DESI Emission Line Galaxies:
Unveiling the Diversity of [OII] Profiles and its Links to Star Formation and Morphology

The Dark Energy Spectroscopic Instrument (DESI) survey (DESI Collaboration et al., 2022) is a Stage-IV project, primarily designed for probing the cosmological parameters of the Universe (Levi et al., 2013; DESI Collaboration et al., 2016a, 2024a). DESI consists of bright-time and dark-time science targets (Cooper et al., 2023; Hahn et al., 2023; Zhou et al., 2023; Raichoor et al., 2023; Chaussidon et al., 2023) with [OII] emission line galaxies (ELGs, Raichoor et al., 2023) being one of the key targets in the program. In order to obtain the desired redshift range of DESI ELGs, a specific target selection scheme is developed for the sources detected in the DESI Legacy Imaging Surveys (Dey et al., 2019), which include $g$, $r$, $z$ bands and near-infrared images from WISE satellite (Wright et al., 2010), via the Tractor algorithm (Lang et al., 2016) with large galaxies masked (Moustakas et al., 2023). To ensure the efficiency of DESI operations, dedicated pipelines are developed for target selection (Myers et al., 2023), survey operations (Schlafly et al., 2023) and fiber assignment (Raichoor et al., 2024).

Spectroscopic data is collected by the DESI instrumentation installed on the 4-meter Mayall Telescope at Kitt Peak National Observatory (DESI Collaboration et al., 2022; Silber et al., 2023; Miller et al., 2023). The instrument has a 3.2 degree diameter field of view covered with 5020 robotic fiber positioners. The wavelength coverage ranges from 3600 $\rm\AA$ to 9800 $\rm\AA$ with spectral resolution from $\sim 2000$ in the shortest wavelength to $\sim 5000$ in the longest wavelength. The raw spectra are processed, reduced and calibrated by an automatic pipeline (Guy et al., 2023). The redshifts of sources are then obtained via an algorithm, called $Redrock$ (Bailey et al., 2023) (See also Brodzeller et al., 2023; Anand et al., 2024), with the redshift accuracy and precision for all types of extragalactic sources, including ELGs, being tested and validated against redshifts obtained from spectra with long exposure times and confirmed via visual inspection (Lan et al., 2023; Alexander et al., 2023).

In this analysis, we make use of the DESI spectra of ELGs observed during the Survey Validation phase (DESI Collaboration et al., 2024a) to explore the [O II]$\lambda\lambda 3726,3729$ emission line profiles. The DESI SV campaign consists of two key phases, the SV1 and the one-percent survey. The SV1 observations include targets selected from a wider parameter space in order to test and finalize the target selection scheme of the DESI main survey. The one-percent survey then adopted the finalized target selection scheme and obtained the observations that cover sky area $\rm\sim 140\,deg^{2}$, about $1\%$ of the DESI final footprint (DESI Collaboration et al., 2024a).

We focus on the ELGs observed in the one-percent survey to inform the properties of ELGs of the DESI main survey. The ELGs are selected within a color-magnitude space defined with $g-r$, $r-z$ colors, g-band magnitude and g-band fiber magnitude for preferentially including star-forming galaxies at $1.1<z<1.63$ (Raichoor et al., 2023).

We first make use of the data from the Early Data Release (DESI Collaboration et al., 2024b) which includes $\sim 280,000$ spectra of ELGs with robust redshift measurements that pass the redshift quality selection for ELGs, $\rm log_{10}\,{\rm SNR}(F_{\rm O\,II})>0.9-0.2\times log_{10}\,{\Delta\chi^{2}}$, where $\rm{\rm SNR}(F_{\rm O\,II})$ is the signal to noise ratio of the [OII] emission lines measured via a double-gaussian fitting (Raichoor et al., 2023) and $\Delta\chi^{2}$ is the difference between the $\chi^{2}$ values from the second best-fit model and the first best-fit model provided by $Redrock$ (Bailey et al., 2023). This selection yields a ELG sample with redshift purity (the fraction of ELGs with $\it{Redrock}$ redshifts and visually inspected redshifts difference smaller than $\sim 1000$ km/s) greater than $99\%$ (Lan et al., 2023). We further select ELGs with $0.6<z<1.63$ and with spectral types identified by $\it{Redrock}$ as galaxies. This selection yields a sample of $\sim 260,000$ ELGs. In addition, using line information available at different redshifts, we remove possible active galactic nuclei (AGN) contamination. The selections remove approximately $4\%$ of DESI ELGs. The detailed selections are described in Appendix A. Approximately $250,000$ ELGs pass the above selection criteria. We note that this sample includes ELGs with LOP (Low Priority) and VLO (Very Low Priority) selections (See Raichoor et al., 2023, for details) for the main DESI survey. Approximately 78% of the sample is LOP ELGs, the fiducial ELG sample for DESI clustering measurements.

To explore the physical properties of DESI ELGs in the context of the whole star-forming galaxy population across redshifts, we utilize the COSMOS2020 catalog (Weaver et al., 2022) which includes approximately 1.7 million sources with photometric redshifts ($z_{photo}$) and physical properties of galaxies estimated based on multi-wavelength broad-band deep imaging datasets. The COSMOS field was covered by the DESI one-percent survey. Therefore, we can compile a sample with a few thousand DESI ELGs with properties derived from deep COSMOS datasets.

Catalog selection: In the COSMOS2020 data release, there are two source catalogs, the CLASSIC catalog and the FARMER catalog, which are constructed based on the SExtractor (Bertin & Arnouts, 1996) and the Tractor (Lang et al., 2016) algorithms respectively for source detection and flux measurements. The primary difference between two methods is that in the CLASSIC catalog, the fluxes of sources are measured with the aperture photometry method while in the FARMER catalog, the fluxes of sources are measured with the forced photometric best-fit models of source light distribution. As shown in Weaver et al. (2022), for sources brighter than 24 mag in Hyper Suprime-Cam z-band, these two methods yield consistent measurements with magnitude deviation lower than 0.05 magnitude. However, the FARMER catalog only includes sources within the UltraVISTA footprint (McCracken et al., 2012), which consists of about half the amount of sources in the CLASSIC catalog with the full COSMOS field coverage. To maximize the number of the matched DESI ELGs within the COSMOS catalog, we use the measurements provided by the CLASSIC catalog.

Photometric redshifts and physical properties: The COSMOS2020 catalog also includes photometric redshifts and the estimated physical properties of galaxies, including the stellar mass ($M_{*}$) and star-formation rate (SFR), based on the LePhare (Ilbert et al., 2006) and EAZY (Brammer et al., 2008) codes. These two algorithms adopt different sets of galaxy spectral energy distribution (SED) templates and different star-formation histories. For the details, we refer the readers to Weaver et al. (2022) and Gould et al. (2023).

In this work, we adopt the photometric redshifts and galaxy properties from the EAZY algorithm. This choice is motivated by the fact that for the DESI ELGs in the COSMOS2020 footprint and with $\rm|z_{DESI}-z_{photo}|<0.1$, the SFR based on the $H\alpha$ emission line luminosity (Kennicutt, 1998; Kennicutt et al., 2009) from the EAZY algorithm has a higher Spearman’s correlation coefficient ($\rho_{s}\simeq 0.72$) with [OII] emission line luminosity, directly measured from the DESI spectra, than the estimated SFR provided by EAZY ($\rho_{s}\simeq 0.68$) and LePhare ($\rho_{s}\simeq 0.66$) codes. More specifically, we use the best-fit $z_{photo}$, the stellar mass, and the SFR based $H\alpha$ emission line luminosity from the EAZY algorithm applied to the CLASSIC catalog. We note that the COSMOS2020 catalog provides dust-reddened $H\alpha$ luminosity. We correct the dust effect by using $A_{H\alpha}=0.81\,A_{V}$ (Kriek & Conroy, 2013) and adopt the $H\alpha$ intrinsic luminosity and SFR relation from Kennicutt et al. (2009) for the Chabrier initial mass function (Chabrier, 2003). All the stellar mass and the SFR of galaxies used in the work are based on the above method. We emphasize that the goal of this research is to explore the relationship between [OII] line profiles and physical properties of galaxies and to compare the physical properties of DESI ELGs with the properties of the overall star-forming galaxy population at similar redshifts. Identifying the most accurate estimates of physical properties of DESI ELGs is beyond the scope of this paper.

Morphological parameters: Besides the photometric redshifts and physical properties, we make use of the non-parametric diagnostics of galaxy morphology provided by the Zurich Estimator of Structural Type catalog (ZEST, Scarlata et al., 2007; COSMOS team, 2007). The catalog includes

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  asymmetry (A), which quantifies the rotational symmetry of galaxy light distribution;

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  concentration (C), which quantifies the concentration of galaxy light distribution;

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  Gini coefficient (G), which quantifies the uniformity of the light distribution,

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  M20, which is second-order moment of the brightest $20\%$ pixels and

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  R80, which is the length of the best-fit ellipse including $80\%$ of total light along semi-major axis in unit of arcsec (”), reflecting the observed size of the galaxy,

(e.g., Abraham et al., 2003; Lotz et al., 2004; Conselice, 2014, for a review). These parameters are derived from Hubble Space Telescope (HST) Advanced Camera for Surveys (ACS) F814W images (Scoville et al., 2007; Koekemoer et al., 2007; Leauthaud et al., 2007) for galaxies with $I_{AB}<24$, a depth sufficient to include all the DESI ELGs (Raichoor et al., 2023). The F814W filter covers the rest-frame near ultraviolet to optical wavelengths of DESI ELGs. At $z\sim 0.6$, the filter covers from $\rm 4400\,\AA$ to $\rm 5900\,\AA$ and at $z\sim 1.6$, it covers from $\rm 2700\,\AA$ to $\rm 3600\,\AA$. The average width of the point spread function for the HST ACS images is $\sim 0.1"$ (Koekemoer et al., 2007) which corresponds to $\sim 0.67$ kpc at $z=0.6$ and $\sim 0.86$ kpc at $z=1.6$.

Combining the information from these three catalogs¹¹1 Except $\sim 0.4\%$ of DESI ELGs within the locations of the stellar masks of the COSMOS2020 catalog, the rest of DESI ELGs in the COSMOS field have matched counterparts within $0.75"$ radius., we produce two samples of DESI ELGs with $\rm|z_{DESI}-z_{photo}|<0.1$:

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  DESI-COSMOS: The first one, DESI-COSMOS, is the combination between the DESI ELGs and COSMOS2020 CLASSIC catalog, which is done by cross-matching sources with 0.75” radius. This yields a sample with $\sim 4,500$ sources having photo-z, stellar mass, and SFR measurements.

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  DESI-ZEST: The second sample, DESI-ZEST, includes the morphological information from the ZEST catalog by matching the DESI-COSMOS sources with the ZEST sources with 0.75” radius. This DESI-ZEST sample is a subset of the DESI-COSMOS sample, consisting of about 2,200 galaxies.

We note that there are rare cases ($\sim 0.3\%$) that one ELG has two or more galaxies within 0.75” radius from the COSMOS2020 or the ZEST catalogs. For such cases, we adopt the properties of the most massive and brightest (in F814W filter) galaxy.

In order to compare the properties of DESI ELGs and that of the overall star-forming galaxies at the similar redshifts, we construct reference samples by selecting star-forming galaxies from the COSMOS2020 catalog that satisfy

This functional form is adopted from Moustakas et al. (2013) for separating star-forming and quiescent galaxies with a modification on the zero point to better include star-forming galaxies based on the adopted SFR. We refer this star-forming galaxy sample from the full COSMOS2020 catalog as COSMOS-SFG. We also cross-match this COSMOS-SFG sample with the ZEST catalog with $0.75"$ radius to obtain a sample of approximately 100,000 star-forming galaxies with morphological parameters based on HST-ACS images. This sample is referred as COSMOS-ZEST. These samples will be used in Section 4.

In order to perform PCA, we shift all the ELG spectra to their rest-frame based on their $\it Redrock$ redshifts and project the spectra on to a common wavelength grid with a pixel size $\rm 0.5\,\AA$ ($\sim 40$ km/s). This pixel size corresponds to the original pixel size of DESI spectra ($\rm 0.8\,\AA$) in the rest-frame of a source at redshift 0.6, the lower bound of the redshift in our analysis. We estimate the continuum of each spectrum using the median value of pixels around [O II]$\lambda\lambda 3726,3729$ emission lines ($\rm 3715<\lambda<3722\,\AA$ and $\rm 3735<\lambda<3742\,\AA$) and subtract the estimated continuum from the spectrum. We then normalize each spectrum by the maximum value of the pixels with $\rm S/N>3$ between $3726\,\rm\AA$ and $3731\,\rm\AA$ of the spectrum. By doing so, the results of PCA is more sensitive to the shape variation of the [O II]$\lambda\lambda 3726,3729$ emission lines, the focus of this study, than the flux difference between spectra. Finally, we remove spectra with any bad pixels and with the median S/N of the [OII] regions between $3726\,\rm\AA$ and $3731\,\rm\AA$ lower than 2. The final sample includes 229,996 ELGs.

The mean spectrum and the eigen-spectra obtained by PCA are shown in Figure 1. The top panel shows the mean spectrum of the ELGs with clear [O II]$\lambda\lambda 3726,3729$ emission lines. The lower four panels show the first four eigen-spectra respectively.

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  1st eigen-spectrum: the 1st eigen-spectrum explains $43\%$ of the variance of the [OII] line region. It has three peaks at 3726 $\rm\AA$, 3728.5 $\rm\AA$, and 3731 $\rm\AA$, which do not coincide with the [O II]$\lambda\lambda 3726,3729$ lines. The [O II]$\lambda\lambda 3726,3729$ lines in the 1st eigen-spectrum are nearly zero. By modulating flux off the line center, this eigen-spectrum broadens the line width of the emission with positive coefficients and reduces the line width with negative coefficients.

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  2nd eigen-spectrum: the 2nd eigen-spectrum explains $11\%$ of the variance. It has two peaks that coincide with the wavelengths of [O II]$\lambda\lambda 3726,3729$ . With a positive value coefficient, this component increases the [O II]$\lambda\lambda 3726,3729$ line strength and with a negative coefficient, it decreases the strength. Therefore, the 2nd eigen-spectrum modulates the amplitude and peakedness of the [O II]$\lambda\lambda 3726,3729$ emission lines.

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  3rd and 4th eigen-spectra: the 3rd and 4th eigen-spectra both explain only $\sim 5\%$ of the variance. They both have positive values around [OII] 3730 line and negative values around [OII] 3727 line. Therefore, these two components can account for the asymmetry of the line profiles induced by both physical and non-physical signals, such as the variation of the line ratio between [OII]$\lambda 3726$ and [OII]$\lambda 3729$ (e.g., Kaasinen et al., 2017) and the residuals of sky lines.

The first two eigen-spectra explain $\sim 54\%$ (43%, 11%) of the total variances of the ELG spectra. In the following, we focus on the first two eigen-spectra and their application in characterizing the DESI ELG [O II]$\lambda\lambda 3726,3729$ line profiles, while we plan to investigate the application of the 3rd and 4th eigen-spectra in future studies.

Using only the first two eigen-spectra, the [O II]$\lambda\lambda 3726,3729$ line profile of each ELG can be described by two coefficients. Figure 2 shows the distribution of Coefficient 1 ($\rm Coeff_{1}$) (x-axis) and Coefficient 2 ($\rm Coeff_{2}$) (y-axis). We find that the [O II]$\lambda\lambda 3726,3729$ line profiles of DESI ELGs cover the parameter space with both coefficient 1 and coefficient 2, ranging from positive to negative values. Based on the ($\rm Coeff_{1},\rm Coeff_{2}$) values, we classify ELGs into four regions using two empirical selection boundaries $\rm Coeff_{2}=0.15\times Coeff_{1}-0.25$ and $\rm Coeff_{1}=0$ and show example spectra in Figure 3:

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  Narrow region (N): $\rm Coeff_{1}<0$ and $\rm Coeff_{2}>0.15\times Coeff_{1}-0.25$. In this region, the doublet of [O II]$\lambda\lambda 3726,3729$ is narrow and is clearly separated.

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  Broad region (B): $\rm Coeff_{1}>0$ and $\rm Coeff_{2}>0.15\times Coeff_{1}-0.25$. With the increase of $\rm Coeff_{1}$ values, the [O II]$\lambda\lambda 3726,3729$ line width becomes broader and the two [OII] lines gradually blend together with increasing $\rm Coeff_{1}$.

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  Double-peak³³3 We note that the [OII] profiles have three peaks which are in fact consisted of two components with overlapping [OII] emission line doublet. For transition with a single line, the emission line profiles are double-peak. Following the literature, we use ”double-peak” galaxies for describing these systems. region (D): $\rm Coeff_{1}>0$ and $\rm Coeff_{2}<0.15\times Coeff_{1}-0.25$. The combination of a positive value of $\rm Coeff_{1}$ and a negative value of $\rm Coeff_{2}$ yields [OII] line profiles with three emission line peaks with the central peak at $\rm\sim 3728.5\,\AA$ as shown in lower right panels of Figure 3. These profiles are consistent with [OII] lines from two components with velocity offsets. The two velocity component spectral features are also observed in other emission lines, such as $\rm H\beta$ and $\rm[OIII]$, for low-z ELGs with double-peak emission lines. Within the selection, there are $\simeq 30,000$ double-peak galaxies identified from the DESI EDR dataset, which is currently the largest double-peak galaxy catalog at $z>0.6$.

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  Outlier region (O): $\rm Coeff_{1}<0$ and $\rm Coeff_{2}<0.15\times Coeff_{1}-0.25$. In this region, the [OII] line profiles are affected by residuals of strong sky emission lines as shown in the lower left panels of Figure 3.

These four regions are highlighted with blue, green orange, and pink colors for narrow, broad, double-peak and outlier emission lines respectively in Figure 2. The histograms on the top and right panels show the number distributions of $\rm Coeff_{1}$ and $\rm Coeff_{2}$ respectively. We find that $\sim 47\%$ of ELGs are in the narrow region, $\sim 38\%$ of ELGs are in the broad region, $\sim 13\%$ are in the double-peak region, and $\sim 2\%$ are in the outlier region. We classify the ELGs into four regions, and emphasize that while based on the coefficients, their distribution is smooth and continuous.

We now explore and describe the relationships between the observed properties of ELGs and $(\rm Coeff_{1},Coeff_{2})$ values. In the upper panels of Figure 4, we first show the median values of galaxy observables in each $\rm Coeff_{1}$ and $\rm Coeff_{2}$ bin, including the number of ELGs, their redshifts, the observed WISE 1 band magnitude, and the observed g-band magnitude from left to right respectively.

Number: The first upper panel from the left shows the number distribution of DESI ELGs as a function of $\rm Coeff_{1}$ and $\rm Coeff_{2}$. As shown in Figure 2, most of the ELGs are in the narrow and broad regions with a small fraction of ELGs in the double-peak region.

Redshifts: The second upper panel shows the median redshifts as a function of $\rm Coeff_{1}-Coeff_{2}$. As can be seen, there is a redshift dependence between the median redshifts and $\rm Coeff_{1}$. ELGs with narrow [O II]$\lambda\lambda 3726,3729$ systems ($\rm Coeff_{1}<0$) have lower median redshifts than [O II]$\lambda\lambda 3726,3729$ with $\rm Coeff_{1}>0$. Additionally, ELGs with $\rm Coeff_{1}$ and $\rm Coeff_{2}$ values near the edge of the entire distribution tend to have median redshifts $z\sim 1.5$. This is due to the fact that the line profiles of those galaxies are affected by sky emission line residuals and therefore have relatively extreme $\rm Coeff_{1}$ and $\rm Coeff_{2}$ values.

Observed WISE 1 band magnitude: The third upper panel of Figure 4 shows the median observed WISE 1-band magnitude of ELGs. There is a trend indicating that ELGs with larger $\rm Coeff_{1}$ values and lower $\rm Coeff_{2}$ values are on average brighter in WISE 1 band. This trend is not driven by the redshift correlation shown in the 2nd panel. It shows an opposite correlation that high-z ELGs with $\rm Coeff_{1}>0$ tend to have brighter observed magnitude than ELGs at low redshifts with $\rm Coeff_{1}<0$. The WISE 1 band ($3.4\,\mu m$) corresponds to $\sim 1.7\,\mu m$ in the rest-frame of ELGs at $z\sim 1$, being sensitive to the stellar mass of galaxies. Therefore, the relationship between the coefficients and WISE 1 magnitude links the relationship between the coefficients and stellar mass.

Observed g-band magnitude: The last upper panel of Figure 4 shows the median g-band observed magnitude. A trend can be observed, showing the brightness of ELGs in g-band increases with the $\rm Coeff_{1}$ values. ELGs with $\rm Coeff_{1}\sim 1$ on average are brighter than the rest of the ELGs. Similarly to the WISE 1 band distribution, this trend is not driven by the redshift correlation shown in the 2nd panel. We also find that the relationship between the coefficients and g-band magnitude differs from the relationship between the coefficients and WISE 1 band magnitude. DESI ELGs tend to have bright median g-band magnitude around $\rm Coeff_{1}>0.5$ and $\rm Coeff_{2}\simeq 0$, while DESI ELGs tend to have bright median WISE 1-band magnitude around $\rm Coeff_{1}>0.5$ but extends to $\rm Coeff_{2}\sim-1$. Considering the g-band covers the ultraviolet wavelength in the rest-frame of ELGs, this difference suggests that the relationship between the coefficients and SFR is not entirely driven by the relationship between the coefficients and stellar mass.

In addition to the photometric properties of DESI ELGs, we extract the [OII] line information by performing spectral fitting analysis with two models. The first one, $F_{s}$, is a single redshift model describing [O II]$\lambda\lambda 3726,3729$ lines with two Gaussian profiles with a single redshift,

where $x$ is the wavelength ($\rm\AA$), $A_{s}$ is the amplitude of the $\rm[OII]\lambda 3726$ line, $\mu_{1}$ is the center wavelength ($3727.092\rm\AA$) of $\rm[OII]\lambda 3726$ line, $\sigma_{s}$ is line width ($\rm\AA$) of the Gaussian profile. $\rm[OII]\lambda 3729$ line is fitted by the second term where we adopt a fixed line ratio $\rm[OII]3729/[OII]3726=1.33$, the ratio between the two lines from the mean spectrum. The second model, $F_{d}$, is a two redshift model describing [O II]$\lambda\lambda 3726,3729$ lines with two sets of two Gaussian profiles, $F_{s}$, with a wavelength offset $\Delta\lambda$,

where $R$ describes the amplitude difference in terms of ratio between the $\rm[OII]\lambda 3726$ lines from two redshifts. With these two models, we obtain the best-fit parameters and the $\chi^{2}$ of the two models for all the ELG [O II]$\lambda\lambda 3726,3729$ profiles. The lower panels of Figure 4 summarizes the fitting results.

p-value: We first quantify the performance of the two models for describing the [O II]$\lambda\lambda 3726,3729$ profiles with F-test by following Maschmann et al. (2020). We estimate $f_{stat}=\frac{(\chi^{2}_{s}-\chi^{2}_{d})/(N_{s}-N_{d})}{\chi_{d}^{2}/N_{d}}$, where $\chi^{2}_{s}$ and $\chi^{2}_{d}$ are the $\chi^{2}$ values of the best-fits from the single and two redshift models and $N_{s}$ and $N_{d}$ are the corresponding degree of freedoms. We convert $f_{stat}$ values into the p-value for this hypothesis test with the null hypothesis being that the $F_{d}$ model does not provide a better fit than the $F_{s}$ model. In other words, lower p-values indicate a higher probability of rejecting the null hypothesis.

The first lower panel of Figure 4 from the left shows the median p-values, indicating that the p-values depend on the $\rm Coeff_{1}$ and $\rm Coeff_{2}$. For systems with negative $\rm Coeff_{1}$ values, the p-values are around 0.5, suggesting that the single redshift model is sufficient to describe the two [OII] lines. The median p-values decrease with the $\rm Coeff_{1}$ values. This indicates that broader line profiles tend to require two components for describing the line profiles, especially the line profiles with three emission line peaks in the double-peak region which have median p-values lower than 0.05 (a commonly adopted threshold for rejecting the null hypothesis).

Line velocity properties: The second and the third lower panels of Figure 4 show the median velocity dispersion of the emission lines estimated from the line width parameter $\sigma_{s}$ of the single redshift model and the median velocity separation estimated from the $\Delta\lambda$ parameter of the two redshift model respectively. We report the velocity dispersion with the spectral resolution effect being corrected. Both parameters increase from the top left corner ($\rm Coeff_{1}<0\ \&\ Coeff_{2}>0$) to the bottom right corner ($\rm Coeff_{1}>0\ \&\ Coeff_{2}<0$). The median velocity dispersion for DESI ELGs in the narrow region, broad region, the double-peak region are $\sim 50$ km/s, $\sim 80$ km/s, and $\sim 100$ km/s respectively. For the systems that require two redshifts, velocity dispersion from the single redshift model partially reflects the velocity offset of the redshift difference shown in the third panel. The median velocity offsets for DESI ELGs in the broad and double-peak regions are $\sim 100$ km/s and $\sim 150$ km/s.

[OII] luminosity: Finally, the last lower panel of Figure 4 shows the median total luminosity (erg/s) of the two [OII] lines estimated with the best-fit of the two redshift model. There is a correlation between [OII] luminosity and $\rm Coeff_{1}$, indicating that ELGs with broader line profiles have on average higher [OII] luminosity, a trend similarly to the g-band magnitude. This trend is detected across the entire redshift range probed in this work. Considering [OII] luminosity as a tracer of star-formation rate (SFR) of galaxies (e.g., Kennicutt, 1998), this result indicates that the SFR of ELGs correlates with the emission line profiles – the broader the line, the higher the SFR.

With the observed and spectral properties of DESI ELGs being explored, in order to better understand the underlying relationship, we now explore the physical properties of DESI ELGs and their connections to the [O II]$\lambda\lambda 3726,3729$ line profiles, using the DESI-COSMOS sample as described in Section 2. Figure 5 shows the median values of ELG stellar mass (left panel) and SFR (right panel) in the $\rm Coeff_{1}$-$\rm Coeff_{2}$ parameter space. The colors reflect the values of stellar mass and SFR. Being consistent with the trend observed in the median values of WISE 1 band magnitude and g-band magnitude shown in Figure 4, the stellar mass and SFR increase with $\rm Coeff_{1}$, demonstrating the overall relationship between the line profiles, stellar mass and SFR.

Given that the stellar mass and SFR of star-forming galaxies correlate with each other, we further investigate the correlation between $\rm Coeff_{1}$ and SFR with a fixed range of stellar mass of ELGs. The results are shown in Figure 6 for three redshift bins from $0.6<z<1$ (left), $1<z<1.25$ (middle), and $1.25<z<1.63$ (right). The upper panels show the stellar mass distributions of ELGs with different $\rm Coeff_{1}$ ranges. The vertical color dashed line shows the median stellar mass for each $\rm Coeff_{1}$ bin, indicating that ELGs with higher $\rm Coeff_{1}$ values on average have higher stellar mass.

The lower panels of Figure 6 show the SFR of ELGs as a function of stellar mass with colors indicating their $\rm Coeff_{1}$ values. The data points with uncertainties are the median values of $\rm log_{10}SFR$ for the four $\rm Coeff_{1}$ bins. The uncertainties are estimated by bootstrapping the sample 1000 times. We find that with a fixed stellar mass, the SFR increases with $\rm Coeff_{1}$. This trend is observed across the stellar mass and redshift ranges of the DESI ELG sample. We also calculate the median SFR of the overall star-forming galaxy population at the same redshift range from the COSMOS-SFG sample defined in Sec 2.2. The grey dashed line in each panel shows the corresponding median trend. As can be seen, the majority of DESI ELGs have SFR higher than the median SFR of the overall star-forming galaxy population. This result indicates that DESI preferentially selects star-forming galaxies with SFR higher than the main sequence galaxies, a conclusion also reached by Yuan et al. (2023) using DESI ELGs with $0.8<z<1.1$ based on a similar analysis.

To summarize, Figure 6 demonstrates that while there is a general trend between the line profiles and the stellar mass and SFR which are coupled together due to the overall stellar mass and SFR correlation, there is an additional correlation between SFR and line profiles when considering ELGs with similar stellar mass. This trend is consistent with the correlation between gas velocity dispersion and SFR of star-forming galaxies observed at different redshifts from the local Universe (e.g., Law et al., 2022), $z\sim 1$ (e.g., Mai et al., 2024), to $z\sim 2$ (e.g., Übler et al., 2019). In the following, we explore the relationship between this excess SFR with respect to the overall star-forming galaxy population and lines profiles and investigate possible mechanisms behind this relationship.

To explore how the excess SFR of ELGs correlates with the line profiles and inform the underlying mechanisms, in addition to the stellar mass and SFR, we use the DESI-ZEST sample which includes five morphological properties derived from HST ACS F814W images from the ZEST catalog (Scarlata et al., 2007) in the analysis: asymmetry (A), Gini coefficient (G), concentration (C), and the second-order moment of the brightest $20\%$ pixels (M20), and R80 parameter reflecting the galaxy size of ELGs. In Appendix B, we summarize the average relationships between line profiles and the morphological properties.

We calculate the differences between the physical and morphological parameters of DESI ELGs and that of overall star-forming galaxies from the COSMOS-ZEST sample at the similar redshifts, stellar mass, and sizes. This analysis allows us to remove the correlations driven by these three parameters. More specifically, for each DESI ELG, we use at least 10 COSMOS-ZEST galaxies as references with redshift difference $|\Delta z|<0.025$, stellar mass difference $\rm|\Delta log_{10}\,M_{*}/M_{\odot}|<0.05$, and size difference $\rm|\Delta R80|<0.025"$. If less than 10 COSMOS-ZEST galaxies are found, we increase the conditions until there are at least 10 galaxies within the selection. Finally, for each ELG, we calculate the difference between the ELG parameter values, SFR, A, G, M20, and C, and the median values of their references as $\Delta\rm log_{10}\,SFR$, $\Delta\rm A$, $\Delta\rm G$, $\Delta\rm M20$, $\Delta\rm C$ respectively.

Figure 7 shows the normalized probability density distributions of the excess values of the parameters. The top three parameters are the controlled parameters, stellar mass, redshift, and size (R80). By construction, the distributions are narrow and center around 0. The lower 5 parameters are the morphological parameters, G, M20, C, A, and the SFR values. We find that while there are mild positive excess of G and M20 parameters and on average lower C parameter in comparison to the reference galaxies, the most significant difference is the asymmetric parameter A. The majority ($\sim 85\%$) of ELGs have the asymmetric parameter A values higher than the reference galaxies with $\rm\Delta A>0$, a trend similar to the trend of the SFR with $\sim 86\%$ ELGs with $\Delta\rm log_{10}\,SFR>0$.

To first explore the correlations between parameters, Table 1 shows the Spearman’s correlation coefficients ($\rho_{s}$) between $\Delta\rm log_{10}\,SFR$ and the spectral PCA coefficient 1 and 2 and the excess values of morphological parameters with the uncertainties estimated by bootstrapping the sample 1000 times. We order the parameters according to their values of Spearman’s correlation coefficients. The results show that

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  the $\Delta\rm log_{10}\,SFR$ correlates with $\rm\Delta A$ with the highest absolute $\rho_{s}\simeq 0.31\pm 0.02$ value among the parameters;

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  the second parameter with high $\rho_{s}\simeq 0.16\pm 0.02$ value is the line profile coefficient, $\rm Coeff_{1}$. We note that $\rho_{s}$ between $M_{*}$ and $\rm\Delta log_{10}SFR$ is $-0.13\pm 0.02$. This demonstrates that the correlation between $\rm Coeff_{1}$ and $\Delta\rm log_{10}\,SFR$ is not driven by stellar mass.

• •

  $\Delta M_{20}$, $\rm Coeff_{2}$, and $\Delta C$ parameters also have some correlations with $\Delta\rm log_{10}\,SFR$.

These results demonstrate that $\Delta\rm log_{10}\,SFR$ of DESI ELGs correlates with both the morphological structures and the spectral profiles of galaxies.

To better understand the interplay between the shape of galaxies and the line profiles, Table 2 shows the $\rho_{s}$ between $\rm Coeff_{1}$ and $\rm Coeff_{2}$ and the excess values of morphological parameters with the uncertainties estimated by bootstrapping the sample 1000 times. As can be seen, $\rm Coeff_{1}$ and $\rm Coeff_{2}$ correlate the most with the $\rm\Delta A$ ($>3\sigma$ detection) and $\rho_{s}$ with other morphological parameters are consistent with no detection ($<3\sigma$). In other words, based on the $\rho_{s}$ values of different parameter pairs, we find that there is a relationship between $\rm\Delta log_{10}SFR$, $\rm\Delta A$, $\rm Coeff_{1}$, and $\rm Coeff_{2}$.

We estimate the median $\rm\Delta A$ and $\rm\Delta log_{10}SFR$ as a function of $\rm Coeff_{1}$ and $\rm Coeff_{2}$ to quantify the relationship. The results are shown in the upper panels of Figure 8, indicating that both median $\rm\Delta A$ (left panel) and median $\rm\Delta log_{10}SFR$ (right panel) increase from negative $\rm Coeff_{1}$ to positive $\rm Coeff_{1}$ and from negative $\rm Coeff_{2}$ to positive $\rm Coeff_{2}$.

We also separate the $\rm Coeff_{1}-Coeff_{2}$ parameter space into 9 regions based on general classification shown in Figure 2:

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  Narrow region: N1 ($\rm Coeff_{1}<-0.65$), N2 ($\rm-0.65<Coeff_{1}<-0.35$), and N3 ($\rm-0.35<Coeff_{1}<0$);

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  Broad region: B1 ($\rm 0<Coeff_{1}<0.35$), B2 ($\rm 0.35<Coeff_{1}<0.65$), B3 ($\rm Coeff_{1}>0.65$);

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  Double-peak region: D1 ($\rm 0<Coeff_{1}<0.35$), D2 ($\rm 0.35<Coeff_{1}<0.65$), D3 ($\rm Coeff_{1}>0.65$).

We calculate the fraction of ELGs with high $\rm\Delta A$ and $\rm\Delta log_{10}SFR$ in each region. The lower panels of Figure 8 summarize the results. The lower left panel show the fractions for $\rm\Delta A>0.1$. We find that the fractions of ELGs with high $\rm\Delta A$ increase from the narrow region ($\rm Coeff_{1}<0$) to the broad region ($\rm Coeff_{1}>0$). The fractions can increase by a factor of 3 from $\sim 0.1$ to $\sim 0.3$. Moreover, for ELGs with $\rm Coeff_{1}>0$, the fraction is higher for ELGs in the broad region ($\rm Coeff_{2}\sim 0$) than in the double-peak region ($\rm Coeff_{2}\leq-0.4$). The lower right panel shows the same measurements with $\rm\Delta log_{10}SFR>0.35$. The overall trends of $\rm\Delta log_{10}SFR$ are consistent with $\rm\Delta A$, showing that ELGs with line profiles in the broad region (B) have relatively higher asymmetry morphology and higher SFR than their reference star-forming galaxies with similar stellar mass, sizes and at the same redshifts. In addition, we perform the same analysis for a control sample which consists of star-forming galaxies from the COSMOS-ZEST sample selected to have similar stellar mass, redshifts, and sizes as the properties of DESI ELGs with $|\rm\Delta log_{10}M_{*}/M_{\odot}|<0.05$, $|\Delta z|<0.025$ and $|\Delta R80|<0.025$ respectively. The color boxes in the lower panels of Figure 8 show the results, indicating that the DESI ELGs have preferentially higher $\rm\Delta A$ and $\rm\Delta log_{10}SFR$ than typical star-forming galaxies.

Finally, we quantify the median $\rm\Delta log_{10}\,SFR$ as a function of $\rm\Delta A$ and line profiles with the results shown in Figure 9. The blue and green data points are measurements from ELGs with $\rm Coeff_{1}<-0.35$ and $\rm Coeff_{1}>0.35$ respectively. The grey data points show the measurements in between. Here we only include ELGs within the narrow and broad regions with $\rm Coeff_{2}>0.15\times Coeff_{1}-0.25$. The measurements indicate that there is a general correlation between $\rm\Delta log_{10}\,SFR$ and $\rm\Delta A$ which has the same slope but different offsets for galaxies with different $\rm Coeff_{1}$. With similar $\rm\Delta A$ values, DESI ELGs with broader [OII] lines have, on average, 0.1 dex higher $\rm\Delta log_{10}SFR$ than those with narrow [OII] lines. This again illustrates the connection between [OII] line profiles, $\rm\Delta A$ and $\rm\Delta log_{10}SFR$ of DESI ELGs.

Utilizing data from the DESI spectroscopic observations and the COSMOS multi-wavelength deep images, we find a relationship between three parameters of DESI ELGs, excess SFR ($\rm\Delta log_{10}SFR$), the asymmetry of galaxy shape ($\rm\Delta A$), and the [OII] line profiles. In the following, we discuss two scenarios that can possibly explain the observed relationship.

Merger scenario: The merging of galaxies has been considered as one of the crucial processes that can transform star-forming galaxies into passive ones. Theoretical works have shown that when two gas-rich galaxies merge, gas flows into the centers of the galaxies and trigger excess star-formation activities (e.g., Hopkins et al., 2008; Lotz et al., 2008; Patton et al., 2020; Bottrell et al., 2023). This merger-induced star-formation activities have also been supported by observational studies. Various observational approaches have been used to identify merging galaxies. For example, making use of data from the Sloan Digital Sky Surveys, one can identify galaxy pairs with a range of impact parameters and use such a sample to explore the difference of the SFR compared with the SFR of controlled isolated galaxies with similar mass (e.g. Ellison et al., 2008, 2010; Behroozi et al., 2015). Another approach is to use the morphological parameters of galaxies derived from imaging datasets to identify possible shape features induced by merging events, such as tidal structures and/or asymmetry (e.g., Lotz et al., 2008; Yesuf et al., 2021). Both simulations and observations have shown that merging events at the closest separation enhance the SFR by approximately a factor of 2 with a fixed stellar mass.

Our results can be explained by this galaxy merger scenario. The excess asymmetry value $\rm\Delta A$ indicates that a sizable fraction of DESI ELGs are disturbed galaxies, e.g. there are approximately $25\%$ of DESI ELGs with $\rm\Delta A>0.1$, while there are only $7\%$ of the controlled sample with $\rm\Delta A>0.1$ (lower panels of Figure 8). Figure 10 shows the HST ACS F814W images of randomly selected DESI ELGs as a function of $\rm\Delta A$. For most of the galaxies with $\rm\Delta A>0.05$, two or multi clumpy structures can be observed at small scales ($<1"$) with disturbed and possibly tidal features. The correlation between $\rm Coeff_{1}$ and $\rm\Delta A$ values provide a further support on this merger scenario — when two interacting galaxies are at a close distance, the emission lines of the two galaxies are included in a single DESI fiber (12 kpc in diameter at $z\sim 1$) with a moderate line-of-sight velocity difference $\Delta v$ which will produce a [O II]$\lambda\lambda 3726,3729$ line profile broader than a typical isolated star-forming galaxy with similar stellar mass. The three observational properties of DESI ELGs, the line profile, the asymmetry of galaxy shape, and the excess SFR, can be all fit within the merger scenario simultaneously.

Disk instability scenario: Another possibility is that the multi clumpy structures shown in Figure 10 are star-forming regions formed due to disk instability (e.g., Dekel et al., 2009; Mandelker et al., 2014) in a single galaxy. Previous studies (e.g., Guo et al., 2015; Murata et al., 2014; Martin et al., 2023; Sattari et al., 2023) have shown that the clumpy fraction, the ratio between the number of star-forming galaxies with at least one off-center clump and the total number of star-forming galaxies, roughly peaks between $z\sim 1$ and $z\sim 2$, overlapping the redshift region of the DESI ELGs, and correlates with SFR with a fixed stellar mass. Bright star-forming clumpy structures can lead to asymmetric light distribution with possible associated emission lines (e.g., Fisher et al., 2017; Oliva-Altamirano et al., 2018) that contribute to the emission line profiles. Moreover, the disk instability is expected to drive turbulent which in turn enhances gas velocity dispersion in galaxies (e.g., Goldbaum et al., 2016). Therefore, this scenario can also produce correlations between $\rm\Delta SFR$, $\Delta A$, and line profiles as observed for DESI ELGs.

The origins of clumpy structures observed in high-redshift galaxies are still under active investigations. Some studies have shown that the clump size and gas kinematics relationship of some clumpy galaxies is consistent with the prediction of the disk instability scenario (e.g., Fisher et al., 2017). However, Ribeiro et al. (2017) have shown that galaxies with only two major clumps tend to have clump mass being inconsistent with the expected mass based on disk instability. The authors argue that galaxies with two major clumps can be ongoing galaxy mergers. In addition, Elmegreen et al. (2021) have shown that the observed appearance of major mergers at high redshifts is similar to the observed appearance of clumpy isolated disk galaxies. These studies indicate the complexity of distinguishing clumps formed by disk instability and galaxy mergers. In the DESI ELG sample, while there are galaxies having only two major clumps, some galaxies have more than two clumps as can be seen in Figure 10. Therefore, it is possible that DESI ELGs include both types of systems.

While estimating the contributions of these two scenarios in the overall DESI ELG population is beyond of the scope of this work, one can combine multi-wavelength deep images with radio observations for spatially resolved gas properties to identify tidal features, characterize the properties of the clumpy structures and resolve the nature of these galaxies.

Our results show that while ELGs in the double-peak region tend to have higher velocity offsets between two velocity components than ELGs in the broad region, ELGs in the double-peak region, especially in D1 and D2 regions, have on average lower $\rm\Delta A$ and $\rm\Delta log_{10}\,SFR$ than ELGs located in the broad (B) region with $\rm Coeff_{1}>0$ and $\rm Coeff_{2}\simeq 0$, as shown in Figure 8.

We propose that this difference might be due to the fact that instead of tracing two galaxies during the merging process or galaxies with violent disk instability, there is higher fraction of ELGs in the double-peak region with the velocity components reflecting the rotating disks of the galaxies without undergoing SFR enhancement events. One possible way to explore these two scenarios is to investigate the galaxy inclination and $\rm\Delta A$ relation of ELGs. The expectation for the rotating disk scenario is that those galaxies tend to be more edge-on with low $\rm\Delta A$. On the other hand, the morphology of two merging galaxies with close separation or galaxies with two major clumps can resemble the morphology of edge-on galaxies. Therefore, merging/clumpy galaxies also tend to look like edge-on galaxies but with higher $\rm\Delta A$ than the rotating disks.

In Figure 11, we examine the distribution of $\rm\Delta A$ and galaxy inclination, using the elongation parameter, the ratio between the lengths of semi-major and semi-minor axes of galaxies, from HST images as a proxy (Leauthaud et al., 2007). We only select ELGs with $\rm 10<log_{10}M_{*}/M_{\odot}<10.5$ to reduce possible effects associated with galaxy mass. The top panel shows the normalized number distributions of the elongation parameter of DESI ELGs in $\rm B1\,\&\,B2$ regions and $\rm D1\,\&\,D2$ regions indicated by green and orange respectively. The middle panel shows the distribution of $\rm\Delta A$ as a function of the elongation parameter and the bottom panel shows the fraction of ELGs with $\rm\Delta A>0.1$ as a function of the elongation parameter for the two types of ELGs. We find that ELGs in $\rm B1\,\&\,B2$ regions and $\rm D1\,\&\,D2$ regions both have a broad range of elongation parameter. The middle and bottom panels show that for ELGs in $\rm D1\,\&\,D2$ regions, the fraction of sources with $\rm\Delta A>0.1$ is consistently being $\sim 0.1$ across all elongation parameter values. In contrast, the fraction of ELGs in $\rm B1\,\&\,B2$ regions with $\rm\Delta A>0.1$ increases with the elongation parameter from 0.2 to 0.4. These observed trends are consistent with the above proposed scenario that mergers/clumpy galaxies tend to have high elongation and high $\rm\Delta A$, while rotating disks tend to have high elongation but with low $\rm\Delta A$. However, we note that the above results are suggestive and spatially resolved kinematics information is needed to conclusively identify the origins of double-peak emission lines observed in DESI ELGs.

Previous studies have also suggested that double-peak emission lines observed in galaxies are associated with rotating disks at the local Universe. For example, Maschmann et al. (2020) found $\sim 5000$ double-peak emission line galaxies from the SDSS spectroscopic dataset. Based on simulations, Maschmann et al. (2023) concluded that the double-peak emission lines can be originated from the central rotating bars of galaxies or minor mergers. Chen et al. (2016) also found that rotating galaxy discs can explain the double-peak emission lines observed in SDSS disc star-forming galaxies.

We now explore the key selection criteria for DESI ELGs which preferentially include galaxies with high SFR and asymmetric morphology. The DESI ELG selections for the main survey are summarized in Table 2 of Raichoor et al. (2023), which includes

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  $g>20$,

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  $\rm g\ band\ fiber\ magnitude\ (gfib)\ <24.1$, and

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  $g-r$ and $r-z$ color boundaries.

To investigate how these selection conditions affect the galaxy properties, we use the COSMOS-ZEST galaxy sample and cross-match the sample with the photometric catalog⁴⁴4DR10 https://www.legacysurvey.org/dr10/catalogs/ from the DESI Legacy Imaging Surveys (Dey et al., 2019) to obtain the photometric information used in the DESI target selections. We then select star-forming galaxies with $\rm log_{10}M_{*}/M_{\odot}>9$, $\rm 1.1<z_{photo}<1.63$ (the parameter space that covers the main DESI ELGs) and $g>20$. For each star-forming galaxy, we follow the same procedure for estimating $\rm\Delta A$ and $\rm\Delta log_{10}SFR$ as the DESI ELG sample by searching for at least 10 galaxies as references with redshift difference $|\Delta z|<0.025$, stellar mass difference $\rm|\Delta log_{10}\,M_{*}/M_{\odot}|<0.05$, and size difference $\rm|\Delta R80|<0.025"$ and increasing the conditions if less than 10 galaxies are found. The $\rm\Delta A$ and $\rm\Delta log_{10}SFR$ are the differences between the values of the galaxies and the median values of the reference galaxies.

With $\rm\Delta A$ and $\rm\Delta log_{10}SFR$ information, we calculate the median $\rm\Delta A$ and $\rm\Delta log_{10}SFR$ as a function of $g-r$, $r-z$ colors, and $\rm gfib$. The upper panels of Figure 12 show the median $\rm\Delta A$ values across the $g-r$ and $r-z$ color space with $\rm gfib<23.6$ (left panel), $\rm 23.6<gfib<24.1$ (middle panel) and $\rm 24.1<gfib<24.6$ (right panel). The black dashed lines are the boundaries for the DESI ELGs LOP sample and the grey dashed lines are the extended region for the VLO sample. As can be seen, galaxies that are brighter in $\rm gfib$ preferentially have higher $\rm\Delta A$ values. A similar trend is observed for $\rm\Delta log_{10}SFR$ as shown in the lower panels of Figure 12 indicating the median $\rm\Delta log_{10}SFR$ values of galaxies. We note that while there is no strong correlation between $\rm\Delta A$ and galaxy colors, a correlation between $\rm\Delta log_{10}SFR$ and galaxy colors can be observed in the middle and right panels. Therefore, we conclude that the g-band fiber magnitude selection is the primary factor for selecting galaxies with more disturbed morphology and higher SFR than the overall star-forming galaxy population at the same redshifts and the (g-r, r-z) color selections are an additional factor modulating the SFR. Note that while $\rm gfib\sim 24.1$ reaches the limiting magnitude of the Legacy Surveys (Dey et al., 2019) with larger uncertainties, we have performed the same analysis with g, r, z-band images with depths $\sim 27-28$ magnitude from Hyper Suprime-Cam (Aihara et al., 2018, 2019) in the COSMOS2020 catalog which yield consistent results.

Recent studies have shown that in order to reproduce the DESI ELG clustering properties, especially the small-scale signals ($\rm\leq 0.2\,Mpc\,h^{-1}$), and obtain physically motivated ELG-halo connection models, additional parameters are required in the halo occupation distribution (HOD) modeling (e.g., Gao et al., 2023; Yuan et al., 2023; Rocher et al., 2023; Gao et al., 2024). These results indicate that the abundance of satellite ELGs in the halos depends on the properties of the central ELGs — a phenomenon called ”conformity” (Wechsler & Tinker, 2018, for a review).

By exploring the properties of ELGs at $0.8<z<1.1$ and their morphology with COSMOS dataset, Yuan et al. (2023) postulate that such conformity signals are driven by galaxy merging induced star formation in both central and satellite galaxies. Our findings of the relationship between SFR, galaxy morphology and the line profiles are consistent with this scenario. In addition, the small-scale enhancement of the clustering amplitude of DESI ELGs is aligned with the results of simulations focusing on galaxy mergers (e.g., Wetzel et al., 2009).

In addition to the behavior of spatial clustering properties of DESI ELGs, Rocher et al. (2023) find that DESI ELGs have an unexpected clustering property in velocity space. They find that on average, the velocity dispersion of the satellite DESI ELGs is larger than the velocity dispersion of dark matter particles by $\sim 30\%$. We argue that this observed property is likely associated with spectral profiles of DESI ELGs having two velocity components along the sightlines. As shown in Figure 4, for two redshift systems, the median value of the line of sight velocity offsets is $\sim\rm 150\,km/s$. However, the current $Redrock$ pipeline typically determines the redshift in the middle of the two velocity components. In this case, this can possibly introduce a $\rm\sim 75\,km/s$ velocity offset of the central galaxy redshifts systematically and adds additional velocity dispersion in the relative velocities between centrals and satellites.

Here we consider a simple case to quantify possible signals. Assuming that the dark matter halo mass of ELGs is $\approx 10^{12}\,M_{\odot}$ (e.g., Rocher et al., 2023) with the corresponding velocity dispersion of dark matter particles being $\rm\sim 100\,km/s$, adding a systematic $\rm 75\,km/s$ offset in the velocity measurements will increase the estimated velocity dispersion by $25\%$, which is similar to the results in Rocher et al. (2023). This demonstrates that this redshift determination effect can be responsible for at least part of the apparent excess velocity dispersion of the satellite galaxies and it needs to be taken into account for the clustering measurements in velocity space.