\volnopage

Vol.0 (20xx) No.0, 000–000

¹¹institutetext: CAS Key Laboratory of Optical Astronomy, National Astronomical Observatories, Beijing 100101, China; [email protected],[email protected]
²²institutetext: University of Chinese Academy of Sciences, Beijing 100049, China
³³institutetext: College of Computer and Information Management & Institute for Astronomical Science, Dezhou University, Dezhou 253023, China
\vs\noReceived 2022 Nov 15; accepted 2023 Mar 16

The Hi gas fraction scaling relation of the Green Pea galaxies

Siqi Liu 1122 A-Li Luo 112233 Wei Zhang 1122 Yan-Xia Zhang 1122 Xiao Kong 11 Yong-Heng Zhao 11

Abstract

Green Pea galaxies are compact galaxies with high star formation rates. However, limited samples of Green Pea galaxies have Hi 21 cm measurements. Whether the Hi gas fraction ( $f_{\rm H{\sc i}}\equiv\rm M_{H\sc I}/M_{\star}$ ) of Green Pea galaxies follows the existing scaling relations between the $f_{\rm H{\sc i}}$ and NUV- $r$ color or linear combinations of color and other physical quantities needs checking. Using archival data of Hi 21cm observations, we investigate the scaling relation of the NUV- $r$ color with the $\rm M_{H\sc I}/M_{\star}$ of 38 Green Pea galaxies, including 17 detections and 21 non-detections. The Hi to stellar mass ratios ( $f_{\rm H{\sc i}}$ ) of Green Pea galaxies deviate from the polynomial form, where a higher Hi gas fraction is predicted given the current NUV- $r$ color, even with the emission lines removed. The blue sources (NUV- $r$ <1) from the comparison sample (ALFALFA-SDSS) follow a similar trend. The Hi gas fraction scaling relations with linear combination forms of $\rm-0.34(NUV-r)-0.64\log(\mu_{\star,z})+5.94$ and $\rm-0.77\log\mu_{\star,i}+0.26\log SFR/M_{\star}+8.53$ , better predict the Hi gas fraction of the Green Pea galaxies. In order to obtain accurate linear combined forms, higher-resolution photometry from space-based telescopes is needed.

keywords:

galaxies: general – galaxies: starburst – radio lines: galaxies

1 Introduction

Green Pea galaxies are well known for their unique color, compactness, high star formation rate (SFR), and are located in isolated environments (Cardamone et al. 2009). They are local analogs to the high- $z$ Ly $\alpha$ emitters due to their low metallicity, low dust content, and high ionization (Izotov et al. 2011; Yang et al. 2016; Jiang et al. 2019).

The observations of the Hi 21cm provide information about the neutral atomic mass, which is the primary fuel for star formation in these galaxies. Presently, there are insufficient studies (Pardy et al. 2014; McKinney et al. 2019; Kanekar et al. 2021) with limited samples of the Green Pea galaxies. Lyman Alpha Reference Sample (LARS) from Pardy et al. (2014) provides an upper limit of one Green Pea galaxy (LARS 14) based on the non-detection of the Hi 21 cm emission line from the Green Bank Telescope (GBT). McKinney et al. (2019) observed one Green Pea galaxy with the Very Large Array (VLA) and found no 21 cm hydrogen hyperfine-structure line detected. Kanekar et al. (2021) provide 19 detections and 21 upper limits on the Green Pea galaxies at $0.02<z<0.1$ from the Arecibo Telescope (Arecibo) and the GBT. They find the Hi-to-stellar mass ratio ( $f_{H\sc I}$ ) in Green Pea galaxies is consistent with the star-forming galaxies in the local Universe but with a much shorter gas depletion time of about 0.6 Gyr.

Scaling relations provide a cheap estimator for the Hi gas fractions in the galaxies. However, there is a lack of blue samples to verify different sets of scaling relations. In this work, we use all of the currently available archival Hi 21 cm measurements of the Green Pea galaxies to verify the Hi gas fraction scaling relations. We find that the scaling relation of the NUV- $r$ with Hi gas fraction for these Green Pea galaxies deviates from the relation in Zhang et al. (2021) of local star-forming galaxies, where a lower fraction of the Hi gas is observed given the current NUV- $r$ color, even with the emission lines removed. The linear combination gas fraction scaling relations (Zhang et al. 2009; Catinella et al. 2010; Li et al. 2012; Zhang et al. 2021) combining the surface mass density, surface brightness, with color or specific star formation rate (sSFR) better predict the Hi gas fraction of the Green Pea galaxies, especially with the form of $\rm-0.34(NUV-r)-0.64\log(\mu_{\star,z})+5.94$ and $\rm-0.77\log\mu_{\star,i}+0.26\log SFR/M_{\star}+8.53$ .

The structure of the paper is as follows. In Section 2, we present Hi 21 cm observation of the Green Pea galaxies and the comparison sample of local star-forming galaxies from ALFALFA-SDSS (Durbala et al. 2020). In Section 3, we discuss the NUV - $r$ color scaling relation, other factors that impact the gas fraction estimation, and the linear combination estimators of the gas fraction. In Section 4, we summarize the result and propose future work.

In this work, we use Wilkinson Microwave Anisotropy Probe (WMAP) 9 cosmology (Hinshaw et al. 2013), AB magnitudes (Oke & Gunn 1983), a Chabrier initial mass function (IMF; Chabrier (2003)), and Bruzual & Charlot (2003) stellar population synthesis (SPS) models.

2 Data

2.1 Green Pea galaxies with Hi 21 cm observations

2.1.1 Hi 21 cm observations

There are limited Green Pea galaxies with Hi observations, including Pardy et al. (2014); McKinney et al. (2019) and Kanekar et al. (2021). All of the samples in this work are from Kanekar et al. (2021).

We include one Green Pea galaxy Lyman Alpha Reference Sample (LARS) 14 from Pardy et al. (2014) according to SDSS and HST images. GBT observation shows no Hi 21 cm emission line. Thus an upper limit of the Hi mass is given with the 3 $\sigma$ detection. McKinney et al. (2019) observed one Green Pea galaxy with the VLA and found no 21 cm hydrogen hyperfine-structure line detected. The upper limit of the Hi mass is obtained assuming a 3 $\sigma$ detection threshold $S_{\rm 21cm}=0.78$ mJy and characteristic emission line width of $W_{\rm 21cm}=36.1$ km s^-1. However, this source is duplicated with GP1608+3528 from Kanekar et al. (2021) observed with Arecibo, with non-detection of Hi 21 cm emission line from both observations. For consistency, we keep the non-detection result from Arecibo for the following discussions.

With a deep search of the Hi 21 cm emission line based on Arecibo and GBT of the Green Pea galaxies, Kanekar et al. (2021) have obtained 19 detections and 21 upper limits of the Hi mass. They are pre-selected from the spectroscopically identified Green Pea galaxies (Jiang et al. 2019) based on the $B$ -band luminosity (Dénes et al. 2014) to have detectable Hi 21 cm. The selected sample covers a wide range of absolute $B-$ band magnitudes ( $-20.0\leq M_{B}\leq-16.1$ ), and gas-phase metallicity ( $\rm-7.6\leq 12+(O/H)\leq 8.35$ ), which is also statistically consistent with the parent Jiang et al. (2019) sample in metallicity, stellar mass, and absolute $B-$ band magnitude. Both the Arecibo and GBT observations use the L-wide receiver and two orthogonal polarizations. The Arecibo observations use a 25 MHz band sub-divided into 4096 spectral channels, while the GBT observations use a 23.44 MHz bandwidth subdivided into 8192 channels. The total integration time on each source ranges from $0.75-4.5$ hrs. All the data are analyzed following the standard procedures with gbtidl, and each spectrum is checked for RFI and systematic effects. The Hi 21 cm emission lines are detected at $\geq 5\sigma$ level. For the non-detections, the upper limits are estimated assuming that the emission line profile is Gaussian with a full width at half maximum (FWHM) of 50 km s ^-1.

We find the positions for the sources in SDSS DR16 (Ahumada et al. 2020) given the name and the redshift of the sources and obtain the cModelMag for the $ugriz$ bands for each of these compact galaxies. For GP0844+0226, we cannot find its SDSS spectrum; and thus exclude it for further analysis. We only include the sources located within the GALEX footprint, which results in 17 Hi 21-cm emission line detections with NUV photometry and 21 Hi 21-cm emission line non-detections with NUV photometry.

We also apply the $k$ -correction with the code Chilingarian et al. (2010) and Chilingarian & Zolotukhin (2012). Because these Green Pea galaxies are isolated sources, we have visually checked them individually in the SDSS and GALEX images to avoid source mismatching. We inherit the results of Hi masses from Kanekar et al. (2021), which are calculated with $\int SdV$ from the Hi 21-cm emission profiles, according to Roberts & Haynes (1994). For the extinction correction, the Galactic extinction from the dust maps of Schlegel et al. (1998) has been applied to both the SDSS magnitudes and the GALEX magnitudes. Furthermore, to be noted, as illustrated in Fig. 6 in Zhang et al. (2021), internal extinction will not affect this Hi gas fraction with the NUV- $r$ relation.

The uni-variate distribution of $\rm M_{H\sc I}$ can be estimated with the Kaplan-Meier (Kaplan & Meier 1958) estimator with confidence bands. We demonstrate the cumulative incidence distribution for the $\rm M_{H\sc I}$ of the Green Pea galaxies in Fig.1 generated with lifelines. At $\rm\log(M_{H\sc I}/M_{\odot})=8.58$ , the probability that the Hi 21 cm emission can be detected is 50%.

Refer to caption — Figure 1: Cumulative incidence curve of the uni-variate $\rm M_{H\sc I}$ distribution estimated with Kaplan-Meier estimator with confidence bands. The dashed lines show that the probability of detection is 50% at $\rm\log(M_{H\sc I}/M_{\odot})=8.58$ .

2.1.2 Mass and SFR

Instead of using the given stellar mass measurement and the SFR measurement from Kanekar et al. (2021), we re-calculate these two quantities to obtain more accurate measurements for the analysis in this work. We cross-match the sources with the AllWISE Multiepoch Photometry Table (Wright et al. 2010; Wright, Edward L. and Eisenhardt, Peter R. M. and Mainzer, Amy K. et al. 2019) to obtain the $W_{1}$ to $W_{4}$ photometry.

For the stellar mass measurement, we fit the sources with multiwavelength photometry with CIGALE (Burgarella et al. 2005; Zhang et al. 2009; Boquien et al. 2019) combining the GALEX NUV, SDSS $ugriz$ , and AllWISE $W_{1}$ to $W_{4}$ photometry. For the configuration of the fitting, we use the delayed $-\tau$ star formation history, BC03 (Bruzual & Charlot 2003), Chabrier IMF (Chabrier 2003), nebular emission lines, the dust attenuated modified starburst model, the dust emission model from Casey (2012), and the Fritz et al. (2006) AGN model.

For the SFR measurement, we combine the IR and UV photometry using the method in Durbala et al. (2020) Section 3.2, where the SFR tracer is robust against extinction. The corrected NUV spectral energy density is $\nu L_{\nu,\rm corrected}=\nu L_{\nu,\rm NUV}+2.26\nu L_{\nu}(22~{}\mbox{$\mu$m})$ . The SFR based on the corrected NUV (Hao et al. 2011; Kennicutt & Evans 2012; Durbala et al. 2020) is calculated as

\displaystyle\rm\log_{10}(SFR_{NUV_{corr}})=\log_{10}(\nu L_{\nu,corrected})-43.17,

(1)

For the source without $W_{4}$ detection (GP_id J0808+1728), we use the measured result from Kanekar et al. (2021).

We compare the mass-SFR relation for these samples with the star-forming main sequence (SFMS) (Speagle et al. 2014) in Fig.2.

The main-sequence SFR- $M_{\star}$ relation from Speagle et al. (2014) is as follows:

	$\displaystyle\log\rm SFR(M_{\ast},t)$	$\displaystyle=$	$\displaystyle(0.84\pm 0.02-0.026\pm 0.003\times t)\log M_{\ast}$		(2)
			$\displaystyle\quad-(6.51\pm 0.24-0.11\pm 0.03\times t),$		(2)

where $t$ is the age of the universe in Gyr. The Green Pea galaxies have much higher SFR compared with the SFMS from $z=0.0$ to $z=0.181$ , where the sSFRs range from $10^{-9}\rm yr^{-1}$ to $10^{-7}\rm yr^{-1}$ .

We list the Hi 21 cm observation results, the mass and SFR measurements from this work in Table 1.

Table 1: Green Pea galaxies with Hi 21 cm measurements

Green Pea	z	Tel.¹	$\bf\nu_{\rm\bf 21\,cm}$	$\bf\int\bf S{\rm\bf d}\bf V$	$\rm\bf{M_{HI}}$	SFR²	$\rm{\bf M_{\bf\star}}$ ³	NUV- $\bf r$ ⁴	$\bf R_{50,z}$ ⁵	$\bf R_{50,\it HST}$ ⁶
identifier			MHz	Jy km s^-1	$10^{8}\;\textrm{M}_{\odot}$	$\textrm{M}_{\odot}$ yr^-1	$10^{8}\;\textrm{M}_{\odot}$		arcsec	arcsec
J0007+0226	$0.0636$	$1$	$1335.52$	$<0.062$	$<12$	$0.8859$	$1.355$	$0.65\pm 0.22$	0.6240	–
J0036+0052	$0.0282$	$1$	$1381.42$	$0.585\pm 0.034$	$22.0\pm 1.3$	$0.2385$	$0.6232$	$0.499\pm 0.024$	1.033	–
J0159+0751	$0.0611$	$1$	$1338.65$	$<0.038$	$<6.9$	$0.8123$	$0.9915$	$0.02\pm 0.29$	2.042	–
J0213+0056	$0.0399$	$2$	$1365.88$	$0.419\pm 0.022$	$31.7\pm 1.7$	$0.7889$	$1.042$	$-0.772\pm 0.057$	0.7293	–
J0801+3823	$0.0376$	$2$	$1368.89$	$<0.051$	$<3.4$	$0.4453$	$2.288$	$0.981\pm 0.025$	0.9185	–
J0808+1728	$0.0442$	$1$	$1360.28$	$<0.044$	$<4.1$	$0.45^{7}$	$0.2902$	$-0.13\pm 0.09$	0.9449	–
J0844+0226	$0.0911$	$1$	$1301.81$	$0.065\pm 0.013$	$26.1\pm 5.4$	$16.39$	$25.93$	$0.751\pm 0.086$	1.110	–
J0852+1216	$0.0759$	$1$	$1320.19$	$<0.050$	$<14$	$19.82$	$13.28$	$0.129\pm 0.032$	1.207	–
J0926+4427 ⁸	$0.1807$	$2$	$1202.71$	$<1.7$	$<3100$	$16.90$	$15.97$	$0.393\pm 0.022$	0.7927	–
J0942+4110	$0.0460$	$2$	$1357.97$	$<0.125$	$<13$	$1.502$	$1.627$	$0.867\pm 0.038$	2.587	–
J1015+3054	$0.0918$	$1$	$1301.04$	$<0.037$	$<15$	$8.735$	$14.17$	$0.774\pm 0.030$	0.8601	–
J1024+0524	$0.0332$	$1$	$1374.76$	$0.074\pm 0.014$	$3.85\pm 0.73$	$1.775$	$2.700$	$0.2419\pm 0.0083$	1.683	–
J1108+2238	$0.0238$	$1$	$1387.37$	$0.155\pm 0.016$	$4.14\pm 0.43$	$0.3054$	$1.056$	$0.758\pm 0.051$	1.248	0.9640
J1134+5006	$0.0260$	$2$	$1384.44$	$0.799\pm 0.065$	$25.4\pm 2.1$	$1.668$	$3.516$	$0.2260\pm 0.0091$	1.057	–
J1148+2546	$0.0451$	$1$	$1359.07$	$3.182\pm 0.078$	$309.0\pm 7.6$	$4.458$	$5.470$	$-0.163\pm 0.036$	1.262	–
J1200+2719	$0.0819$	$1$	$1312.91$	$0.310\pm 0.028$	$100.6\pm 9.0$	$3.256$	$5.169$	$-0.188\pm 0.083$	0.8862	–
J1224+0105	$0.0398$	$2$	$1365.99$	$<0.063$	$<4.8$	$0.5906$	$2.341$	$0.632\pm 0.025$	1.242	–
J1224+3724	$0.0404$	$2$	$1365.25$	$<0.077$	$<5.9$	$1.069$	$1.369$	$0.023\pm 0.058$	0.9575	–
J1226+0415	$0.0942$	$1$	$1298.10$	$<0.073$	$<32$	$3.528$	$5.218$	$0.069\pm 0.037$	0.9608	–
J1253-0312	$0.0227$	$2$	$1388.89$	$0.235\pm 0.021$	$56.9\pm 5.1$	$10.34$	$4.832$	$0.569\pm 0.021$	1.088	–
J1319+0050	$0.0477$	$1$	$1355.78$	$0.234\pm 0.025$	$21.7\pm 2.3$	$0.9432$	$3.892$	$1.175\pm 0.031$	0.8985	–
J1329+1700	$0.0942$	$1$	$1298.16$	$<0.086$	$<37$	$16.89$	$2.679$	$0.169\pm 0.042$	0.7646	–
J1345+0442	$0.0304$	$1$	$1378.47$	$0.650\pm 0.026$	$28.5\pm 1.1$	$1.308$	$1.369$	$-0.538\pm 0.029$	0.8460	0.4181
J1359+5726	$0.0338$	$2$	$1373.93$	$<0.095$	$<5.1$	$3.282$	$5.480$	$-0.011\pm 0.020$	1.034	–
J1423+2257	$0.0328$	$1$	$1375.24$	$<0.025$	$<1.3$	$0.6637$	$1.425$	$0.389\pm 0.061$	1.024	–
J1432+5152	$0.0256$	$2$	$1384.94$	$<0.079$	$<2.4$	$0.4168$	$1.695$	$0.819\pm 0.018$	1.169	–
J1448-0110	$0.0274$	$2$	$1382.50$	$<0.054$	$<1.9$	$1.609$	$2.542$	$0.885\pm 0.012$	1.059	–
J1451-0056	$0.0432$	$2$	$1361.59$	$0.288\pm 0.029$	$25.6\pm 2.6$	$1.280$	$3.020$	$-0.152\pm 0.015$	0.9594	–
J1455+3808	$0.0277$	$2$	$1382.13$	$0.855\pm 0.047$	$31.0\pm 1.7$	$0.7575$	$0.853$	$0.023\pm 0.029$	0.9091	0.5770
J1509+3731	$0.0326$	$2$	$1375.58$	$<0.088$	$<4.4$	$1.239$	$1.354$	$0.882\pm 0.063$	1.617	–
J1509+4543	$0.0481$	$2$	$1355.18$	$0.543\pm 0.081$	$60.0\pm 8.9$	$2.101$	$5.471$	$0.308\pm 0.040$	1.160	–
J1518+1955	$0.0751$	$1$	$1321.19$	$<0.041$	$<11$	$5.309$	$14.69$	$0.509\pm 0.019$	0.9274	–
J1545+0858	$0.0377$	$1$	$1368.76$	$0.302\pm 0.019$	$17.8\pm 1.1$	$2.938$	$1.942$	$0.052\pm 0.045$	0.6910	–
J1547+2203	$0.0314$	$1$	$1377.15$	$<0.053$	$<2.5$	$0.6915$	$1.721$	$1.436\pm 0.025$	1.121	–
J1608+3528 ⁹	$0.0327$	$1$	$1375.38$	$<0.12$	$<0.61$	$0.1891$	$0.2809$	$0.68\pm 0.16$	1.022	–
J1624-0022	$0.0313$	$1$	$1377.27$	$0.134\pm 0.021$	$62.2\pm 9.8$	$2.832$	$4.472$	$0.729\pm 0.039$	1.253	–
J2114-0036	$0.0447$	$2$	$1359.59$	$0.173\pm 0.020$	$16.5\pm 1.9$	$0.6017$	$2.014$	$0.297\pm 0.084$	1.187	–
J2302+0049	$0.0331$	$1$	$1374.91$	$<0.050$	$<2.6$	$0.2756$	$0.6311$	$0.102\pm 0.026$	0.9076	–

¹ Following the notation in Kanekar et al. (2021), we use Arecibo $\equiv 1$ , GBT $\equiv 2$ to note the telescope used for the observations.
² The SFR is measured combining UV and IR photometry (Durbala et al. 2020)
³ The stellar mass is measured with multi-wavelength photometry fitting combining the GALEX NUV, SDSS $ugriz$ , and AllWISE $W_{1}$ to $W_{4}$ photometry.
⁴ The NUV- $r$ color has been $k$ -corrected.
⁵ From SDSS DR16 (Ahumada et al. 2020).
⁶ The entries are from HST COS instrument (Kanekar et al. 2019).
⁷ Inherited from Kanekar et al. (2021).
⁸ From Pardy et al. (2014).
⁹ In duplication with the VLA observation of McKinney et al. (2019).

2.2 Star forming galaxies with Hi 21-cm observation

For the comparison sample, we use the detections in the ALFALFA-SDSS catalog (Durbala et al. 2020). We adopt the stellar mass measurement using infrared photometry from the unWISE catalog based on Section 3.1 in Durbala et al. (2020) referred to as $M_{\star,\rm McGaugh}$ (McGaugh & Schombert 2015). Our analysis employs the SFR measurements based on UV and IR photometry from Durbala et al. (2020) Section 3.2 quoted as $\rm SFR_{NUV_{cor}}$ . The mass and redshift distribution for all of these sources is demonstrated in Fig.3.

3 The scaling relations of the Hi gas fraction

In this section, we revisit the scaling relation of the NUV- $r$ color with the Hi gas fraction and demonstrate the deviation of the observed Hi gas fraction of Green Pea galaxies to the predicted values. Then, we consider other factors that might impact the scaling relations of the Hi gas fractions and provide the scaling relations with linear combination forms, which combine color, surface mass density, surface brightness, or sSFR, that better predict the Hi gas fraction.

3.1 The scaling relation of the Hi gas fraction with NUV- $r$ color

Traditionally, different colors have been used to infer the Hi gas fraction of the star-forming galaxies, like the optical-optical color $u-r$ and the optical-NIR color $u-K$ in Kannappan (2004), with a scatter of 0.4 dex. Martin et al. (2005) demonstrate the correlation of the $g-i$ color and the NUV- $r$ color to the gas fraction in their Fig.5. Later studies aim to improve the photometric estimators of Hi gas fraction by introducing the surface mass density and surface brightness. Zhang et al. (2009) provide an estimator based on the optical color $g-r$ and the $i-$ band surface brightness $\mu_{i}$ reaching a smaller scatter as 0.3 dex. In Zhang et al. (2021), both the $g-i$ color and the NUV- $r$ color are correlated with the Hi gas fraction, where a bluer color represents a higher gas fraction based on the low- $z$ calibrating sample consisting of 660 local galaxies. NUV- $r$ color is better to predict the Hi gas fraction with a larger dynamic span (see Fig.5 in Zhang et al. (2021)). Zhang et al. (2021) explain with the following statement: “the ultra-violet emission of a galaxy mainly traces the light from the young stars in an optical thin environment and the extended gas in the outer disk of the galaxies are not absorbed by dust."

We apply the scaling relation of the NUV- $r$ color with the Hi gas fraction in Fig.4. It is noticed that the observed Hi gas fractions of the Green Pea galaxies deviate from the polynomial fit in Zhang et al. (2021), where more Hi gas is predicted from the NUV- $r$ color.

The emission lines contribute significantly to the broad-band color, therefore, we also display the NUV- $r$ color with the emission lines masked. The synthetic photometry of the $ugriz$ bands is obtained by convolving the spectra with the corresponding filters, and the magnitude difference is the difference between the synthetic photometry with the original spectra and the spectra with the emission lines masked. It is obvious in Fig.4, with the emission lines removed, the NUV- $r$ colors become bluer, and therefore deviate more from the Zhang et al. (2021) NUV- $r$ color scaling relation.

Furthermore, there are a non-negligible amount (141) of blue samples (NUV- $r$ <1) in the ALFALFA-SDSS catalog. These sources are marked with gray squares in Fig.4. where the predicted $f_{\rm H\sc I}$ is higher than the observed Hi gas fraction for these blue samples. We have carefully checked these sources in the SDSS images and have found that the majority of the sources are more likely diffuse H ii regions or bright star-forming regions in large galaxies. It is obvious in Fig.4 that these samples also deviate from the polynomial form NUV- $r$ scaling relation of Hi gas fraction in Zhang et al. (2021), where the observed values are lower than the predicted values, similar to the Green Pea galaxies. With the optical emission lines removed, the NUV- $r$ color of these blue samples will become bluer as well, moving left in Fig.4.

3.2 Other factors that impact the Hi gas fraction

Due to the non-negligible offset between the observed Hi gas fraction and the predicted Hi from the NUV- $r$ scaling relation, we consider additional parameters to better estimate the Hi gas fraction for the Green Pea galaxies and the blue samples from ALFALFA-SDSS.

Four possible factors that will impact the measured NUV- $r$ with Hi gas fraction scaling relation are investigated: the $g-r$ color, the sSFR, surface brightness $\mu_{i}$ and the surface mass density $\log\mu_{\star}$ as discussed in Zhang et al. (2009); Catinella et al. (2010); Li et al. (2012); Zhang et al. (2021). Following the definitions in Zhang et al. (2009), we define the surface mass density as $\rm\log(\mu_{\star,z})=\log(\rm M_{\star})-\log(2\pi\rm R^{2}_{50,z})$ , where the $\rm M_{\star}$ is the stellar mass and the $\rm R_{50,z}$ is the radius (in units of kpc) enclosing 50% of the total Petrosian $z-$ band flux obtained from photoObjAll in SDSS. Similarly, the surface brightness is defined as $\rm\mu_{i}=m_{i}+2.5(2\pi\rm R^{2}_{50,i})$ , where the $m_{i}$ is the apparent cModelMag of the $i-$ band and the $\rm R_{50,i}$ is the radius (in units of kpc) enclosing 50 percent of the total Petrosian $z-$ band flux in units of arcsecond. Green Pea galaxies are compact galaxies and are barely resolved in the SDSS images, where it is still reliable to use the measurement from SDSS. Three Green Pea galaxies have obtained acquisition images from the COS instrument in the UV of HST (Kanekar et al. 2019), with 200 s exposure time each. We use SExtractor (Bertin & Arnouts 1996) to measure the Petrosian $R_{50,\rm HST}$ for these three sources: J1108+2238 is 0.964 arcsec, J1345+0442 is 0.418 arcsec, and J1455+3808 is 0.577 arcsec. These radii in the UV $R_{50,\rm HST}$ are smaller than the $R_{50,z}$ . The comparison of the Hi gas fraction with the $g-r$ color, the sSFR, surface mass density, and the surface brightness for Green Pea galaxies and the ALFALFA-SDSS samples are demonstrated in Fig.5, as well as the distribution of the $g-r$ color and the surface brightness with the emission lines removed for the Green Pea galaxies. With the emission lines removed, the Green Pea galaxies occupy similar $g-r$ color, which intrinsically traces mainly the small- to intermediate-mass stars, similar to the ALFALFA-SDSS samples. However, the Green Pea galaxies are dominated by massive stars from ongoing starbursts, thus they deviate from the ALFALFA-SDSS samples in the NUV- $r$ color with the emission lines removed.

It is natural to consider including the surface mass density, the surface brightness, and the sSFR into the scaling relation of the Hi gas fraction. We consider the differences between the Hi gas fraction predicted by the NUV- $r$ color and the observed gas fraction as the offset and demonstrate the relation of these three quantities with the offset in Fig.6.

There is a positive correlation between the offset and the surface mass density and the sSFR as demonstrated in the left and right panels of Fig.6, while the surface brightness anti-correlates with the surface brightness in the middle panel.

3.3 The scaling relations of the Hi gas fraction with linear combination forms

We test four sets of linear combination Hi gas fraction estimators based on the relations in Zhang et al. (2009, 2021). To be noted, that there are other forms of linear combination estimators in Catinella et al. (2010); Li et al. (2012). Following the relation in Zhang et al. (2021), for the blue sources with NUV- $r<$ 3.5, we check whether a linear combination of NUV- $r$ color and the stellar surface mass density will predict the Hi gas fraction more accurately. The top left panel in Fig.7 demonstrates the distribution of the Green Pea galaxies and the blue samples (NUV- $r<3.5$ ) from ALFALFA-SDSS catalog (Durbala et al. 2020), with the form of $\rm-0.34(NUV-r)-0.64\log(\mu_{\star,z})+5.94$ .

Three other sets of the linear combination Hi gas fraction estimators from Zhang et al. (2009) that use the optical color, sSFR, surface brightness, and surface mass density are also applied for the Green Pea galaxies.

The Green Pea galaxies with Hi 21 cm detections and non-detections distribute above and below the linear relation, in agreement with the linear estimator prediction. Among the four sets of linear combination gas fraction estimators, the first estimator $\rm-0.34(NUV-r)-0.64\log(\mu_{\star,z})+5.94$ (Zhang et al. 2021), and the fourth estimator $\rm-0.77\log\mu_{\star,i}+0.26\log SFR/M_{\star}+8.53$ (Zhang et al. 2009) result in smaller scatters. Even with the impact of the emission lines taken into consideration, the first estimator can still predict the gas fraction robustly. This is reasonable due to (1) a broader dynamic range of the NUV- $r$ color compared with the $g-r$ color (Zhang et al. 2021), (2) the NUV- $r$ color is dominated by the emission from massive stars compared with $g-r$ where mainly from the low- to intermediate-mass (discussed in Section 3.2), (3) this is a more dedicated scaling relation tuned towards the blue samples (NUV- $r$ <1).

However, these measurements are based on barely resolved ¹¹1We obtain the FWHM of the PSF for the same band from photoObjAll in SDSS and find the $R_{50,z}$ of the Green Pea galaxies are larger than half of the psfFWHM. measurements of these compact galaxies, where the measured $R_{50}$ is not accurate. For three Green Pea galaxies with morphological information from HST, we calculate the surface mass density and surface brightness with the $R_{50,\it HST}$ . In Fig.7, these measurements are marked with green stars, they are connected to the measurements based on SDSS $R_{50}$ with green lines. More accurate optical imaging with the upcoming ground-based and space-based facilities will be helpful to accurately measure the surface mass density and the surface brightness of the Green Pea galaxies. This will be helpful for better calibrating the scaling relations of the Hi gas fraction and reducing the scatter, serving as cheap and convenient $f_{\rm H\sc I}$ estimators for potential application to large samples of star-forming galaxies.

4 Result

Based on the archival data of the Hi mass measurements from Kanekar et al. (2021), we compare 38 Green Pea galaxies, including 17 detections and 21 non-detections, to the comparison sample of local star-forming galaxies from ALFALFA-SDSS (Durbala et al. 2020), to check the Hi gas fraction scaling relations. We find that the Green Pea galaxies deviate from the Zhang et al. (2021) NUV- $r$ polynomial form, where the observed gas fractions are lower than the predictions, even with the emission lines removed from the $r-$ band photometry.

The offsets between the predicted Hi gas fraction and the measured Hi gas fraction correlate with the surface mass density, the surface brightness, and the sSFR. Therefore, these three quantities are included in the scaling relations of the Hi gas fraction with linear combination forms. The forms of $\rm-0.34(NUV-r)-0.64\log(\mu_{\star,z})+5.94$ , and $\rm-0.77\log\mu_{\star,i}+0.26\log SFR/M_{\star}+8.53$ (Zhang et al. 2009, 2021), better predict the Hi gas fraction of the Green Pea galaxies. In order to obtain accurate linear combined forms with smaller scatter, higher-resolution photometry from space-based telescopes is needed.

There are a large amount of optically identified Green Pea galaxies (Jiang et al. 2019; Liu et al. 2022), where the median NUV- $r$ color for these samples is 1.13 and presumably high Hi gas fractions. We have verified in this work that the predicted Hi gas fractions from the scaling relations with the linear combination forms agree well with the observed Hi gas fraction. The Hi gas fraction of these Green Pea galaxies and other types of blue star-forming galaxies can be estimated and applied for other analyses.

Acknowledgements.

This work is supported by the National Science Foundation of China (Nos. 12273075 and 12090041). This publication makes use of data products from the Wide-field Infrared Survey Explorer, which is a joint project of the University of California, Los Angeles, and the Jet Propulsion Laboratory/California Institute of Technology, funded by the National Aeronautics and Space Administration. W. Zhang acknowledges support from the National Key R&D Program of China (No. 2021YFA1600401, 2021YFA1600400), and the Guangxi Natural Science Foundation (No. 2019GXNSFFA245008). This research uses Astropy (Astropy Collaboration et al. 2013, 2018), TOPCAT (Taylor 2005), Scipy (Virtanen et al. 2020), Numpy (Harris et al. 2020), lifelines (Davidson-Pilon 2019), pandas (Wes McKinney 2010; pandas development team 2020) and Matplotlib (Hunter 2007)

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