EMPRESS. XII. Statistics on the Dynamics and Gas Mass Fraction of Extremely Metal-poor Galaxies

We present the demography of the dynamics and gas mass fraction of 33 extremely metal-poor galaxies (EMPGs) with metallicities of 0.015–0.195 Z ⊙ and low stellar masses of 104–108 M ⊙ in the local universe. We conduct deep optical integral field spectroscopy (IFS) for the low-mass EMPGs with the medium-high resolution (R = 7500) grism of the 8 m Subaru FOCAS IFU instrument by the EMPRESS 3D survey, and investigate the Hα emission of the EMPGs. Exploiting the resolution high enough for the low-mass galaxies, we derive gas dynamics with the Hα lines by the fitting of three-dimensional disk models. We obtain an average maximum rotation velocity (v rot) of 15 ± 3 km s−1 and an average intrinsic velocity dispersion (σ 0) of 27 ± 10 km s−1 for 15 spatially resolved EMPGs out of 33 EMPGs, and find that all 15 EMPGs have v rot/σ 0 < 1 suggesting dispersion-dominated systems. There is a clear decreasing trend of v rot/σ 0 with the decreasing stellar mass and metallicity. We derive the gas mass fraction (f gas) for all 33 EMPGs, and find no clear dependence on stellar mass and metallicity. These v rot/σ 0 and f gas trends should be compared with young high-z galaxies observed by the forthcoming JWST IFS programs to understand the physical origins of the EMPGs in the local universe.


INTRODUCTION
Classical galaxy formation theory suggests galaxy initially forms as angular-momentum supported disks (White & Rees 1978;Fall & Efstathiou 1980;Blumenthal et al. 1984).Primordial galaxies evolve into the various types of galaxies we see today involving complex interplay between different processes: accretion of cold gas, minor and major mergers, stellar and activegalactic-nuclei feedback.One way to understand the evolution of primordial galaxies and the complex interplay is to study the dynamics of high-z galaxies.Rizzo et al. (2020Rizzo et al. ( , 2021) ) analyze the kinematics of z ∼ 4 − 5 galaxies and obtain large maximum rotation velocity (v rot ) that is ∼10 times the velocity dispersion (σ 0 ).Tokuoka et al. (2022) identifies a z ∼ 9 galaxy that possibly presents clear rotation.Given that galaxies in Rizzo et al. (2020) and Tokuoka et al. (2022) reside in low-mass dark matter (DM) halos with halo masses of ∼ 10 10 M ⊙ and ∼ 10 9 M ⊙ , respectively, the disk structure may not be stable but easily disrupted by inflow or outflow.Simulations of Dekel et al. (2020) suggest a critical DM halo mass of M h < 2 × 10 11 M ⊙ , below which disk cannot survive and the galaxy becomes dispersion-dominated.
Although the dynamics of high-z galaxies can be investigated with the state-of-the-art observation facilities (e.g., James Webb Space Telescope, hereafter JWST), local dwarf galaxies with recent starbursts are also important test-beds of galaxy evolution theories due to their apparent brightness.Local galaxies are advantageous for conducting deep observations with high spectral and spatial resolutions, such as optical integral filed spectroscopy.The spatially resolved Hα recombination line can be used to trace the kinematics of ionized gas (e.g., Green et al. 2014;Barat et al. 2020).Among local dwarf galaxies, EMPGs are considered as local counterparts of high-z primordial galaxies having gas-phase metallicity (hereafter metallicity) below 10% Z ⊙ .EMPGs typically have low stellar masses ≲ 10 8 M ⊙ and high specific star formation rates ≳ 1 Gyr −1 suggestive of shallow gravitational potential and recent starburst, respectively.Kinematics of EMPGs can provide us a hint of the important mechanism (e.g., inflow/outflow) during the early stage of galaxy formation.Despite that EMPGs may differ from primordial galaxies on numerous aspects (star formation histories, stellar population, etc.), we aim to provide a clear correlation between dynamics and metallicity/stellar mass that can be extrapolated to high-z primordial galaxies.Two important quantities indicating the detailed gas dynamical state are the relative level of rotation, via the v rot /σ 0 ratio, and the mass composition, via the gas mass fraction (f gas ).
Recently, a project "Extremely Metal-Poor Representatives Explored by the Subaru Survey (EMPRESS)" has been launched (Kojima et al. 2020, here after Paper I). EMPRESS aims to select faint EMPG photometric candidates from Subaru/Hyper Suprime-Cam (HSC; Miyazaki et al. 2018) deep optical (i lim = 26 mag; Aihara et al. 2019) images, which are 2 dex deeper than those of SDSS.Conducting follow-up spectroscopic observations of the EMPG photometric candidates, EM-PRESS has identified new 12 EMPGs with low stellar masses of 10 4.2 -10 6.6 M ⊙ (Papers I, IV; Nakajima et al. 2022, hereafter Paper V;Xu et al. 2022, hereafter Paper VI). Remarkably, J1631+4426 has been reported to have a metallicity of 0.016 Z ⊙ , which is the lowest metallicity identified so far (Paper I; c.f. Thuan et al. 2022).
This paper is the twelfth paper of EMPRESS, reporting a demography of Hα kinematics of EMPGs observed with Subaru/Faint Object Camera and Spectrograph (FOCAS) IFU (Ozaki et al. 2020) in a series of the Subaru Intensive Program entitled EMPRESS 3D (PI: M. Ouchi).So far, EMPRESS has released 8 papers related to EMPGs, each of which reports the survey design (Paper I), high Fe/O ratios suggestive of massive stars (Kojima et al. 2021, hereafter Paper II;Isobe et al. 2022a, hereafter Paper IV), morphology (Isobe et al. 2021, hereafter Paper III), low-Z ends of metallicity diagnostics (Paper V), outflows (Paper VI), the shape of incident spectrum that reproduces high-ionization lines (Umeda et al. 2022, hereafter Paper VII), the primordial He abundance (Matsumoto et al. 2022, hereafter Paper VIII), and pioneer results of Hα kinematics (Isobe et al. 2022b, hereafter Paper IX).
The paper is structured as follows.Section 2 explains our observations and dataset.Section 3 describes how we derive rotation velocity, velocity dispersion and gas mass fraction.We discuss and summarize our findings in Sections 4 and 5, respectively.Throughout the paper we assume a solar metallicity of 12+log(O/H) = 8.69 (Asplund et al. 2021) and adopt a cosmological model with H 0 = 70 km s −1 Mpc −1 , Ω Λ = 0.7, and Ω m = 0.3.

Observations
In the EMPRESS 3D project, we conducted observations for the 32 targets over 9 half-nights in 2021-2022.We conducted the observations using FOCAS IFU mounted on Subaru Telescope.We took science frames using the low-resolution (R ∼ 900) 300B grism and the mid-high-resolution (R ∼ 7500) VPH680 grism (hereafter low-and high-resolution data, respectively).The low-resolution data were successfully taken for all the 32 targets (see Kimihiko Nakjima et al. in prep.).Paper IX reports the first six targets with high-resolution data taken in 2021 that enables us to study the dynamics of EMPGs.In 2022, we further obtained highresolution data for 20 targets.In total, we obtained low-resolution data for 32 objects and high-resolution data for 26 (= 6 + 20) targets.
Here we describe the observations in 2022 when we observed 21 targets.Because of the relatively high redshift of J1234+3901, we used the VPH850 grim (R ∼ 1350) to take the high-resolution data.The observation nights were April 20th, 21st, 22nd, and October 17th, 2022, with typical seeing sizes of 0.6 ′′ , 0.5 ′′ , 0.8 ′′ , and 0.4 ′′ , respectively.There were thin clouds at the beginning of observations on April 21st.On the other nights, the sky was clear.We took calibration data for flat fielding and wavelength calibration in the beginning of observa-Xu et al.
tions.We observed standard stars in the beginning or at the end of the observations.We found no detection in the high-resolution data of J1044+6306 and successfully obtained high-resolution data for 20(= 21 − 1) targets.The observations are summarized in Table 1.

Data reductions
We use a reduction pipeline software of FOCAS IFU (Ozaki et al. 2020) based on PyRAF (Tody 1986) and Astropy (Astropy Collaboration et al. 2013, 2018, 2022).The software performs bias subtraction, flat-fielding, wavelength calibration, cosmic ray removal, and flux calibration.The software outputs three-dimensional (3D) data cubes of integral field spectroscopy (IFS) with and without sky background subtraction.The 3D data cubes cover a filed-of-view (FoV) of 13.5 ′′ × 10 ′′ with 64 × 23 spaxels, which corresponds to a pixel scale of 0.215 ′′ /pix and 0.435 ′′ /pix in the x-and y-axis, respectively.For the low-resolution data, the 3D data cubes cover the wavelengths of 3500 − 8000 Å.For the high-resolution data, the 3D data cubes cover the wavelengths of 6500−7500 Å and 6000 − 10000 Å for the VPH650 and VPH850 grim, respectively.We estimate the flux uncertainties containing read-out noises and photon noises of sky and object emissions.

Deblending of spatial components
Our data includes EMPGs that have multiple spatial components as shown in the photometric images.The multiple components can also be seen in the Hα flux maps derived from our IFU data (see Figure 1 and Section 3.2).In this study, we aim to discuss the properties of individual components exploiting the spatial resolution of the IFU data.We define the components based on the morphology of the Hα flux map using the tool of source detection and deblending in Photutils, an Astropy package.We carefully choose the flux threshold to include only components that have photometric counterparts in the SDSS catalog.Twenty targets appear to have only one component of our interest.From 5 EMPGs which are J0057-0941, J2104-0035, J2115-1734, DDO 68, and I Zw 18, we extract 2 components.For J0125+0759, we extract 3 components.We label the components with suffices, where the brightest one is labeled with #1.For I Zw 18, we separate I Zw 18-NW and I Zw 18-SE.For DDO 68, we use the labels of #2 and #3 in consistency with the notations in previous studies (e.g., Pustilnik et al. 2005).Although the origin of the multiple components in one system is debatable, we treat each component as an individual EMPG in this study, which means our sample consists of 33 (= 20 + 5 × 2 + 3) EMPGs in total.

Gas mass fraction
Gas mass surface density (Σ gas ) can be estimated from the SFR surface density adopting the Kennicutt-Schmidt law (Kennicutt 1998): We estimate the SFR surface density (Σ SFR ) from the Hα flux using the relation from Kennicutt (1998), assuming the initial mass function (IMF) of Chabrier (2003): We fit a Gaussian profile to the spectrum of emission line using the low-resolution data which offers a better signal-to-noise ratio (S/N) for the Hα lines.
Gas mass fraction is defined as the ratio between the gas mass and the total baryonic mass within one effective radius: We sum up Σ gas for the spaxles within r e to obtain M gas (r < r e ).The value of r e is derived by fitting a Sersic profile to the Hα flux maps.The fitting procedure is integrated in the rotation disk models for the 15 spatially-resolved EMPGs (see Section 3.2) and conducted separately using galfit (Peng et al. 2002(Peng et al. , 2010) ) for the other 18(= 33 − 15) EMPGs.For the stellar masses, there are 15 EMPGs whose stellar masses are measured in previous studies (Table 2).To estimate the stellar masses for the other EMPGs, we first obtain the i−band magnitudes for all the 33 EMPGs from the SDSS catalog.We obtain an average mass-to-light ratio of 0.12 between the stellar mass and i−band magnitude using the 15 EMPGs with known stellar masses.For the other 18(= 33 − 15) EMPGs, we derive the stellar masses from the absolute i−band magnitudes assuming the mass-to-light ratio.We assume the effective radius of stellar component (r e, * ) can be approximated by r e and estimate M * (r < r e ) by dividing the stellar masses by 2. We check the possible systematic errors given by our analysis method.We confirm that the gas mass fraction is consistent between the 15 galaxies whose stellar masses are derived from a fixed mass-to-light ratio and the rest of the sample.Since some EMPGs are identified from multiple components in one field of view (Section 2.4), we make sure the consistency between the i−band aperture and the spaxels used for M gas (r < r e ).Interestingly, we find the multiple components in one system generally have similar f gas , implying that the multiple components may have similar star formation history.We evaluate the uncertainty of M * (r < r e ) assuming r e, * ranges from r e /2 to 2r e .We take the 0.3 dex scatter of Kennicutt-Schmidt law as the uncertainty of M gas (r < r e ).The calibration from Kennicutt (1998) may underestimate the gas mass for metal-poor galaxies (e.g., Shi et al. 2014).Therefore, we add an upper error of 1 dex to our estimation of M gas (r < r e ) following Paper IX.We propagate these uncertainties to obtain the error of f gas .The results are summarized in Table 2.In the bottom panels of Figure 2, we show f gas as a function of stellar mass and metallicity.We obtain an median value of f gas ∼ 0.9 larger than those of more massive galaxies in Barat et al. (2020), which suggests EMPGs are likely to be gas-rich systems.
The average and standard deviation of f gas is 0.8 and 0.2, respectively.Six galaxies (J0057-0941, J0943+3326, J2104-0035, I Zw 18-NW/-SE, and Leo P) are 1σ below the average having f gas < 0.6.One possibility of finding low f gas is the existence of old stellar population (e.g., I Zw 18; Vaduvescu et al. 2005;Aloisi et al. 2007).We find Leo P may be relatively gas-deficient with f gas = 0.12 +0.75 −0.08 although with a large uncertainty.value is relatively small among EMPGs, which is consistent with our results.
For our EMPGs, we find no clear correlation between f gas and stellar mass or metallicity.It may seem that only high f gas ≳ 0.9 can be found for EMPGs with M * < 10 5 M ⊙ .However, the fact that apparently bright EMPGs are preferred by our sample selection may lead to selection bias towards high f gas EMPGs.We consider the selection bias by simply assuming an Hα surface brightness of 1 × 10 −17 erg s −1 cm −2 arcsec −2 , which is roughly the detection limit of our low-resolution data (Ozaki et al. 2020).We apply the Hα surface brightness to Equations 1 and 2 to derive the limiting Σ gas for observable EMPGs.Isobe et al. (2021) measure the effective radius of 27 EMPGs and obtain r e ∼ 200 +450 −110 pc.We take the minimum (maximum) value of 100 pc (1000 pc) to integrate the Σ gas as the limiting gas mass.Finally, we calculate the limiting f gas as a function of M * using Equation 3. In the bottom-left panel of Figure 2, we show two grey regions bellow the limit f gas , where the lighter (darker) color corresponds to the case of minimum (maximum) r e values.We find the correlation between f gas and M * is possibly biased below 10 6 M ⊙ .On the other hand, there is no clear correlation between f gas and M * above 10 6 M ⊙ .

Gas kinematics
We derive the kinematical properties of our EMPGs from the Hα lines.The spatial distribution of line-ofsight velocity (v l.o.s. ) and velocity dispersion (σ) can be derived by fitting a Gaussian profile to each spaxel of the high-resolution data.For the line-of-sight velocity, we derive the velocity from the central wavelength (λ Hα ): where λ 0 represents the systemic wavelength.For EMPGs that can be fitted by a rotation disk model (see below), λ 0 is the observed wavelength at the cen- ter of the disk model.Otherwise, we adopt the central wavelength in the spaxel where the flux of Hα is largest among all the spaxels.The value of λ shift is given by the slit-width effect that is caused by a flux gradient parallel to the wavelength direction (see Section 3.2 in Paper IX) and c is the speed of light.For the velocity dispersion, we subtract the instrumental broadening (σ inst ) from the line width (σ Hα ): We estimate a typical value of σ inst = 17±2 km s −1 from the line widths of unresolved skylines, where the uncertainty is the standard deviation of σ inst from different spaxels.We show the Hα flux, velocity and dispersion maps in Figures 1 and 6-9.Assuming that the line-of-sight velocities are given by disk rotation, we can derive the maximum rotation velocity (v rot ) that can be compared to the velocity dispersion to study how EMPGs are dynamically supported.We model the disk rotation using a software named GalPak 3D (Bouché et al. 2015).We follow the method described in Paper IX to prepare the input data cube.Because GalPak 3D requires the input data cube to have the same pixel scale on the x-and y-axis, we interpolate the data cube on the y-axis to have a pixel scale of ∼ 0.217 ′′ /pix.We also correct the wavelength by the slit-width effect.We only use the spaxels within the apertures that are determined by the source detection procedure in Section 2.4 and mask out the rest of the 3D data cube.We mask out the spaxels with S/N(Hα)< 3. We calculate the 84th percentile of σ for the spaxels left and mask out the spaxels with σ larger than the 84 percentile because the spaxles with large σ could be strongly turbulent (Egorov et al. 2021).We then fit the 3D data cube by a thick disk model.Specifically, we choose a disk model with the disk height equals to one third of the effective radius.The Hα surface brightness is an exponential function of radius, i.e., Sersic profile with a Sersic index of one.We choose the arctan rotation curve with two parameters, maximum rotation velocity (v rot ) and turn-over radius (r v ).The disk model consists of 10 parameters in total that are x-and y-coordinates of the center, total flux, effective radius (r e ), r v , inclination (i), position angle, systemic velocity, v rot , and intrinsic dispersion (σ 0 ).The intrinsic dispersion is free from the broadening given by instrument, the local isotropic velocity dispersion driven by disk self-gravity, and the mixture of the line-of-sight velocities due to the disk thickness (Bouché et al. 2015).We fit the disk model to all the 33 EMPGs.For EMPGs with compact sizes, we find the best-fit r e is below the seeing size, in which case the parameters are not well constrained (see Section 4.3 in Bouché et al. 2015).We thus only report 9 spatially resolved EMPGs with reliable v max and σ 0 measurements that are shown in Table 2.The measurements of v rot and σ 0 for the 6 EMPGs given by Paper IX are also included.We obtain average values of v rot = 15 km s −1 and σ 0 = 27 km s −1 , with standard errors of 3 km s −1 and 10 km s −1 , respectively.We confirm that all of the 15(= 9 + 6) EMPGs have v rot /σ 0 < 1, indicating that they may be dispersion dominated (Förster Schreiber et al. 2009).
We show v rot /σ 0 as a function of M * and metallicity in the top panels of Figure 2. We also include the v rot /σ 0 values of dwarf galaxies investigated by the DYNAMO survey (Green et al. 2014) and the SHαDE survey (Barat et al. 2020) as comparisons.Their results are also derived from the ionized gas.We show that EMPGs have low v rot /σ 0 that is smaller than those of more massive galaxies and comparable to those of low-mass galaxies.J0057-0941-#1 6.50±0.87-2.67 7.33 −0.17 of dispersion dominated galaxies having an average v rot /σ 0 = 0.48 ± 0.28.As a comparison, dwarf galaxies (10 6 < M * < 10 9 M ⊙ ) studied in Barat et al. (2020) have an average v rot /σ 0 of 0.84.de los Reyes et al. ( 2023) also obtain low v rot /σ 0 ≲ 2 based on the stellar kinematics of local dwarf galaxies (10 7 < M * < 10 9 M ⊙ ) and suggest a positive correlation that is independent of environmental effect.We note that EMPGs are selected with low-metallicity and high specific star formation rate (log(sSFR/Gyr −1 ) ∼ 1 − 3; Kojima et al. 2020) compared to the more uniform samples used by Barat et al. (2020) and de los Reyes et al. (2023).It is curious whether the correlation between v rot /σ 0 and M * are still present for EMPGs that undergo recent star formation.We divide our sample into two stellar mass bins of M * < 10 6 M ⊙ and > 10 6 M ⊙ .We obtain v rot /σ 0 = 0.24 ± 0.16 and 0.64 ± 0.22, respectively.As shown in Figure 2, EMPGs with M * < 10 6 M ⊙ have smaller v rot /σ 0 than those with M * > 10 6 M ⊙ with at least 1σ significance.For the 6 galaxies (HS 0822+3542, DDO 68-#2, -#3, Leo P, J1452+0241, and J1631+4426) with M * < 10 6 M ⊙ , we find only weak velocity gradient in the velocity maps shown in Figure 1, consistent with the conclusion that they may not present any rotation.For local group dwarf spheroidals with 10 3.5 M ⊙ < M * < 10 8 M ⊙ , Wheeler+17 study the stellar kinematics and find no clear correlation between v rot /σ 0 and M * .delosReyes+23 also obtain low v rot /σ 0 based on the stellar kinematics of local dwarf galaxies and suggest a positive correlation that is independent of environmental effect.We note that our EMPGs are different from the dwarf galaxies investigated by Wheeler+17 and delosReyes+23 as EMPGs are young systems that probably undergo the first star formation activity.
In this study we present a reasonably large sample of EMPGs to investigate the correlation between v rot /σ 0 and metallicity.We find a positive correlation as shown in the top right panel of Figure 2 with a Pearson coefficient of 0.50 (p = 0.06).The small v rot /σ 0 for the EMPGs with the smallest metallicity probably suggests that they are experiencing the first star formation activity due to gas inflow.To test this hypothesis, we include the classification of EMPGs based on the spatial distribution of metallicity that is taken from a companion paper.Kimihiko Nakajima et al. (in prep.)divide our EMPGs into four categories: Category A with a metal poor region in the center and relatively metal enriched around it, Category B with only metal poor region, Category C in the transitioned phase, and the unresolved Category D. One scenario to explain the metallicity distribution of Category A EMPGs is that cold gas inflow accretes directly into the center of EMPGs (e.g., Sánchez Almeida et al. 2014, Kimihiko Nakajima et al. in prep.).In Figure 3, we show v rot /σ 0 as a function of metallicity with each EMPG color coded by the categories.Surprisingly, EMPGs of Category A have v rot /σ 0 ∼ 0.68 ± 0.10 on average which is larger than that v rot /σ 0 ∼ 0.34 ± 0.08 for EMPGs of Category B, at 1σ significance.In a Category A EMPG, the metal poorest region is surrounded by the metal enriched regions that may represent an older stellar population.The older stellar population may have already formed a rotation disk which is destroyed by the latest gas inflow.For a Category B EMPG, neither older stellar population nor rotation are detected.The EMPGs in Category B may undergo its first chemical evolutionary event that could be triggered by gas accretion.
Whether stable rotation disk can build up in low-mass star-forming galaxies like EMPGs needs to be tested with simulations (see also the discussions in Paper IX). Hopkins et al. (2023) show that a sufficiently centrallyconcentrated mass profile is crucial for the initial formation of a disk.However, it is still a difficult task to resolve the profile of mass concentration (e.g., Genzel et al. 2020) for compact low-mass young galaxies by observations.High spatial resolution with future observational facilities may help us understand how EMPGs start the recent star formation and why they appear to be dispersion dominated.On the other hand, observations of primordial galaxies at high-z (e.g., with JWST) are useful to reveal the relation between dynamics and star formation at the early stage of galaxy formation.

Mass profiles
For the 15 EMPGs with v rot and σ 0 measurements, we can compare the radial profile of gas mass and stellar mass to that of the dynamical mass.The dynamical mass enclosed by radius r can be calculated with: We derive the enclosed dynamical, stellar, gas, and DM mass enclosed by radius r following the procedures in Paper IX.We follow the same procedure as Paper IX and assume a Sersic profile and Navarro-Frenk-White (NFW; Navarro et al. 1996) profile for the stellar mass and DM mass, respectively.The results are plotted in Figure 4 for the 15 EMPGs, including the 6 EMPGs presented in Paper IX.For 14 out of the 15 EMPGs, the mass profile of gas mass contribute to most of the dynamical mass, which is consistent with the large f gas we derived.In general, we find EMPGs are likely puffly gasrich systems supported by the random motion that may be supplied by gas inflow, stellar feedback, or galaxygalaxy interaction.

Toomre Q parameter
The Toomre Q parameter is used by many kinematic studies as an indicator of the gravitational stability of disk galaxies (e.g., Genzel et al. 2011).In general, if the Q value of a rotating disk is greater than unity (i.e., Q > 1), the disk is thought to be gravitationally stable.On the other hand, the disk is gravitationally unstable if Q < 1.However, it remains an open question on what observable scales the Toomre Q parameter is a reliable indicator of gravitational stability (e.g., Romeo & Agertz 2014).Paper IX also suggests that it is unclear if this criterion is applicable for the EMPGs because they may not have rotating disks.To compare with previous kinematics studies, we calculate the average of Q within a disk that is called the global Q (e.g., Aumer et al. 2010) in the same manner as Paper IX: where the parameter a ranges from 1 to 2 depending on the gas distribution.We assume a = √ 2 which corresponds to a disk with constant rotational velocity (Genzel et al. 2011).The differences of Toomre Q parameters is less than a factor of 2 if a different value of a is assumed.
We obtain a global Q of 1 − 70 for 15 EMPGs with a median value of 4.Although all of the 15 EMPGs have global Q larger than unity suggestive of stable disk, the large global Q is inconsistent with the star-forming nature of EMPGs as pointed out in Paper IX.In Figure 5 we plot the global Q as a function of stellar mass and metallicity.We find no clear correlation between the global Q and stellar mass or metallicity.It is possible that EMPGs have a large variety of dynamics, or the global Q does not provide a good constraint on the gravitational stability of EMPGs.It is difficult to conclude whether or not EMPGs generally have stable disk without high-resolution observations for both gas and stellar component (e.g., Romeo 2020; Romeo et al. 2020) using next-generation facilities such as ngVLA.

SUMMARY
We present demography of the dynamics and gasmass fraction of 33 EMPGs with metallicities of 0.015 − 0.195 Z ⊙ and low stellar masses of 10 4 − 10 8 M ⊙ in the local universe.We conduct deep optical integralfield spectroscopy (IFS) for the low-mass EMPGs with the medium high resolution (R = 7500) grism of the 8m-Subaru FOCAS IFU instrument by the EMPRESS 3D survey, and investigate Hα emission of the EMPGs (Section 2).Exploiting the resolution high enough for the low-mass galaxies, we derive gas dynamics with the Hα lines by the fitting of 3-dimensional disk models.We obtain an average maximum rotation velocity (v rot ) of 15±3 km s −1 and an average intrinsic velocity dispersion (σ 0 ) of 27 ± 10 km s −1 for 15 spatially resolved EMPGs out of the 33 EMPGs, and find that all of the 15 EMPGs have v rot /σ 0 < 1 suggesting dispersion dominated systems (Section 3.2).There is a clear decreasing trend of v rot /σ 0 with the decreasing stellar mass and metallicity (Section 4).We derive the gas mass fraction (f gas ) for all of the 33 EMPGs, and find no clear dependence on stellar mass and metallicity (Section 3.1).Our results suggest EMPGs are gas-rich dispersion-dominated systems, whose dynamical properties likely depend on the current stellar mass and previous star formation history.
Xu et al.

Figure 1 .
Figure 1.From left to right: SDSS cut-out, Hα flux map, line-of-sight velocity map, and velocity dispersion map for each EMPG whose high-resolution data is reported in this study and Paper IX. Spaxels with S/N(Hα) > 3 are plotted.The red rectangle on the SDSS cut-out indicates the pointing position of our IFU observations while the arrow indicates the direction of x-axis.The x-and y-axes are presented in arcsec.The black contours represent the Hα flux in the range of log(FHα/erg s −1 cm −2 ) = −17 to −14.5 with a step of 0.5 dex.The red circles highlight the apertures we obtained by source detection (see Section 2.4).Within the apertures we fit disk rotation models.Bernstein-Cooper et al. (2014) conduct Hi observations and obtain f gas ∼ 0.7 for Leo P. They claim the f gas

Figure 3 .
Figure 3. Same as the top-right panel of Figure 2 but colorcoded by the categories given by Kimihiko Nakajima et al. (in prep.).The y-axis is changed to linear scale.The category A EMPGs have surrounding metal enriched regions that may come from older stellar population while category B EMPGs only show metal poor regions given by the recent star formation.The category C EMPGs are possibly in a transition stage.

Figure 4 .
Figure 4. Enclosed mass profiles.The red, yellow, cyan, and black curves represent dynamical, stellar, gas, and DM mass profiles, respectively.The vertical dotted lines show the effective radius of Hα.The edge of the plots correspond to the outer most radii used for the kinematic analysis.

Figure 5 .
Figure 5.The global Toomre Q parameter as a function of M * (left) and metallicity (right).The red triangles indicate the four EMPGs with large global Toomre Q values that are out of the y-axis range.All of the EMPGs shown in this plot have Q > 1.

Table 1 .
Summary of medium-high resolution FOCAS-IFU observations

Table 2 .
Summary of Galaxy Properties