arXiv subjects

Akinori Matsumoto

Publications and source records attributed to Akinori Matsumoto.

14 recordsLinked to original sources

arXiv2026

A New Constraint on the Optical Depth from the Reionization History Independent of CMB Large-Scale E-Mode Polarization

Recent studies report a mild discrepancy between BAO and CMB measurements within the $Λ$CDM framework. This discrepancy could be explained if the optical depth $τ$ inferred from the CMB large-scale E-mode polarization is underestimated, which may be biased by foreground-subtraction or instrumental systematics. In this work, we present a determination of $τ$ independent of the large-scale E-mode polarization, using the latest measurements of the redshift evolution of the neutral hydrogen fraction $x_\mathrm{HI}(z)$, which is constrained by Lyman-$α$ forest and damping-wing absorption measurements at $z\sim5$--$14$, based on ground-based optical and JWST observations. Combining $x_\mathrm{HI}(z)$ with the Planck CMB power spectra excluding the large-scale E-mode polarization, we obtain $τ=0.0552^{+0.0019}_{-0.0026}(\mathrm{stat.})^{+0.0075}_{-0.0049}(\mathrm{sys.})$, where the systematic uncertainty accounts for possible absorption-modeling effects in the inference of $x_\mathrm{HI}(z)$. This constraint is consistent with previous CMB results including the large-scale E-mode polarization. With this measurement, we resolve the degeneracy in the $τ$--$Ω_{\rm m}$ plane and find a $2.4σ$ tension with the DESI DR2 BAO results, thereby confirming the claimed mild discrepancy suggestive of physics beyond $Λ$CDM. Finally, we derive an upper limit on the sum of neutrino masses, $Σm_ν< 0.0550\,(0.0717)\,{\rm eV}$ at the 95\%\,(99\%) confidence level. This limit favors the normal mass ordering and, when combined with the lower limits from neutrino oscillation experiments, yields a further constraint, $Σm_ν= 0.0594_{-0.0007}^{+0.0113}\,{\rm eV}$. However, the cosmological upper limit and the oscillation-based lower limit show a mild $2.2σ$ tension, providing an independent indication of possible physics beyond $Λ$CDM.

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arXiv2026

EMPRESS. XV. A New Determination of the Primordial Helium Abundance Suggesting a Moderately Low $Y_\mathrm{P}$ Value

We present a new constraint on the primordial helium abundance, $Y_\mathrm{P}$, based on Subaru observations. A major source of uncertainty in previous $Y_\mathrm{P}$ determinations is the lack of extremely metal-poor galaxies (EMPGs; $0.01-0.1\,Z_\odot$), which have metallicities a few to ten times lower than the metal-poor galaxies (MPGs; $0.1-0.4\,Z_\odot$) predominantly used in earlier studies, requiring substantial extrapolation to zero metallicity. Here, we perform Subaru near-infrared spectroscopy of 29 galaxies, including 14 EMPGs. By incorporating existing optical spectra, we derive He/H for each galaxy using photoionization modeling of helium and hydrogen emission lines, including the He \textsc{i} 10830Å\, line to break the density--temperature degeneracy. After carefully selecting galaxies with robust He/H determinations, and adding 58 galaxies from previous studies, we obtain $Y_\mathrm{P} = 0.2402^{+0.0040}_{-0.0040}$. This $Y_\mathrm{P}$ value is $\sim1σ$ lower than most of the previous estimates, but agrees with recent determinations using EMPGs and the CMB constraint from the Atacama Cosmology Telescope (ACT) experiment. Our result indicates $N_\mathrm{eff} = 2.54^{+0.20}_{-0.25}$, showing a mild ($\sim2σ$) tension with the Standard Model and Planck results. These tensions may suggest a nonzero lepton asymmetry $(ξ_\mathrm{e}\neq0)$, which would alleviate the tension with $ξ_\mathrm{e} = 0.05^{+0.02}_{-0.03}$. More observations of EMPGs and further assessments of systematic uncertainties are essential to test the potential tension more rigorously.

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arXiv2025

Near-infrared Variability Detected in the Young Star-Forming Dwarf Galaxy SBS 0335-052E

SBS~0335-052E is a young star-forming dwarf galaxy with a total stellar mass of $M_{*} \lesssim 10^{8}~M_{\odot}$ and an extremely low metallicity ($Z \sim 1/40~Z_{\odot}$), which has long been considered to be devoid of an active galactic nucleus (AGN). Here we report the detection of temporal flux variability of SBS~0335-052E in near-infrared (NIR) 3-4\ ${\rm μ}$m bands on timescales of several years, showing dimming and brightening of up to 50\% over 14~years, based on archival data from the Wide-field Infrared Survey Explorer. Our spectral energy distribution (SED) fitting of archival ultraviolet (UV)-NIR photometry, including AGN SED models, indicates that the variable NIR emission arises from an edge-on AGN dust torus. The UV-optical emission from the accretion disk is obscured and does not reach us, leading to the dominance of the host galaxy's young stellar population in the UV-optical wavelengths. This analysis favors the presence of a Compton-thick, heavily obscured AGN in SBS~0335-052E, consistent with its observed X-ray weakness. From the SED fitting, we estimate an AGN bolometric luminosity of $L_{\rm bol} = 1.2\times10^{43}\ {\rm erg\ s^{-1}}$, which implies a black hole mass of $M_{\rm BH} \simeq 10^{5}\ M_\odot$ if the AGN is accreting at the Eddington limit. If confirmed, SBS~0335-052E would be the least massive galaxy known to host an AGN, likely harboring an intermediate-mass black hole.

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arXiv2025

Probing Chemical Enrichment in Extremely Metal-Poor Galaxies

The chemical composition of galaxies offers vital insights into their formation and evolution. In particular, the relationship between helium abundance (He/H) and metallicity serves as a key diagnostic for estimating the primordial helium yield from Big Bang nucleosynthesis. We investigate the chemical enrichment history of low-metallicity galaxies, focusing especially on extremely metal-poor galaxies (EMPGs), using one-zone chemical evolution models. Adopting elemental yields from Limongi and Chieffi (2018), our models reach He/H ~ 0.089 at (O/H) $\times 10^5<20$, yet they fall short of reproducing the elevated He/H values observed in low redshift dwarf galaxies. In contrast, the observed Fe/O ratios in EMPGs are successfully reproduced using both the Nomoto et al. (2013) and Limongi and Chieffi (2018) yield sets. To address the helium discrepancy, we incorporate supermassive stars (SMSs) as Pop III stars in our models. We find that SMSs can significantly enhance He/H, depending on the mass-loss prescription. When only 10 percent of the SMS mass is ejected, the model yields the steepest slope in the (O/H) $\times 10^5$ - He/H relation. Alternatively, if the entire outer envelope up to the CO core is expelled, the model can reproduce the high He/H ratios observed in high-redshift galaxies (He/H > 0.1). Additionally, these SMS-enriched models also predict elevated N/O ratios, in agreement with recent JWST observations of the early universe.

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arXiv2024

EMPRESS. X. Spatially resolved mass-metallicity relation in extremely metal-poor galaxies: evidence of episodic star-formation fueled by a metal-poor gas infall

Using the Subaru/FOCAS IFU capability, we examine the spatially resolved relationships between gas-phase metallicity, stellar mass, and star-formation rate surface densities (Sigma_* and Sigma_SFR, respectively) in extremely metal-poor galaxies (EMPGs) in the local universe. Our analysis includes 24 EMPGs, comprising 9,177 spaxels, which span a unique parameter space of local metallicity (12+log(O/H) = 6.9 to 7.9) and stellar mass surface density (Sigma_* ~ 10^5 to 10^7 Msun/kpc^2), extending beyond the range of existing large integral-field spectroscopic surveys. Through spatially resolved emission line diagnostics based on the [NII] BPT-diagram, we verify the absence of evolved active galactic nuclei in these EMPGs. Our findings reveal that, while the resolved mass-metallicity relation exhibits significant scatter in the low-mass regime, this scatter is closely correlated with local star-formation surface density. Specifically, metallicity decreases as Sigma_SFR increases for a given Sigma_*. Notably, half of the EMPGs show a distinct metal-poor horizontal branch on the resolved mass-metallicity relation. This feature typically appears at the peak clump with the highest Sigma_* and Sigma_SFR and is surrounded by a relatively metal-enriched ambient region. These findings support a scenario in which metal-poor gas infall fuels episodic star formation in EMPGs, consistent with the kinematic properties observed in these systems. In addition, we identify four EMPGs with exceptionally low central metallicities (12+log(O/H) <~ 7.2), which display only a metal-poor clump without a surrounding metal-rich region. This suggests that such ultra-low metallicity EMPGs, at less than a few percent of the solar metallicity, may serve as valuable analogs for galaxies in the early stages of galaxy evolution.

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arXiv2024

SILVERRUSH. XIV. Lya Luminosity Functions and Angular Correlation Functions from ~20,000 Lya Emitters at z~2.2-7.3 from upto 24 ${\rm deg}^2$ HSC-SSP and CHORUS Surveys: Linking the Post-Reionization Epoch to the Heart of Reionization

We present the luminosity functions (LFs) and angular correlation functions (ACFs) derived from 18,960 Ly$α$ emitters (LAEs) at $z=2.2-7.3$ over a wide survey area of $\lesssim24 {\rm deg^2}$ that are identified in the narrowband data of the Hyper Suprime-Cam Subaru Strategic Program (HSC-SSP) and the Cosmic HydrOgen Reionization Unveiled with Subaru (CHORUS) surveys. Confirming the large sample with the 241 spectroscopically identified LAEs, we determine Ly$α$ LFs and ACFs in the brighter luminosity range down to $0.5L_{\star}$, and confirm that our measurements are consistent with previous studies but offer significantly reduced statistical uncertainties. The improved precision of our ACFs allows us to clearly detect one-halo terms at some redshifts, and provides large-scale bias measurements that indicate hosting halo masses of $\sim 10^{11} M_\odot$ over $z\simeq 2-7$. By comparing our Ly$α$ LF (ACF) measurements with reionization models, we estimate the neutral hydrogen fractions in the intergalactic medium to be $x_{\rm \HI}<0.05$ (=${0.06}^{+0.12}_{-0.03}$), $0.15^{+0.10}_{-0.08}$ (${0.21}^{+0.19}_{-0.14}$), $0.18^{+0.14}_{-0.12}$, and $0.75^{+0.09}_{-0.13}$ at $z=5.7$, $6.6$, $7.0$, and $7.3$, respectively. Our findings suggest that the neutral hydrogen fraction remains relatively low, $x_{\rm \HI} \lesssim 0.2$, at $z=5-7$, but increases sharply at $z > 7$, reaching $x_{\rm \HI} \sim 0.9$ by $z \simeq 8-9$, as indicated by recent JWST studies. The combination of our results from LAE observations with recent JWST observations suggests that the major epoch of reionization occurred around $z \sim 7-8$, likely driven by the emergence of massive sources emitting significant ionizing photons.

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arXiv2024

Balmer Decrement Anomalies in Galaxies at z ~ 6 Found by JWST Observations: Density-Bounded Nebulae or Excited H I Clouds?

We investigate the physical origins of the Balmer decrement anomalies in GS-NDG-9422 (Cameron et al. 2023) and RXCJ2248-ID (Topping et al. 2024) galaxies at $z\sim 6$ whose $\mathrm{H}α/\mathrm{H}β$ values are significantly smaller than $2.7$, the latter of which also shows anomalous $\mathrm{H}γ/\mathrm{H}β$ and $\mathrm{H}δ/\mathrm{H}β$ values beyond the errors. Because the anomalous Balmer decrements are not reproduced under the Case B recombination, we explore the nebulae with the optical depths smaller and larger than the Case B recombination by physical modeling. We find two cases quantitatively explaining the anomalies; 1) density-bounded nebulae that are opaque only up to around Ly$γ$-Ly8 transitions and 2) ionization-bounded nebulae partly/fully surrounded by optically-thick excited H{\sc i} clouds. The case of 1) produces more H$β$ photons via Ly$γ$ absorption in the nebulae, requiring fine tuning in optical depth values, while this case helps ionizing photon escape for cosmic reionization. The case of 2) needs the optically-thick excited H{\sc i} clouds with $N_2\simeq 10^{12}-10^{13}$ $\mathrm{cm^{-2}}$, where $N_2$ is the column density of the hydrogen atom with the principal quantum number of $n=2$. Interestingly, the high $N_2$ values qualitatively agree with the recent claims for GS-NDG-9422 with the strong nebular continuum requiring a number of $2s$-state electrons and for RXCJ2248-ID with the dense ionized regions likely coexisting with the optically-thick clouds. While the physical origin of the optically-thick excited H{\sc i} clouds is unclear, these results may suggest gas clouds with excessive collisional excitation caused by an amount of accretion and supernovae in the high-$z$ galaxies.

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arXiv2024

Strong He I Emission Lines in High N/O Galaxies at $z \sim 6$ Identified in JWST Spectra: High He/H Abundance Ratios or High Electron Densities?

We present HeI/H$β$-flux and He/H-abundance ratios in three JWST galaxies with significant constraints on N/O-abundance ratios, GS-NDG-9422, RXCJ2248-ID, and GLASS150008 at $z\sim 6$ mostly with the spectroscopic coverage from HeI$λ$4471 and HeII$λ$4686 to HeI$λ$7065, comparing with 68 local-dwarf galaxies. We find that these high-$z$ galaxies present strong HeI emission with HeI/H$β$ flux ratios generally larger than those of local-dwarf galaxies. We derive He/H with all of the detected HeI, HeII, and $2-3$ hydrogen Balmer lines in the same manner as the local He/H determination conducted for cosmology studies. These high-$z$ galaxies show He overabundance He/H$\gtrsim 0.10$ or high electron density $n_\mathrm{e}\sim 10^{3-4}$ cm$^{-3}$ much larger than local values at low O/H, $12+\log \mathrm{(O/H)}=7-8$. In contrast, we obtain low He/H and $n_\mathrm{e}$ values for our local-dwarf galaxies by the same technique with the same helium and hydrogen lines, and confirm that the difference between the high-$z$ and local-dwarf galaxies are not mimicked by systematics. While two scenarios of 1) He overabundance and 2) high electron density are not clearly concluded, we find that there is a positive correlation on the He/H-N/O or $n_\mathrm{e}$-N/O plane by the comparison of the high-$z$ and local-dwarf galaxies. The scenario 1) suggests that the overabundant helium and nitrogen are not explained by the standard chemical enrichment of core-collapse supernovae, but the CNO-cycle products and equilibrium ratios, respectively. The scenario 2) indicates that the strong helium lines are originated from the central dense clouds of the high-$z$ galaxies by excessive collisional excitation.

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arXiv2024

EMPRESS. XIV. Strong High Ionization Lines of Young Galaxies at $z=0-8$: Ionizing Spectra Consistent with the Intermediate Mass Black Holes with $M_{\rm BH}\sim 10^3-10^6\ M_\odot$

We present ionizing spectra estimated at 13.6--100 eV for ten dwarf galaxies with strong high ionization lines of He {\sc {ii}}$λ$4686 and [Ne {\sc{v}}]$λ$3426 ([Ne {\sc{iv}}]$λ$2424) at $z=0$ ($z=8$) that are identified in our Keck/LRIS spectroscopy and the literature (the JWST ERO program). With the flux ratios of these high ionization lines and $>10$ low-ionization lines of hydrogen, helium, oxygen, neon, and sulfur, we determine ionizing spectra consisting of stellar and non-thermal power-law radiation by photoionization modeling with free parameters of nebular properties including metallicity and ionization parameter, cancelling out abundance ratio differences. We find that all of the observed flux ratios are well reproduced by the photoinization models with the power law index $α_{\rm EUV}$ of $α_{\rm EUV}\sim (-1)-0$ and the luminosity $L_{\rm EUV}$ of $L_{\rm EUV}\sim 10^{40}-10^{42}$ erg s$^{-1}$ at $\sim 55-100$ eV for six galaxies, while four galaxies include large systematics in $α_{\rm EUV}$ caused by stellar radiation contamination. We then compare $α_{\rm EUV}$ and $L_{\rm EUV}$ of these six galaxies with those predicted by the black hole (BH) accretion disk models, and find that $α_{\rm EUV}$ and $L_{\rm EUV}$ are similar to those of the intermediate mass black holes (IMBHs) in BH accretion disk models {albeit with possibilities of the other scenarios.} Confirming these results with a known IMBH having a mass $M_{\rm BH}$ of $M_{\rm BH}=10^{5.75} \ M_\odot$, we find that four local galaxies and one $z=7.665$ galaxy have ionizing spectra consistent with those of IMBHs with $M_{\rm BH} \sim 10^3-10^5 \ M_\odot$.

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arXiv2024

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

We present demography of the dynamics and gas-mass fraction of 33 extremely metal-poor galaxies (EMPGs) with metallicities of $0.015-0.195~Z_\odot$ and low stellar masses of $10^4-10^8~M_\odot$ 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 8m-Subaru FOCAS IFU instrument by the EMPRESS 3D survey, and investigate H$α$ emission of the EMPGs. Exploiting the resolution high enough for the low-mass galaxies, we derive gas dynamics with the H$α$ lines by the fitting of 3-dimensional disk models. We obtain an average maximum rotation velocity ($v_\mathrm{rot}$) of $15\pm3~\mathrm{km~s^{-1}}$ and an average intrinsic velocity dispersion ($σ_0$) of $27\pm10~\mathrm{km~s^{-1}}$ for 15 spatially resolved EMPGs out of the 33 EMPGs, and find that all of the 15 EMPGs have $v_\mathrm{rot}/σ_0<1$ suggesting dispersion dominated systems. There is a clear decreasing trend of $v_\mathrm{rot}/σ_0$ with the decreasing stellar mass and metallicity. We derive the gas mass fraction ($f_\mathrm{gas}$) for all of the 33 EMPGs, and find no clear dependence on stellar mass and metallicity. These $v_\mathrm{rot}/σ_0$ and $f_\mathrm{gas}$ 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.

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arXiv2023

SILVERRUSH. XIII. A Catalog of 20,567 Ly$α$ Emitters at $z=2-7$ Identified in the Full-depth Data of the Subaru/HSC-SSP and CHORUS Surveys

We present 20,567 Ly$α$ emitters (LAEs) at $z=2.2-7.3$ that are photometrically identified by the SILVERRUSH program in a large survey area up to 25 deg$^2$ with deep images of five broadband filters (grizy) and seven narrowband filters targeting Ly$α$ lines at $z=2.2$, $3.3$, $4.9$, $5.7$, $6.6$, $7.0$, and $7.3$ taken by the Hyper Suprime-Cam Subaru Strategic Program (HSC-SSP) and the Cosmic HydrOgen Reionization Unveiled with Subaru (CHORUS) survey. We select secure $>5σ$ sources showing narrowband color excesses via Ly$α$ break screening, taking into account the spatial inhomogeneity of limiting magnitudes. After removing spurious sources by careful masking and visual inspection of coadded and multi-epoch images obtained over the 7 yr of the surveys, we construct LAE samples consisting of 6995, 4641, 726, 6124, 2058, 18, and 5 LAEs at $z=2.2$, 3.3, 4.9, 5.7, 6.6, 7.0, and 7.3, respectively, although the $z=7.3$ candidates are tentative. Our LAE catalogs contain 241 spectroscopically confirmed LAEs at the expected redshifts from previous work. We demonstrate that the number counts of our LAEs are consistent with previous studies with similar LAE selection criteria. The LAE catalogs will be made public on our project webpage with detailed descriptions of the content and ancillary information about the masks and limiting magnitudes.

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arXiv2023

EMPRESS. IX. Extremely Metal-Poor Galaxies are Very Gas-Rich Dispersion-Dominated Systems: Will JWST Witness Gaseous Turbulent High-z Primordial Galaxies?

We present kinematics of 6 local extremely metal-poor galaxies (EMPGs) with low metallicities ($0.016-0.098\ Z_{\odot}$) and low stellar masses ($10^{4.7}-10^{7.6} M_{\odot}$). Taking deep medium-high resolution ($R\sim7500$) integral-field spectra with 8.2-m Subaru, we resolve the small inner velocity gradients and dispersions of the EMPGs with H$α$ emission. Carefully masking out sub-structures originated by inflow and/or outflow, we fit 3-dimensional disk models to the observed H$α$ flux, velocity, and velocity-dispersion maps. All the EMPGs show rotational velocities ($v_{\rm rot}$) of 5--23 km s$^{-1}$ smaller than the velocity dispersions ($σ_{0}$) of 17--31 km s$^{-1}$, indicating dispersion-dominated ($v_{\rm rot}/σ_{0}=0.29-0.80<1$) systems affected by inflow and/or outflow. Except for two EMPGs with large uncertainties, we find that the EMPGs have very large gas-mass fractions of $f_{\rm gas}\simeq 0.9-1.0$. Comparing our results with other H$α$ kinematics studies, we find that $v_{\rm rot}/σ_{0}$ decreases and $f_{\rm gas}$ increases with decreasing metallicity, decreasing stellar mass, and increasing specific star-formation rate. We also find that simulated high-$z$ ($z\sim 7$) forming galaxies have gas fractions and dynamics similar to the observed EMPGs. Our EMPG observations and the simulations suggest that primordial galaxies are gas-rich dispersion-dominated systems, which would be identified by the forthcoming James Webb Space Telescope (JWST) observations at $z\sim 7$.

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arXiv2022

EMPRESS. VIII. A New Determination of Primordial He Abundance with Extremely Metal-Poor Galaxies: A Suggestion of the Lepton Asymmetry and Implications for the Hubble Tension

The primordial He abundance $Y_\mathrm{P}$ is a powerful probe of cosmology. Currently, $Y_\mathrm{P}$ is best determined by observations of metal-poor galaxies, while there are only a few known local extremely metal-poor ($<0.1 Z_\odot$) galaxies (EMPGs) having reliable He/H measurements with HeI$λ$10830 near-infrared (NIR) emission. Here we present deep Subaru NIR spectroscopy for 10 EMPGs. Combining the existing optical data, He/H values of 5 out of the 10 EMPGs are reliably derived by the Markov chain Monte Carlo algorithm. Adding the existing 3 EMPGs and 51 moderately metal-poor ($0.1-0.4 Z_\odot$) galaxies with reliable He/H estimates, we obtain $Y_\mathrm{P}=0.2370^{+0.0034}_{-0.0033}$ by linear regression in the $\mathrm{(He/H)}-\mathrm{(O/H)}$ plane, where we increase the number of EMPGs from 3 to 8 anchoring He/H of the most metal-poor gas in galaxies. Although our $Y_\mathrm{P}$ measurement and previous measurements are consistent, our result is slightly ($\sim 1σ$) smaller due to our EMPGs. With our $Y_\mathrm{P}$ and the existing primordial deuterium $D_\mathrm{P}$ measurement, we constrain the effective number of neutrino species $N_\mathrm{eff}$ and the baryon-to-photon ratio $η$ showing $\gtrsim 1-2σ$ tensions with the Standard Model and Planck Collaboration et al. (2020). Motivated by the tensions, we allow the degeneracy parameter of electron-neutrino $ξ_e$ to vary as well as $N_\mathrm{eff}$ and $η$. We obtain $ξ_e = 0.05^{+0.03}_{-0.02}$, $N_\mathrm{eff}=3.11^{+0.34}_{-0.31}$, and $η\times10^{10}=6.08^{+0.06}_{-0.06}$ from the $Y_\mathrm{P}$ and $D_\mathrm{P}$ measurements with a prior of $η$ taken from Planck Collaboration et al. (2020). Our constraints suggest a lepton asymmetry and allow for a high value of $N_\mathrm{eff}$ within the $1σ$ level, which could mitigate the Hubble tension.

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arXiv2022

EMPRESS. VII. Ionizing Spectrum Shapes of Extremely Metal-Poor Galaxies: Uncovering the Origins of Strong HeII and the Impact on Cosmic Reionization

Strong high-ionization lines such as HeII of young galaxies are puzzling at high and low redshift. Although recent studies suggest the existence of non-thermal sources, whether their ionizing spectra can consistently explain multiple major emission lines remains a question. Here we derive the general shapes of the ionizing spectra for three local extremely metal-poor galaxies (EMPGs) that show strong HeII$λ$4686. We parameterize the ionizing spectra composed of a blackbody and power-law radiation mimicking various stellar and non-thermal sources. We use photoionization models for nebulae, and determine seven parameters of the ionizing spectra and nebulae by Markov Chain Monte Carlo methods, carefully avoiding systematics of abundance ratios. We obtain the general shapes of ionizing spectra explaining $\sim 10$ major emission lines within observational errors with smooth connections from observed X-ray and optical continua. We find that an ionizing spectrum of one EMPG has a blackbody-dominated shape, while the others have convex downward shapes at $>13.6$ eV, which indicate a diversity of the ionizing spectrum shapes. We confirm that the convex downward shapes are fundamentally different from ordinary stellar spectrum shapes, and that the spectrum shapes of these galaxies are generally explained by the combination of the stellar and ultra-luminous X-ray sources. Comparisons with stellar synthesis models suggest that the diversity of the spectrum shapes arises from differences in the stellar age. If galaxies at $z\gtrsim 6$ are similar to the EMPGs, high energy ($>54.4$ eV) photons of the non-stellar sources negligibly contribute to cosmic reionization due to relatively weak radiation.

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