The most distant, luminous, dusty star-forming galaxies: redshifts from NOEMA and ALMA spectral scans
Y. Fudamoto R. J. Ivison I. Oteo M. Krips Z. Y. Zhang A. Weiss H. Dannerbauer A. Omont S. C. Chapman L. Christensen V. Arumugam F. Bertoldi M. Bremer D. L. Clements L. Dunne S. A. Eales J. Greenslade S. Maddox P. Martinez-Navajas M. Michalowski I. Pérez-Fournon D. Riechers J. M. Simpson B. Stalder E. Valiante P. van der Werf
astro-ph.GA


firstpage–lastpage
[
    Jorge Drumond Silva
    December 30, 2023
=======================





  We present 1.3- and/or 3-mm continuum images and 3-mm spectral
  scans, obtained using NOEMA and ALMA, of 21 distant, dusty,
  star-forming galaxies (DSFGs). Our sample is a subset of the
  galaxies selected by <cit.> on the basis of their
  extremely red far-infrared (far-IR) colours and low Herschel flux densities; most are thus expected to be
  unlensed, extraordinarily luminous starbursts at z 4,
  modulo the considerable cross-section to gravitational lensing
  implied by their redshift. We observed 17 of these galaxies
  with NOEMA and four with ALMA, scanning through the 3-mm
  atmospheric window.  We have obtained secure redshifts for
  seven galaxies via detection of multiple CO lines, one of them
  a lensed system at z=6.027 (two others are also found to be
  lensed); a single emission line was detected in another four
  galaxies, one of which has been shown elsewhere to lie at
  z=4.002.  Where we find no spectroscopic redshifts, the
  galaxies are generally less luminous by 0.3–0.4 dex, which
  goes some way to explaining our failure to detect line
  emission. We show that this sample contains amongst the most
  luminous known star-forming galaxies.  Due to their extreme
  star-formation activity, these galaxies will consume their
  molecular gas in 100 Myr, despite their high molecular
  gas masses, and are therefore plausible progenitors of the
  massive, `red-and-dead' elliptical galaxies at z ≈ 3.





galaxies: high-redshift – galaxies: starburst – galaxies: ISM  – ISM: molecules 




§ INTRODUCTION


It has been known since the 1970s and 1980s that a large fraction
of the energy produced by vigorously star-forming galaxies in the
nearby Universe is radiated by cool dust which mingles with their
reservoirs of molecular gas <cit.>.  A decade on,
the existence of a more distant population of dusty galaxies was
inferred by <cit.> from the detection of the cosmic
far-IR background using FIRAS aboard the Cosmic Background
  Explorer, individual examples of which were quickly detected
by <cit.> in the submillimeter (submm) waveband.  If
their initial stellar mass function (IMF) is normal, these
galaxies form stars at tremendous rates, sometimes
>1000  M_⊙  yr^-1 <cit.>.
Deeper submm observations in cosmological deep fields
<cit.> confirmed the
abundance of these so-called submm galaxies (SMGs), sometimes
known now as dusty, star-forming galaxies <cit.>.

In the decades since then, the SPIRE camera <cit.>
aboard Herschel <cit.> and the SCUBA-2 camera
<cit.> on the James Clerk Maxwell Telescope (JCMT)
have together detected orders of magnitude more of these DSFGs.
Conventional optical and near-IR spectroscopic observations
confirmed that DSFGs are considerably more abundant
(≈ 1,000×) at high redshift than in the local
Universe, with a redshift distribution for those selected at
850 μm that peaks at z∼1–3
<cit.>.  Those selected at >1 mm
by the South Pole Telescope <cit.>
are more distant while those selected at the far-IR wavelengths
imaged by Herschel are typically at z<2.

In the local Universe, massive early-type galaxies have old
stellar populations, >2 Gyr, and are therefore red in
optical color – so-called `red-and-dead' galaxies.  They have
little gas or dust, and star-formation activity has ceased
<cit.>.
The majority of these galaxies experienced an intense phase of
star formation around 5–10 Gyr ago <cit.>,
and current observational evidence suggests that DSFGs at
z≈ 2 are their likely progenitors.

It is also well established that there exists a population of massive
elliptical galaxies at z∼ 2–3.  It has been claimed that most of
these are high-redshift analogs of local, massive red-and-dead
galaxies <cit.>.  The existence of these galaxies at z∼2–3 suggests
intense star-formation episodes must occur at even higher redshifts,
perhaps implying that DSFGs are common at z 4
<cit.>.

Only a small number of DSFGs were known at z 4 until
recently, most of them gravitationally lensed
<cit.>.  To address this issue,
<cit.> recently exploited the widest available far-IR
imaging survey, H-ATLAS <cit.>, to create a sample
of the faintest, reddest dusty galaxies, further improving their
photometric redshifts via ground-based photometry from SCUBA-2
<cit.> and LABOCA <cit.>.  The galaxies
thus selected are expected to be largely
unlensed[Despite expecting a low lensing fraction,
   and others have shown that strongly
  lensed galaxies are common at z>4 due to the increase with
  redshift of the optical depth to lensing and the magnification
  bias; <cit.> present high-resolution ALMA imaging
  of this sample, showing that the fraction of lensed galaxies is
  indeed relatively high.], luminous and very distant.  Their
vigorous star-formation activity thus tallies with the
star-formation history required to build up the large mass of
stars found in spheroidal galaxies at z≈ 2.

To confirm that the ultrared DSFGs selected by 
do lie at z 4, which will strengthen their links with
red-and-dead galaxies at z∼2-3, requires robust spectroscopic
confirmation of their photometric redshifts.  This is non-trivial when
working in the traditional optical and near-IR regime, verging on
impossible with current telescopes and instrumentation.  Following the
success of <cit.>, who scanned the 3-mm atmospheric window to
determine the redshift of one of the brightest, reddest, lensed
galaxies to emerge from H-ATLAS <cit.>, we
have therefore obtained 3-mm spectral scans of 21 ultrared DSFGs from
the  sample, as well as interferometric 0.85- and
1.3-mm imaging to better pinpoint their positions.

Our primary objective here is to determine robust spectroscopic
redshifts for these DSFGs, via the detection of multiple molecular
and/or atomic emission lines.  Using these to fine-tune the
far-IR/submm photometric techniques employed by 
then allows us to more reliably determine the space density of DSFGs
at z 4.  In addition, we use our improved measurements of IR
luminosity and our CO line luminosities to estimate physical
properties, such as SFR and molecular gas mass.  Finally, we compare
these derived properties with those of other DSFGs at low and high
redshifts, subject as usual to the considerable uncertainties imposed
by α_ CO and the assumed IMF.

Where applicable, we assume a flat Universe with
(Ω_m,Ω_Λ,h_0) = (0.3,0.7,0.7).  In this
cosmology, an arcsecond corresponds to 7.1 kpc at z=4.





§ SAMPLE SELECTION





 Our targets – see Table <ref> – were chosen from the faint,
`ultrared' galaxy sample of <cit.>, taking those best suited
to the latitudes of the telescopes we employ, with photometric
redshifts consistent with z4. Here, we briefly summarize the
selection method used, referring readers to <cit.> for more
details.

The sample was selected from the SPIRE images used to construct H-ATLAS Data Release 1 <cit.>, employing an optimal
extraction kernel to minimize the effects of source confusion, which
is especially pernicious at 500 μm. The reddest galaxies were
isolated based on their SPIRE colors, such that
S_500/S_250≥1.5 and S_500/S_350≥0.85, where S_250
is the flux density measured at 250 μm (see Fig. <ref>).
The galaxies thus selected have a median S_500∼ 50 mJy, such
that the majority are not expected to be lensed gravitationally
<cit.>.

The reddest of these SPIRE-selected galaxies were then imaged
with SCUBA-2 <cit.> on the 15-m JCMT and/or with
LABOCA <cit.> on the 12-m Atacama Pathfinder Telescope
(APEX) so that better photometric redshifts could be determined.
These data are also utilized here, in <ref>, to aid
us in spatially localizing any line emission.  Of the 109 objects
thus targeted by , 17 galaxies were selected
for further observations with the Institute Radioastronomie
Millimetrique's (IRAM's) Northern Extended Millimeter Array
(NOEMA) and four galaxies for further observations with the
Atacama Large Millimeter Array (ALMA), based on their
accessibility to those telescopes and their high photometric
redshifts. The SPIRE flux densities and photometric redshifts
determined by <cit.> are listed in Table <ref>.



§ OBSERVATIONS







 §.§ NOEMA 3-mm spectral scans


Our observations with
NOEMA[http://iram-institute.org/EN/noema-project.php] were
conducted as two programs (Program IDs: W05A, X0C6; Co-PIs:
R. J. Ivison, M. Krips). Table <ref> lists the galaxies
observed.  Both projects acquired data using five or six antennas in
NOEMA's most compact (D) configuration. W05A was carried out between
2012 June and 2013 April, and 14 targets were observed. X0C6 took
place between 2013 November and 2014 June, where four targets were
observed. One target, G09-83808, was observed during both periods.

We employed multiple receiver tunings together with the WideX
correlator – which provides 3.6 GHz of instantaneous
dual-polarization bandwidth – to cover the 80–101.6-GHz part of
the 3-mm atmospheric window, in which we expect to find at least
one ^12CO transition for galaxies at z>3.6 – see, for
example, Figure 2 of <cit.>, where for 3.6<z<7.5 we
always expect ^12CO(4–3), ^12CO(5–4) and/or
^12CO(6–5) in our frequency search range, with other lines
such as C i(1–0) and H_2O(211–202) also present for
some redshifts.

Different approaches were used during the two projects to maximize the
probability of detecting multiple emission lines from each target,
necessary to yield an unambiguous redshift <cit.>. In W05A, once a single emission line was detected
during an initial sweep of the 3-mm atmospheric window, the remaining
3-mm tunings were skipped and we instead tuned to a higher frequency,
outside the 3-mm band, to search for a higher CO transition, having
used the initial line and/or continuum detection to quantize the
possibilities as well as to improve the photometric redshift
estimate. In X0C6, spectra covering the 3-mm atmospheric window were
obtained for all targets (∼21 GHz in total), then targets with
emission lines were observed again to search for emission lines at
higher frequencies, in the 2-mm band.  Some of the targets
therefore have less than 21 GHz of coverage (e.g. NGP-190387,
NGP-126191 and G09-59393); others have coverage larger than 21 GHz
(NGP-284357, NGP-246114 and G09-81106). Average on-source time per
tuning was 20 min for W05A, and 120 min for X0C6, of which 15 and
90 min remained after flagging, respectively.

Calibration of the data was carried out by using the gildas
package[http://www.iram.fr/IRAMFR/GILDAS]. The typical
resulting r.m.s. noise levels were 2.7 and 1.1 mJy beam^-1
in 100- channels for data taken in W05A and X0C6. Calibrated
visibilities were converted into FITS format for export, then
into MS format to be imaged by casa <cit.>. The
average synthesized beam size was 5fwhm during both
runs, with considerable diversity in beam shape due to the
relatively short tracks.

To study any 3-mm continuum emission from our targets, we
integrated our data over all observed frequencies, imaging with
the clean task in casa, with a map size of
1^'× 1^', sufficient to cover the 3-mm
primary beam.



 §.§ ALMA 3-mm spectral scans


Four ultrared galaxies were observed using ALMA (see
Table <ref>), with five separate tunings to cover the 3-mm
window (Program ID: 2013.1.00499.S; PI: A. Conley). Data were
acquired during 2014 July 02–03 and August 28, with typically
8.6–9.7 min spent on-source for each tuning, in addition to
20 min of calibration – pointing, phase, flux density (Neptune)
and bandpass.

Data were calibrated using the ALMA pipeline, with only minor flagging
required. Calibrated data were imaged using clean within casa, using the natural weighting scheme to maximize sensitivity.

The resulting r.m.s. noise levels ranged between 0.73 and
0.80 mJy beam^-1 in channels binned to 100 . Because the
observations were carried out on several different dates, with
different antenna configurations, at frequencies ranging from 84 to
115 GHz, the resulting synthesized beamsizes varied between 0.6 and
1.2” fwhm.

As with our NOEMA data, 3-mm continuum images were created using
all the available data, with a map size of
1^'× 1^'.



 §.§ NOEMA 1.3-mm continuum observations



We have also carried out 1.3-mm observations of ten galaxies
lacking continuum detections, and hence accurate positions, in
our earlier 3-mm work. Table <ref> lists those targets
observed during 2015 December (Program ID: W15ET; PI: M. Krips),
again using the most compact NOEMA configuration, with six
antennas. The typical resulting synthesized beam size was
∼ 1.5” fwhm. Calibration was accomplished following
the standard procedures, using gildas, with little need for
significant flagging. The average time spent on-source was
25 min, yielding typical noise level of 0.47 mJy beam^-1.

We also use data from an earlier programme which observed another five
of our targets – G09-81106, G09-83808, NGP-101333, NGP-126191 and
NGP-246114 – taken during 2013 in the compact 6C configuration, with
a typical resulting synthesized beam size of 1.0”× 1.3” fwhm, the major axis at a position angle of 25^∘ (Program ID:
W0BD; Co-PIs: F. Bertoldi, I. Perez-Fournon).



§ RESULTS



If detecting faint line emission from distant galaxies is
challenging, doing so in the absence of an accurate position is
considerably more so.  For this reason, our first step is to
explore the 3-mm continuum images described in <ref>,
hoping that thermal dust emission from our luminous, dusty
starbursts will betray the precise position of our targets.



 §.§ Continuum emission



To determine the significance of any continuum emission, we measured
the r.m.s. noise level of the maps, and then created the
signal-to-noise ratio (SNR) images shown in Fig. <ref>.
 
All four sources observed at 3 mm with ALMA are clearly detected in
continuum, at >8σ significance.

For the objects observed at 3 mm with NOEMA, the sensitivity is much
reduced compared to ALMA, so we begin by overlaying the 3-mm continuum
images with contours from the deep SCUBA-2 850-μm imaging of
<cit.>, where the unsmoothed fwhm of the SCUBA-2
images is around 13”, and the r.m.s. pointing accuracy of the JCMT
for a single visit to a target is ∼ 2–3”.

We then searched for faint 3-mm continuum sources coincident with
SCUBA-2 850-μm emission, finding eight plausible sites.  We
discount the faint 3-mm emission seen towards G09-59393, favoring
the 1.3-mm position a few arcsec to the east, which is
considerably more significant.  The most dubious of the others is
NGP-113609, although the close proximity of the 3-mm peak to the
SCUBA-2 850-μm emission lends extra confidence.  NGP-126191
displays ≥4-σ emission; again, the near-coincidence
with 850-μm and/or 1.3-mm emission gives additional
confidence.  For the five remaining sources, 3-mm continuum
emission was detected at >5σ.

Of the targets observed in continuum at 1.3 mm using NOEMA, we were
able to measure positions and flux densities for 13 of 15.

The flux densities and coordinates of all these continuum detections
are quoted in Tables <ref> and <ref>, respectively,
corrected for primary beam attenuation, including the small number of
tentative examples (which are marked as such).  The contribution from
emission lines to the continuum flux density is negligible, as we
shall see in what follows.

It is worth noting here that none of the ultrared galaxies observed in
1.3- or 3-mm continuum are revealed as doubles, as would be expected
in the simulations of <cit.>, though it remains possible
that some or all of the ∼ 20% of targets that remain undetected
in continuum have been pushed below our interfeometric detection
threshold by multiplicity.







 §.§ Searching for emission lines


To determine reliable, unambiguous redshifts for a DSFG, we must
detect two or more emission lines.  Ideally we must extract their
spectra at known positions, typically betrayed by interferometric
continuum detection in the cases of DSFGs, thereby maximising the
significance of any line detections. If we extract spectra blindly, we
must correct our statistics for the number of independent sightlines
explored.  Here, our known positions come from the 1.3- and 3-mm
continuum imaging with NOEMA and ALMA, as described in
<ref>; for the 17 sources with reliable coordinates
(Table <ref>), we extracted spectra at the precise positions
of the corresponding continuum detections. 

In the three cases where we have no continuum detection at either 1.3
or 3 mm, tagged as such in Table <ref>, we searched blindly
for emission lines in data cubes that had not been corrected for the
primary beam response.  We convolved these data cubes along their
frequency axis with box-car kernels of width 3, 4 and 7 channels,
corresponding to velocity widths of ≈ 200–500 km s^-1,
typical for DSFG emission lines <cit.>.  For each
convolved cube we created a SNR cube, then searched for peaks above
5σ, where the significance of detections at this stage have not
been corrected for the number of independent sightlines we have
explored.  We also performed the same blind line-search procedure on
continuum-detected sources to look for any additional line emission.
Only known lines were recovered.

As a result of these emission-line searches, we detected multiple (two
or more) emission lines from seven of our targets, one of these
following the detection of three lines by <cit.>, as well as
single emission lines from four targets, where more lines have been
detected subsequently in one case <cit.>.  We thus report
the first eight robust, accurate, unambiguous redshifts for faint,
largely unlensed and thus intrinsically very luminous starbursts.

For all the detected emission lines, we have fitted single-component
Gaussians, measuring the frequency of the line center, and its fwhm.  Continuum emission was subtracted with the UVCONTSUB task in
casa, using all available channels except those close to
emission lines.  The flux of each emission line has been measured with
the casa IMFIT task, from the zeroth moment map (created by
integrating along the frequency axis across the emission line).  There
are no significant discrepencies between these values and those found
from the Gaussian fits.  The measured properties of the emission lines
are summarized in Table <ref>.



 §.§ Unambiguous redshifts via detection of multiple emission lines




We detect multiple emission lines towards seven of our targets, such
that the redshifts of these sources and species/transitions of the
emission lines are confirmed unambiguously.  The properties of those
sources are discussed in <ref>.

For NGP-190387, two emission lines are detected at 85.10 and at
106.23 GHz (see Fig. <ref>), CO(4–3) and CO(5–4) at
z=4.420 (z=4.418 and 4.425, respectively, for the two
lines). NGP-190387 lies close to a group of three faint
(K_ AB≈ 21–22) galaxies, likely at z1, revealed by
NIRI on the 8-m Gemini North telescope (Fig. <ref>), which amplify
the DSFG gravitationally by a factor we cannot constrain meaningfully
at the present time.

Towards G09-81106 we have detected two emission lines, CO(4–3)
and CO(5–4), at 83.36 and 104.19 GHz (Fig. <ref>),
both at z=4.531.  There is no suggestion of gravitational
lensing for G09-81106, either via the presence of unusually
bright near-IR galaxies in the field, or via its submm morphology
as seen in high-resolution ALMA continuum imaging
<cit.>.

Towards G09-83808 we have detected two faint emission lines, at 82.02
and 98.39 GHz (Fig. <ref>), corresponding to CO(5–4) and
CO(6–5) at z=6.026±0.001 and 6.028±0.001, respectively, so an
average of 6.027±0.001.  These lines were also noted by
<cit.> in a spectrum obtained using the Large Millimeter
Telescope.  G09-83808 is near-coincident with a foreground galaxy,
seen clearly in near-IR imaging from the VIKING survey <cit.>, indicative of gravitationally lensing.
This foreground galaxy has a spectroscopic redshift of 0.778, obtained
using X-shooter on the 8-m Very Large Telescope (see
Fig. <ref>).  A lens model based on the morphology
determined by high-resolution ALMA continuum imaging predicts a
gravitional amplification of 8.2± 0.3 <cit.>.





For NGP-284357, we find at least two emission lines, at 97.75 and
136.9 GHz (Fig. <ref>). If these are CO(5–4) and CO(7–6),
the redshifts are 4.895 and 4.892, respectively, so an average of
z=4.894.  At this redshift, the fine-structure lines of neutral
carbon are expected at 83.54 and 137.41 GHz, respectively, and we see
strong hints of corresponding emission – a discrete feature where
C i(1–0) is expected, and C i(2–1) appears to be
broadening the CO(7–6) line.

In the case of NGP-246114, two emission lines are detected at 95.08
and 142.71 GHz (Fig. <ref>), which must be CO(4–3) and
CO(6–5) at z=3.849 and 3.845, respectively, so an average of
z=3.847.

SGP-196076 has been studied in detail by <cit.>, who referred
to the galaxy as SGP-38326, an H-ATLAS nomenclature pre-dating
<cit.>; for further details we refer the readers to that
paper.  Summarising the main results obtained from our 3-mm spectral
scans of SGP-196076: we have detected the CO(5–4) and CO(4–3)
transitions at 84.97 and 106.19 GHz, so at z=4.425
(Fig. <ref>). C i is also seen, at low
significance. Both the continuum emission, from dust, and the CO(5–4)
line emission, indicate clearly that SGP-196076 comprises multiple
(≥ 3) components, with the star formation in each one presumably
triggered by their close proximity – a ongoing merger or strong
interaction.  <cit.> explored the velocity field of the two
largest components, via their CO and [C ii] emission, finding
ordered disk-like rotation.

SGP-261206 displays emission lines at 87.95 and 109.01 GHz
(Fig. <ref>), CO(4–3) and CO(5–4) at
z=4.242± 0.001, around 1.7σ below its photometric
redshift. C i is also seen, at low significance. Very
dust-obscured, distant galaxies should not be coincident with
near-IR sources at the depth of our available imaging, unless
those near-IR sources are gravitationally lensing the dusty
galaxy.  However, the K-band image[Gravitational
  lensing is found likely for three of the galaxies in this
  sample, as revealed by K-band imaging – see Fig. <ref>;
  the rest are devoid of close near-IR counterparts, though the
  depth of the available near-IR imaging does not exclude the
  possibility of distant (z 1) lenses.] of SGP-261206 shown
in Fig. <ref>, from VIKING <cit.>, contains a clear
K-band counterpart, coincident with the dust emission. This
suggests that SGP-261206 is gravitationally lensed by the
foreground galaxy detected in the near-IR image, a hint confirmed
by high-resolution ALMA imaging <cit.>.





  §.§.§ CO line ratios


Our spectra allow us to determine line luminosity ratios for those
galaxies for which multiple lines were detected, typically anchored to
^12CO J=5–4.

In Table <ref> we list the CO line luminosity ratios (i.e.L^'_CO(i - i-1)/L^'_CO(j - j-1))
which we find are consistent with the average values found for SMGs by
<cit.>.





  §.§.§ Rest-frame stacking


For the eight spectra for which we have accurate, unambiguous
redshifts, we can shift the data to the corresponding rest-frame
frequencies and stack them to search for features fainter than
the relatively bright ^12CO lines, following
<cit.> and <cit.>.  The resulting stacked
spectrum is shown in Fig. <ref> where we find the
expected ^12CO ladder between J=4–3 and J=7–6, the
latter broadened by C i(2–1), as well as weak C i(1–0) line emission.  Absorption due to the collisionally
excited H_2O 1_1,0–1_0,1 ground
transition[Due to its very high critical density, this
  line is very difficult to excite in emission, but it can be
  seen relatively easily in absorption, where there is strong
  background continuum.  In the cold ISM, water is normally
  frozen out, forming icy mantles on dust grains; detecting this
  transition in absorption suggests water is gaseous, perhaps
  because of turbulence or shock heating.] may be seen, at low
(≈2.5σ) significance.





  §.§.§ Detection of single emission lines



Towards four of our galaxies, single emission lines were detected,
insufficient to determine the redshift of the source unambiguously, as
the species and/or transition of the emission line is
unknown. However, combining the redshift constraint available by
virtue of far-IR/submm color, often only a handful of strong emission
lines become plausible candidates.

Towards NGP-126191 we detected a clear emission line at 85.77 GHz
(Fig. <ref>), with a fwhm of 570± 180 km s^-1.
As outlined earlier, this line emission is ≈ 3” from weak
3-mm continuum emission, which may be spurious, or may be from a
companion, or the dust emission may be slightly displaced from the
line emission – a relatively common finding amongst DSFGs
<cit.>.  With
a far-IR/submm photometric redshift of 4.9, the most likely
identification for this emission line is ^12CO(4–3) at z=4.38;
however, ^12CO(5-4) would then be expected at 107.1 GHz, with a
similar significance given the typical spectral-line energy
distributions of DSFGs, and such a line is not detected
(Fig. <ref>).  ^12CO(3–2) and ^12CO(5–4) are the
other most likely possibilities, at z=3.03 and z=5.71.

Towards NGP-111912 we detected a weak emission line at 95.15 GHz
(Fig. <ref>), with a fwhm of 440± 200 km s^-1.
The line emission is coincident spatially with 1.3-mm continuum
emission (Fig. <ref>).  With a photometric redshift estimate
of 3.28^+0.36_-0.26, the emission line may be ^12CO(4–3) at
z=3.84, in which case we would not expect any other lines in our
current frequency coverage, consistent with our data.

SGP-32338 is a similar case: we detected an emission line at
101.07 GHz, with a fwhm of 630± 80 km s^-1.  The line
emission is again coincident with its 3-mm continuum emission
(Fig. <ref>).  The photometric redshift,
4.51^+0.47_-0.39, makes ^12CO(5–4) at z=4.70 the most
likely candidate emission line.  Because the line lies close to the
center of the spectral coverage, we would not then expect to detect
any other lines, despite the high sensitivity and the wide frequency
range available.

Follow-up observations are required to determine unambiguous redshifts
for these three galaxies.

In SGP-354388, dubbed the `Great Red Hope' because it is amongst
the reddest galaxies seen by Herschel, our ALMA spectrum
reveals a line at 98.34 GHz, coincident with 3-mm continuum
emission.  Extensive further follow-up observations of
SGP-354388, reported by <cit.>, confirm that the line
at 98.34 GHz is, in fact, the C i(1–0) transition at
z=4.002±0.001, a rare ≈2σ deviation from the
photometric redshift which can be attributed at least partially
to dusty galaxies surrounding SGP-354388, at the same redshift,
which contaminate the flux densities measured at ≥500 μm
by SPIRE and LABOCA <cit.>.





  §.§.§ Galaxies where no emission lines are detected



In our remaining spectral scans, regardless of whether or not we
have secure positions via continuum detections, we have found no
compelling evidence of line emission (Fig. <ref>).
Note that the mean [median] log_10 far-IR luminosity of this
subsample, 13.2 [13.1], for an average [median] photometric
redshift of 3.79 [3.70], which is 0.3–0.4 dex below that of the
sample in which line emission has been detected.  For a fwhm line width of 500  and typical brightness
temperature and /CO ratios (see later, <ref>), this
equates to a peak line flux density in CO(4–3) of 1.6
[1.4] mJy, comparable to the r.m.s noise levels in our spectral
scans, which goes some considerable way towards explaining why we
detected no line emission for this sub-sample.







 §.§ Spectral energy distributions



Since we have added continuum flux density measurements at 1.3 and/or
3 mm for many of our targets, as well as some unambiguous
spectroscopic redshifts, it is worth repeating the SED fits performed
by <cit.>.  We have constructed the SEDs of our targets,
utilizing data from SPIRE at 250, 350 and 500 μm, from SCUBA-2 at
850 μm <cit.>, from NOEMA at 1.3 mm, and from NOEMA
and/or ALMA at 3 mm – see Table <ref>.  For details of the
SED fits for SGP-32386, we refer readers to <cit.>.

Like , we employ SED templates representative of
high-redshift DSFGs: the average SEDs from <cit.>,
<cit.> and <cit.>, and the observed SEDs of
individual targets – the Cosmic Eyelash <cit.>, HFLS 3 <cit.>, G15.141 <cit.>
and Arp 220 <cit.>.

We have restricted our SED work to the sources with unambiguous
redshift determinations, such that we need shift only the flux
density scale of the templates to fit the observed SEDs. We
adopted the lowest χ^2 values, calculated from the
difference between the templates and the observed flux densities,
with inverse weighting of the flux density uncertainties.  These
best-fitting SEDs are plotted in Fig. <ref>, with the
corresponding IR luminosities (L_ 8-1000 μ m) and SFRs
listed in Table <ref>, the latter calculated using the
calibration of <cit.>, <cit.> and
<cit.>, with a Salpeter IMF <cit.>.  On the basis of high-resolution ALMA
continuum and line observations, <cit.> found that
SGP-196076 at z=4.425 comprises at least three components,
their on-going merger driving large masses of turbulent gas to
form stars, as is ubiquitous amongst objects with such high
intrinsic IR luminosties <cit.>.



  §.§.§ Modified blackbody fits


To better quantify the thermal dust emission we have performed SED
fits using modified blackbody (MBB) spectra, again by minimizing
χ^2.  We adopted an optically thin model with single dust
temperature (i.e.S_ν(T_ d)∝ (ν/ν_
    c)^β B_ν(T_ d)), where ν_c is the frequency
at which the optical depth is unity, B_ν(T_ d) is Planck
function at frequency, ν, and dust temperature, T_ d, and
β is the dust emissivity index.  We fixed ν_ c to
1.5 THz <cit.> and adopted
κ_850 μ m = 0.15  m^2 kg^-1
<cit.>.  Dust emissivity, β, being poorly
constrained by our data, was fixed to values of 1.5, 2.0 or 2.5
<cit.>.

The assumption of a single dust temperature means that we are
measuring the emission-weighted mean dust temperature and dust mass of
all the dust components in the galaxy.  Another advantage of this
approach is that it allows us to compare directly with other
high-redshift DSFGs, which are usually described in terms of
single-temperature MBB fits (see Table <ref>).  Finally, the
modest sampling of our SEDs, especially at the short wavelengths
required to constrain hot dust components, prevents meaningful
multi-temperature MBB fitting.

The best MBB fits are plotted in Fig. <ref>.  Minimum χ^2
were obtained with β=1.5 for NGP-190387, β=2.0 for
NGP-246114 and NGP-284357.  G09-81106 proved difficult to reconcile
with a value of β below 2.5 – probably the result of using a
single temperature MBB <cit.>.  Changing
β results in an increase/decrease of the dust temperature by
∼ 2–3 k, and the dust mass by ∼ 0.1 dex.  The
resulting dust temperatures are in the range ∼31–36 k,
and dust masses, ∼ 0.2–4.1×10^9 M_⊙. For their
high IR luminosities, the dust temperatures of our galaxies are
relatively low <cit.>.  Individual values
of T_ d and M_ d are listed in Table <ref>.







 §.§ Molecular gas masses


Although low-J transitions of CO, or C i, are much preferred
when tracing the remaining reservoirs of molecular hydrogen
<cit.>, we can estimate those gas masses from
higher-J CO lines by assuming the average CO line ratio for SMGs, as
measured by <cit.>
and <cit.>, and tabulated by the latter:
L^'_CO(7-6)/L^'_CO(1-0) = 0.18,
L^'_CO(6-5)/L^'_CO(1-0) = 0.21,
L^'_CO(5-4)/L^'_CO(1-0) = 0.32 and
L^'_CO(4-3)/L^'_CO(1-0) = 0.41,
bearing in mind that there can be large variations.  We find that
L_ IR-L^'_ CO as derived from different – usually
neighbouring – transitions are consistent.  We have taken the average
L^'_CO(1-0) from the available high-J CO
transitions, then calculated the molecular gas masses using
α_ CO=0.8  M_⊙ (K km s^-1 pc^2)^-1,
the value often assumed for high-redshift starbursts and local ULIRGs
since the work of <cit.>. Estimates of gas-to-dust mass
ratios then lie in the range 50–140, consistent with those of local
galaxies. Our M_ H_2 estimates are listed in
Table <ref>. 

Since luminous CO(5–4) and CO(4–3) emission can be generated by the
presence of a massive molecular gas reservoir, or by a much smaller
amount of highly excited molecular gas, follow-up observations of
low-J CO transitions are required to better determine
M_ H_2, modulo the effects of cosmic rays laid out by
<cit.>.





 §.§ L_ IR - L^'_ CO correlation



The relationship between star formation and total molecular gas
content is often shown via a plot of the key observables, L_ IR
versus L^'_ CO, and can reveal if and how star-formation
efficiency (SFE) changes with the amount of molecular gas available
for star formation.  We have constructed a plot of
L_ IR - L^'_ CO using our z>4 IR-luminous
galaxies, other high-redshift unlensed DSFGs
<cit.> and local U/LIRGS
<cit.> — see Fig. <ref>.  A linear fit to all
the data has a slope, 1.15±0.02 <cit.>.

Caution is required here, however, since most of the high-redshift
targets, ours included, are detected in mid-J CO transitions. Using
only CO(1–0) observations, with self-consistent determinations of IR
luminosity, <cit.> reported a slope significantly below
unity, showing that adopting mid-J CO transitions for high-redshift
galaxies and CO(1–0) transitions for low-redshift galaxies may
artificially steepen the slope.  Differential amplification is likely
also an issue for the lensed galaxies in Fig. <ref>, where the
amplifications derived for the dust, the CO(1–0) and/or high-J CO
lines likely differ significantly. Finally, we note that several
studies have suggested that our adopted value of α_ CO is
too low, including <cit.> and <cit.>; indeed,
if we were to apply the formalism of <cit.>, who use
optically thin long-wavelength dust emission to probe the mass of
molecular gas, we arrive at a value ∼ 3.5× higher, the
equivalent of α_ CO≈ 3 
  M_⊙ (K km s^-1 pc^2)^-1.



 §.§ Depletion timescale


The average gas-depletion timescale of our galaxies, t_ depl,
is around 50 Myr, modulo the possibility of considerably higher gas
masses noted in <ref>.  Taken at face value, this t_ depl
is consistent with the idea that our targets are rapidly building a
significant mass of stars, which may be picked up in a later phase at
z∼2–3 as massive `red-and-dead' galaxies by near-IR imaging
surveys <cit.>.



§ CONCLUSIONS


We report spectral scans of Herschel-selected ultra-red
galaxies with photometric redshifts estimated to lie at
≳4. For each of 21 galaxies we have covered
Δν≈ 20 GHz using ALMA and NOEMA in the 3-mm
waveband.  We have determined the redshifts of seven galaxies
unambiguously, in the range z=3.85–6.03, detecting multiple
emission lines, usually CO rotational transitions. One of these
redshifts was determined independently by <cit.>.

For an additional four galaxies, single emission lines are
detected, one of which has been shown by <cit.> to lie
at z=4.002. Candidate redshifts are suggested, based on their
photometric redshifts. Follow-up observations are required to
measure their redshifts unambiguously, except in that one case.

Since the comparison of photometric and spectroscopic redshifts
for this sample by <cit.>, two new spectroscopic
redshifts have been determined, one below and one above the
respective photometric redshifts.  Although the offsets for these
two galaxies are larger than the expected uncertainties in
z_ phot, the overall scatter in
(z_ phot - z_ spec) / (1 + z_ spec) is still
consistent with (actually, slightly better than) that of the
training set. In the worst case, the offset can be understood in
terms of contamination of flux densities measured at
≥500 μm by a cluster of dusty galaxies
<cit.>.

Our sample of redshift-confirmed galaxies contains extraordinarily
IR-luminous starbursts, with an average SFR of
≈ 2900 M_⊙ yr^-1.  They are also among the most
massive known, in terms of molecular gas mass, and dust mass, with
M_ H_2≈ 1.8×10^11  M_⊙ on average, and
M_ d∼ 0.9–4.1×10^9 M_⊙.

Lurking amongst our IR-luminous galaxies we find three lensed systems.
These would otherwise have been hailed as the most luminous known
starbursts.  It is notable that the vast majority of the brightest
systems selected by Herschel have been revealed as either lensed
galaxies, groups/clusters of starburst galaxies, starbursts with
buried AGN, or some combination of the three
<cit.>, which suggests strongly that there
exists a limit to the luminosity of individual starbursting galaxies.

Combining local U/LIRGs, other high-redshifts DSFGs and our new
redshift-confirmed galaxies, the resulting
L_ IR - L^'_ CO correlation has slope close to
unity, 1.14±0.02, suggesting slightly higher
  star-formation efficiency in the most IR-bright galaxies.
 
The gas-depletion timescale of our galaxies, around 50 Myr, is
consistent with the idea that our targets may be picked up in a later
phase at z∼2–3 as massive `red-and-dead' galaxies by near-IR
imaging surveys.
 


§ ACKNOWLEDGEMENTS


RJI, IO, VA, LD, SM, JMS and ZYZ acknowledge support from the
European Research Council in the form of the Advanced
Investigator Programme, 321302, COSMICISM.  JMS also acknowledges
financial support through an EACOA fellowship.  DR acknowledges
support from the National Science Foundation under grant number
AST-1614213. HD acknowledges financial support from the Spanish
Ministry of Economy and Competitiveness (MINECO) under the 2014
Ramón y Cajal program, MINECO RYC-2014-15686. We thank the
referee, Francoise Combes, for her rapid and constructive
feedback. This work was based on observations carried out with
the IRAM Interferometer, NOEMA, supported by INSU/CNRS (France),
MPG (Germany), and IGN (Spain).  This paper makes use of the
following ALMA data: ADS/JAO.ALMA#2013.1.00499.S. ALMA is a
partnership of ESO (representing its member states), NSF (USA)
and NINS (Japan), together with NRC (Canada) and NSC and ASIAA
(Taiwan) and KASI (Republic of Korea), in cooperation with the
Republic of Chile.  The Joint ALMA Observatory is operated by
ESO, AUI/NRAO and NAOJ. Based on observations collected at the
European Organisation for Astronomical Research in the Southern
Hemisphere under ESO programme 090.A-0891(A).  Based on
observations obtained at the Gemini Observatory, which is
operated by the Association of Universities for Research in
Astronomy, Inc., under a cooperative agreement with the NSF on
behalf of the Gemini partnership: the National Science Foundation
(United States), the National Research Council (Canada), CONICYT
(Chile), Ministerio de Ciencia, Tecnología e Innovación
Productiva (Argentina), and Ministério da Ciência,
Tecnologia e Inovação (Brazil).







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