THE ALMA SPECTROSCOPIC SURVEY IN THE HUBBLE ULTRA DEEP FIELD: IMPLICATIONS FOR SPECTRAL LINE INTENSITY MAPPING AT MILLIMETER WAVELENGTHS AND CMB SPECTRAL DISTORTIONS

Intensity mapping of the cumulative CO and other millimeter and submillimeter line emission from early galaxies has been proposed as a new means to probe very large-scale structures in the distant universe (Carilli 2011; Gong et al. 2011, 2012; Yue et al. 2015). Intensity mapping entails low spatial and spectral resolution imaging of the sky to obtain the mean brightness due to the cumulative emission from myriad discrete cosmic sources. While interferometric arrays like ALMA, the JVLA, and NOEMA, can detect CO and [C ii] 158 μm (and in cases of high luminosity sources, other lines), from individual galaxies at high redshift, the fields of view are very small, and the integration times are long. These telescopes are inadequate for measuring the galaxy distribution on the very large scales relevant to cosmological questions, such as the baryon acoustic oscillations at intermediate redshifts, or the large-scale distribution of galaxies that reionize the universe. The latter is of particular interest for cross correlation studies with very wide field, low-resolution H i 21 cm images of the intergalactic medium during cosmic reionization (Lidz et al. 2011).

The integrated millimeter and submillimieter line emission from early galaxies has also been recognized as a possible significant contaminant of measurements of the spectral and spatial fluctuations of the cosmic microwave background (CMB; Righi et al. 2008a, 2008b; Chluba & Sunyaev 2012; de Zotti et al. 2015; Mashian et al. 2016). For example, modeling suggests (Mashian et al. 2016) that the integrated CO line emission could be significantly higher than the primordial spectral distortions due to other cosmological effects (e.g., Chluba & Sunyaev 2012; Sunyaev & Khatri 2013; Tashiro 2014), and may be measurable with next generation instruments like the Primordial Inflation Explorer (PIXIE; Kogut et al. 2014).¹⁴

Numerous calculations have been done to predict the mean sky brightness due to emission lines from CO at intermediate and high redshift, and [C ii] 158 μm emission at very high redshift (see Section 2). These predictions are based on either empirical estimates using proxies for the line emission, such as the cosmic star formation rate density, or large scale cosmological simulations of galaxy formation, with recipes to relate proxy measurements or simulated properties to line luminosities.

In this paper, we present direct measurements of the summed line luminosity from individual sources in bands around 99 and 242 GHz. These measurements are based on the ALMA spectral deep field observations (ASPECS) program, corresponding to a broad band spectral line deep field of the UDF at 1.25 and 3 mm (Aravena et al. 2016a; Decarli et al. 2016a; Walter et al. 2016). From these measurement, we derive the mean brightness temperature at a given observing frequency due to high redshift galaxies. As a pilot study with ALMA, the fields are necessarily small, and the number of galaxies few. However, the measured quantity is direct: line emission from early galaxies. Hence, no modeling or conversion factors are required.

The dominant contribution to the integrated line brightness from high redshift galaxies in the 99 GHz band is due to rotational transitions of CO from galaxies at intermediate to high redshift. Other molecular tracers, such as high dipole moment molecules like HCN and HCO⁺, are typically 10 times, or more, fainter than CO, while the atomic fine structure lines would be from galaxies at improbable redshifts (z ∼ 20; see Carilli & Walter 2013). At 242 GHz, the integrated line brightness will be some combination of higher order CO lines from intermediate and high redshift galaxies, plus a possible contribution from [C ii] 158 μm line emission from galaxies at z ∼ 6 to 7, and other fine structure lines at lower redshift. We consider each in turn.

Considering CO in the 99 GHz band, predictions of the mean CO sky brightness from early galaxies have taken two approaches. First is an empirical use of the measured evolution of the cosmic star formation rate density, and/or the cosmic far-infrared (FIR) background, converted to CO luminosity by adopting a CO-to-FIR or star formation rate conversion factor (Righi et al. 2008a, 2008b; Lidz et al. 2011; de Zotti et al. 2015). A related calculation is to consider the star formation rate density required to reionize the neutral intergalactic medium at high redshift, subsequently converted to CO luminosity using said conversion factors (Carilli 2011; Gong et al. 2011). While based on celestial measurements, these methods involve significant uncertainties inherent in both the determination of the cosmic star formation rate density, and more importantly, the assumed "star formation law" relating CO luminosity to FIR luminosity, or to star formation rate (Kennicutt & Evans 2012; Carilli & Walter 2013). The latter may entail a dual conversion of star formation rate to total gas mass, then total gas mass to CO luminosity. There is the additional uncertainty in the assumed gas excitation when modeling the contribution to the mean brightess at a given observing frequency from different CO transitions from galaxies at different redshifts.

The second method for predicting the mean CO sky brightness is through cosmological numerical simulations (Gong et al. 2011; Li et al. 2016; Mashian et al. 2016). Such simulations can be normalized to e.g., an observed galaxy luminosity function at a given redshift, although ultimately, even the most detailed simulations rely on recipes to convert from simulated to observable quantities. This is particularly difficult in the case of tracer molecules, such as CO, while also including their excitation state.

In summary, the predictions at around 100 GHz for the mean brightness from CO lines from intermediate and high redshift galaxies range from 1.5 μK (Righi et al. 2008a, 2008b) to about 10 μK (Marshian et al. 2016).

Two recent observations have set upper limits to the CO brightness from distant galaxies using CO intensity mapping. The first entailed a cross correlation of WMAP images with maps of very large-scale structures from the SDSS, namely the photometric quasar sample and the luminous red galaxy sample (Pullen et al. 2013). The cross correlation technique removes numerous systematic errors. Pullen et al. estimate upper limits to the mean brightness temperature of CO 1-0 or 2-1 of about 10 μK in the 30–90 GHz range. The second was an interferometric measurement of the brightness fluctuations at 30 GHz using the Sunyaev–Zel'dovich Array (Keating et al. 2015). Keating et al. quote an upper limit to the CO 1-0 mean brightness of ∼5 μK from z ∼ 3 galaxies. Since both these measurements rely on modeling of the spatial structure in the signal, they depend on the assumed underlying structural parameters.

Considering the 242 GHz band, predictions also vary considerably. The most detailed modeling to date, including analysis of lines from CO, [C ii], and [C i], is presented in Yue et al. (2015). They use large scale cosmological simulations, plus physically motivated conversion factors (Pallottini et al. 2015; Vallini et al. 2015), to derive the line luminosities from early galaxies. They predict a [C ii] 158 μm brightness of ∼0.05 μK around 242 GHz from z ∼ 6.5 galaxies. At this frequency, they obtain a similar contribution from the [C i] lines at rest frame frequencies of 492 and 809 GHz, from lower redshift galaxies. The dominant line contribution to the mean brightness at 242 GHz in their models comes from CO emission from galaxies at intermediate to high redshift, for which they derive a mean brightness of ∼0.45 μK. Note that, in their models, the [C ii] contribution increases rapidly with increasing observing frequency, to ∼0.4 μK at 316 GHz (comparable to CO), due to galaxies at z ∼ 5. Conversely, Gong et al. (2012) perform an analytic calculation of the expected [C ii] surface brightness based on interstellar medium physics and halo statistics, and predict a substantially larger contribution of [C ii] at 242 GHz of ∼0.3 μK.

The ASPECS results are described in Walter et al. (2016), Aravena et al. (2016a), Decarli et al. (2016a). In brief, we surveyed a ∼1 arcmin² field in the UDF to a 3-σ depth of ∼0.05 Jy km s⁻¹ (assuming line widths of 200 km s⁻¹) over the frequency range 84–115 GHz (3 mm), and of ∼0.13 Jy km s⁻¹ over the frequency range 212–272 GHz. In the analysis below, we adopt the mean frequencies for each band, which are 99 and 242 GHz.

The observations are sensitive to galaxies over a wide range in redshift, depending on CO transition. The typical CO luminosity limits are ∼2 × 10⁹ K km s⁻¹ pc² at 3 mm and 6 ×  10⁸ K km s⁻¹ pc² at 1 mm at 1 < z < 3. The implied gas mass limits will depend on which CO transition is being considered, at which redshift, and depend critically on assumed CO excitation, in particular for the high order transitions, since the total gas mass is derived by extrapolation to low order. For reference, at the typical redshifts and transitions of the detected galaxies, these limits imply galaxies with gas masses of 3 to 10 × 10⁹ M_⊙, for a Galactic conversion factor of CO 1-0 luminosity to total molecular gas mass. We discuss this point further in Section 5.1. For [C ii] at very high redshift (z ∼ 6.5), our observations are sensitive to galaxies with star formation rates ≥10 M_⊙ yr⁻¹, using the de Looze et al. (2011) conversion.

Line emitting galaxies were identified using multiple three-dimenional search algorithms, and a series of tests were made for completeness and fidelity (Walter et al. 2016). Once a line candidate was identified, a search was made for an optical or near-IR (NIR) counterpart. Decarli et al. (2016a) discuss how a given line is identified as a specific CO transition. In some cases, the detection (or the lack of detection) of multiple CO transitions over the broad frequency range constrains the redshift determination. If an optical/NIR counterpart is present, literature information on the redshift of the source (via spectroscopy or SED fitting of the photometry) was also used. The lack of an optical counterpart is used to rule out low redshift interpretations in some cases. Ultimately, for some sources there can be ambiguity as to the transition in question, and therefore the redshift. This is dealt with via a bootstrapping approach (see Decarli et al. 2016a). However, in the context of the analysis below, this is not an issue, since we simply sum all the lines detected in the blind survey in a give observing band, independent of what transition and redshift the line happens to be.

For completeness, Figure 1 shows a compilation of all the candidate line detections in the survey, as presented in Walter et al. (2016). There are a total of 21 candidate lines above 5σ. In six cases, line identifications are unequivocally confirmed, through detection of other CO transitions, and/or an optical galaxy with a spectroscopic redshift. For the rest of the lines, extensive quantitative tests are made, and we only include lines with a >60% "fidelity" rating. See Decarli et al. (2016a) for more details on the statistical analysis, and Walter et al. (2016) for total intensity CO images, and optical images, of all the candidates. At this fidelilty level, we expect to have roughly as many spurious detections as sources missing from the survey due to noise fluctuations (Decarli et al. 2016a).

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The mean line brightness temperatures are calculated using an empirical approach of summing the lines detected in the blind survey. The process is simple. Table 2 in Walter et al. (2016) lists the lines detected according to the blind search criteria outlined in Section 3. We sum the total flux from all the lines detected in a given band, in Jy km s⁻¹, which is equivalent dimensionally to Jy Hz or erg s⁻¹ cm⁻². We then divide by the total bandwidth covered in the blind survey, which results in a mean flux density over the full band and over the full field, S_ν, in Jy. The mean brightness temperature at the observed wavelength, λ_obs, is then derived using the angular area of the field employed in the blind search, Ω_f, under the Rayleigh–Jeans appoximation: ${T}_{B}\sim 1360\,{S}_{\nu }\,{\lambda }_{\mathrm{obs}}^{2}\,{{\rm{\Omega }}}_{f}^{-1}\,{\rm{K}}$,  where λ_obs is in centimeters and Ω_f is in arcsec².

For the 99 GHz band, the total flux for the 10 lines detected in the band is 2.53 ± 0.25 Jy km s⁻¹ = (8.3 ± 0.08) × 10⁵ Jy Hz. The total bandwidth is 31 GHz, so the mean flux density across the band is ${S}_{\nu }=(2.7\pm 0.27)\times {10}^{-5}$ Jy. The field covered by the survey was 3600 arcsec². Hence, the mean brightness temperature, T_B = 0.94 ± 0.09 μK.

For the 242 GHz band, the total flux for the 11 lines detected in the band is 6.93 ± 0.42 Jy km s⁻¹ = (5.6 ± 0.34) × 10⁶ Jy Hz. The total bandwidth is 60 GHz, so the mean flux density across the band is ${S}_{\nu }=(9.3\pm 0.6)\times {10}^{-5}$ Jy. The field covered by the survey was also 3600 arcsec². Hence, the mean brightness temperature, T_B = 0.55 ± 0.033 μK.

5.1. Limits

5.2. Comparison to Predictions and CMB Spectral Distortions

We thank the referee for useful comments that improved the paper. FW acknowledges support through ERC grant COSMIC–DAWN. MA acknowledges partial support from FONDECYT through grant 1140099. Support for RD was provided by the DFG priority program 1573 "The physics of the interstellar medium." DR acknowledges support from the National Science Foundation under grant number AST-#1614213 to Cornell University. FB acknowledges support by the Collaborative Research Council 956, sub-project A1, funded by the Deutsche Forschungsgemeinschaft (DFG). This paper makes use of the following ALMA data: ADS/JAO.ALMA#2013.1.00146.S and ADS/JAO.ALMA#2013.1.00718.S. ALMA is a partnership of ESO (representing its member states), NSF (USA), and NINS (Japan), together with NRC (Canada), 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. The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc.