HETDEX Public Source Catalog 1: 220 K Sources Including Over 50 K Lyα Emitters from an Untargeted Wide-area Spectroscopic Survey^*

An accurate description of sky sensitivity and coverage is essential for HETDEX. Each IFU consists of 448 fibers that are divided into two spectrograph channels. Each channel has a 2064 × 2064 detector. We use two amplifiers per spectrograph channel and bin 2× in the spectral direction during readout. Thus, each IFU consists of four amplifier channels, labeled "RU," "RL," "LL," and "LU" as demonstrated in the left panel of Figure 2. Each amplifier generates an FITS image that is 1032 × 1032, each with 112 fiber spectra. With a full 78 IFU installation, each single exposure consists of data from 312 CCD amplifiers, which corresponds to about 35,000 fiber spectra. Our standard three-dithered observation set generates 936 FITS files, each an image of a single amplifier, and 104,000 fiber spectra. Although the IFU spectrographs are designed to be identical, in practice, there are important variations from amplifier to amplifier that we track (see, for example, Figure 6 from Gebhardt et al. 2021). Over its lifetime, including calibration frames, HETDEX will generate about 20 million FITS files. Each one of the amplifier images consisting of 112 fiber images is considered individually for quality assessment.

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Over the first 3 yr of the HETDEX survey, we have seen a variety of detector and calibration issues. These include dead amplifiers, variable electronic noise, low count rates, and scrambled pixels. Calibration issues include vignetting of some IFUs, saturation problems from bright objects, astrometric uncertainties from fields with low number of stars, large variation in throughput over a dither set, large variations in the wavelength solution for some spectrographs, among others. We robustly track these issues and find that for a given exposure set, about 92% of the FITS files are useful and make it into the catalog. This percentage has increased over the years as we have fixed various detector issues, and we expect an even higher rate of return in the future.

2.1.1. Detector Issues

Instrument deficiencies can result in a number of failures. Specific detectors may exhibit low response or spatially distorted features that cannot be removed by flat-field corrections. These failures can vary with time and significantly impact our detection methods. Certain failures result in the creation of many false detections and can dramatically affect our detected sample. Building from an initial sample that was visually flagged, we have developed a set of criteria from statistics generated by our image calibration that automatically identifies substandard amplifier readouts. These criteria are summarized in Table 2. We provide the quality inclusion criterion limits for each statistic and a short description. We also indicate the fraction of amplifiers that pass each criteria. Ultimately, an amplifier must satisfy all of the criteria to be included. Unfortunately not all issues can be caught automatically, and an extensive list of detector issues for each detector are maintained ²³ so that both the catalog and the survey selection function are consistently masked. For this catalog release, about 92% of the FITS files pass our quality control, although we note that the first year of observations were particularly poor with the fraction of usable data below 90%. The quality fraction generally averages about 94% in recent years. An example where a specific amplifier is removed from the survey is shown in the right panel of Figure 3. The IFU at roughly $20^\circ \,11^{\prime}$, $00^\circ \,02^{\prime}$ has a single amplifier masked out of the catalog.

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Table 2. Statistics in Image Processing Used for Amplifier Quality Assessment

Quality Criteria	Quality Fraction	Description
im_median > 0.05	98.7%	Median counts in unprocessed amplifier image frame
−10 < background < 100	98.0%	Median counts value in sky-subtracted image
0.2 < sky_sub_rms < 1.5	99.3%	rms in sky-subtracted image counts
sky_sub_rms_rel < 1.5	97.7%	Ratio of sky rms in individual amplifier relative to all other amplifiers in all IFUs within the same exposure
n_cont < 35	98.7%	Number of fibers above a certain count threshold. A good indication of an amplifier saturated by a bright star or nearby galaxy.
norm < 0.5	99.3%	Relative normalization for a dithered exposure.
maskfraction < 0.2	98.3%	Rejected if more than 20% of the frame is masked

Note. Inclusion quality criteria for each image statistic, the fraction of amplifiers that pass the criteria and a short description are listed. Each HETDEX IFU is fed to four amplifiers, each containing spectral information for 112 fibers. For HETDEX survey data, we consider each amplifier to be an independent observation with its own quality criteria.

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2.1.2. Calibration Failures

2.1.3. Observation Quality Criteria

2.1.4. Pixel Masks

Galaxies larger than roughly 1' are excluded from our catalog using the positions and optically defined elliptical apertures provided by the Third Reference Catalog of Bright Galaxies (RC3; de Vaucouleurs et al. 1991) and the Uppsala General Catalogue of Galaxies (UGC; Nilson 1973). The spring field contains 644 such galaxies; the fall field, 447. For each galaxy, we use the catalogs' basic parameters for position, position angle, ellipticity, and D25 semimajor axis (i.e., the size of the galaxy defined by its B-band isophote at 25.0 mag arcsec⁻²). Each galaxy is visually inspected through photometric imaging to confirm that these default values are reasonable. Where the parameters are uncertain, they are corrected to values listed in the NASA/IPAC Extragalactic Database ²⁴ or through visual inspection of the galaxy in SDSS g-band images. All detections that fall within 1.5× the D25 scale of a bright galaxy's elliptical aperture are removed. This factor was determined by examining the HETDEX spectra at different scalings and ensuring that all detections related to the bright galaxy were encompassed in the aperture mask. These galaxy masks are consistently applied to the HETDEX catalog and accompanying survey area mask through the HETDEX python-based, software repository hetdex-api ²⁵ to provide proper survey volume accounting.

Both satellites and meteors generate signals that produce detections in both our emission-line and continuum emission catalogs. Meteors largely appear as line emission at multiple wavelengths and therefore contaminate our LAE samples because of their lack of strong continuum underlying the emission. Fiber spectra from HDR2 contain at least 31 meteors resulting in thousands of spatially extended emission-line detections, as the meteor travels across the HET focal plane. We use a systematic search method for these objects as part of our Emission Line Explorer software tool (ELiXer; Davis et al. 2023). Strong line emission appearing in just a single dithered HETDEX observation is flagged as a meteor candidate. For any observation with over 10 associated meteor candidate emission-line detections, we visually inspect the detections to confirm the presence of the meteor. We create a simple linear mask by fitting to the positions of the flagged meteor detections. This mask extends 12'' above and below the linear fit to the meteor positions; in many cases, a smaller mask could be used, but this width is needed for the brightest events. We therefore chose to be conservative with this mask. This linear mask is consistently applied to both the line emission and continuum emission raw catalogs as well as to our survey area mask.

Satellites are identified when the continuum flux density measured in the HETDEX spectral data differs from that estimated within photometric imaging data (see Figure 3 in Gebhardt et al. 2021 for an example of a satellite trail across the HETDEX FOV). Each HETDEX detection is processed with the ELiXer software tool, in which forced aperture photometry is performed on all available imaging. If any reported photometric measurement is more than two magnitudes fainter than the measured HETDEX value, the source is rejected as it indicates the signal is from a transient source, such as a satellite, only briefly observed at that point in the sky. Visual inspection confirmed that the majority of these detections are indeed satellites, scattered light from bright star or artifacts caused by improper flux calibration. For more discussion about finding transient sources in HETDEX, see Vinko et al. (2022).

Two independent, but complementary, object detection search techniques are performed as part of the main HETDEX reduction pipeline: one to identify emission lines, the other to detect continuum sources. In the second internal data release for HETDEX (HDR2), a search was performed across 210 million flux-calibrated fibers as described in detail in Section 7 of Gebhardt et al. (2021). We briefly summarize the procedures here. During this process, no imaging preselection is used and the HETDEX data itself provides object detection. Both the emission line and continuum detection algorithms are designed to identify point-sources and account for the variable image quality, or point-spread function (PSF) of each independent HETDEX three-dither observation. To move from object detection to source classification, the outputs from both object detection methods are combined as described in Section 3.3 below.

3.1.1. Spectral Extraction

3.1.2. Line Emission Search

3.1.3. Emission-Line Fits and Criteria

The raw emission-line database is produced from all available HETDEX observations and consists of both real sources and artifacts that can arise from the data quality issues described in Section 2.1. Each raw line detection is subjected to a series of tests, which check whether the candidate line is close to a large galaxy, a meteor trail, a known detector feature, or subject to a poorly performing amplifier. A criterion is then applied, based on the S/N measured in the continuum-subtracted emission line, the Gaussian width of the fitted line in Angstroms, σ, and the quality of line fit, χ², measured in a ±2 × σ wide spectral window. Specifically, to be classified as a detection, a line must satisfy either

$$\begin{eqnarray}5.5\lt {\rm{S}}/{\rm{N}}\lt 6.5\,\,\&\,\,1.7\,\AA \lt \sigma \lt 6\,\AA \,\,\&\,\,{\chi }^{2}\lt 1.2\end{eqnarray} \tag{ 1 }$$

or

$$\begin{eqnarray}{\rm{S}}/{\rm{N}}\gt 6.5\,\,\&\,\,1.7\,\AA \lt \sigma \lt 14\,\AA \,\,\&\,\,{\chi }^{2}\lt 2.5\,\,\&\,\,g\gt 19\end{eqnarray} \tag{ 2 }$$

where g, hereafter labeled g_HETDEX, is an equivalent broadband photometric measurement obtained by summing up the flux densities in the HETDEX spectrum, weighted by the SDSS g-band filter curve.

This combination of constraints means that high line width sources can have poorer fits (i.e., a higher χ²) if they also have a relatively high S/N and faint g_HETDEX. Sources in the high line width regime tend to suffer from a higher contamination rate, due to calibration issues or the existence of broad continuum emission from nearby galaxies and late-type stars. However, the broad-line identifications do contain interesting high-z sources, including AGNs (see the HETDEX AGN Catalog; Liu et al. 2022) and extended Lyα emitters (Mentuch Cooper et al. 2023, in preparation). We therefore allow a more liberal χ² quality of fit for these objects, as their lines are not typically well described by a single Gaussian line model (especially in the case of AGNs). Additional to the above criteria, narrow emission-line detections are cataloged in the wavelength range between 3510 and 5490 Å while broad-line features are only cataloged between 3550 and 5460 Å, as many spurious high line width sources were identified by the detection software on the spectral edges.

Detector artifacts are a major issue with some HETDEX spectra. In some cases, the fiber spectrum is poorly calibrated, resulting in measured continuum flux that is negative, leading to a false-positive detection. To mitigate this issue, we apply a lower cut of −3 × 10⁻¹⁷ erg s⁻¹ cm⁻² Å⁻¹ to the local continuum measured in the Gaussian line fit. Additionally, the fiber profile quality of fit can also help identify detector artifacts. If the quality fit of the fiber profile solution, ${\chi }_{\mathrm{fiber}}^{2}$, is high, we remove the detection. In practice this value is measured for each of the five highest weight fibers in an aperture extraction, 5 Å above and below the central wavelength of the detected emission line. If any of the fibers in this spectral window have a ${\chi }_{\mathrm{fiber}}^{2}\gt 4.5$ or ${\chi }_{\mathrm{fiber}}^{2}\gt 3$ and continuum < 0.5 × 10⁻¹⁷ erg s⁻¹ cm⁻² Å⁻¹, the detection is removed from further consideration. We opted for this dual criterion because fibers with a significant continuum signal can produce higher reduced ${\chi }_{\mathrm{fiber}}^{2}$ values; we are particularly concerned with finding artifacts in the low continuum regime, where their presence can lead to false-positive LAE candidates.

Our final curated line emission detection catalog consists of 236,354 line emission detections. They can be identified in the Detection Info Table (see Table 6) in the column det_type==line. The line flux sensitivity limit for a HETDEX line emission source depends on observed wavelength, image quality, exposure time, other observing conditions, and instrument component inconsistencies, but, on average, 50% completeness is reached at roughly ∼7 × 10⁻¹⁷ erg s⁻¹ cm⁻². The reader is referred to Section 8.2 of Gebhardt et al. (2021) for a detailed discussion on HETDEX emission-line sensitivity and completeness with an updated discussion on these topics and the HETDEX selection function to be presented in D. Farrow et al. (2023, in preparation).

3.1.4. Continuum Emission Search

The HETDEX AGN catalog from the same internal data release, HDR2, is presented in Liu et al. (2022), and contains the same base sample that is included in the catalog presented in this paper. There are, however, several selection differences between Liu et al. (2022) and the current work; some of these add candidates that are not in the Liu et al. (2022) HETDEX AGN catalog, while others reject Liu et al. (2022) objects.

The catalog presented here includes additional data quality criteria that limit the sample relative to Liu et al. (2022). For example, some frames with poor observational conditions or sources on amplifiers that failed our quality assessment remain in the HETDEX AGN catalog, which mitigated these issues through visual inspection. Our sample is also limited to the HETDEX fall and spring fields, as well as the COSMOS and GOODS-N legacy fields, whereas the AGN catalog includes additional data from a North Ecliptic Pole survey (Chavez Ortiz et al. 2023, submitted).

Roughly a quarter of the AGN sample overlap with the curated line emission catalog and the continuum detection catalog; the main divergence between the catalogs arises from AGNs that exhibit broad-line emission that is not well fit by the Gaussian model implemented in the HETDEX line detection algorithm. These detections occupy both high line width and high χ² parameter space and do not meet the line parameter criteria for line emission in our curated line detection catalog. As described in Liu et al. (2022), visual inspection of this broad-line emission sample is essential for classifying a source as an AGN rather than a calibration artifact.

We include the AGN catalog in our combined source catalog and allow individual detections to be grouped according to the process described in Section 3.3. This approach allows for additional line and continuum emission detections to be associated with the AGN source and assigns an AGN classification and its associated redshift.

Both the line emission and continuum emission pipelines are designed to identify point-source emission. For LAEs, the primary target of interest for HETDEX, and many [O ii] emitting galaxies, the point-source approximation is valid for HET image quality. However, ∼40% of the S/N > 5.5 detections identified in the emission-line and continuum source pipeline have multiple identifications. This situation can arise in extended objects, where emission is found at more than one spatial location, or with sources where more than a single emission-line has been detected. Similarly, bright astronomical sources can have both line emission and continuum emission, leading to entries in both the continuum and line curated catalogs.

The overlap in point-source brightness between the detection samples is shown in Figure 5. As expected, the continuum sources have much brighter g_HETDEX values than the objects found by the line detection algorithm. Starting near g_HETDEX ≈ 20, there is considerable overlap in the catalogs, while at magnitudes fainter than g_HETDEX ≈ 22, the line emission sources dominate. A particularly important challenge to creating a robust LAE sample is extended [O ii] line emission surrounding low-z galaxies; these features can often be confused for Lyα emission due to the lack of detectable continuum emission at large galactocentric radii. To mitigate the impact of these contaminants and to properly associate extended line emission to a single emission-line source, we apply a 3D friend-of-friends (FOF) clustering algorithm to our list of line detections. Our code ²⁶ uses cKDtree from SciPy (Virtanen et al. 2020) but is modified to use normalized coordinates in a pseudo-spherical space consisting of projected separation on sky and normalized wavelength difference. Specifically, we adopt a spatial linking length of 6'' and a linking length in the spectral direction of 8 Å. Information for the 3D clustering of the emission-line detections is provided in the columns wave_group_XX of the Detection Info Table (see Table 6). These columns contain the identification for the wave group, its mean equatorial coordinate, and mean central wavelength. Also included is the group's semimajor wave_group_a and semiminor wave_group_b axes, as determined from the line flux-weighted first-order moment of the line detection group. These values can be considered as a rough approximation to the extended group's emission-line size, but we caution that many sources that consist of just two matched line detections will be elongated in shape, while sources that have incomplete IFU coverage (as in the cases with extended [O ii]-emitting galaxies) will be limited by the IFU edge of fiber coverage.

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In addition to 3D clustering in wavelength and position, we also link all detections on sky together with a spatial linking length of 2''. This will ensure that sources with emission lines at multiple wavelengths will be grouped as one source. If those lines are themselves extended, then this step will group extended emission at multiple wavelengths together, as is the case for nearby galaxies that might, for example, exhibit extended [O ii] Hβ and [O iii] emission at multiple wavelengths. For blended objects or cases where a background object lies behind an extended foreground group, we accept that this linking may cause background detections to be lost and ultimately merged into the foreground object. Some of these sources may be quite interesting, particularly those with the potential to be gravitationally lensed, as demonstrated for the sample in Laseter et al. (2022). For fainter source groups that are ultimately classified as LAEs after detection grouping, we separate these sources spatially and assign a redshift according to each detection's observed wavelength assuming it to be Lyα. Although we note a possible exception is if the line emission wavelengths contain a pair of emission lines that can be associated with a common redshift, such as Lyα, He ii, and C iv. Redshift assignment and source classification are described further in Section 4.

For each source, we select a single representative detection for each source observation. This is listed as selected_det==True in the Detection Info Table (columns described in Table 6) and detectid in the Source Observation Table (column reference is found in Table 3). This detectid corresponds to the detection member with the brightest (i.e., smallest) g_HETDEX value for all sources that are not LAEs. For LAEs, we use the highest S/N Lyα line detection as the selected representative detectid. To remove detections that are identified by the HETDEX detection pipeline due to sharp discontinuities in the detection spectrum that do not correspond to true line emission, we opt to remove all emission lines with a line width greater than 6 Å that are not identified as a representative source (with selected_det==True) or are not included in the AGN catalog.

Examples of the data (broadband images, reconstructed IFU images, and spectra) for a range of objects in the catalog are presented in Figures 6 (z < 0.5) and 7 (1.9 < z < 3.3). Individual detections are overplotted on the imaging data in the left panel in each row. Line emission detections are marked by orange crosses, and continuum detections are marked by green crosses. The spectrum for a single representative detection for the source group (identified by selected_det==True) is shown at the right. Yellow bars indicate line emission detections. In the first example in Figure 6, multiple emission lines are found, but notably a line near 5250 Å is missing from the curated catalog. This is because the other emission-lines causes the single Gaussian fit of that detection to have a poor quality of fit and does not make it to the curated catalog based on line parameter quality criteria. Continuum-subtracted emission, line flux maps, shown in the middle column, at the observed wavelength indicated in the text at the top, demonstrate differences between the line emission distribution and continuum emission morphology as shown in the imaging data on the left.

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For every galaxy with z_hetdex < 0.5, we measure spatially resolved [O ii] line fluxes at the galaxy's redshift in addition to those provided by the HETDEX line detection algorithm that are point-source, PSF-weighted line flux values. We note that while a resolved line emitter can appear as multiple detections in the line database, some flux will inevitably be missed even if each detection is summed. In addition, the line detection pipeline used for this catalog release contained an upper limit on the continuum value, so some very bright line emitting galaxies are completely missing from our line emission database, even though they are found in the HETDEX continuum catalog.

A major strength of the wide-IFU (dithered) coverage with HETDEX is that the observations automatically produce an emission-line map of resolved galaxies. However, due to the IFU layout in the HET's focal plane, many of these systems have incomplete coverage, as their light extends off the edge of their IFU. The angular resolution of our imaging observations is substantially better than the IFU fibers. As a result, object shapes and sizes are better measured from direct imaging.

Object shapes are automatically included in HETDEX's ELiXer classification tool (Davis et al. 2023), as it applies Source Extraction and Photometry (SEP; Barbary 2016) to all available broadband imaging at the location of each HETDEX detection. This step provides the major and minor axes of an ellipse fit to the second-order moment of each object's surface brightness distribution (Bertin & Arnouts 1996). We use the ELiXer catalog selected=True option and preferentially choose r-band over g-band measurements to define each galaxy's elliptical aperture. In general, the r-band imaging we have obtained has a fainter limiting magnitude, and significantly better image quality. The image selection can be found in the columns catalog_name_aper and filter_name_aper in Table 6. Elliptical parameters for each low-z galaxy can be found in both Tables 3 and 6 under the columns major, minor, and theta. Additionally the aperture center and the measured continuum aperture magnitude are in Table 6 in the columns ra_aper, dec_aper, mag_aper, and mag_aper_err.

Figure 8 presents the major axis distribution of the low-z sample. More than three-quarters of the sample has a major axis larger than 3'' and is thus spatially resolved by VIRUS. We create continuum-subtracted line flux and flux uncertainty maps for each source's [O ii] emission by summing the fiber data in a ±15 Å window around the wavelength of observed [O ii], redshifted from λ 3727.8 Å according to z_hetdex. We then subtract local spectral continuum by making two narrowband-like images, each 50 Å wide, shifted by an additional 10 Å blue and red of the line emission. We subtract the average of these two images from the line flux map to produce a continuum-subtracted line-flux map.

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The flux and associated error in the galaxy's elliptical aperture is summed using the photutils software package (Bradley et al. 2021). The resulting aperture and dust-corrected aperture fluxes are found in columns flux_aper and flux_aper_err. The photometric information has an aperture correction applied, im_apcor, for sources that lack full IFU coverage. For each source, we opt to use the flux_aper value for flux_oii if the value is positive and the major axis of the low-z galaxy is greater than 2''.

3.4.1. Comparison to SDSS [O ii] Line Fluxes

Since the HETDEX survey fields lie completely within the SDSS footprint, we can compare spectra that are in common between the two surveys. Figure 9 presents HETDEX measurements of the continuum-subtracted emission-line fluxes for [O ii] emitting galaxies found in the MPA-JHU value-added catalogs from SDSS DR8 ²⁷ (based on the methods described in Brinchmann et al. 2004; Tremonti et al. 2004). In the top-left, for optimal comparison, the HETDEX line fluxes are measured in a circular 3'' diameter aperture to match the 3'' diameter fibers of SDSS. The figure demonstrates that for forced aperture line fluxes, the HETDEX measurements are well matched to SDSS 3'' values to an rms of 26% for objects with line fluxes above of ∼3 × 10⁻¹⁶ erg s⁻¹ cm⁻². Differences in positioning are mitigated by placing apertures exactly at the location quoted by SDSS; however, the derived line fluxes also depend on how the continuum is measured, and our IFU data have a different spatial profile than that of the single SDSS fiber.

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Comparisons between the pipeline point-source fluxes show much greater scatter in the top-right panel in Figure 9. As with the forced line fluxes, differences in the measurement method can create scatter, but here the bigger culprit is positioning. The HETDEX detection pipeline is designed to peak on the highest S/N line detection in a spatial grid of 1D extracted spectral data. This peak can vary from the location of the SDSS fiber by up to 1''. The bottom-right panel shows the distribution of sky separations between the SDSS fiber and the position of best HETDEX peak detection. In cases where the SDSS fiber is on the edge of the IFU, some flux is lost and underestimated in the pipeline point-source fluxes. In addition, fewer data points are shown here because the continuum detection search was performed with an upper limit threshold on counts, thus excluding the brightest [O ii]-emitting galaxies.

The middle-left panel compares HETDEX aperture fluxes, flux_aper, with SDSS measurements. Here, the HETDEX values lie significantly above those of SDSS due to the larger aperture area. The middle-right shows the optimal HETDEX [O ii] line flux, flux_oii in the catalog, which can be either from the HETDEX pipeline or the aperture flux measurement. It is assigned flux_aper if it is a positive value and the major axis of the galaxy based on broadband imaging is greater than 2''. Otherwise the line flux measured comes from the flux measured from the HETDEX pipeline. The flag listed as flag_aper is 1 if flux_aper is used, 0 if flux is used, and -1 if it is not relevant, as is the case for LAEs, AGN, stars, and low-z galaxies (LZGs). As shown in the bottom-left of Figure 9, the galaxies in the comparison have a wide range of sizes, so it is not surprising that the HETDEX spatially resolved fluxes are much larger than the fiber fluxes from SDSS.

Reported fluxes are provided both as measured at the top of the atmosphere, and corrected for Galactic extinction. The python software package dustmaps (Green 2018) is employed to access the local Milky Way dust reddening values for each source's coordinates as measured by Schlegel et al. (1998). The software returns the locally measured color excess value, E(B − V), based on a source coordinate. We assume the ratio of V-band extinction, A_V , to color excess, E(B − V), to be R_V = 3.1 and apply a factor of 2.742 to measure the local V-band extinction as A_V = 2.742 × E(B − V) according to the re-calibration using SDSS stars of the Schlegel et al. (1998) maps by Schlafly & Finkbeiner (2011). A_V values range from 0.01–1.44 with a median value of 0.04. Dust correction of line fluxes is applied at the central wavelength of the line emission according to the R_V = 3.1 extinction curve of Fitzpatrick (1999), implemented using the open-source python software extinction. ²⁸ The measured values are designated with the notation XXX_obs, where XXX_obs can be flux_obs, flux_obs_err, continuum_obs, or continuum_obs_err without any dust correction, while those without the obs suffix have the local dust correction applied. Included source spectra are also offered with and without an applied dust correction. Their format is described further in Section 5.

The continuum sample comprises objects in the magnitude range of 14 ≲ g ≲ 21.5. In contrast, the line-emission sample probes a broad range of continuum levels, with a quarter of the curated, high-quality sample having g_HETDEX > 25, which we consider to be the approximate sensitivity limit of HETDEX 1D spectra.

The line emission algorithms probe a wide range of sources, which include galaxies with no detectable continua and bright objects with multiple emission-line entries in our detection catalog. Depending on the choice of line-fit parameters, the detection algorithms also include high line width detections that are actually sharp discontinuities in the spectra, caused by absorption features in late-type stars, while others are due to the broad, complex emission lines of AGNs.

For the brighter continuum spectra, we employ the software package Diagnose to determine a source's classification and redshift (see Section 4.1.1). For fainter objects, we rely on the properties of the line emission and assumptions about the expected luminosity function and equivalent width distribution of line emitting sources to assign a redshift; this process is described in detail in Davis et al. (2023) and briefly summarized in Section 4.1.2. If any source contains a detection that is found within the HETDEX AGN Catalog, then the redshift and classification from Liu et al. (2022) is applied, as detailed in Section 4.1.3.

4.1.1. Diagnose

4.1.2. Emission Line eXplorer (ELiXer)

4.1.3. AGN Catalog Redshifts

A sequence of logic is implemented to assign a redshift and classification to each source. We highlight the general logic in the bottom part of the flowchart presented in Figure 4 and describe the details here.

The method of the assigned redshift is found in the column z_src_redshift. If any detection in the group is found in the HETDEX AGN catalog, the redshift from Liu et al. (2022) is assigned to the source group, the source type is labeled agn, and the source's redshift confidence is taken from the z_flag column from the HETDEX AGN Catalog. This value is 1 if either the redshift is derived from multiple emission lines or the object has an SDSS counterpart with a measured redshift consistent with the HETDEX observations. A small (2.2%) fraction of our catalog (4976/223,641) is assigned its redshift from the HETDEX AGN Catalog and can be found in the catalog under z_src_redshift==Liu+2022.

For source groups that contain one or more detections with g_HETDEX < 22 mag and a Diagnose classification, we adopt the Diagnose redshift, z_diagnose. We assign a confidence to this redshift of z_conf=0.9 (an arbitrary high-confident number here, but we aim to provide better calibration of our redshift assignment in the future) as redshifts assigned from Diagnose are highly reliable, with a 97.1% accuracy for our sample (described further in Section 4.3). If the detection has a STELLAR classification, we assign source_type=star and z_hetdex=0. We note that additional classification information can be found from the Diagnose spectral fits in columns (z_diagnose, cls_diagnose, stellartype in Table 6 (described in the Appendix). If the Diagnose classification is GALAXY, we label the source type as oii if an [O ii] emission line is present in the spectrum with a line flux value, flux_oii, reported, and lzg (low-z galaxy) if no emission line has been detected. If the Diagnose classification is QSO, we assign a source type of agn. Less than half (41.1%, 91,885/223,641) of the catalog redshifts are assigned using Diagnose and can be isolated in the catalog under z_src_redshift==Diagnose.

For all other source groups, we rely on ELiXer to assign source redshifts. For the public HDR2 catalog that is limited to higher S/N > 5.5 detections, 60.7% (135,789/223,641) sources are classified by ELiXer. A few steps of logic are involved when making the final selection, which we briefly outline here. For a single emission-line source group, we simply assign the ELiXer redshift, best_z, to z_hetdex. We also transfer the ELiXer redshift confidence, best_pz (described in detail in Davis et al. 2023) to z_conf. The redshift confidence should not be used for selection criteria, however, as we have not calibrated it. This will be applied in later HETDEX catalogs.

If multiple line detections are found, we first check to see if any of the detections are part of a common wavelength linked group. We then use the redshift for the detection closest to the center of the wave group (listed as the minimum value of src_separation for the detection group). Next we check to see if any of the detections are confidently at low-z, with plya_classification < 0.4. This value is empirically chosen to maximize the LAE recovery fraction (96%), while minimizing the [O ii] contamination fraction (at 3%). It also differs from the built-in threshold (plya_classification = 0.5) that ELiXer users for its redshift assignment, as this earlier software version was found to put low-quality LAE candidates at 0.4 < plya_classification < 0.5. If this is the case, we assign the ELiXer best_z to the detection closest to the source group center. This can result in background line emitters getting blended with the foreground source and ultimately not classified as an LAE or more distant galaxy. If neither of these cases are found, we go through the source group assigned redshifts and make a choice of which is the best redshift to use.

If the collection of redshifts has a standard deviation less than 0.02, then we can simply assign the redshift of the detection closest to the source center. This will happen if the source is an extended Lyα-emitter or if observed emission lines are a pair match such as Lyα and C iv. Extended Lyα-emitters will be analyzed in a future HETDEX paper but can be found in this catalog by searching for sources with a defined wave_group_id at z_hetdex >1.88. Both AGN and LAE source types (e.g., via a logical search of source_type = =lae or agn) can exhibit extended emission. If the standard deviation of z_hetdex in the detection grouping is larger than 0.02 and all detections are classified as high-z according to ELiXer's best_z, then we assume the detections to be independent from each other and be line-of-sight interlopers. We disassociate the group of detections and assign each detection a unique source_id, and classify each detection as an LAE at redshift corresponding to Lyα the observed line wavelength. Sources that have been assigned their redshift from ELiXer are found in Table 6 under z_src_redshift=='elixer'.

Examples of the source classification and redshift assignment for a range of objects in the catalog are presented in Figures 6 (z < 0.5) and 7 1.9 < z < 3.3).

To assess the accuracy of our redshift assignments, we can compare our cataloged values, z_hetdex, to spectroscopically determined redshifts from other surveys. These literature redshifts are generally quite reliable, as they tend to be derived from spectra with higher spectral resolution, and/or broader wavelength coverage than that from HETDEX. However, because these targets were often pre-selected from broadband imaging data, they also tend to have continuum magnitudes significantly brighter than the bulk of the HETDEX detections.

In the COSMOS legacy field, we use redshifts from zCOSMOS DR3 (Lilly et al. 2009) and the DEIMOS 10k Sample (Hasinger et al. 2018); in the GOODS-N legacy field, the redshifts come from Reddy et al. (2006), Barger et al. (2008), Wirth et al. (2004, 2015), PEARS (Ferreras et al. 2009), and DEEP3 (Cooper et al. 2011). Redshifts are also used from MOSDEF (Kriek et al. 2015) and 3D-HST (Momcheva et al. 2016), which cover multiple deep legacy fields. Finally, we also use measurements from the SDSS DR16 Redshift Catalog (Ahumada et al. 2020), which covers brighter objects over all of our fields. For all of these data, we apply quality criteria to select the surveys' most confident redshifts as described in their corresponding papers.

Shown in Figure 10, 4675 of our catalog sources have a spectroscopic redshift match within 12. The source type breakdown of the catalog-matched sources is 134 LAEs, 1592 AGNs, 2560 [O ii]-emitting low-z galaxies, 311 other LZGs without [O ii] line emission, and 78 stars. The accuracy of our combined redshift assignment method is 96.1% (88.4%), where accuracy is defined as agreement with an external spectroscopic redshift value to within Δz < 0.02 (Δz < 0.005). Restricting the matches to those sources with redshifts assigned from the HETDEX AGN Catalog, 98.2% (1564/1592) are in agreement. The redshift assignment for AGNs, however, included cross-matches to AGN spectroscopic redshifts from SDSS DR14 (Paris et al. 2018), which were adopted if they agreed with line emission measured in the HETDEX data. Removing the AGN population from the catalog and considering just Diagnose and ELiXer redshift assignments, the net redshift accuracy to within Δz < 0.02 is 95.0% (2929/3083). The sample assigned redshifts by Diagnose are 95.7% (1994/2084) accurate; this result is slightly higher than that reported by G. Zeimann et al. (2023, in preparation) because we have excluded the poorer performing AGN/Quasar assignments, which are affected by narrower wavelength coverage of VIRUS. The remaining redshifts assigned by ELiXer have a relatively poorer redshift accuracy of 93.6% (935/999) primarily because ELiXer is the catchall for all of the remaining sources that are not bright enough for Diagnose nor are they visually classified as an AGNs. False-positive line-emission detections, which generally do not have associated continuum emission, fall into this category, as do transient detections (such as missed meteor and satellite features), and local line emitters with little continuum (e.g., young stellar objects, active late-type stars, and planetary nebulae). Finally, the overall density of faint line emitters is considerably larger than that for bright continuum sources, so some line-of-sight mismatches with external redshift catalogs are likely.

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One approach to measure the true success rate of identifying [O ii] and Lyα sources and mitigate possible contamination from false positives and other interlopers is to only consider line detections at observed wavelengths that match the spectroscopic redshift from the external catalogs at either the observed frame of [O ii] or Lyα. This requirement increases the accuracy of ELiXer to 95.24% and the accuracy of HETDEX redshift assignments to 96.8%. For greater in-depth discussion on assigning classifications with ELiXer and its success rates, see Davis et al. (2023).

The unique count of astronomical sources is 51,863 LAEs, 123,891 [O ii] emitting galaxies, 4976 AGN, 5274 LZGs, and 37,916 stars. Since the HETDEX observations contain several fields with repeated observations, a number of the sources have more than one entry. Thus the total number of source detections is greater than the number of unique sources, and consists of 40,088 stars, 129,511 [O ii] emitters, 4971 AGN, 5399 LZGs, and 52,681 LAEs. In the catalog, each source is allocated a common integer source_id and source_name where the latter descriptor follows the IAU standard, i.e., of the form HETDEX J123449.19+511733.7. To search for repeated observations of the same object, the unique integer observation identifier shotid can be used. Since multiple detections can comprise a single source, we have provided the additional column selected_det==True in Table 6 to indicate which detection best represents the source. If a source is observed multiple times, multiple selected_det==True entries are in the catalog.

By field, the breakdown of sources for dex-spring: 172,831, dex-fall: 56,251, cosmos: 2447, and goods-n: 1121, which is presented relative to field size and IFU count in Table 1. In Figure 11, the g_HETDEX magnitude distribution is shown. The vertical dashed line shows the approximate limiting magnitude of observations; while the precise value varies with the observing conditions, below g_HETDEX ≈ 25, the "magnitude" is mostly the result of summed noise. Note that the median continuum magnitude for S/N > 5.5 LAEs is g_HETDEX ∼25.9, far below this threshold. In this sample, 84.7% of the LAEs have g_HETDEX > 24.5.

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The LAE sample used to produce the bright-end Lyα luminosity function presented by Zhang et al. (2021) overlaps with the sample in this catalog. Their sample is derived from an earlier version of the catalog presented here. It also consists of an augmented LAE sample found by force extracting HETDEX spectra on known imaging sources in Hyper Suprime-Cam r-band (HSC-r; Miyazaki et al. 2018) data and performing an independent line emission search. As they required HSC-r band coverage for their work, their coverage consists of ∼45% (11.4 deg²) of the coverage presented in this catalog (25.0 deg²). Cross-matching between both catalogs shows that 91% of LAE candidates in Zhang et al. (2021) are recovered in our final source catalog and 95% in the raw line emission-line database. The primary reason LAE candidates (about 1000 LAE candidates) are not in the catalog presented here is they fail from stricter observational quality criteria cuts, updated masking, and different line parameter criteria. Visual inspection suggests about three-quarters of the missing sample are false positives due to noise and artifacts, while the rest are confident LAE candidates that are culled due to quality cuts. We do note that a substantial fraction (about 10%) of their LAE candidates are misclassified. Many of these LAEs are actually low-redshift emission-line sources (primarily due to [O ii] emission, but some are due to Hβ, [O iii], and other line emission) in the HETDEX Source Catalog.

Low-z, [O ii] emitting galaxies are the most numerous in our catalog. These objects span a wide range of magnitudes ranging from g_HETDEX ∼ 17.5 to below the catalog's sensitivity limit (based on a threshold continuum requirement for object detection not the sensitivity limit of HETDEX observations), with a median value of g_HETDEX ∼ 22.4. The faint end of this distribution overlaps that of the LAEs and illustrates the need for additional observational criteria in determining whether a line emitter is from a low-z galaxy or from Lyα.

The third panel in Figure 11 shows the AGN g_HETDEX distribution. This distribution has a median magnitude that is slightly brighter than that for the [O ii] galaxies, g_HETDEX ∼ 22.0, and contains both bright continuum sources with broad-line emission and a fainter population in which either multiple emission lines (i.e., Lyα, C iv, and He ii) or a single broad emission feature is found. In some cases, broad extended line emission can have very little continuum associated with it, and it is often spatially extended, suggesting the possibility that the heating mechanism is perhaps not due to an AGN.

The LZG population is mostly detected in the continuum detection search, although a detection of line emission can also result if there is a continuum peak within two absorption troughs or if there is an abrupt change in an object's continuum level. Not surprisingly, LZG galaxies are generally brighter than [O ii] emitters, with a median g_HETDEX of 20.4 mag, and they are much less numerous. But there is considerable overlap in the populations, and both object classes are present in our continuum catalog. Initially, many [O ii] galaxies were missed by our line-emission search, and were only discovered by measuring spatially resolved [O ii] aperture fluxes (see Section 3.4). If we consider just continuum detected sources, which can loosely be considered analogous to a magnitude-limited survey, then 16.3% of the low-z galaxies have no measured line emission, while 82.9% have measured continuum-subtracted [O ii] emission. Alternatively, if we consider all HETDEX low-z detections (both emission-line and continuum objects) then just 2.7% of the catalog consists of LZGs, and 97.2% are [O ii] systems.

Both the HETDEX line and continuum emission catalogs contain entries from stellar emission. As with LZGs, discontinuity jumps in the continuum can be mistaken for emission features; our spatial clustering ensures that duel detections are properly merged into a single source. The stars in the HETDEX catalog can be as bright as g_HETDEX ∼ 12.3 with a median value of g_HETDEX≈19.0. The number of stars in this catalog is considerably smaller than that reported in the HETDEX-Gaia catalog (Hawkins et al. 2021), due to the very different selection criteria and methods of detection applied. In Hawkins et al. (2021), spectral extractions were performed at the known locations of 10 < G < 22 Gaia DR2 stars (Gaia Collaboration et al. 2018) using the same data release (HDR2) presented here. Their catalog consisted of 98,736 unique stellar candidates; our catalog contains 37,916 of these objects.

The major difference between the two catalogs lies in the heterogeneous sensitivity of the HETDEX continuum detection level. At magnitudes of g_HETDEX < 15, bright stars and galaxies saturate the detectors, making it impossible to properly perform a flux calibration. When this happens, the detector may be useless for HETDEX science, but may still produce detectable and classifiable stellar spectra. Moreover, as discussed in Section 2.1, frames with bright stars or additional detector issues will fail our observation quality criteria and are removed from the survey; the forced extraction methods performed by Hawkins et al. (2021) did not apply these additional criteria, and so will include more objects. In addition, our continuum detection search was essentially count limited, rather than magnitude limited. Depending on observing conditions, this restricted our continuum-selected sample to objects brighter than g ∼ 21–22.5. Finally, we note that it appears the HETDEX-Gaia catalog has some likely galaxy contaminants: out of the 37,916 overlapping sources, 87.3% were classified in the HETDEX Source Catalog as stars, 3.9% as AGNs, 6.6% as [O ii] galaxies, and 2.0% as LZGs. Indeed when measuring radial velocities, Hawkins et al. (2021) report low-level (∼2%) contamination by galaxies.

As described in Section 3.1.3, the Gaussian amplitude (which provides the line flux), line width (σ), and continuum level are the free parameters of the emission-line fit. The central location of the line detection is determined by rastering the line fit at high spatial resolution to maximize on S/N of the fit. Table 6 reports theses values and the quality of fit, χ². We employ variable cuts on the line parameters when we create the curated line emission catalog (as discussed in Section 3.1.3 and described in Equations (1) and (2)). The internal HETDEX Source Catalog is limited to line emission detections with S/N > 4.8, while the public version excludes all LAEs with S/N < 5.5. At the lower value, confidence in the line detection goes down, and the visual line fits are of poor quality.

In Figure 12, we plot the S/N distribution for the LAEs and [O ii] galaxies in the top and bottom panels, respectively. The lighter colors are for the full sample included in the catalog; the solid region is for an isolated "confirmed" sample with at least three independent observations. Many of these objects are from the science verification fields, which were subjected to multiple visits (see Section 6.3.2 for a complete discussion). The sample of sources confirmed by multiple observations has a similar S/N distribution as the objects in the full catalog, although the number counts go significantly down at higher S/N as sample variance plagues the "confirmed" sample. For both samples, as expected, the number of sources increases as S/N decreases. Unsurprisingly, the [O ii] galaxies extend to much higher S/N than the LAEs.

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The left panel of Figure 13 shows the distribution of Lyα and [O ii] line fluxes for the two main line emission samples. Lyα line flux values range from 3.4–1030 × 10⁻¹⁷ erg s⁻¹ cm⁻² Å⁻¹ where the 10th, 50th, and 90th percentiles are 8.3, 14.5, and 32.8 × 10⁻¹⁷ erg s⁻¹ cm⁻² Å⁻¹, respectively. The [O ii] line fluxes range from 3.7–2960 × 10⁻¹⁷ erg s⁻¹ cm⁻² Å⁻¹ where the 10th, 50th, and 90th percentiles are 10.2, 20.0, and 53.2 × 10⁻¹⁷ erg s⁻¹ cm⁻² Å⁻¹, respectively. Distributions for the AGN sample can be found in Liu et al. (2022). Some line emission sources were observed multiple times in this release, and have multiple measurements in the catalog. These can be isolated by searching for a common source_id value but a different observation ID (shotid) value. The rms scatter in repeated line measurements is 13.1% if comparison sources are required to be within 05. This value increases to 13.8% without any sky separation requirement, suggesting source position plays a role in line flux accuracy, as discussed earlier in Section 3.4.1. Simulations described in Gebhardt et al. (2021) suggest an even higher statistical uncertainty of 25%–30% that is signal-to-noise dependent. A better flux accuracy is measured in the presented catalog likely due to a stricter S/N requirement of 5.5.

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A comparison to two external samples of published line flux values is shown in Figure 14. Here we compare a strictly LAE sample from the SC4K survey (Sobral et al. 2018) shown in blue, as well as a mix of [O ii] and Lyα-emitting galaxies from the HETDEX Pilot Survey (HPS; Adams et al. 2011). SC4K uses 16 different narrowband and medium-band filters over the COSMOS field to select a large sample of LAEs. For these emitters, we require a match to within 1'' spatially and within 300 Å of the HETDEX emission-line wavelength. We find that 50 LAEs and 17 AGNs overlap with our catalog. We find 30% of the HETDEX line fluxes are more than three times the reported SC4K fluxes with 50% of these being AGNs in our catalog. SC4K measures their fluxes in 2'' apertures, and the continuum is measured in multiple narrowband filters potentially leading to inconsistencies in the measurement, which is most significant for the AGN sources. Designed as an HETDEX validation survey, HPS is similar in design to HETDEX. HPS used the VIRUS prototype IFU (VIRUS-P; Hill et al. 2008) on the 2.7 m Harlan J. Smith telescope at the McDonald. Three-dithered exposures provide similar coverage at similar resolving power, with the main difference being VIRUS-P's larger fiber size (42 compared to VIRUS's 15 diameter fibers). Data is reduced in a completely independent pipeline from the current HETDEX pipeline, and line fluxes are measured differently. In total, 179 detections overlap within 8 Å spectrally and 1'' spatially; 128 of these are O iis, 37 are LAEs, and 12 are AGNs. The bottom panel shows that the line flux differences (HETDEX—HPS) are consistent to within 1σ of the combined lines flux uncertainties 92% of the time.

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The fitted Gaussian line width distributions for the [O ii] and LAE samples have roughly the same range. As shown in the middle panel of Figure 13, Lyα emitters show a broader distribution and have a higher frequency of broad-line emitters relative to the [O ii] sample, as might be expected (Kulas et al. 2012; Chonis et al. 2013). The figure also shows a substantial decrease in the distribution at σ = 6: our fitting criteria removes all lower signal-to-noise (S/N < 6.5) lines with σ > 6 (see Equation (1)). The drop off suggests we are losing real sources with this criteria, especially in the LAE sample at a 0.001% level. Fortunately, the HETDEX AGN Catalog selection does explore this parameter space. In the higher line width regime, visual inspection confirms the existence of many artifacts due to issues involving both the detector and the calibration.

We run each line and continuum detection through our source classifying software ELiXer (Davis et al. 2023) to obtain photometric magnitudes at the direct location of the HETDEX detection. We use the multiwavelength coverage provided by the Hyper Suprime-Cam through the Subaru Strategic Program (HSC-SSP; Aihara et al. 2018, 2022) as well as internally obtained HSC-r-band imaging as described in Davis et al. (2023). Data reduction and source detections were performed with version 6.7 of the HSC pipeline, hscPipe (Bosch et al. 2018), and produced r-band images with a 10σ limit of r = 25.1 mag in a 2'' diameter circular aperture.

The magnitude distribution of imaging counterpart to HETDEX sources, as measured in the HSC r band, are shown in Figure 15 for the LAE and OII catalog sources. We show the full sample in shaded opacity while highlighting the confirmed samples in solid colors to show the overall consistencies in the two populations. [O ii] galaxies are brighter than the LAEs with a median value of r = 21.6. In contrast, the LAE sample has a median magnitude of r = 24.7, but we note that this distribution is biased due to the sensitivity limit of the r-band imaging data.

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6.3.1.  g-band Magnitude Comparison

In Section 6.1, we described the g_HETDEX magnitude distributions for the catalog. Continuum sensitivity from a single extracted HETDEX spectrum varies based on observing conditions, but is generally reliable to g_HETDEX ∼ 25, although the uncertainties can be large. We compare these magnitudes with g-band measurements calculated with our ELiXer software on g-band data from the HSC-SSP program, which reach a sensitivity of g = 26.5 mag.

In Figure 16, the difference in magnitude is plotted as a function of g_HETDEX. The stellar sample shows an offset of 0.05 mag with a scatter of 0.51 mag. The [O ii] sample has an offset of 0.14 mag with a scatter of 0.41 mag. The LZG has the largest offset of −0.34 mag with a scatter of 0.57 mag. The AGN sample has an offset of 0.13 mag with a scatter of 0.54 mag. For both the [O ii] and LZG samples, the aperture effects are important, as HETDEX magnitudes are for point-source measurements and the HSC-SSP measurements are for varying apertures. We intentionally exclude any sources with a major axis greater than 3'' to mitigate aperture affects. Unsurprisingly, the faint LAE sample that pushes the sensitivity limits of HETDEX shows the largest scatter of 0.59 mag, but a modest offset of 0.17 mag. An overall trend line shows that the offset is largest at faint magnitudes where a lower S/N in the HETDEX spectra leads to a lower integrated flux.

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6.3.2. Imaging Counterpart Fraction

In HSC r-band, our preferred photometric data set, many LAEs in our sample have no apparent counterpart. This is not surprising given that the LAE sample exhibits stellar masses ranging from ∼10⁸–10¹⁰ M_⊙ (Hagen et al. 2016; Oyarzún et al. 2017; McCarron et al. 2022). However, we also recognize that a lack of imaging counterparts can be an indication of potential false-positive contamination. This is specific to the high-z sample since the low-z identifications require that a continuum be detected in either the spectral data or the accompanying imaging. Thus, by definition, the [O ii] sample has less contamination from noise and artifacts.

One way to investigate the amount of contamination present in our sample is to compare the fraction of confirmed LAEs with imaging counterparts to that of the full catalog sample. There are a number of ways to confirm the presence of line emission for an HETDEX detection. For example, sources confirmed by other instruments can confirm an object as real (as well as provide confirmation of the redshift and classification). Alternatively, we can use the HETDEX data themselves: if line emission is detected in three or more independent observations, we confirm the source to be real. Although HETDEX tiling is designed to visit the sky just once, there are a number of science verification fields (in legacy regions such as COSMOS and GOODS-N) that HETDEX has visited on numerous occasions. In a few cases, observations were redone, due to substandard observing conditions. Although the unacceptable observations are not in our final catalog, the emission-line detections remain in the raw line database and are used for object verification. Finally, in a few cases, the corners of IFUs overlap (see, for example, the overlap in the right panel of Figure 3), due to tiling changes associated with the increasing number of active IFUs over time. We call the set of objects identified in three or more independent observations our "confirmed" sample. We show the S/N and HSC-r-band imaging counterpart magnitudes for the confirmed sample relative to the full catalog sample in Figures 12 and 15. The similar distributions indicate the sample is representative of the full catalog.

We consider two different catalog samples, all of which require accompanying HSC-r imaging coverage, for this test: the publicly provided catalog LAE sample (n = 39,083) and OII sample (n = 86,357). We compare these to their counterparts in the confirmed data set: n = 422 for the LAE sample, n = 1529 for the OII sample. To be in these subsamples, we require that each source be contained on an HSC r-band image, which we assume to have a depth better than r = 26.2 mag (5σ limit). For each sample, we calculate the number of HETDEX detections with an r-band counterpart as measured in either one of two ways: (1) through on-demand source extraction applied to the HSC image using the ELiXer software tool, or (2) a forced extraction at the exact position of the HETDEX detection and measured within an r = 15 circular aperture.

In Table 5, we summarize the net fraction of LAEs and OII galaxies with HSC r-band counterparts. The first thing to note is that the fractions for the confirmed sample and the main sample are consistent to within a few percentage points. This implies that the catalog is relatively free of contamination by false positives. In a catalog with many false detections, the fraction of LAEs with counterparts would be much greater in the confirmed sample than in the main sample.

Table 5. HSC r-band Imaging Counterpart Fraction

	Full Catalog	Confirmed
LAE	55.8% (21,824/39,083)	52.4% (221/422)
O ii	99.3% (85,754/86,357)	99.2% (1517/1529)

Note. The "Confirmed" sample of line emitters consists of objects that have been independently detected in three different observations. The detected objects have r-band counterparts brighter than r = 26.2.

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In Figure 17, we consider how the fraction of objects with r-band counterparts depends on the S/N of the line (top) and g_HETDEX (bottom). The counterpart fraction increases with the S/N on the LAE emission line. This implies the brighter emitters tend to also have higher line flux in our catalog as seen in previous LAE studies where equivalent width has a minimal dependence on line luminosity (e.g., Gronwall et al. 2007; Ciardullo et al. 2012). By design, nearly all OII sources are present in the r-band images, as a continuum detection (either through imaging or spectroscopy) is needed for a detection to be classified as OII. There are some OII detections that have faint g_HETDEX values and are consequently less likely to be observable in the r. These are sources that have been classified as OII by ELiXer even though they have a very weak continuum. Upon inspection, these often tend to be false positives, due either to calibration issues or satellites.

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The measured imaging counterpart fraction demonstrates the strength of an IFU-based LAE survey. Just over half of the LAE sample have image counterparts brighter than r = 26.2. A survey based on imaging preselection at this sensitivity would miss half of the objects that HETDEX is using to trace the large-scale structure of the 1.9 < z < 3.5 universe.

6.3.3. Source Positioning

Table 6 contains selected output from the ELiXer catalog about the imaging counterparts of HETDEX detections. Included in these data are the separations between the HETDEX sources and the position of the most likely imaging counterparts (labeled as counterpart_dist). Figure 18 shows distributions of these separations for each source type. The LAE sample shows the widest distribution. This is primarily attributed to a poorer ability to center low-S/N emission lines within the PSF-weighted VIRUS spectral extraction. McCarron et al. (2022) found in deep GOODS-N HST imaging that HETDEX imaging counterparts can be up to 1'' in separation from the HETDEX detection center.

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The star sample in orange at the bottom shows the tightest distribution with a median sky separation of 027. This is comparable to our astrometric uncertainties (∼02). OII galaxies, AGNs, and LZGs, have a wider distribution as there can be differences in where the source center lies.

In Figure 19, we show the emission-line luminosities for LAEs and the OII galaxies. The Lyα line luminosities range from 1.84 × 10⁴² erg s⁻¹ to 2.85 × 10⁴⁴ erg s⁻¹ with a median value of 8.31 × 10⁴² erg s⁻¹. For each LAE source, the corresponding Lyα flux and luminosity are found in the columns flux_lya and lum_lya. For the OII galaxies, 87.9% of the values (as indicated by flag_aper==1) are from resolved aperture line fluxes (flux_aper); the rest are assumed to be pointlike sources and come from HETDEX pipeline (flux). The selected OII flux values can be found in the Source Observation Table (see Table 3) in the column flux_oii, and the luminosities are given in column lum_oii. The [O ii] line luminosities of our sample range from 6.13 × 10³² erg s⁻¹ to 1.76 × 10⁴⁴ erg s⁻¹ with a median value of 1.96 × 10⁴⁰ erg s⁻¹.

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In Figure 20, we show the redshift distribution of the low-z and high-z galaxy samples. For the low-z sample, galaxies with (source_type==oii) and without (source_type==lzg) [O ii] line emission are shown together; their counts increase with z, as the greater volume at higher z is more important than the accompanying decrease in survey depth. The dip at z_hetdex ∼ 0.21 in the low-z sample (and at z_hetdex ∼ 2.7 in the high-z data set) is due to a mask that is applied at the center of 50% of the detectors as well as an increase in night sky emission. Night sky emission, particularly in the blue, causes marked decreases in number counts in the lower-redshift regions of both data sets but is most notable at high-z. The brightest sky lines are marked by light yellow bars in Figure 20. At these epochs, the loss in depth due to increased distance outweighs the volume effect. Sample variance can play a small role in the variation in counts, but given the size of the survey, this should largely be mitigated. The remaining variability in counts as a function of wavelength is due to the complex sensitivity variations caused by variable observing conditions, detector spectral response, and fiber-to-fiber (and amplifier-to-amplifier) variations. Details concerning HETDEX's complex selection will be described in D. Farrow et al. (2022, in preparation).

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HETDEX is designed to search for faint, low-S/N emission lines in a large amount of data. HDR2 consists of 208 million fiber spectra, each with 1036 spectral resolution elements. This means examining over 210 billion resolution elements. Noise is ultimately the biggest contaminator in our catalog, and the vast majority of our spectra observe the blank sky. Attempts to quantify the HETDEX false-positive rate are ongoing but here we briefly summarize our efforts to confirm sources.

Multiple methods are used to measure the confirmation rate of HETDEX line emission sources. The method that provides the highest number of confirmed sources involves using the HETDEX data themselves. As described in Section 6.3.2, we assume that any emission-line source found in three independent observations is real. We create a validation sample by considering every OII and LAE in the catalog and checking to see if the location of the source has been targeted multiple times. This is done by cross-matching the catalog with the fiber database. If a source has fiber coverage from at least six observations, we put it in the validation sample. We note that just because a sky position has fiber coverage, that does not mean the observation is useful, as varying observing conditions may prevent a real source from being observed. Ultimately the confirmation rate provides only an upper limit on our false-positive rate. Consequently, we also use spectroscopic redshifts from the literature to validate HETDEX detections if the redshift matches the redshift in the literature to within Δz < 0.02

For the S/N > 5.5 validation sample, 91.0% of LAEs are confirmed; for the OII sample, the fraction is 99.3%. The combined fraction is 98.1% because of the high fraction of [O ii]-emitting galaxies in the catalog (123,891) compared to the number of S/N > 5.5 LAEs (51,863).