The GADOT Galaxy Survey: Dense Gas and Feedback in Herschel-selected Starburst Galaxies at Redshifts 2 to 6

We successfully detect CO(J = 9→8) emission toward all 16 galaxies in the sample at peak S/Ns of 5–16 in the continuum-subtracted moment-0 maps (except for HeLMS-65, which is detected at a peak S/N of 4.2; Figure 1). The continuum subtraction was carried out in the visibility plane, and accounts for the spectral slope of the continuum where measurable within the line-free spectral ranges. The line emission is only marginally resolved at best in all cases except for HeLMS-9, which is resolved into two components. Line spectra were extracted centered on the peak positions of the line-averaged emission (Figure 6).

Line parameters were obtained from Gaussian fitting to the CO line profiles, using two Gaussian components where appropriate. Other lines in the bandpass were fitted simultaneously with additional Gaussian functions to include reliable estimates of the uncertainties of all fitting parameters, and the integrated line fluxes were compared to those found from two-dimensional Gaussian fitting to the emission in the moment-0 maps to warrant internal consistency. The resulting line fluxes are reported in Table 2, and the line luminosities are given in Table 4.

We successfully detect OH⁺(1₁→0₁) emission or absorption toward all 16 galaxies in the sample, and OH⁺(1₂→0₁) toward all 4 galaxies in which the line was covered (Figures 3 and 4). OH⁺ absorption (emission) is detected or tentatively detected in 14/16 (10/16) sources. 2/16 sources show OH⁺ emission, but no absorption. 6/16 sources show OH⁺ absorption, but no emission. 8/16 sources show evidence for both absorption and emission components when tentative detections are included. Three of the absorption lines are tentatively detected at peak S/Ns of 2.4–2.9, two are detected at moderate peak S/Ns of 3.3, and the remaining 12 lines are detected solidly at peak S/Ns of 4.6–11 (all S/Ns were estimated based on the continuum-subtracted moment-0 maps). The peak postions of the absorption features are always coincident with the continuum peak positions within the relative uncertainties. One of the emission lines is tentatively detected at a peak S/N of 2.5, five are detected at moderate peak S/Ns of 3.2–3.7, and seven are detected solidly at peak S/Ns of 4.1–9.1 (two sources, HeLMS-9 and 45, show multiple emission components). All detections are plausible, but independent confirmation is required for all features with S/N < 4 (S/N < 5 for sources that show potential spatial offsets from the CO and continuum peaks).

Line spectra were extracted centered on the peak positions of the line-averaged emission (Figures 7 and 8). Separate spectra were extracted for absorption and emission peaks where the positions may not coincide (HeLMS-44, 59, and 65, and HLock-102), and/or where multiple emission components are detected (HeLMS-9 and 45 only). Most of the offsets are marginal due to the moderate S/N of the emission components (see discussion in Section 3.3) and the potential interplay between emission/absorption components (such that OH⁺ emission may be partially masked due to foreground OH⁺ absorption in some velocity ranges; see more detailed discussion below). As such, while our data may suggest that spatial offsets between absorption/emission components such as previously observed in ADFS-27 (Riechers et al. 2021) may not be uncommon, we defer a more general interpretation of absorption/emission peak position offsets to future work on higher-resolution data. Within the uncertainties, the OH⁺(1₁→0₁) and OH⁺(1₂→0₁) lines show the same profiles and velocities for all sources where both were covered, with the possible exception of HeLMS-62, where the absorption component of the former may be broader. The S/N of the OH⁺(1₂→0₁) line in HeLMS-28 is too limited to warrant further interpretation, but it is possible that the red wing of the line is partially filled in by NH₂ emission, making the OH⁺(1₂→0₁) line profile appear more asymmetric than the OH⁺(1₁→0₁) line (see Section 3.3 for further discussion). Because of the limited width of the bandpass, the OH⁺(1₁→0₁) features are only partially covered for HeLMS-59 and 62, but the OH⁺(1₂→0₁) lines are virtually fully covered. As such, part of the interpretation of these sources is based on the latter lines alone.

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Line parameters were obtained from Gaussian fitting to the OH⁺ line profiles, using two Gaussian components where appropriate. The CO(J = 9→8) lines (and other lines where appropriate) were fitted simultaneously with additional Gaussian functions to include reliable estimates of the uncertainties of all fitting parameters, and the integrated line fluxes were compared to those in the moment-0 maps to warrant internal consistency. The resulting line fluxes are reported in Table 2. HeLMS-9 shows a blueshifted OH⁺ emission component that is sufficiently broad to be partially blended with the CO(J = 9→8) line. To reliably separate both lines, we thus compared the CO(J = 9→8) line profile to the CO(J = 5→4) line profile (Figure 9), which shows a line width that is consistent with our multicomponent fits to the CO(J = 9→8) and OH⁺ features. The complexity of the OH⁺ emission in this source (both spatially and spectrally) warrants further follow-up observations for a more detailed component separation.

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Velocity shifts between the CO(J = 9→8) (representing the systemic redshift) and OH⁺ absorption and emission lines from the Gaussian fitting are provided in Table 3. All shifts were calculated at the centroid positions of each line. Values in parentheses are consistent with no shifts at the current S/N of our data. Nine sources show no significant velocity shifts in the absorption lines, while four and three sources show significant red- and blueshifts of the OH⁺ absorption, respectively. The absorption velocity shifts are in the range of ∼130–360 km s⁻¹, which is typically less than the CO(J = 9→8) line widths. Two sources show no significant velocity shifts in the emission lines, three show significant blueshifts, and five show significant redshifts. One source, HeLMS-9, shows components that are both blue- and redshifted, where the latter component is closer to the CO(J = 9→8) and OH⁺ absorption peaks. The emission velocity shifts are in the range of ∼30–1000 km s⁻¹. The highest redshifts exceed the CO(J = 9→8) line widths.

Table 3. Line Shifts and OH⁺ Optical Depths

Name	Redshift	${{\rm{v}}}_{0}^{\mathrm{OH}+,\mathrm{abs}}$–v${}_{0}^{\mathrm{CO}}$	${{\rm{v}}}_{0}^{\mathrm{OH}+,\mathrm{em}}$–v${}_{0}^{\mathrm{CO}}$	Origin	τOH+	τOH+ dv	N(OH+) a	$L{{\prime} }_{{\mathrm{OH}}^{+}(1-0)}^{\,\mathrm{em}}$ b
		( km s−1)	( km s−1)			( km s−1)	(1014 cm−2)	(1010 Ll )
HeLMS-5	2.2919	258 ± 33	(795 ± 63)	ambiguous	${1.3}_{-0.4}^{+0.7}$	${343}_{-109}^{+186}$	${16.7}_{-5.3}^{+9.0}$	0.50 ± 0.20
HXMM-01	2.3079	(–457 ± 36)		ambiguous	${0.32}_{-0.12}^{+0.14}$	${116}_{-44}^{+50}$	${5.6}_{-2.1}^{+2.4}$
HeLMS-9	2.3934	(68 ± 35)	–341 ± 48(e)	ambiguous	${0.25}_{-0.11}^{+0.10}$	${53}_{-21}^{+23}$	${2.6}_{-1.0}^{+1.1}$	1.69 ± 0.40
			313 ± 77(w)
HeLMS-61	2.4022		–26 ± 10	inflow?				1.01 ± 0.14
			–232 ± 11
HeLMS-45	2.4726	(–6 ± 17)	(622 ± 18)(ne)	outflow	${0.55}_{-0.13}^{+0.15}$	${173}_{-41}^{+47}$	${8.4}_{-2.0}^{+2.3}$	1.47 ± 0.29
			397 ± 25(sw)
J0210+0016	2.5534		–32 ± 15	inflow?				4.52 ± 0.70
HeLMS-44	2.6895	177 ± 36	1026 ± 61	outflow?	${0.30}_{-0.04}^{+0.05}$	${179}_{-26}^{+27}$	${8.7}_{-1.3}^{+1.3}$	1.09 ± 0.32
Orochi	3.3903	–132 ± 41		outflow	0.43 ± 0.09	${146}_{-29}^{+32}$	${7.1}_{-1.4}^{+1.5}$
HeLMS-59 c	3.4346	213 ± 20	94 ± 60	inflow	${0.26}_{-0.10}^{+0.11}$	${88}_{-33}^{+36}$	${2.5}_{-0.9}^{+1.0}$	1.66 ± 0.45
HeLMS-62 c	3.5027	–363 ± 15	561 ± 37	outflow	${0.46}_{-0.09}^{+0.10}$	${199}_{-39}^{+43}$	${11.1}_{-1.3}^{+1.4}$	3.88 ± 0.89
HeLMS-65	3.7966	(136 ± 20)	–197 ± 40	inflow	${1.88}_{-1.19}^{+\infty }$	${244}_{-154}^{+\infty }$	${11.9}_{-7.5}^{+\infty }$	1.25 ± 0.38
		(502 ± 36)
HeLMS-28	4.1625	(20 ± 28)		ambiguous	${0.40}_{-0.05}^{+0.06}$	${161}_{-21}^{+23}$	${7.8}_{-1.0}^{+1.1}$
HeLMS-10	4.3726	(49 ± 49)		ambiguous	${0.57}_{-0.21}^{+0.27}$	${83}_{-31}^{+39}$	${4.0}_{-1.5}^{+1.9}$
HXMM-30	5.094	(16 ± 139)		ambiguous	${1.43}_{-0.45}^{+0.83}$	${1109}_{-346}^{+642}$	${54}_{-17}^{+31}$
HeLMS-34	5.1614	(–133 ± 150)		ambiguous	${0.75}_{-0.21}^{+0.27}$	${417}_{-120}^{+153}$	${20.3}_{-5.8}^{+7.5}$
HLock-102	5.2915	(–152 ± 159)	544 ± 193	outflow	${1.90}_{-0.76}^{+\infty }$	${381}_{-152}^{+\infty }$	${18.5}_{-7.4}^{+\infty }$	4.33 ± 0.80
ADFS-27 d	5.6550	–216 ± 16	233 ± 10	outflow	0.35 ± 0.04	234 ± 26	11.4 ± 1.2	0.20 ± 0.02
HFLS3 d	6.3369	179 ± 74	⋯ e	ambiguous	${0.49}_{-0.17}^{+0.21}$	${205}_{-72}^{+87}$	${10.0}_{-3.5}^{+4.2}$	>1.48

Notes. Tentative detections are indicated in italic font. Values in parentheses are consistent with no velocity shifts (tentative detections are included in this category by default). "Origin" is the most likely interpretation based on the presence of P-Cygni (outflow) or inverse P-Cygni (inflow) profiles, or when not available or ambiguous, the blue- or redshift of the absorption and emission components.

^a These values can be translated into approximate neutral H i column densities by assuming a relative abundance of [OH⁺/H] = –7.8, i.e., by multiplying the listed values by a factor of 6.3 × 10⁷ (e.g., Bialy et al. 2019). ^b Given in units of L_l = K km s⁻¹ pc². Apparent values not corrected for gravitational magnification where applicable. ^c Velocity shifts and $L{{\prime} }_{{\mathrm{OH}}^{+}(1-0)}^{\,\mathrm{em}}$ are reported relative to OH⁺ 1₂→0₁ instead of 1₁→0₁ due to the incomplete coverage of the latter by our observations. ^d Adopted from Riechers et al. (2013, 2021). ^e Component not fully covered by the bandpass.

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Table 4. Herschel/SPIRE and 870 μm fluxes, CO(J = 9→8) Luminosities, and Parameters Obtained from Dust Spectral Energy Distribution Fitting to Our Sample and Four Sources in the Literature (Including Two Secondary Sources from the Master Sample)

Name	Redshift	S250	S350	S500	S870 a	Tdust	βIR	λpeak	λ0	LFIR b , c	LIR b , c , d	$L{{\prime} }_{\mathrm{CO}(9-8)}$ b , e	LCO(9−8) b	References
		(mJy)	(mJy)	(mJy)	(mJy)	(K)		(μm)	(μm)	(1012 L⊙)	(1012 L⊙)	(1010 Ll )	(108 L⊙)
HeLMS-5	2.2919	312 ± 6	244 ± 7	168 ± 8	49 ± 5	${66.5}_{-6.8}^{+5.1}$	${2.05}_{-0.45}^{+0.48}$	${74}_{-3}^{+4}$	${205}_{-52}^{+22}$	${40.0}_{-1.6}^{+1.4}$	${68.1}_{-5.7}^{+6.7}$	2.92 ± 0.45	10.4 ± 1.6	1
HXMM-01	2.3079	180 ± 7	192 ± 8	132 ± 7	29 ± 3	${57.8}_{-2.8}^{+1.4}$	${2.52}_{-0.11}^{+0.18}$	${88}_{-2}^{+4}$	${236}_{-37}^{+11}$	${22.8}_{-0.4}^{+1.0}$	${37.3}_{-1.5}^{+1.8}$	2.37 ± 0.39	8.5 ± 1.4	1
HeLMS-9	2.3934	166 ± 6	195 ± 6	135 ± 7		${43.0}_{-8.6}^{+7.3}$	${1.82}_{-0.23}^{+0.23}$	${95}_{-2}^{+3}$	${138}_{-89}^{+58}$	${21.2}_{-1.6}^{+1.5}$	${33.4}_{-7.0}^{+1.1}$	2.32 ± 0.45	8.3 ± 1.6	1
HeLMS-61	2.4022	148 ± 6	187 ± 6	147 ± 9		${42.7}_{-7.3}^{+5.4}$	${1.91}_{-0.31}^{+0.32}$	${101}_{-3}^{+4}$	${170}_{-87}^{+51}$	${19.3}_{-1.4}^{+1.3}$	${30.3}_{-5.7}^{+0.7}$	1.33 ± 0.17	4.73 ± 0.60	1
HeLMS-45	2.4726	214 ± 7	218 ± 7	172 ± 9		${58.0}_{-3.6}^{+2.7}$	${2.70}_{-0.35}^{+0.38}$	${87}_{-3}^{+4}$	${208}_{-24}^{+8}$	${31.2}_{-1.5}^{+1.3}$	${46.3}_{-4.5}^{+2.8}$	6.92 ± 0.99	24.7 ± 3.5	1
J0210+0016	2.5534	826 ± 7	912 ± 7	717 ± 8	167 ± 4	${59.8}_{-8.6}^{+6.3}$	${2.01}_{-0.14}^{+0.07}$	${87}_{-3}^{+5}$	${256}_{-80}^{+63}$	${130.6}_{-6.8}^{+3.4}$	${262.0}_{-91.5}^{+70.0}$	7.43 ± 0.66	26.5 ± 2.4	1
HeLMS-44	2.6895	271 ± 6	336 ± 6	263 ± 8		${50.3}_{-4.2}^{+2.2}$	${2.15}_{-0.26}^{+0.28}$	${93}_{-1}^{+3}$	${197}_{-51}^{+3}$	${47.7}_{-2.0}^{+1.5}$	${73.7}_{-11.6}^{+0.2}$	4.86 ± 0.80	17.3 ± 2.9	1
Orochi	3.3903	92 ± 7	122 ± 8	113 ± 7	63 ± 6	${55.0}_{-1.5}^{+1.3}$	${2.75}_{-0.27}^{+0.26}$	${93}_{-2}^{+3}$	${274}_{-16}^{+11}$	${27.4}_{-0.8}^{+1.0}$	${48.7}_{-1.1}^{+1.3}$	2.50 ± 0.38	8.9 ± 1.4	1
HeLMS-59	3.4346	193 ± 7	252 ± 6	202 ± 8		${53.7}_{-9.4}^{+6.6}$	${1.69}_{-0.20}^{+0.18}$	${79}_{-1}^{+2}$	${127}_{-77}^{+50}$	${60.1}_{-1.6}^{+1.6}$	${92.5}_{-14.2}^{+5.0}$	5.65 ± 0.63	20.1 ± 2.3	1
HeLMS-62	3.5027	151 ± 6	209 ± 6	205 ± 8		${56.1}_{-2.1}^{+2.0}$	${2.21}_{-0.43}^{+0.44}$	${88}_{-2}^{+3}$	${209}_{-26}^{+22}$	${52.1}_{-1.2}^{+1.2}$	${76.8}_{-4.8}^{+2.1}$	7.7 ± 1.5	27.6 ± 5.4	1
HeLMS-65	3.7966	36 ± 7	49 ± 6	72 ± 7	23 ± 4	${53.6}_{-7.9}^{+7.7}$	${2.10}_{-0.21}^{+0.21}$	${90}_{-7}^{+7}$	${205}_{-51}^{+50}$	${15.7}_{-1.4}^{+1.4}$	${24.2}_{-4.1}^{+3.1}$	1.20 ± 0.28	4.3 ± 1.0	1
HeLMS-28	4.1625	113 ± 7	177 ± 6	209 ± 8	82 ± 4	${53.8}_{-6.8}^{+5.0}$	${1.74}_{-0.17}^{+0.16}$	${82}_{-2}^{+2}$	${150}_{-48}^{+24}$	${63.5}_{-1.6}^{+1.7}$	${97.3}_{-12.2}^{+18.5}$	7.21 ± 0.60	25.7 ± 2.2	1
HeLMS-10	4.3726	88 ± 6	129 ± 6	155 ± 7	82 ± 5	${58.8}_{-3.2}^{+3.8}$	${1.66}_{-0.33}^{+0.32}$	${82}_{-3}^{+3}$	${208}_{-39}^{+40}$	${53.7}_{-1.6}^{+1.6}$	${88.0}_{-12.0}^{+14.8}$	4.39 ± 0.78	15.7 ± 2.8	1
HXMM-30	5.094	30 ± 5	50 ± 8	55 ± 7	28 ± 2	${74.2}_{-4.6}^{+4.7}$	${2.64}_{-0.39}^{+0.37}$	${69}_{-4}^{+4}$	${242}_{-34}^{+29}$	${24.7}_{-1.7}^{+1.8}$	${44.1}_{-6.4}^{+4.2}$	2.56 ± 0.52	9.2 ± 1.9	1
HeLMS-34	5.1614	62 ± 6	104 ± 6	116 ± 7	41 ± 3	${63.0}_{-8.3}^{+7.8}$	${1.36}_{-0.18}^{+0.14}$	${66}_{-2}^{+2}$	${93}_{-64}^{+50}$	${53.8}_{-2.0}^{+2.1}$	${86.5}_{-7.8}^{+5.1}$	6.98 ± 0.67	24.9 ± 2.4	1
HLock-102	5.2915	56 ± 4	118 ± 4	139 ± 4	70 ± 7	${55.7}_{-7.5}^{+5.1}$	${1.80}_{-0.08}^{+0.07}$	${73}_{-1}^{+2}$	${99}_{-43}^{+31}$	${68.2}_{-1.3}^{+1.5}$	${96.7}_{-5.0}^{+3.4}$	12.1 ± 1.9	43.1 ± 6.7	1
ADFS-27	5.6550	14 ± 2	19 ± 2	24 ± 2	25 ± 2	${59.2}_{-4.1}^{+3.3}$	${2.52}_{-0.17}^{+0.19}$	${85}_{-4}^{+5}$	${191}_{-19}^{+11}$	${15.8}_{-1.9}^{+1.0}$	${23.8}_{-2.2}^{+2.3}$	2.48 ± 0.06	8.84 ± 0.20	2, 3
HFLS3	6.3369	12 ± 2	32 ± 2	47 ± 3	33 ± 2	${63.3}_{-5.8}^{+5.4}$	${1.94}_{-0.09}^{+0.07}$	${73}_{-1}^{+2}$	${142}_{-27}^{+25}$	${29.3}_{-1.3}^{+1.4}$	${55.0}_{-2.2}^{+3.0}$	4.51 ± 0.73	16.1 ± 2.6	4, 5
Literature:
SDP-17b f	2.3051	354 ± 7	339 ± 8	220 ± 9	55 ± 3	${60.3}_{-4.8}^{+2.8}$	${2.32}_{-0.24}^{+0.25}$	${83}_{-3}^{+4}$	${204}_{-27}^{+13}$	${45.3}_{-2.2}^{+1.7}$	${70.9}_{-9.5}^{+3.6}$			6
Eyelash	2.3259	366 ± 55	429 ± 64	325 ± 49	106 ± 12	${48.3}_{-2.0}^{+1.1}$	${2.81}_{-0.17}^{+0.18}$	${105}_{-2}^{+3}$	${223}_{-25}^{+10}$	${44.9}_{-1.9}^{+2.9}$	${66.2}_{-2.8}^{+4.1}$	1.19 ± 0.56	4.2 ± 2.0	7, 8
HerBS-89a	2.9497	72 ± 6	103 ± 6	96 ± 7	53 ± 4	${49.7}_{-2.8}^{+2.6}$	${2.27}_{-0.10}^{+0.10}$	${102}_{-5}^{+5}$	${256}_{-22}^{+20}$	${16.8}_{-1.0}^{+1.0}$	${26.0}_{-3.1}^{+0.7}$	0.88 ± 0.10	3.14 ± 0.37	9
HLock-01 f	2.9574	425 ± 10	340 ± 10	233 ± 11	53 ± 1	${77.4}_{-3.0}^{+2.0}$	${1.93}_{-0.19}^{+0.17}$	${64}_{-1}^{+1}$	${151}_{-20}^{+15}$	${87.1}_{-1.1}^{+1.9}$	${176.7}_{-2.8}^{+4.7}$	6.3 ± 1.6	22.5 ± 5.8	10, 11, 12

Notes. [1] this work; [2–5] Riechers et al. (2013, 2017, 2020b, 2021); [6] Bussmann et al. (2013); [7] Swinbank et al. (2010); [8] Danielson et al. (2011); [9] Berta et al. (2021); [10] Conley et al. (2011); [11] Riechers et al. (2011); [12] Scott et al. (2011).

^a Fluxes for J0210+0016, HeLMS-28, 10, HLock-102, and HerBS-89a are measured at 850 μm. Fluxes for HeLMS-5, HFLS3, SDP-17b, the Eyelash, and HLock-01 are measured at 880 μm. ^b Apparent values not corrected for gravitational magnification where applicable. Published lens magnification factors are HeLMS-5 μ_L = 8.3 ± 0.6 (Dye et al. 2018); HXMM-01 subcomponents: μ_L = 1.39 ± 0.19; 1.21 ± 0.01; 1.29 ± 0.15 (Bussmann et al. 2015); J0210+0016 μ_L = 14.7 ± 0.3 (Geach et al. 2018); Orochi μ_L = 5.33 ± 0.19 (Bussmann et al. 2015); HLock-102 μ_L = 12.5 ± 1.2 (Riechers et al. 2020b); HFLS3 μ_L = 1.8 ± 0.6 (Riechers et al. 2020b); SDP17b μ_L = 4.9 ± 0.7 (Bussmann et al. 2013); Eyelash μ_L = 37.5 ± 4.5 (Swinbank et al. 2011); HerBS-89a μ_L = 5.05 ± 0.03 (Berta et al. 2021); HLock-01 μ_L = 10.9 ± 0.7 (Gavazzi et al. 2011). ^c L_FIR (L_IR) is integrated over the 42.5–122.5 μm (8–1000 μm) range in the rest frame. ^d Multiply L_IR by a factor of 1.0 × 10⁻¹⁰ to obtain apparent star formation rates (SFRs), under the assumption of a Chabrier (2003) stellar initial mass function. ^e Given in units of L_l = K km s⁻¹ pc². ^f Source is also part of the GADOT master sample, but not reanalyzed with the same methods as used for the sample studied here.

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Blueshifted absorption and redshifted emission components (i.e., P-Cygni profiles) are expected for gas that is outflowing along the line of sight, while the opposite (i.e., inverse P-Cygni profiles) is expected for inflows. As such, the highest velocity emission components may be associated with outflowing gas beyond the escape velocities of their host galaxies. We caution that the centroid velocities alone may not always be sufficient to distinguish between inflows and outflows. As an example, the OH⁺ emission centroid of HeLMS-59 appears to be significantly redshifted relative to CO from the spectral line fit alone (which would suggest an outflow), but it shows an inverse P-Cygni profile, and the strongest part of the emission is seen at blueshifted velocities. Thus, HeLMS-59 is most likely dominated by infalling material, even though we cannot rule out the presence of some outflowing gas. Overall, our sample appears to show similar numbers of examples of outflows and inflows based on velocity shifts alone under the assumption of simple spherical geometries, and a 3:2 ratio ¹⁰ when combining line profiles and velocity shifts, but observations at higher spatial resolution are desirable to study the gas kinematics and balance of outflows versus inflows on scales that come closer to resolving the starburst nuclei.

The OH⁺(1₂→0₁) absorption feature in Orochi shows evidence for line emission both red- and blueward of the line (see the spectra extracted centered on the peak positions of the emission in Figure 8). Because no such emission is seen near the OH⁺(1₁→0₁) absorption feature, these components are unlikely to be due to OH⁺ emission, despite the fact that they appear to be symmetrically offset from the continuum peak position (Figure 5). ¹¹

We identify the blueward component at ∼221.651–221.963 GHz (corresponding to –830 to –400 km s⁻¹ relative to the systemic redshift of OH⁺) detected at an S/N of ∼3.5 with NH(1₂→0₁) line emission (which has 21 components at 974.3156 to 974.6078 GHz, with the strongest component at 974.4784 GHz, redshifted to 221.9246–221.9912 GHz and 221.9617 GHz, respectively). If correct, this would imply that the line centroid is redshifted by 185 ± 24 km s⁻¹ relative to the systemic velocity, at a line full width at half maximum (FWHM) of 273 ± 61 km s⁻¹ (i.e., comparable to that of the OH⁺ absorption). Because this is significantly narrower than the CO(J = 9→8) emission line, we cannot rule out that its red wing may be partially affected by absorption due to the (blueshifted) OH⁺ line. This, however, is unlikely to be a strong effect due to the similarity in shape of both detected OH⁺ absorption lines. We thus consider this identification to be plausible. We measure a line flux of 1.59 ± 0.45 Jy km s⁻¹, which corresponds to a line luminosity of $L{{\prime} }_{\mathrm{NH}(1-0)}$ = 1.1 ± 0.3 × 10¹⁰ K km s⁻¹ pc².

We identify the redward component at ∼220.853–221.228 GHz (corresponding to +170 to +680 km s⁻¹ relative to the systemic redshift of OH⁺) detected at an S/N of >5 with NH₂(3₁₂→3₀₃) line emission (which has seven of its components at 970.7079–970.7927 GHz, with the strongest component at 970.7883 GHz, redshifted to 221.1029–221.1222 GHz and 221.1212 GHz, respectively). If correct, the line centroid velocity of 17 ± 130 km s⁻¹ would be consistent with the systemic redshift, and the line FWHM of 549 ± 225 km s⁻¹ would be consistent with that of CO(J = 9→8). The relatively large uncertainties on the line width are due to the proximity to the OH⁺ absorption feature. We thus consider this identification to be plausible as well. We measure a line flux of 3.5 ± 1.2 Jy km s⁻¹, which corresponds to a line luminosity of $L{{\prime} }_{\mathrm{NH}2(312-303)}$ = 2.5 ± 0.8 × 10¹⁰ K km s⁻¹ pc². Higher S/N measurements are desirable to more reliably deblend the different emission/absorption components, to investigate any red- or blueshifting of lines, and to more precisely constrain the significance of any positional offsets for the NH and NH₂ detections at z = 3.4 in Orochi.

As discussed in the previous section, the OH⁺(1₂→0₁) absorption feature in HeLMS-28 appears to be more asymmetric and potentially narrower than the OH⁺(1₁→0₁) absorption feature. The shallower absorption is found at the velocities where NH₂(3₁₂→3₀₃) emission would be expected. While the current S/N is too limited to attempt a reliable deblending, we thus consider it possible that NH₂ emission contributes to the apparent OH⁺(1₂→0₁) profile. As a consequence, we base our further interpretation of this source mainly on the OH⁺(1₁→0₁) line.

We find a strong correlation between the CO(J = 9→8) line (${L}_{\mathrm{CO}(9-8)}^{{\prime} }$) and FIR dust continuum luminosities for the GADOT sample (Figure 11 left). This relation is reminiscent of that found for nearby star-forming galaxies (e.g., Liu et al. 2015), consistent with the idea that the CO(J = 9→8) emission is associated with warm, dense molecular gas in the star-forming regions. The GADOT sample is consistent with the linear slope of the relation found for the lower-luminosity nearby galaxies, but the sample appears to be systematically offset toward higher CO(J = 9→8) luminosity.

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At first glance, one may conclude that this could be due to the fact that most GADOT sources are strongly lensed, given that no magnification correction has been applied. However, given the linear slope of the relation, such corrections would only be important if there is differential lensing between the ∼70–100 μm dust near the peak of the SEDs and the warm, dense molecular gas. Moreover, the observed offset is in the opposite direction of what would be expected for differential lensing between a compact, warm dust component and a more extended molecular gas component.

Another possibility would be that the gas excitation in the GADOT sample is systematically higher than in the nearby galaxies. To further investigate this issue, Figure 11 highlights the galaxies that overlap with the Class I, II, and III samples of the HerCULES survey (Rosenberg et al. 2015), where a higher class corresponds to a higher CO excitation. Indeed, Class I sources appear to show systematically lower CO(J = 9→8) to FIR luminosity ratios than the Class II and III samples, and Class II sources appear to preferentially fall within the intermediate range. This is consistent with the idea that differences in CO excitation may be responsible for a significant portion of the observed scatter of the relation. Class III sources show the broadest scatter, with about half of them being below the relation, in a similar region as the GADOT sources. The strongest outlier is the binary AGN NGC 6240, which shows the highest ${L}_{\mathrm{CO}(9-8)}^{{\prime} }$/L_FIR ratio of the entire combined low- and high-redshift sample. The high CO line to dust continuum luminosity ratio in NGC 6240 is thought to be due to shock excitation (e.g., Meijerink et al. 2013). At face value, our findings may therefore suggest more prevalent shock excitation (rather than stronger radiative excitation due to the warm dust or hidden AGNs) in DSFGs at z = 2–6 than in most nearby star-forming galaxies, perhaps due to slow-moving shocks. A possible alternative explanation would be that these galaxies exhibit increased cosmic-ray energy densities that lead to an increased CO excitation. ¹²

We also find a weak correlation between the OH⁺ line emission components (${L}_{{\mathrm{OH}}^{+}(1-0)}^{{\prime} \,\mathrm{em}}$) and FIR dust continuum luminosities for the GADOT sample (Figure 11 right), with a best fit of log(L_FIR/L_⊙)=(5.5 ± 2.5)+(0.35 ± 0.10)log(${L}_{{\mathrm{OH}}^{+}(1-0)}^{{\prime} \,\mathrm{em}}$/L_l ), where L_l =K km s⁻¹ pc². The OH⁺ emission components are consistent with being associated with shock-heated, dense gas components impacted by galactic winds (e.g., Falgarone et al. 2017; Riechers et al. 2021). As discussed above, the presence of shock-heated gas is consistent with the strong CO(J = 9→8) emission across the GADOT sample. Thus, while we cannot make strong inferences based on this relation alone, and while alternative scenarios cannot be ruled out, our findings for the CO and OH⁺ emission paint a consistent picture for the heating and excitation mechanisms in z = 2–6 DSFGs.

The OH⁺ absorption components are likely associated with cool (≲100 K), low-density (<100 cm⁻³), spatially extended gas components along the line of sight to the warm dust continuum emission from the starbursts (e.g., Falgarone et al. 2017; Riechers et al. 2021).

To better understand the implications of the OH⁺ absorption detections in our sample, we have calculated the peak optical depths τ_OH+ = –ln(f_trans) and the velocity-integrated optical depths τ_OH+ dv (which is a quantity similar to the line equivalent width) for the GADOT sample. Here, f_trans is the fraction of the continuum emission that is still transmitted. The resulting values are summarized in Table 3. The GADOT sample has a median τ_OH+ = 0.56 ± 0.25 and a median τ_OH+ dv = 220 ± 110 km s⁻¹. This corresponds to a median OH⁺ column density of N(OH⁺) = (1.0 ± 0.6)×10¹⁵ cm⁻², or a median hydrogen column density of N(H) = (6.3 ± 3.8)×10²² cm⁻² (see Table 3 for the underlying assumptions). For a typical DSFG diameter of 2 kpc (e.g., ADFS-27; Riechers et al. 2021), this corresponds to a neutral hydrogen mass of M(H) ∼ 2 × 10⁹ M_⊙.

We then compare the results to SED-based physical quantities that are, to first order, independent of lensing magnification. In the top row of Figure 12, T_dust, λ₀, and λ_peak are shown as a function of redshift. There are no clear trends except for a potential weak increase in T_dust toward higher redshift, and a corresponding weak blueshifting of λ_peak. This weak trend is likely primarily due to the underlying selection function of Herschel at 250–500 μm and is thus consistent with no strong underlying redshift evolution within the uncertainties.

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The remaining panels show the same quantities in relation to the peak and integral optical depths. There is no detectable trend with λ₀, such that we do not find evidence for increased OH⁺ absorption in systems that have higher dust opacity near the wavelengths of the OH⁺ lines. This is perhaps expected because the OH⁺ absorption is caused by gas in front of the dust continuum. On the other hand, there appears to be a significant trend of increased OH⁺ absorption depth toward higher dust temperatures (or correspondingly, toward shorter wavelengths of the SED peak). The trend appears to be tighter for the integral optical depth (see Table 5).

There are two potential factors that may explain such a trend. First, the OH⁺ 2 → 1 lines (which reduce the upper level populations of the 1₁→0₁ and 1₂→0₁ transitions if seen in absorption) lie at ∼1892–2029 GHz, or 148–158 μm, i.e., close to or shortward of λ₀ for most of the GADOT sample. These transitions are observed in absorption in the archetypal ultra-luminous infrared galaxy (ULIRG) Arp 220 (González-Alfonso et al. 2013), and tentatively, in the z = 6.34 starburst HFLS3 (based on the data shown by Riechers et al. 2013). As such, it is conceivable that the observed trend could be due to the increased availability of 148–158 μm photons as the SED peak shifts toward shorter wavelengths, which results in an increased pumping efficiency out of the upper level of the 1₁→0₁ and 1₂→0₁ transitions.

Second, the sources with higher T_dust may simply be warmer because they are more compact, such that they have higher Σ_FIR and Σ_SFR surface densities. Smaller sizes then lead to a higher density of supernovae once the most massive stars end their life cycles. Because the supernova rate is proportional to the rate of cosmic-ray production, this would result in an increased cosmic-ray energy density. The central regions of the high T_dust DSFGs in the GADOT sample thus may resemble giant cosmic-ray-dominated regions, rather than ensembles of photon-dominated regions, i.e., similar to what has been discussed for ULIRG nuclei (e.g., Papadopoulos Papadopoulos 2010; González-Alfonso et al. 2013). Because cosmic rays are likely the main production mechanism for molecular ions such as OH⁺, the increased cosmic-ray energy density would then result in an increased abundance of OH⁺ for higher T_dust sources, causing stronger OH⁺ absorption and therefore higher OH⁺ optical depth. High cosmic-ray energy densities could also explain the comparatively high CO excitation in this sample, as a possible alternative to the shock-induced CO excitation scenario.

In principle, the OH⁺ abundance can also be increased in environments exposed to radiation fields associated with X-ray dominated regions (XDRs) around AGN (see also the discussion by González-Alfonso et al. 2013). At the same time, AGN can increase the dust temperature as an additional heating source. A contribution like this can certainly be relevant for local enhancements near an AGN. However, given the high optical depth of the dust, it is unlikely that the radiation from AGN can penetrate to large radii even if buried AGN are present in our sample, such that it remains unclear that the OH⁺ production could be sufficiently increased on large enough scales to fully explain the observed trend.