969, J Chem Phys, 50, 4501
  * Bertoldi et al. (2003a) Bertoldi, F. et al. 2003, A&A, 409, L47
  * Bertoldi et al. (2003b) Bertoldi, F., Carilli, C. L., Cox, P., Fan, X., Strauss, M. A., Beelen, A., Omont, A., Zylka, R., 2003, A&A, 406, L55
  * Borys et al. (2003) Borys, C., Chapman, S., Halpern, M., Scott, D., 2003, MNRAS, 344, 385
  * Borys et al. (2004) Borys, C., Scott, D., Chapman, S., Halpern, M., Nandra, K., Pope, A., 2004, MNRAS, 355, 485
  * Bottorff et al. (1998) Bottorff, M., Lamothe, J. Momjian, E. Verner, E. Vinković, D. & Ferland, G. 1998, PASP, 110, 1040
  * Brinchmann et al. (1998) Brinchmann, J. et al. 1998, ApJ, 499, 112
  * Caillault & Helfand (1985) Caillault, J.-P., Helfand, D. J., 1985, ApJ, 289, 279
  * Charmandaris et al. (2002) Charmandaris, V. et al. 2002, A&A, 391, 429
  * Condon et al. (1991) Condon J. J., Huang Z.-P., Yin Q. F., Thuan, T. X., 1991, ApJ, 378, 65
  * Curtis et al. (2005) Curtis, D. B., Rajaram, B., Toon, O. B., Tolbert, M. A., 2005, Applied Optics, 44, 4102
  * Cutri et al. (2003) Cutri R. M., Skrutskie M. F., Van Dyk S., et al. 2003, 2MASS All Sky Data Release
  * Dartois et al. (1998) Dartois, E., et al. 1998, A&A, 338, L21
  * Dickinson et al. (2006) Dickinson, M. et al., in prep.
  * Downes et al. (1999) Downes D. et al., 1999, A&A, 347, 809
  * Dudley & Wynn-Williams (1997) Dudley. C. C. & Wynn-Williams, C. G. 1997, ApJ, 488, 720
  * Dudley (1999) Dudley C. C., 1999, MNRAS, 304, 549
  * Dunlop et al. (2004) Dunlop, J. S. et al. 2004, MNRAS, 350, 769
  * Dunne et. al (2000) Dunne, L., Eales, S., Edmunds, M., Ivison, R., Alexander, P., Clements, D. L. 2000, MNRAS. 315, 115
  * Elvis et al. (1994) Elvis, M., Wilkes, B. J., McDowell, J. C., Green, R. F., Bechtold, J., Willner, S. P., 1994, ApJS, 95, 1
  * Fan et al. (2003) Fan, X., et al. 2004, AJ, 125, 1649
  * Fan et al. (2004) Fan, X., et al., 2004, AJ, 128, 515
  * Fernández-Soto et al. (1999) Fernández-Soto, A., Lanzetta, K. M., Yahil, A., 1999, ApJ, 513, 34
  * Frayer et al. (2006) Frayer, D. T., et al., 2006, ApJ, 647, L9
  * Geballe et al. (2006) Geballe, T. R., Goto, M., Usuda, T., Oka, T., McCall, B. J. 2006, ApJ, 644, 907
  * Genzel et al. (1998) Genzel, R. et al. 1998, ApJ, 498, 579
  * Gerakines et al. (2005) Gerakines P. A., Bray J. J., Davis A., Richey C. R., 2005, ApJ, 620, 1140
  * Giavalisco et al. (2004) Giavalisco M. et al., 2004, ApJ, 600, L93
  * González-Alfonso et al. (2004) González-Alfonso, E., Smith, H. A., Fischer, J., Cernicharo, J., 2004, ApJ, 613, 247
  * Greenberg et al. (1995) Greenberg, J. M., Li, A. Mendoza-Gomez, C. X., Schutte, W. A., Gerakines, P. A. & de Groot, M. 1995, ApJ, 455, L 177
  * Hagen et al. (1983) Hagen, W., Greenberg, J. M. & Tielens, A. G. G. M. 1983, A&AS, 51, 389
  * Heger & Woosley (2002) Heger, A. & Woosley, S. E. 2002, ApJ, 567, 532
  * Helou et al. (1985) Helou, G., Soifer, B. T., Rowan-Robinson, M., 1985, ApJ, 298, L7
  * Hoogzaad et al. (2002) Hoogzaad S. N., Molster E. F., Dominik C., Waters L. B. F. M., Barlow M. J., de Koter A., 2002, A&A, 389, 547
  * Huchra (1977) Huchra, J. P., 1977, ApJS, 35, 171
  * Hughes et al. (1998) Hughes D. H. et al., 1998, Nature, 394, 241
  * Imanishi & Dudley (2000) Imanishi, M., Dudley, C. C., 2000, ApJ, 545, 701
  * Imanishi et al. (2001) Imanishi, M., Dudley, C. C., Maloney, P. R., 2001, ApJ, 558, L93
  * Imanishi & Maloney (2003) Imanishi, M., Maloney, P. R., 2003, ApJ, 588, 165
  * Imanishi et al. (2006a) Imanishi, M., Dudley, C. C., Maloney, P. R., 2006, ApJ, 367, 114
  * Imanishi (2006) Imanishi, M., 2006, AJ, 131, 2406
  * Imanishi et al. (2006b) Imanishi, M., Dudley, C. C., Maiolino, R., Maloney, P. R., Nakagawa, T., Risaliti, G. 2006, ApJ, submitted
  * Jimenez (2000) Jimenez et al. 2000, ApJ, 532, 152
  * Kim & Sanders (1998) Kim, D.-C. & Sanders, D. B. 1998, ApJS, 119, 41
  * Kim, Veilleux & Sanders (2002) Kim D.-C., Veilleux S., Sanders D. B. 2002, ApJS, 143, 277
  * Klaas et al. (2000) Klaas, U., Laureijs, R. J., Radovich, M., Schulz, B., Wilke, K., 2000, ISOPHOT Calibration Accuracies, SAI/1998-092/Dc, Ver. 4
  * Klaas et al. (2001) Klaas, U. et al. 2001, A&A, 379, 823
  * Le & Dermer (2007) Le, T., Dermer, C. D., 2006, ApJ, 661, 394L
  * Leitherer et al. (1999) Leitherer, C. et al. 1999, ApJS, 123, 3
  * Lis et al. (1998) Lis, D. C., Serabyn, E., Keene, J., Dowell, C. D., Benford, D. J., Phillips, T. G., Hunter, T. R. & Wang, N. 1998, ApJ, 509, 299
  * Lisenfeld et. al (2000) Lisenfeld, U., Isaak, K. G., Hills, R. 2000, MNRAS, 312, 433
  * Maloney & Reynolds (2000) Maloney, P. R. & Reynolds, C. S. 2000, ApJ, 545, 23
  * McCutcheon et al. (1995) McCutcheon, W. H., Sato, T. Purton, C. R. Matthews, H. E. & Dewdney, P. E. 1995, AJ, 110, 1762
  * Mihos & Hernquist (1996) Mihos, J. C., Hernquist, L., 1996, ApJ, 464, 64
  * Monet et al. (1998) Monet D., Canzian B., Harris H., Reid N., Rhodes A., Sell S. 1998, US Naval Obs. Flagstaff Station 1977, 1243
  * Moore & Hudson (1992) Moore, M. H. & Hudson, R. L. 1992, ApJ, 401, 353
  * Moshir et al. (1990) Moshir M. et al. RAS Faint Source Catalogue, version 2.0
  * Nenkova et al. (2002) Nenkova,M., Ivezić, Z., Elitzur, M., 2002, ApJ, 570, L9
  * Nolta et al. (2004) Nolta, M. R. et al. 2004, ApJ, 608, 10
  * Nozawa et al. (2003) Nozawa, T., Kozasa, T., Umeda, H., Maeda, K., Nomoto, K., 2003, ApJ, 598, 785
  * Osterbrock (1993) Osterbrock, D. E., 1993, ApJ, 404, 551
  * Persson et al. (1979) Persson, S. E., Frogel, J. A., Aaronson, M., 1979, ApJS, 39, 61
  * Pope et al. (2005) Pope, A., Borys, C., Scott, D. Conselice, C., Dickinson, M., Mobasher, B., 2005, MNRAS, 358, 149
  * Riess et al. (2004) Riess, A. G. et al. 2004, ApJ, 607, 665
  * Rigopoulou et al. (1996) Rigopoulou, D., Lawrence, A., Rowan-Robinson, M. 1996, MNRAS, 278, 1049
  * Risaliti et al. (2006) Risaliti, G., et al., 2006, MNRAS, 365, 303
  * Robson et al. (2004) Robson, I., Priddey, R. S., Isaak, K. G., McMahon, R. G., 2004, MNRAS, 351, L29
  * Roche & Aitken (1984) Roche, P. F.,Aitken, D. K.., 1984, MNRAS, 208, 481
  * Roussel et al. (2003) Roussel, H., Helou, G., Beck, R., Condon, J. J., Bosma, A., Matthews, K., Jarrett, T. H., 2003, ApJ, 593, 733
  * Sanders (2000) Sanders, D. B. 2000, AdSpR, 25, 2251
  * Sanders et al. (1995) Sander D. B., Egami E., Lipari S., Mirabel I. F., Soifer, B. T., 1995, AJ, 110, 1993
  * Sanders & Mirabel (1996) Sanders, D. B. & Mirabel, I. F. 1996, ARAA, 37, 749
  * Saunders et al. (1990) Saunders, W., Rowan-Robinson, M., Lawrence, A., Efstathiou, G., Kaiser, N., Ellis, R. S., Frenk, C. S., 1990, MNRAS, 242, 318
  * Schober et al. (2000) Schober, H., Koza, M. M., Tölle, A., Masciovecchio, C., Sette, F., Fujara, F. 2000, PhRvL, 85, 4100
  * Schneider et al. (2004) Schneider, R., Ferrara, A., Salvaterra, R., 2004, MNRAS, 351, 1379
  * Scoville et al. (1991) Scoville, N. Z. et al. 1991, ApJ, 366, L8
  * Soifer et al. (1987) Soifer B. T. et al., 1987, ApJ, 320, 238
  * Soifer et al. (1999) Soifer, B. T., Neugebauer, G., Matthews, Becklin, E. E., Ressler, M., K., Werner, M. W., Weinberger, A. J., Egami, E., 1999, AJ, 118, 2065
  * Soifer et al. (2002) Soifer, B. T., Neugebauer, G., Matthews, K., Egami, E., Weinberger, A. J., 2002, AJ, 124, 2980
  * Smith et al. (1994) Smith, R. G. et al. 1994, MNRAS, 271, 481
  * Spergel et al. (2006) Spergel, D. N. et al. 2006, ApJ, submitted
  * Spergel et al. (2003) Spergel, D. N. et al. 2003, ApJS, 148, 175
  * Spoon et al. (2002) Spoon, H. W. W. et al. 2002, A&A, 414, 873
  * Spoon et al. (2006) Spoon, H. W. W., et al., 2006, ApJ, 638, 759
  * Stockton et al. (2004) Stockton, A., Canalizo, G., Maihara, T. 2004, ApJ, 605, 37
  * Temi et al. (2005) Temi, P., Mathews, W. G., Fabrizio, B., 2005, ApJ, 622, 235
  * Verma et al. (2002) Verma, A., Rowan-Robinson, M., McMahon, R., Efstathiou, A., 2002, MNRAS, 335, 574
  * Wang et al. (2004) Wang, W.-H., Cowie, L. L., Barger, A. J. 2004, ApJ, 613, 655
  * Weedman et al. (2005) Weedman, D. W., et al. 2005, ApJ, 633, 706
  * Willot et al. (2003) Willott, C. J., McLure, R. J., Jarvis, M. J., 2003, ApJ, 587, L15
  * Whittet et al. (1988) Whittet, D. C. B., Bode, M. F., Longmore, A. J., Adamson, A. J., McFadzean, A. D., Aitken, D. K., Roche, P. F., 1988, MNRAS, 233, 321
  * Xilouris et al. (2004) Xilouris, E. M., Madden, S. C., Galliano, F., Vigroux, L., Sauvage, M., 2004, A&A, 416, 41
  * Yun et al. (2001) Yun M. S., Reddy N. A., Condon J. J., 2001, ApJ, 554, 803

Figure 1:  Upper Panel: Data from Imanishi & Maloney (2003) is reproduced for
IRAS 00188-0856 together with a model (solid line) subsequently employed in
the lower panel. The model consists of an $\alpha=2$ (flux density
$f_{\nu}\propto\nu^{-\alpha}$) power-law continuum to which absorption is
applied together with an unabsorbed component which is a combination of an
archival spectrum of M 82 (ISO SWAA11600319) and a blackbody of temperature
2500 K to represent additional stellar photospheric emission (displayed in the
lower panel long-dashed line). The two absorption components used are: (1) a
volatile admixture (H2O:CO=2:1) of amorphous ice measured at 10 K (Hagen et
al. 1983) and (2) the refractory EURECA-B curve presented by Greenberg et al.
(1995). The effects of absorption by the refractory material are shown with
the dot-dashed line and those of the combined volatile and refractory
absorption with the dashed line. The volatile and refractory components have
approximately equal contributions to the absorption at 3 $\mu$m but the
refractory component contributes little at the short wavelength edge
suggesting that a volatile component is required. Lower Panel: The same model
(solid line), now adjusted to lower optical depth in the refractory component
to better match the 6 $\mu$m absorption and with a smaller additive M 82
component is applied to longer wavelength data. Here, the effects of silicate
absorption have also been included based on fig. 5 of Dudley & Wynn-Williams
(1997) but oddly shifted to the red by about 0.6 $\mu$m at 10 $\mu$m, perhaps
owing to differing composition. The inset shows the effects of adding the
spectrum of M 82 as in the upper panel and without this component in the model
at all (bounding dotted lines). The spectral resolution of the model matches
that of the data in the inset. The short-dashed line is an emission model
described more fully in the text (Sec. 4.1). Data sources for IRAS 00188-0856
in descending order in the legend are from Imanishi & Maloney (2003); Monet et
al. (1998); Cutri et al. (2003); Moshir et al. (1990); and Charmandaris et al.
(2002). R and K’ data are in rough agreement with the photometry given by Kim,
Veilleux & Sanders (2002).  Figure 2:  Highly processed data products from the
ISO Archive (hpdp_05100540_2.tar and hpdp_65000608_2.tar with minimal ISAP
post processing) are compared with a 43 $\mu$m ice absorption feature derived
from the spectrum of HD 161796 (also from the ISO archive: SWAA52100537). The
diamonds and circles are data for Mkn 231 and IRAS 17208$-$0014 respectively.
The solid lines are derived from the ISO SWS spectrum of HD 161796 using a
single temperature (140 K) to estimate emissivity after the manner of Roche &
Aitken (1984) and then converted to absorption. The inset is described in the
text. Figure 3:  Observational data for IRAS 14348-1447 (filled circles) are
plotted at their rest wavelength in Jy as reported by Klaas et al. (2001).
Horizontal bars indicate filter passbands. The solid line shows an optically
thin (in the FIR) ice emission model whose $\beta$ parameter (100 and
300–900$\mu$m) is $\sim 2.3$ as compared to $\sim 1.9$ for a bare (refractory)
core. Adjustment of the core to smaller $\beta$ would result in a smaller
$\beta$ for the mantled grain as well. In fitting the model data at 95 and 450
$\mu$m were matched and various mantle-to-core volume ratios were compared
with photometry between these wavelengths. The dashed line reproduces the fit
proposed by Klaas et al. (2001) which is quite optically thick in the FIR and
has $\beta$=2.  Figure 4:  Observational data for QSO J1154+5251 (filled
circles and arrow) are plotted at their rest wavelength in mJy as reported by
Bertoldi et al. (2003a) (3 mm); Bertoldi et al. (2003b) (1.2 mm); Robson et
al. (2004) (850 and 450 $\mu$m); Beelen et al. (2006) (350 $\mu$m). The lines
represent emission models. The dashed and dot-dashed are single temperature
models using refractory and ice mantled dust respectively while the solid line
two temperature ice model with colder ice obscuring warmer ice.  Figure 5: The
observed frame 450-to-850 flux density ratio calculated for a series of
emission models is plotted as a function of redshift together with 9 observed
lower limits (large filled symbols), 34 observed upper limits (medium open
symbols), and two detections (smallest symbols). Individual 450 $\mu$m source
and detection identifications are given in the legend. The models, also in the
legend, are more fully described in the text.  Figure 6: Brightness in mJy at
the observed wavelength 450 $\mu$m is plotted as a function of redshift for a
set of models. Four of the models are carried over from Fig. 5: The solid line
represents 150 K ice, the triple dot dashed line, 50 K ice, the dot dashed
line 30 K ice and the long dashed line 60 K refractory dust. A fifth model
(short dashed line) is taken from the solid line in Fig. 4: 71 K ice is
obscured by 24 K ice. Infrared luminosities for the models are constant as a
function of redshift and are $2\times 10^{13}$ L⊙: long-dashed, dot-dashed,
and triple-dot-dashed lines, $2\times 10^{14}$ L⊙: solid line, and $1\times
10^{13}$ L⊙: short-dashed line. We remark that just as standard dust shows
roughly redshift independent brightness at 850 $\mu$m, so too does T=50 K ice
(triple dot dashed line) at 450 $\mu$m. The filled circle is QSO J1148+5251.
Figure 7:  Observational data for HDF 850.1 (filled circles) are plotted for a
rest wavelength and luminosity scale corresponding to a redshift of 12.6 and
accounting for the effects of gravitational lensing by reducing the apparent
luminosity by a factor of 3. The data, except for the $Z$ band limit, are
reported or summarized in Dunlop et al. (2004). The $Z$ band limit is measured
from GOODS ACS data (Giavalisco et al. 2004) by subtracting the image of the
lensing galaxy from itself after a rotation of 180°. The limit is 2$\sigma$
drawn from the weight image for an 0$\farcs$5 aperture centered at the IRAM
position (Downes et al. 1999) and corresponds to $Z-K^{\prime}>3.5$ (Vega).
Data for the lensing source (filled diamonds) should be read relative to the
HDF 850.1 data (filled circles) as the scalings in wavelength and luminosity
do not apply. Here the $I-K^{\prime}$ photometry are from Dunlop et al. (2004)
while the 3.6–24 $\mu$m points are measured from GOODS IRAC and MIPS images
(Dickinson et al. 2006). The IRAC data are 6$\farcs$0 diameter aperture
photometry subtracting an equal area outer annulus. The 24 $\mu$m datum is
obtained through radial profile fitting after subtraction of a confusing
source and is perhaps a 2.5$\sigma$ measurement of 20 $\mu$Jy. The dashed line
is scaled ($z=1.1$ wrt observed frame; Fernández-Soto et al. 1999) data for
the elliptical galaxy NGC 1399 (Persson et al. 1979;Athey et al. 2002) and the
triple-dot-dashed line is for the galaxy NGC 3928 (Huchra 1977; 2MASS;
Xilouris et al. 2004) with the shaded region between them showing the age
dependent range of mid-infrared flux suggested by models for elliptical
galaxies reported by Temi et al. (2005). The models shown as solid lines are
described more fully in the text. Figure 8:  The 850 $\mu$m brightness as a
function of redshift is shown for three calculated SEDs. The solid line
corresponds to the FIR SED shown in Fig. 1. The long-dashed line corresponds
to an optically thin $T=45$, $\beta=1.2$ modified blackbody similar to the
Scoville et al. (1991) fit for Arp 220. The short-dashed line corresponds to
the FIR SED shown in Fig. 7 all normalized to the FIR luminosity of IRAS
00188-0856. The arrows for the solid, dot-dashed, and dashed lines indicate
redshifts for HDF 850.1 estimated using Fig. 1, Dunlop et al. (2004), and Fig.
7 respectively. The numbers at the right are a conversion of the vertical
scale for the gravitational lens amplification factor of three estimated for
HDF 850.1.

Figure 1:

Figure 2:

Figure 3:

Figure 4:

Figure 5:

Figure 6:

Figure 7:

Figure 8: