EMPRESS. III. Morphology, Stellar Population, and Dynamics of Extremely Metal-poor Galaxies (EMPGs): Are EMPGs Local Analogs of High-z Young Galaxies?^*

We utilize the imaging data set of HSC-SSP S18A that were taken with five broadband filters, grizy, in 2014 March–2018 January, and that were released by the HSC Collaboration in 2018 (Aihara et al. 2019). In the HSC S18A imaging data, the effective area and the i-band limiting magnitude are ∼500 deg² (Paper I) and ∼26 mag (for point sources, Ono et al. 2018), respectively. Because the HSC y-band image is ∼1 mag shallower than the other broadband images, we do not use the HSC y-band data but four broadband (griz) data for our analysis.

Before we explain our sample, we need to clarify the photometric sample of Paper I. The Paper I photometric sample consists of EMPG candidates identified with the data of HSC and SDSS, which are called HSC EMPG candidates and SDSS EMPG candidates, respectively. In this paper, we do not use SDSS EMPG candidates, because the SDSS EMPG candidates include more contaminants than the HSC EMPG candidates (Paper I). The catalog of the HSC EMPG candidates is developed with the HSC-SSP S17A and S18A data (Aihara et al. 2019) that are wide and deep enough to search for rare and faint EMPGs. The HSC EMPG candidates are selected from ∼46 million sources whose photometric measurements are brighter than 5σ limiting magnitudes in all of the four broadbands, g < 26.5, r < 26.0, i < 25.8, and z < 25.2 mag (Ono et al. 2018). The catalog consisting of these sources is referred to as the HSC source catalog.

With the HSC source catalog, Paper I isolates EMPGs from contaminants such as other types of galaxies, Galactic stars, and quasars. Paper I aims to find galaxies at z ≲ 0.03 with EW₀(Hα) > 800 Å and $12+\mathrm{log}({\rm{O}}/{\rm{H}})=6.69$–7.69. Because it is difficult to distinguish EMPGs from the contaminants on two color diagrams such as r − i versus g − r, Paper I constructs a machine-learning classifier based on a deep neural network (DNN) with a training data set. The training data set is composed of mock photometric measurements for model spectra of EMPGs and the contaminants. The DNN allows us to isolate EMPGs from the contaminants with nonlinear boundaries in the multidimensional color space. Paper I finally obtains 27 HSC EMPG candidates from the HSC source catalog. Paper I conducts spectroscopic follow-up observations for four out of the 27 HSC EMPG candidates, and confirm that all four HSC EMPG candidates are truly emission-line galaxies with the low metallicity of $12+\mathrm{log}({\rm{O}}/{\rm{H}})=6.90$–8.27 (i.e., 1.6–38% Z_⊙). Because two out of the four HSC EMPG candidates meet the EMPG criterion of $12+\mathrm{log}({\rm{O}}/{\rm{H}})\lt 7.69$ (i.e., <10% Z_⊙), Paper I concludes that these two candidates are quantitatively confirmed as EMPGs. There remain two (= 4−2) spectroscopically confirmed HSC EMPG candidates with $12+\mathrm{log}({\rm{O}}/{\rm{H}})=7.72$–8.27 (i.e., 11%–38% Z_⊙). One of the two HSC EMPG candidates shows low metallicity of $12+\mathrm{log}({\rm{O}}/{\rm{H}})=7.72$ (i.e., 11% Z_⊙), almost meeting the EMPG criterion of $12+\mathrm{log}({\rm{O}}/{\rm{H}})\lt 7.69$ (i.e., <10% Z_⊙). The other HSC EMPG candidate shows moderately low metallicity of $12+\mathrm{log}({\rm{O}}/{\rm{H}})=8.27$ (i.e., 38% Z_⊙), falling in the regime of metal-poor galaxies (MPGs). Thus, the candidate is referred to as MPG, hereafter. There remain 23 (= 27−4) HSC EMPG candidates that are not spectroscopically confirmed in Paper I. We obtain r_e for 15 of the 27 HSC EMPG candidates. Three out of the 15 HSC EMPG candidates have spectra, while 12 out of them do not have spectra. We thus refer to the three EMPGs with <11% Z_⊙ and the 12 EMPG candidates with no spectra as HSC spectroscopic EMPGs and HSC photometric EMPGs, respectively (see Figure 1). Hereafter we refer to the 15 objects as HSC EMPGs.

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Here, we estimate the purity of the HSC photometric EMPGs. Paper I has reported only four out of the 27 HSC EMPG candidates that are spectroscopically observed, and the number of spectroscopic objects is too small to reliably estimate the purity. We have added other 13 HSC EMPG candidates whose spectra are recently taken with Keck/LRIS (Isobe et al. 2021, in preparation), and obtained 17 ( = 4+13) HSC EMPG candidates with spectroscopic results. We find that 12 out of the 17 HSC EMPG candidates with spectra (12/17 = 71%) are real EMPGs with ≲10% Z_⊙, while the rest of them (5/17 = 29%) are contaminants. Thus, our machine-learning classifier accomplishes 71% purity for the HSC EMPG candidates, indicative that 71% of the HSC photometric EMPGs are real EMPGs. ¹⁷ For the 12 spectroscopically confirmed EMPGs, we derive the median redshift with the 16th and 84th percentiles $z={0.030}_{-0.017}^{+0.015}$. Thus, we assume z = 0.03 for the HSC photometric EMPGs to measure their sizes, stellar masses, and SFRs.

For the completeness of results, we also utilize a catalog of EMPGs compiled by S16. S16 selected EMPGs in the full set of 788677 galaxy spectra at z < 0.25 from the Sloan Digital Sky Survey (SDSS) Data Release 7. S16 aims to find galaxies showing a high line ratio of [O iii]λ4363/[O iii]λ λ 4959, 5007, which is an indicator of gas with high electron temperature. Because metals are the main coolants of gas (e.g., Pagel et al. 1979), low-metallicity gas should exhibit higher temperatures. Using the automated classification algorithm, k-means (e.g., Sánchez Almeida et al. 2010), S16 narrowed down the large data set of the SDSS galaxy spectra according to the spectral shape in the range of λ = 4200–5200 Å, which contains [O iii]λ4363, [O iii]λ4959, and [O iii]λ5007 lines. After the classification, S16 obtained 1281 EMPG candidates. S16 calculated metallicities of the 1281 candidates to identify that 196 out of the candidates meet the low metallicities of 2%–10% Z_⊙, which meet the EMPG criterion. In order to evaluate r_e precisely in the same manner as HSC EMPGs, we utilize 13 out of the 196 EMPGs that have griz-band data in the HSC-SSP S18A data release. We obtain 12 EMPGs whose r_e values are successfully measured. Hereafter, we refer to the 12 EMPGs as S16 spectroscopic EMPGs (see Figure 1).

In order to increase the sample size, we analyze both HSC EMPGs and S16 spectroscopic EMPGs. We refer to the sum of HSC EMPGs and S16 spectroscopic EMPGs as ALL EMPGs (see Figure 1). Metallicities of ALL EMPGs, so far identified, are 0.01–0.1 Z_⊙.

Figure 1 presents the HSC gri-composite images of ALL EMPGs. We find that most of the EMPGs have tails. Hereafter, we refer to the tails as EMPG tails. Here, we define the EMPG tail as an object brighter than the 5σ limiting magnitude of the HSC i band (25.8 mag) within 10 kpc from the EMPG. After conducting multicomponent SB profile fitting (Section 3.2), we find that 23 out of the 27 EMPGs have EMPG tails, many of which appear to be galaxies in HSC deep images. We measure sizes and stellar masses of the EMPG tails in the same manner as the EMPGs.

We measure the galaxy size with the HSC i-band images. One of the reasons is that the i-band imaging data allow us to trace the spatial distribution of the stellar continuum because the i-band measurements are less affected by strong emission lines such as Hα and [O iii]. Another reason is that the median seeing of the HSC i-band images (FWHM ∼ 0.56'') is also smaller than that of the other four HSC broadband images (Aihara et al. 2019). We fit a Sérsic profile to the SB profile of each EMPG. The Sérsic profile can be written as

$$\begin{eqnarray}&&I(r,n)={I}_{e}\exp \left[-\kappa (n)\left\{{\left(\displaystyle \frac{r}{{r}_{e}}\right)}^{1/n}-1\right\}\right],\end{eqnarray} \tag{ 1 }$$

where r_e and n represent the effective radius and the Sérsic index, respectively. The function, κ(n), is the implicit function that satisfies Γ(2n) = 2γ(2n, κ(n)), where Γ and γ are the gamma function and the incomplete gamma function, respectively (Graham & Driver 2005). The Sérsic profiles with n = 1 and n = 4 are generally obtained from the disk and elliptical galaxies, respectively. Because most of the EMPGs have EMPG tails (Section 3.1), we utilize the multicomponent SB profile fitting code, Galfit (Peng 2010), to derive r_e and n of the EMPGs (and the EMPG tails simultaneously).

Here, we explain the procedure of our SB profile fitting. First, we fit the SB profiles of first single Sérsic profiles to those of the EMPGs by the χ² minimization technique. The code Galfit can convolve the model functions with a point-spread function, which is supplied by the HSC-SSP data release. We obtain best-fit models and residual images. The residual images are obtained by subtracting the best-fit model from an original image. If there remain no obvious sources in the residual images, we complete the fitting of the EMPG with the best-fit model. If there exist clear sources in the residual images, we execute two-component Sérsic profile fitting. ¹⁸ Physical properties of the first and the second Sérsic profiles are regarded as those of the EMPGs and EMPG tails, respectively. The best-fit models provide physical properties of r_e , n, apparent i-band magnitudes m_i , galaxy positions, axis ratios q, and position angles. We search n in the range of n = 0.7–4.2 because n sometimes diverges at n = 0 or n → ∞ . We omit objects from the samples in cases where the SB profile is too complicated to fit. We estimate the 16th, 50th, and 84th percentiles of the parameters by performing Monte Carlo simulations. We create 100 mock images by cutting out each EMPG (and EMPG tail) and embedding them in nearby blank regions. We also consider that an error of each pixel is normally distributed with a variance value supplied by the HSC-SSP data release. Figure 2 presents examples of the SB profile fitting. The size and n results are listed in Tables 1–4.

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Table 1. Properties of the HSC EMPGs

Name	ID	Redshift	re	n	$\mathrm{log}({M}_{* })$	$\mathrm{log}(\mathrm{SFR})$
			(pc)		M⊙	(M⊙ yr−1)
(1)	(2)	(3)	(4)	(5)	(6)	(7)
KS1	J2314+0154	0.03265	${104}_{-5}^{+12}$	<0.7	${6.01}_{-0.16}^{+0.10}$	−0.851 ± 0.001
KS2	J1631+4426	0.03125	${137}_{-7}^{+9}$	${1.08}_{-0.13}^{+0.15}$	${6.12}_{-0.03}^{+0.02}$	−1.276 ± 0.002
KS3	J1142−0038	0.02035	${219}_{-13}^{+189}$	${2.79}_{-0.39}^{+1.41}$	${4.97}_{-0.00}^{+0.01}$	−1.066 ± 0.002
KP1	J0912−0104	⋯	${89.3}_{-12.4}^{+9.4}$	${0.83}_{-0.13}^{+0.37}$	${5.61}_{-0.11}^{+0.07}$	$-{1.7}_{-0.4}^{+0.2}$
KP2	J2321+0125	⋯	${377}_{-75}^{+87}$	${0.80}_{-0.10}^{+0.43}$	${4.81}_{-0.22}^{+0.26}$	$-{2.0}_{-0.4}^{+0.2}$
KP3	J2355+0200	⋯	${416}_{-51}^{+54}$	${0.80}_{-0.10}^{+0.14}$	5.47 ± 0.02	$-{1.0}_{-0.4}^{+0.2}$
KP4	J2236+0444	⋯	${159}_{-12}^{+13}$	${0.80}_{-0.10}^{+0.28}$	5.92 ± 0.02	$-{1.7}_{-0.4}^{+0.2}$
KP5	J1411−0032	⋯	${45.9}_{-1.7}^{+2.5}$	${0.7}_{-0.0}^{+0.4}$	${5.93}_{-0.01}^{+0.02}$	$-{1.3}_{-0.4}^{+0.2}$
KP6	J0834+0103	⋯	${116}_{-12}^{+8}$	${0.7}_{-0.0}^{+0.6}$	4.86 ± 0.01	$-{1.6}_{-0.4}^{+0.2}$
KP7	J0226−0517	⋯	${60.5}_{-11.7}^{+1.1}$	${1.16}_{-0.07}^{+0.91}$	${5.51}_{-0.03}^{+0.04}$	$-{1.2}_{-0.4}^{+0.2}$
KP8	J0156−0421	⋯	${199}_{-14}^{+23}$	${1.12}_{-0.42}^{+0.75}$	4.96 ± 0.04	$-{1.6}_{-0.4}^{+0.2}$
KP9	J0935−0115	⋯	${86.0}_{-1.3}^{+0.8}$	<0.7	${6.79}_{-0.05}^{+0.09}$	$-{0.4}_{-0.4}^{+0.2}$
KP10	J0937−0040	⋯	159 ± 1	${1.72}_{-0.02}^{+0.03}$	${6.45}_{-0.09}^{+0.04}$	$-{0.4}_{-0.4}^{+0.2}$
KP11	J1210−0103	⋯	${589}_{-126}^{+227}$	${1.59}_{-0.38}^{+0.69}$	${4.99}_{-0.08}^{+0.10}$	$-{1.6}_{-0.4}^{+0.2}$
KP12	J0845+0131	⋯	${122}_{-7}^{+6}$	${1.72}_{-0.34}^{+2.48}$	${5.38}_{-0.02}^{+0.01}$	$-{1.2}_{-0.4}^{+0.2}$

Note. (1) Name. (2) ID. (3): Spec-z. Typical uncertainties are Δz ∼ 10⁻⁶ (I). (4) Median effective radius in the 16th and 84th percentiles (Section 3.2). (5) Median Sérsic index in the 16th and 84th percentiles. If we obtain n = 0.7 for all of the mock images, we describe the situation as n < 0.7 (Section 3.2). (6) Median stellar mass at the 16th and 84th percentiles (Section 3.3). (7) SFR (Section 3.4).

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Table 2. Properties of S16 Spectroscopic EMPGs

Name	# in	ID	Redshift	re	n	$\mathrm{log}({M}_{* })$	$\mathrm{log}(\mathrm{SFR})$
	S16			(pc)		(M⊙)	(M⊙ yr−1)
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)
SS1	110	J1217−0154	0.02047	${1520}_{-20}^{+30}$	1.29 ± 0.03	8.0	−1.959 ± 0.004
SS2	148	J1419+0109	0.00814	${80.8}_{-1.9}^{+0.5}$	<0.7	7.2	−2.210 ± 0.005
SS3	152	J1427−0143	0.00602	${343}_{-11}^{+10}$	${1.38}_{-0.04}^{+0.03}$	6.0	−2.660 ± 0.004
SS4	153	J1429+0107	0.02969	${422}_{-0}^{+1}$	0.92 ± 0.00	8.3	−0.975 ± 0.003
SS5	158	J1444+4237	0.00213	${37.7}_{-6.4}^{+8.1}$	${4.2}_{-0.5}^{+0.0}$	5.0	−3.560 ± 0.003
SS6	186	J2211+0048	0.06459	${662}_{-2}^{+4}$	0.85 ± 0.02	8.3	−0.883 ± 0.003
SS7	187	J2212+0108	0.21011	2650 ± 30	${1.50}_{-0.03}^{+0.04}$	8.5	0.418 ± 0.005
SS8	191	J2302+0049	0.03312	273 ± 1	${1.38}_{-0.02}^{+0.05}$	7.4	−0.631 ± 0.004
SS9	192	J2327−0051	0.02343	${494}_{-2}^{+3}$	1.01 ± 0.01	8.0	−1.730 ± 0.005
SS10	193	J2334+0029	0.02384	${684}_{-88}^{+64}$	>4.2	7.9	−1.461 ± 0.004
SS11	194	J2335−0025	0.07672	${1260}_{-0}^{+10}$	${1.18}_{-0.01}^{+0.02}$	8.6	−0.595 ± 0.005
SS12	195	J2340−0053	0.01883	${176}_{-4}^{+2}$	<0.7	7.7	−1.747 ± 0.005

Note. (1) Name. (2) Number that appeared in S16. (3) ID. (4) Spec-z. Typical uncertainties are Δz ≲ 10⁻⁵. (5) Median effective radius at the 16th and 84th percentiles (Section 3.2). (6) Median Sérsic index at the 16th and 84th percentiles (Section 3.2). (7) Median stellar mass (Section 3.3). (8) SFR (Section 3.4).

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Table 4. Properties of the EMPG Tails

Name	re	n	$\mathrm{log}({M}_{* })$
	(kpc)		(M⊙)
(1)	(2)	(3)	(4)
KS1 tail	${3.37}_{-0.29}^{+0.34}$	${2.51}_{-0.15}^{+0.18}$	${7.47}_{-0.03}^{+0.04}$
KS2 tail	${0.805}_{-0.054}^{+0.063}$	<0.7	${6.94}_{-0.34}^{+0.45}$
KS3 tail	${3.99}_{-0.64}^{+1.67}$	${1.93}_{-0.16}^{+0.37}$	8.01 ± 0.08
KP2 tail	${0.481}_{-0.016}^{+0.023}$	<0.7	${6.50}_{-0.35}^{+0.39}$
KP3 tail	${0.705}_{-0.045}^{+0.104}$	<0.7	${6.30}_{-0.24}^{+0.38}$
KP5 tail	2.62 ± 0.05	0.93 ± 0.02	7.98 ± 0.04
KP6 tail	${1.98}_{-0.02}^{+0.07}$	${0.97}_{-0.02}^{+0.05}$	8.39 ± 0.08
KP7 tail	${1.87}_{-0.02}^{+0.01}$	${0.79}_{-0.03}^{+0.04}$	${7.86}_{-0.10}^{+0.08}$
KP9 tail	${1.23}_{-0.07}^{+0.11}$	${0.95}_{-0.08}^{+0.12}$	${7.12}_{-0.13}^{+0.26}$
KP10 tail	${1.63}_{-0.00}^{+0.01}$	<0.7	${8.05}_{-0.15}^{+0.09}$
KP11 tail	${1.29}_{-0.11}^{+0.18}$	${0.7}_{-0.0}^{+0.1}$	${6.50}_{-0.21}^{+0.35}$
KP12 tail	${1.02}_{-0.11}^{+0.45}$	${0.89}_{-0.19}^{+0.34}$	${6.57}_{-0.20}^{+0.34}$
SS2 tail	${6.66}_{-0.53}^{+0.09}$	${2.10}_{-0.07}^{+0.03}$	${7.33}_{-0.15}^{+0.13}$
SS3 tail	${0.822}_{-0.028}^{+0.026}$	${1.55}_{-0.03}^{+0.04}$	${6.16}_{-0.09}^{+0.11}$
SS4 tail	${2.77}_{-0.03}^{+0.02}$	1.60 ± 0.02	${8.82}_{-0.11}^{+0.07}$
SS5 tail	${1.84}_{-0.21}^{+0.11}$	<0.7	${7.36}_{-0.10}^{+0.22}$
SS6 tail	${1.64}_{-0.02}^{+0.03}$	${1.43}_{-0.02}^{+0.03}$	${7.80}_{-0.07}^{+0.10}$
SS7 tail	${1.90}_{-0.18}^{+0.26}$	${4.2}_{-0.2}^{+0.0}$	8.33 ± 0.08
SS8 tail	0.321 ± 0.002	${0.89}_{-0.01}^{+0.03}$	${7.12}_{-0.18}^{+0.16}$
SS9 tail	${1.31}_{-0.01}^{+0.03}$	${1.22}_{-0.02}^{+0.03}$	${7.85}_{-0.05}^{+0.14}$
SS10 tail	${1.41}_{-0.00}^{+0.04}$	${1.02}_{-0.01}^{+0.04}$	${7.88}_{-0.05}^{+0.14}$
SS11 tail	4.23 ± 0.02	<0.7	${8.75}_{-0.04}^{+0.02}$
SS12 tail	${0.645}_{-0.007}^{+0.008}$	0.77 ± 0.01	${7.47}_{-0.09}^{+0.20}$

Note. (1) Name. (2) Median effective radius at the 16th and 84th percentiles (Section 3.2). (3) Median Sérsic index at the 16th and 84th percentiles (Section 3.2). (4) Median stellar mass at the 16th and 84th percentiles (Section 3.3).

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We estimate stellar masses with the spectral energy distribution (SED) interpretation code, beagle (Chevallard & Charlot 2016). The beagle code calculates both the stellar continuum and the nebular emission using the stellar population synthesis code (Bruzual & Charlot 2003) and the photoionization code of Gutkin et al. (2016) that are computed with cloudy (Ferland et al. 2013). We adopt the Charlot & Fall (2000) law to the models for dust attenuation. In the SED fitting, we use griz-band photometry provided by the HSC-SSP S18A photometry catalog. Settings of the SED fitting for the EMPGs are the same as in Paper I. Because Paper I reports that most of our EMPGs with spectra show a small color excess of E(B − V) ∼ 0, we also assume no dust attenuation in the EMPGs. Assuming the constant star formation history, we run the beagle code with four free parameters of the metallicity, the maximum stellar age, the stellar mass, and the ionization parameter in the range of Z=0.006–0.3 Z_⊙, $\mathrm{log}(\mathrm{Age}/\mathrm{yr})\,=4.0$–9.0, $\mathrm{log}({M}_{* }/{M}_{\odot })=4.0$–9.0, and $\mathrm{log}(U)=(-2.5)$–(−0.5), respectively. This time we assume the maximum stellar age of the EMPGs less than 1 Gyr, because the EMPGs do not show prominent Balmer breaks (Paper I) indicative that the EMPGs are much younger than ∼1 Gyr. An example of the SED fitting is shown in Figure 3. We also conduct SED fitting for the EMPG tails, while parameter ranges of the fitting are different from those for the EMPGs. Assuming the constant star formation history, we run the beagle code with five free parameters of the metallicity, the maximum stellar age, the stellar mass, the ionization parameter, and the dust attenuation in the range of Z = 0.01–1 Z_⊙, $\mathrm{log}(\mathrm{Age}/\mathrm{yr})=8.0$–12.0, $\mathrm{log}({M}_{* }/{M}_{\odot })\,=4.0$–9.0, $\mathrm{log}(U)=(-5.0)$–(−2.5), and τ_V = 0–20, respectively. We find that eight EMPG tails are missed in the HSC-SSP photometry catalog probably because the eight EMPG tails are not only faint (∼20 mag) but also near their EMPG (∼1''), while the other 15 (= 23–8) EMPG tails are included. We first estimate stellar masses of the 15 EMPG tails by the SED fitting described above. Then we obtain a mass–luminosity (M_* and absolute i-band luminosity M_i ) relation,

$$\begin{eqnarray}&&\mathrm{log}({M}_{* }/{M}_{\odot })=-0.345\,{M}_{i}+2.02,\end{eqnarray} \tag{ 2 }$$

by the linear fitting to the stellar masses and i-band luminosities of the 15 EMPG tails. For the eight EMPG tails missed in the HSC-SSP photometry catalog, we instead use i-band magnitudes obtained by our SB profile fitting (Section 3.2). Then, we apply the mass–luminosity relation (Equation (2)) to estimate stellar masses of the eight EMPG tails.

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Stellar masses of the EMPGs and the EMPG tails are listed in Tables 1–4. In these tables, we show only median values of the stellar masses because errors provided by the SED fitting do not include any uncertainty arising from different assumptions. This uncertainty is ∼0.1 dex, which is larger than a typical error of ∼0.05 dex provided by the SED fitting.

We derive SFRs from Hα fluxes F(Hα). Regarding the HSC spectroscopic EMPGs, we use dust- and aperture-corrected Hα fluxes obtained by spectroscopy in Paper I. For S16 spectroscopic EMPGs, we utilize aperture-corrected Hα fluxes of SDSS DR16 that are derived with the methods of Brinchmann et al. (2004), Kauffmann et al. (2003), and Tremonti et al. (2004). On the other hand, we estimate Hα fluxes of the HSC photometric EMPGs with riz-band photometry. The HSC EMPGs show large r-band excesses by r − i ∼ − 0.8, which are mainly caused by the strong Hα line (Section 2.2). Here, we describe how to estimate the flux density (per unit frequency) of the r-band continuum f_r,cont. Because the observed iz-band flux densities, f_i,tot and f_z,tot, are less affected by strong emission lines (Section 3.2), we regard f_i,tot and f_z,tot as tracers of the stellar continuum. The Bruzual & Charlot (1993) synthesis model shows that young starburst galaxies have stellar continua whose flux densities per unit frequency is constant. We thus estimate f_r,cont as an average of f_i,tot and f_z,tot. We calculate F(Hα) as follows:

$$\begin{eqnarray}&&F({\rm{H}}\alpha )=({f}_{r,\mathrm{tot}}-{f}_{r,\mathrm{cont}.})\times \displaystyle \frac{c}{{\lambda }_{r}^{2}}\times {\rm{\Delta }}{\lambda }_{r},\end{eqnarray} \tag{ 3 }$$

where f_r,tot, λ_r and Δλ_r represent the observed r-band flux density, the central wavelength of the HSC r-band filter, and the width of the HSC r-band filter in wavelength, respectively. The F(Hα) error calculated from riz-band photometric errors is at most ∼10%. Emission lines other than Hα in the HSC r, i, and z bands can increase the flux densities by only ∼11%, 4%, and 6%, respectively. Consequently, the estimated Hα flux can be changed by only ∼6%. We calculate F(Hα) of the HSC spectroscopic EMPGs, and confirm that the values of F(Hα) are consistent with those derived from the spectra within ∼60%. Because this ∼60% difference is the most dominant error of the F(Hα) estimation, we adopt ±60% as the F(Hα) error of the HSC photometric EMPGs. We utilize the Kennicutt relation (Kennicutt 1998) to derive SFRs:

$$\begin{eqnarray}&&\mathrm{SFR}=7.9\times {10}^{-42}L({\rm{H}}\alpha ),\end{eqnarray} \tag{ 4 }$$

where SFR and L(Hα) are in units of M_⊙ yr⁻¹ and erg s⁻¹, respectively. We note that Kennicutt (1998) adopt the power-law initial mass function (IMF) of Salpeter (1955) to derive Equation (4). However, the top-heavy Chabrier (2003) IMF is more appropriate than the Salpeter IMF for young galaxies such as the HSC EMPGs (Paper I). We divide the SFR of Equation (4) by 1.8, which is based on the Chabrier IMF (Madau & Dickinson 2014). The SFR results are listed in Tables 1 and 2.

Regarding ALL EMPGs, we obtain a median effective radius of ${r}_{e}={200}_{-110}^{+450}$ pc, Sérsic index of $n={1.1}_{-0.4}^{+0.6}$, stellar mass of $\mathrm{log}({M}_{* }/{M}_{\odot })={6.0}_{-1.0}^{+2.0}$, and SFR of $\mathrm{log}(\mathrm{SFR}/{M}_{\odot }\,{\mathrm{yr}}^{-1})\,=-{1.3}_{-0.6}^{+0.7}$ with the range of ±68% distributions, respectively. The small values of r_e ∼ 200 pc and n ∼ 1 suggest that the EMPGs have very compact disks. The median size of the EMPGs is also comparable to those of the heads of metal-poor tadpole galaxies (FWHM ∼ 200 pc; Sánchez Almeida et al. 2015) even though their method of measuring and the interpretation of the morphological structure are different from ours. As shown in Figure 4, the median M_* of the HSC EMPGs is ∼2 dex smaller than that of S16 spectroscopic EMPGs, which makes the EMPGs cover the wide M_* range of $\mathrm{log}({M}_{* }/{M}_{\odot })=4.5$–8.6. The HSC EMPGs have small M_* comparable to those of Galactic star clusters. All the results are listed in Tables 1 and 2.

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On the other hand, we find that a median effective radius, Sérsic index, and stellar mass of the EMPG tails with the range of ±68% distributions are ${r}_{e}={1.6}_{-0.9}^{+1.4}$ kpc, $n={0.9}_{-0.2}^{+0.8}$, and $\mathrm{log}({M}_{* }/{M}_{\odot })={7.5}_{-0.9}^{+0.7}$, respectively (Table 4). The stellar mass ratio between EMPGs and EMPG tails (M_*,tail/M_*,EMPG ∼ 32) is comparable to the ratio between head and tail of tadpole galaxies (M_*,tail/M_*,head ∼ 12; Elmegreen et al. 2012), which implies that heads of the tadpole galaxies and the EMPG with the EMPG tail are similar populations.

Figure 5 represents the distribution of r_e and M_* of the EMPGs and EMPG tails. We add the data of star-forming galaxies (SFGs) at z ∼ 0 (gray) and z ∼ 6 (yellow). We also plot r_e and M_* of local dwarf galaxies. We created Figure 6 to compare the distributions of the EMPGs and EMPG tails to the z ∼ 0 and 6 SFGs (left), the local dwarf galaxies (center), and clumps of clumpy galaxies and normal galaxies (right). As described in the left panel of Figure 6, we find that most of the EMPGs, except for a few (KP9, SS2, and SS12), fall on the r_e –M_* relation of z ∼ 0 SFGs rather than z ∼ 6 SFGs. The EMPGs have r_e values larger than those of z ∼ 6 SFGs at a given M_*. Compared to local dwarf galaxies as shown in the center panel of Figure 6, some of the EMPGs have the values of r_e and M_* similar to those of dSphs and dIrrs. The other EMPGs fall on the region between dSphs and GCs. Comparing the right panel of Figure 6 with the left panel of Figure 6, we find that the clumps of Elmegreen et al. (2013) have size–mass relations similar to those of z ∼ 0 SFGs. Thus, we arrive at the same finding as we compare the EMPGs with z ∼ 0 SFGs. It should be noted that the sizes of the clumps reported by Elmegreen et al. (2013) do not necessarily represent effective radii.

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As well as the EMPGs, the majority of the EMPG tails have a r_e –M_* relation similar to that of z ∼ 0 SFGs. We also find that the EMPG tails are located on the distributions of dSphs, dIrrs, and UDGs.

In Section 4.2, we report that the EMPGs overlap the distributions of z ∼ 0 SFGs on the r_e –M_* plane (Figure 6, left). Now we present the SFR–M_* distribution of the EMPGs to compare with those of z ∼ 0 and 6 main sequences (Shibuya et al. 2015). As shown in Figure 7, the EMPGs fall on both the z ∼ 0 MS and the extrapolation of z ∼ 6 MS. We confirm that KP9 is located around the extrapolation of the z ∼ 6 MS, whereas SS2 and SS12 lie on the z ∼ 0 MS.

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In Section 4.2, we also point out that some of the EMPGs have r_e and M_* comparable to those of dSphs and dIrrs. Now we compare the EMPGs to dIrrs whose SFR and M_* values are reported by Zhang et al. (2012). As shown in Figure 7, the majority of the EMPGs, except for a few, have sSFR values higher than those of dIrrs. We note that star formation activities of dSphs are already quenched (Weisz et al. 2014), i.e., SFR values of dSphs are too small to plot.

In Section 4.2, we compare the EMPGs to several types of galaxies and clumps in the r_e –M_* space. In this section, we discuss which type of galaxies can be a counterpart of the EMPG based on the properties that we report in Section 4.

5.1.1. Comparison with SFGs

5.1.2. Comparison with Local Dwarf Galaxies

5.1.3. Comparison with Clumps

In Section 4.2, we point out the size–mass relations of the clumps are similar to those of z ∼ 0 SFGs. Thus, if we use only the r_e –M_* relations, we cannot tell whether the EMPGs are clumps of the EMPG tails or individual galaxies. Wuyts et al. (2012) report that z ∼ 1–2 clumpy galaxies have clumps whose V-band SBs are at most ∼1 dex larger than the SB profile of the host galaxies, although such relations have not been investigated for the clumps of Elmegreen et al. (2013). The SB excesses possibly get smaller in the i band because the i-band luminosity is less affected by strong emission lines (Section 3.2) and thus stellar ages. If a clump nevertheless has an i-band SB more than ∼1 dex larger than that of the host galaxy, the clump may be a system that is separate from the host galaxy. Therefore, estimating how much i-band SB of the EMPGs exceed the EMPG-tail SB profile is important to understand whether the EMPGs are likely to be star-forming clumps of the EMPG tails. Here, we derive i-band SBs of the EMPGs, Σ_EMPG, normalized by i-band SBs of the EMPG tails, Σ_tail. The ratio $\mathrm{log}({{\rm{\Sigma }}}_{\mathrm{EMPG}}/{{\rm{\Sigma }}}_{\mathrm{tail}})$ can be calculated by

$$\begin{eqnarray}&&\mathrm{log}({{\rm{\Sigma }}}_{\mathrm{EMPG}}/{{\rm{\Sigma }}}_{\mathrm{tail}})=-0.4({\bar{\mu }}_{{\rm{e}},\mathrm{EMPG}}-{\bar{\mu }}_{{\rm{e}},\mathrm{tail}}),\end{eqnarray} \tag{ 5 }$$

where

$$\begin{eqnarray}\begin{array}{rcl}{\bar{\mu }}_{{\rm{e}},\mathrm{EMPG}} & = & {M}_{i,\mathrm{EMPG}}+2.5\mathrm{log}(2\pi {r}_{{\rm{e}},\mathrm{EMPG}}^{2}),\\ {\bar{\mu }}_{{\rm{e}},\mathrm{tail}} & = & {M}_{i,\mathrm{tail}}+2.5\mathrm{log}(2\pi {r}_{{\rm{e}},\mathrm{tail}}^{2}),\end{array}\end{eqnarray} \tag{ 6 }$$

where M_i,EMPG and M_i,tail are absolute magnitudes of the EMPGs and the EMPG tails, respectively. The projected distance r_p between each pair of EMPG and EMPG tail is derived from the best-fit coordinates obtained by the SB Sérsic profile fitting (Section 3.2). Figure 8 presents the distribution of Σ_EMPG/Σ_tail and r_p /r_e,tail. For comparison, we derive the normalized SB profile of the EMPG tails from SB of the 2D Sérsic profile at a given (r_p /r_e,tail) divided by the average SB within r_e,tail. The black solid curve represents the normalized SB profile with n = 0.93 that is the median n of the EMPG tails. The gray shaded region represents how much the SB profile of the EMPG tails varies when we change n from 0.7–1.76. The n range corresponds to the ±68% percentiles of Sérsic indices of the EMPG tails, and 19 out of the 23 EMPG tails have n within the range. We find 10 out of the 23 EMPGs with the EMPG tail (10/23 = 43%) have Σ_EMPG/Σ_tail at most ∼1 dex larger than the normalized SB profile of the typical EMPG tail (black solid curve). The SB excesses are comparable to those of the star-forming clumps of Wuyts et al. (2012). We conclude that 43% of the EMPGs are likely to be star-forming clumps of the EMPG tails.

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Conversely, we identify the rest 13 EMPGs with the EMPG tail (13/23 = 57%) whose Σ_EMPG/Σ_tail are at least ∼2 dex larger than the normalized SB profile of the typical EMPG tail. Although KS1 tail has a relatively large n of 2.51, we confirm that Σ_EMPG/Σ_tail of KS1 is >2 dex larger than the SB profile of KS1 tail (the blue solid curve). The 13 EMPGs do not resemble the clumps in the z ∼ 1–2 clumpy galaxies (Wuyts et al. 2012), which implies that the 13 EMPGs are a population different from that of clumps in galaxies. These large SB excesses cannot possibly be explained by only ages because starbursts lose their i-band luminosity by only ∼1 dex for the first 1 Gyr (regarding metal-poor models; Leitherer et al. 1999). The SBs of the 13 EMPGs cannot be equal to those of the EMPG tails even after 1 Gyr, unless the EMPGs grow in size by a factor of ≳3.

In Section 4.2, we find that many of the EMPG tails fall around the r_e –M_* relation of dSphs, dIrrs, and UDGs. We can exclude dSphs from a counterpart candidate of the EMPG tails because most of dSphs are located near the host galaxies (within a virial radius; McConnachie 2012), while the EMPG tails are located in an isolated environment (more isolated than typical local galaxies, e.g., Filho et al. 2015; Paper I). In contrast, dIrrs are relatively apart from the host galaxies (McConnachie 2012). UDGs are classified into two groups: those in galaxy clusters (Van Dokkum et al. 2015) and those in blank fields (field UDGs; Prole et al. 2019a). Thus, the EMPG tails may be in environments similar to those of field UDGs. A number of field UDGs reported by Prole et al. (2019a) (especially the UDG in the middle left panel of Figure 9) have blue star-forming clumps or galaxies, which are also similar to the EMPG tails. Additionally, typical UDGs have n < 1.5 (Prole et al. 2019a), which are also supported by the result of zoom-in cosmological simulations (Di Cintio et al. 2017).

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In this section, we discuss dynamical relations between the EMPGs and EMPG tails. In our sample, the KS1 tail is the only EMPG tail whose spectrum is available, which allows us to evaluate whether KS1 is dynamically related to the KS1 tail. As shown in Figure 8, KS1 has the i-band SB more than ∼2 dex larger than the normalized SB profile of the typical EMPG tail, implying that KS1 is a different system that has not been reported yet. MPG (see Section 2.2) also has a tail (hereafter MPG tail) whose spectrum is available. Figure 10 (Figure 11) presents spectra of KS1 (MPG) and the KS1 tail (MPG tail). We measure barycenters of Hα emission lines. To estimate errors of the barycenters, we fluctuate the observed spectrum based on a noise spectrum that contains photon noise. We embed the fluctuated spectrum into a continuum spectrum that is randomly selected from the wavelength range of 5100–5800 Å. We repeat the procedure 1000 times for each EMPG or EMPG tail.vWe finally obtain the barycenter differences at the 16 and 84th percentiles of Δλ = 2.2 ± 0.7 and 0.6 ± 0.4 Å for KS1 and MPG, respectively (the right top panels of Figures 10 and 11). The barycenter differences correspond to the relative velocities at the 16th and 84th percentiles of ΔV = 101 ± 32 and ΔV = 27 ± 17 km s⁻¹, respectively. Using best-fit coordinates of KS1 and the KS1 tail obtained by the SB Sérsic profile fitting (Section 3.2), the projected distance r_p between KS1 and the KS1 tail is 9.83 kpc. Similarly, the value of r_p between MPG and the MPG tail is 2.40 kpc. For both KS1 and MPG, errors of the r_p are smaller than 0.01 kpc. Because ΔV and r_p are smaller than ∼100 km s⁻¹ and 10 kpc, respectively, KS1 (MPG) may be dynamically related to the KS1 tail (MPG tail).

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In figure 12, we plot ΔV and r_p of KS1 (top) and MPG (bottom). Here, we investigate whether KS1 (MPG) is the structure on the dynamical system of KS1 tail (MPG tail). In Section 4.1, we identify that the EMPG tails have low Sérsic indices of n ∼ 1 that is indicative of disk galaxies. Moreover, the images of the KS1 tail and MPG tail show internal structures similar to spiral arms on disk galaxies (the bottom left panels of Figures 10 and 11). These morphological properties indicate that the KS1 tail and MPG tail are probably disk galaxies that are dynamically supported by rotational motions. We thus estimate rotation curves of the EMPG tails.

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Below, we draw rotation curves of the KS1 tail and MPG tail and discuss how KS1 and MPG are dynamically associated with the KS1 tail and MPG tail, respectively. Because r_p of KS1 (MPG) is larger than r_e of the KS1 tail (MPG tail), dynamics around KS1 (MPG) is dominated by the DM halo of the KS1 tail (MPG tail). We assume the density profile of the DM halo of the EMPG tail as a Navarro–Frenk–White (NFW) profile derived with CDM models (Navarro et al. 1996). The circular velocity of the NFW halo V_c (r) can be calculated by

$$\begin{eqnarray}&&{\left(\displaystyle \frac{{V}_{c}(r)}{{V}_{200}}\right)}^{2}=\displaystyle \frac{1}{r/{r}_{200}}\displaystyle \frac{\mathrm{ln}[1+C(r/{r}_{200})]-\tfrac{C(r/{r}_{200})}{1+C(r/{r}_{200})}}{\mathrm{ln}(1+C)-\tfrac{C}{1+C}},\end{eqnarray} \tag{ 7 }$$

where V₂₀₀, r, and r₂₀₀ represent the virial velocity, the radius, and the virial radius, respectively. The parameter C describes the concentration, which is roughly correlated with the SB (Navarro 1998). We assume C = 5 for galaxies with low SBs (Navarro 1998). The values of V₂₀₀ and r₂₀₀ in units of kilometer per second and kiloparsec are described with

$$\begin{eqnarray}&&{V}_{200}={\left(\displaystyle \frac{{M}_{200}}{2.33\times {10}^{5}\,{M}_{\odot }}\right)}^{1/3}\end{eqnarray} \tag{ 8 }$$

and

$$\begin{eqnarray}&&{r}_{200}=\displaystyle \frac{{{GM}}_{200}}{{V}_{200}^{2}},\end{eqnarray} \tag{ 9 }$$

respectively, where G is the gravitational constant of 6.67 × 10⁻⁸ cm³ s⁻² g⁻¹. Here, M₂₀₀ is the DM halo mass. We obtain the relations between M_* and M₂₀₀, both in units of the stellar mass, assuming the stellar-to-halo mass relations for low-mass galaxies (Brook et al. 2014)

$$\begin{eqnarray}&&{M}_{* }={\left(\displaystyle \frac{{M}_{200}}{79.6\times {10}^{6}\,{M}_{\odot }}\right)}^{3.1}\end{eqnarray} \tag{ 10 }$$

that is applicable for UDGs and LSBGs (Prole et al. 2019b). The virial velocity and the virial radius of the KS1 tail (MPG tail) are estimated to be V₂₀₀ = 51.8 (45.7 km s⁻¹) and r₂₀₀ = 51.9 (45.7 kpc), respectively. Comparing the r_p values between KS1 (MPG) and the KS1 tail (MPG tail), we find that KS1 (MPG) is located within the virial radius of the KS1 tail (MPG tail). Then we estimate the inclinations i of the EMPG tails using the relation of

$$\begin{eqnarray}&&{\cos }^{2}i=\displaystyle \frac{{q}^{2}-{q}_{0}^{2}}{1-{q}_{0}^{2}},\end{eqnarray} \tag{ 11 }$$

where q and q₀ are the axis ratios of the EMPG tail with arbitrary i and i = 90°, respectively. We adopt q₀ = 0.3, which is applicable for disk galaxies (Fouque et al. 1990). KS1 tail and MPG tail have q of 0.74 and 0.90, respectively. Substituting q in Equation (11), we obtain i = 45° and i = 27°, respectively.

Using Equations (7) and (11), we calculate the rotation curve along the line of sight ${\rm{\Delta }}V(r)={V}_{c}(r)\sin i$ from M_*. The black curves in Figure 12 show the rotation curves of the KS1 tail and MPG tail. The gray curves indicate the maximum velocity cases corresponding to the edge-on (i = 90°) cases of the KS1 tail and MPG tail. We find that ΔV between KS1 and the KS1 tail is significantly higher than ΔV expected by the rotation curve even in the maximum velocity case (ΔV ∼ 40 km s⁻¹ at r_p ∼ 10 kpc). This velocity excess indicates that KS1 is dynamically independent of a disk structure of the KS1 tail. Such a velocity excess is not be seen in previously known tadpole galaxies (Sánchez Almeida et al. 2013; Olmo-García et al. 2017; see Section 1). At the same time, we find MPG whose ΔV is comparable to the rotation velocity (Figure 12 bottom), indicative that MPG is a system similar to the tadpole galaxies. Thus, we do not think the methodological differences cause the discrepancy between KS1 and the tadpole galaxies.

The bottom left panel of Figure 10 indicates that KS1 and the KS1 tail are connected with a filamentary structure. One possible scenario is that KS1 is located in the filamentary structure with a large proper motion. However, KS1 is unlikely a clump in the KS1 tail due to the large SB difference with respect to the KS1 tail as shown in Section 5.1.3. The filamentary structure may be a gas stream now accreting onto the KS1 tail as shown in Figure 1 of Tumlinson et al. (2017), ¹⁹ or a tidal tail created by gravitational interactions between KS1 and the KS1 tail. In either case, we are likely to identify the metal-poor star-forming system just now infalling into the EMPG tail, which supports the idea more directly that the matter of the extremely metal-poor starbursts come from outside of the EMPG tails (Sánchez Almeida et al. 2015; see Section 1).

There is also a possibility that some other EMPGs, especially 57% of the EMPGs with large SB differences like KS1 (Section 5.1.3), have large velocity excesses with respect to the EMPG tails. To investigate such EMPGs, we need long-slit or integral-field spectroscopy for EMPGs.