arXiv subjects

Naoto Kobayashi

Publications and source records attributed to Naoto Kobayashi.

At least 37 records · Page 2Linked to original sources

arXiv2022

Effective temperatures of red supergiants estimated from line-depth ratios of iron lines in the YJ bands, 0.97--1.32 micron

Determining the effective temperatures (Teff) of red supergiants (RSGs) observationally is important in many fields of stellar physics and galactic astronomy, yet some significant difficulties remain due to model uncertainty originating majorly in the extended atmosphere of RSGs. Here we propose the line-depth ratio (LDR) method in which we use only Fe I lines. As opposed to the conventional LDR method with lines of multiple species involved, the LDR of this kind is insensitive to the surface gravity effects and expected to circumvent the uncertainty originating in the upper atmosphere of RSGs. Therefore, the LDR--Teff relations that we calibrated empirically with red giants may be directly applied to RSGs, though various differences, e.g., caused by the three-dimensional non-LTE effects, between the two groups of objects need to be kept in mind. Using the near-infrared YJ-band spectra of nine well-known solar-metal red giants observed with the WINERED high-resolution spectrograph, we selected 12 pairs of Fe I lines least contaminated with other lines. Applying their LDR--Teff relations to ten nearby RSGs, the resultant Teff with the internal precision of 30--70 K shows good agreement with previous observational results assuming one-dimensional LTE and with Geneva's stellar evolution model. We found no evidence of significant systematic bias caused by various differences, including those in the size of the non-LTE effects, between red giants and RSGs except for one line pair which we rejected because the non-LTE effects may be as large as ~250 K. Nevertheless, it is difficult to evaluate the systematic bias, and further study is required, e.g., with including the three-dimensional non-LTE calculations of all the lines involved.

astro-ph.SR↗

arXiv2022

A Very Metal-poor RR Lyrae Star with a Disk Orbit Found in the Solar Neighborhood

Metal-deficient stars are important tracers for understanding the early formation of the Galaxy. Recent large-scale surveys with both photometric and spectroscopic data have reported an increasing number of metal-deficient stars whose kinematic features are consistent with those of the disk stellar populations. We report the discovery of an RR~Lyrae variable (hereafter RRL) that is located within the thick disk and has an orbit consistent with the thick-disk kinematics. Our target RRL (HD 331986) is located at around 1 kpc from the Sun and, with V=11.3, is among the 130 brightest RRLs known so far. However, this object was scarcely studied because it is in the midplane of the Galaxy, the Galactic latitude around -1 deg. Its near-infrared spectrum (0.91-1.32 micron) shows no absorption line except hydrogen lines of the Paschen series, suggesting [Fe/H] less than -2.5. It is the most metal-deficient RRL, at least, among the RRLs whose orbits are consistent with the disk kinematics, although we cannot determine to which of the disk and the halo it belongs. This unique RRL would provide us with essential clues for studying the early formation of stars in the inner Galaxy with further investigations, including high-resolution optical spectroscopy.

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arXiv2021

Discovery of the Fastest Early Optical Emission from Overluminous SN Ia 2020hvf: A Thermonuclear Explosion within a Dense Circumstellar Environment

In this Letter we report a discovery of a prominent flash of a peculiar overluminous Type Ia supernova, SN 2020hvf, in about 5 hours of the supernova explosion by the first wide-field mosaic CMOS sensor imager, the Tomo-e Gozen Camera. The fast evolution of the early flash was captured by intensive intranight observations via the Tomo-e Gozen high-cadence survey. Numerical simulations show that such a prominent and fast early emission is most likely generated from an interaction between $0.01~M_{\odot}$ circumstellar material (CSM) extending to a distance of $\sim$$10^{13}~\text{cm}$ and supernova ejecta soon after the explosion, indicating a confined dense CSM formation at the final evolution stage of the progenitor of SN 2020hvf. Based on the CSM-ejecta interaction-induced early flash, the overluminous light curve, and the high ejecta velocity of SN 2020hvf, we suggest that the SN 2020hvf may originate from a thermonuclear explosion of a super-Chandrasekhar-mass white dwarf ("super-$M\rm_{Ch}$ WD"). Systematical investigations on explosion mechanisms and hydrodynamic simulations of the super-$M\rm_{Ch}$ WD explosion are required to further test the suggested scenario and understand the progenitor of this peculiar supernova.

astro-ph.HE↗

arXiv2021

Low-metallicity Young Clusters in the Outer Galaxy. III. Sh 2-127

In deep near-infrared imaging of the low-metallicity (${\rm [O/H]}=-0.7$ dex) H II region Sh 2-127 (S127) with Subaru/MOIRCS, we detected two young clusters with 413 members (S127A) in a slightly extended H II region and another with 338 members (S127B) in a compact H II region. The limiting magnitude was $K=21.3$ mag (10$σ$), corresponding to a mass detection limit of $\sim$0.2 $M_\odot$. These clusters are an order of magnitude larger than previously studied young low-metallicity clusters and larger than the majority of solar neighborhood young clusters. Fits to the K-band luminosity functions indicate very young cluster ages of 0.5 Myr for S127A and 0.1-0.5 Myr for S127B, consistent with the large extinction (up to $A_V\simeq20$ mag) from thick molecular clouds and the presence of a compact H II region and class I source candidates, and suggest that the initial mass function (IMF) of the low-metallicity clusters is indistinguishable from typical solar neighborhood IMFs. Disk fractions of $28\% \pm 3\%$ for S127A and $40\% \pm 4\%$ for S127B are significantly lower than those of similarly aged solar neighborhood clusters ($\sim$50$\%$-60$\%$). The disk fraction for S127B is higher than those of previously studied low-metallicity clusters ($<$30 $\%$), probably due to S127B's age. This suggests that a large fraction of very young stars in low-metallicity environments have disks, but the disks are lost on a very short timescale. These results are consistent with our previous studies of low-metallicity star-forming regions, suggesting that a solar neighborhood IMF and low disk fraction are typical characteristics for low-metallicity regions, regardless of cluster scales.

astro-ph.GA↗

arXiv2021

Relationship between Radar Cross Section and Optical Magnitude based on Radar and Optical Simultaneous Observations of Faint Meteors

Radar and optical simultaneous observations of meteors are important to understand the size distribution of the interplanetary dust. However, faint meteors detected by high power large aperture radar observations, which are typically as faint as 10 mag. in optical, have not been detected until recently in optical observations, mainly due to insufficient sensitivity of the optical observations. In this paper, two radar and optical simultaneous observations were organized. The first observation was carried out in 2009 to 2010 using Middle and Upper Atmosphere Radar (MU radar) and an image-intensified CCD camera. The second observation was carried out in 2018 using the MU radar and a mosaic CMOS camera, Tomo-e Gozen, mounted on the 1.05-m Kiso Schmidt Telescope. In total, 331 simultaneous meteors were detected. The relationship between radar cross sections and optical V-band magnitudes was well approximated by a linear function. A transformation function from the radar cross section to the V-band magnitude was derived for sporadic meteors. The transformation function was applied to about 150,000 meteors detected by the MU radar in 2009--2015, large part of which are sporadic, and a luminosity function was derived in the magnitude range of $-1.5$ to $9.5$ mag. The luminosity function was well approximated by a single power-law function with the population index of $r = 3.52{\pm}0.12$. The present observation indicates that the MU radar has capability to detect interplanetary dust of $10^{-5}$ to $10^{0}$ g in mass as meteors.

astro-ph.EP↗

arXiv2021

Eclipsing Binary Populations across the Northern Galactic Plane from the KISOGP survey

We present a catalog of eclipsing binaries in the northern Galactic Plane from the Kiso Wide-Field Camera Intensive Survey of the Galactic Plane (KISOGP). We visually identified 7055 eclipsing binaries spread across $\sim$330 square degrees, including 4197 W Ursa Majoris/EW-, 1458 $β$ Lyrae/EB-, and 1400 Algol/EA-type eclipsing binaries. For all systems, $I$-band light curves were used to obtain accurate system parameters. We derived the distances and extinction values for the EW-type objects from their period--luminosity relation. We also obtained the structure of the thin disk from the distribution of our sample of eclipsing binary systems, combined with those of high-mass star-forming regions and Cepheid tracers. We found that the thin disk is inhomogeneous in number density as a function of Galactic longitude. Using this new set of distance tracers, we constrain the detailed structure of the thin disk. Finally, we report a global parallax zero-point offset of $ Δπ=-42.1\pm1.9\mbox{(stat.)}\pm12.9\mbox{(syst.)}$ $μ$as between our carefully calibrated EW-type eclipsing binary positions and those provided by Gaia Early Data Release 3. Implementation of the officially recommended parallax zero-point correction results in a significantly reduced offset. Additionally, we provide a photometric characterization of our EW-type eclipsing binaries that can be applied to further analyses.

astro-ph.SR↗

arXiv2020

Mg II and Fe II fluxes of luminous quasars at z ~ 2.7 and evaluation of the Baldwin effect in the flux-to-abundance conversion method for quasars

To investigate the chemical abundance of broad-line region clouds in quasars at high redshifts, we performed near-infrared spectroscopy of six luminous quasars at z ~ 2.7 with the WINERED spectrograph mounted on the New Technology Telescope (NTT) at the La Silla Observatory, Chile. The measured Fe II/Mg II flux ratios nearly matched with the published data for 0.7 < z < 1.6, suggesting that there is no evolution over a long period of cosmic time, which is consistent with previous studies. To derive the chemical abundances from the measured equivalent widths (EWs), their dependence on nonabundance factors must be corrected. In our previous paper, we proposed a method to derive the [Mg/Fe] abundance ratio and the [Fe/H] abundance by correcting the dependence of EW(Mg II) and EW(Fe II) on the Eddington ratio. To the best of our knowledge, that was the first report to discuss the star-formation history through a direct comparison with chemical evolution models. In the present study, we further investigated the dependence of EWs on luminosity, which is known as the Baldwin effect (BEff). Additional correction for the BEff significantly affects the derived chemical abundances for the six luminous quasars at z ~ 2.7, and the resultant abundances agree well with the prediction of chemical evolution models. Given that most distant quasars found thus far are biased toward luminous ones, the correction of the measured EWs for the BEff is crucial for extending the chemical evolution study to higher redshifts.

astro-ph.GA↗

arXiv2020

The effect of surface gravity on line-depth ratios in the wavelength range 0.97-1.32 μm

A line-depth ratio (LDR) of two spectral lines with different excitation potentials is expected to be correlated with the effective temperature ($T_\mathrm{eff}$). It is possible to determine $T_\mathrm{eff}$ of a star with a precision of tens of Kelvin if dozens or hundreds of tight LDR-$T_\mathrm{eff}$ relations can be used. Most of the previous studies on the LDR method were limited to optical wavelengths, but Taniguchi and collaborators reported 81 LDR relations in the $YJ$ band, 0.97-1.32 $μ\mathrm{m}$, in 2018. However, with their sample of only 10 giants, it was impossible to account for the effects of surface gravity and metallicity on the LDRs well. Here we investigate the gravity effect based on $YJ$-band spectra of 63 stars including dwarfs, giants, and supergiants observed with the WINERED spectrograph. We found that some LDR-$T_\mathrm{eff}$ relations show clear offsets between the sequence of dwarfs and those of giants/supergiants. The difference between the ionization potentials of the elements considered in each line pair and the corresponding difference in the depths can, at least partly, explain the dependency of the LDR on the surface gravity. In order to expand the stellar parameter ranges that the LDR method can cover with high precision, we obtained new sets of LDR-$T_\mathrm{eff}$ relations for solar-metal G0-K4 dwarfs and F7-K5 supergiants, respectively. The typical precision that can be achieved with our relations is 10-30 K for both dwarfs and supergiants.

astro-ph.SR↗

arXiv2019

Identification of Absorption Lines of Heavy Metals in the Wavelength Range 0.97--1.32 Micron

Stellar absorption lines of heavy elements can give us various insights into the chemical evolution of the Galaxy and nearby galaxies. Recently developed spectrographs for the near-infrared wavelengths are becoming more and more powerful for producing a large number of high-quality spectra, but identification and characterization of the absorption lines in the infrared range remain to be fulfilled. We searched for lines of the elements heavier than the iron group, i.e., those heavier than Ni, in the Y (9760--11100 AA) and J (11600--13200 AA) bands. We considered the lines in three catalogs, i.e., Vienna Atomic Line Database (VALD), the compilation by R. Kurucz, and the list published in 1999 by Melendez and Barbuy. Candidate lines were selected based on synthetic spectra and the confirmation was done by using WINERED spectra of 13 supergiants and giants within FGK spectral types (spanning 4000--7200 K in the effective temperature). We have detected lines of Zn I, Sr II, Y II, Zr I, Ba II, Sm II, Eu II, and Dy II, in the order of atomic number. Although the number of the lines is small, 23 in total, they are potentially useful diagnostic lines of the Galactic chemical evolution, especially in the regions for which interstellar extinction hampers detailed chemical analyses with spectra in shorter wavelengths. We also report the detection of lines whose presence was not predicted by the synthetic spectra created with the above three line lists.

astro-ph.SR↗

arXiv2019

An optical search for transients lasting a few seconds

Using a prototype of the Tomo-e Gozen wide-field CMOS mosaic camera, we acquire wide-field optical images at a cadence of 2 Hz and search them for transient sources of duration 1.5 to 11.5 seconds. Over the course of eight nights, our survey encompasses the equivalent of roughly two days on one square degree, to a fluence equivalent to a limiting magnitude about $V = 15.6$ in a 1-second exposure. After examining by eye the candidates identified by a software pipeline, we find no sources which meet all our criteria. We compute upper limits to the rate of optical transients consistent with our survey, and compare those to the rates expected and observed for representative sources of ephemeral optical light.

astro-ph.IM↗

arXiv2019

New constraint on the atmosphere of (50000) Quaoar from a stellar occultation

We report observations of a stellar occultation by the classical Kuiper belt object (50000) Quaoar occurred on 28 June 2019. A single-chord high-cadence (2 Hz) photometry dataset was obtained with the Tomo-e Gozen CMOS camera mounted on the 1.05 m Schmidt telescope at Kiso Observatory. The obtained ingress and egress data do not show any indication of atmospheric refraction and allow to set new $1σ$ and $3σ$ upper limits of 6 and 16 nbar, respectively, for the surface pressure of a pure methane atmosphere. These upper limits are lower than the saturation vapor pressure of methane at Quaoar's expected mean surface temperature ($T \sim 44$ K) and imply the absence of a $\sim$10 nbar-level global atmosphere formed by methane ice on Quaoar's surface.

astro-ph.EP↗

arXiv2019

Possible progression of mass flow processes around young intermediate-mass stars based on high-resolution near-infrared spectroscopy. I. Taurus

We used the WINERED spectrograph to perform near-infrared high-resolution spectroscopy (resolving power $R = 28$,000) of 13 young intermediate-mass stars in the Taurus star-forming region. Based on the presence of near- and mid-infrared continuum emission, young intermediate-mass stars can be classified into three different evolutionary stages: Phases I, II, and III in the order of evolution. Our obtained spectra ($λ= 0.91$--1.35\,$μ$m) depict \HeI $λ$10830 and P$β$ lines that are sensitive to magnetospheric accretion and winds. We also investigate five sources each for P$β$ and \ion{He}{1} lines that were obtained from previous studies along with our targets. We observe that the P$β$ profile morphologies in Phases I and II corresponded to an extensive variety of emission features; however, these features are not detected in Phase III. We also observe that the He I profile morphologies are mostly broad subcontinuum absorption lines in Phase I, narrow subcontinuum absorption lines in Phase II, and centered subcontinuum absorption features in Phase III. Our results indicate that the profile morphologies exhibit a progression of the dominant mass flow processes: stellar wind and probably magnetospheric accretion in the very early stage, magnetospheric accretion and disk wind in the subsequent stage, and no activities in the final stage. These interpretations further suggest that opacity in protoplanetary disks plays an important role in mass flow processes. Results also indicate that \ion{He}{1} absorption features in Phase III sources, associated with chromospheric activities even in such young phases, are characteristics of intermediate-mass stars.

astro-ph.SR↗

arXiv2019

First detection of $A$--$X$ (0,0) bands of interstellar C$_2$ and CN

We report the first detection of C$_2$ $A^1Π_u$--$X^1Σ_g^+$ (0,0) and CN $A^2Π_u$--$X^2Σ^+$ (0,0) absorption bands in the interstellar medium. The detection was made using the near-infrared (0.91--1.35 $μ$m) high-resolution ($R=20,000$ and 68,000) spectra of Cygnus OB2 No.\,12 collected with the WINERED spectrograph mounted on the 1.3 m Araki telescope. The $A$--$X$ (1,0) bands of C$_2$ and CN were detected simultaneously. These near-infrared bands have larger oscillator strengths, compared with the $A$--$X$ (2,0) bands of C$_2$ and CN in the optical. In the spectrum of the C$_2$ (0,0) band with $R=68,000$, three velocity components in the line of sight could be resolved and the lines were detected up to high rotational levels ($J''\sim20$). By analyzing the rotational distribution of C$_2$, we could estimate the kinetic temperature and gas density of the clouds with high accuracy. Furthermore, we marginally detected weak lines of $^{12}$C$^{13}$C for the first time in the interstellar medium. Assuming that the rotational distribution and the oscillator strengths of the relevant transitions of $^{12}$C$_2$ and $^{12}$C$^{13}$C are the same, the carbon isotope ratio was estimated to be $^{12}\text{C}/^{13}\text{C}=50$--100, which is consistent with the ratio in the local interstellar medium. We also calculated the oscillator strength ratio of the C$_2$ (0,0) and (1,0) bands from the observed band strengths. Unfortunately, our result could not discern theoretical and experimental results because of the uncertainties. High-resolution data to resolve the velocity components will be necessary for both bands in order to put stronger constraints on the oscillator strength ratios.

astro-ph.GA↗

arXiv2019

FeI lines in 0.91-1.33 ${\rm μ}$m spectra of red giants for measuring the microturbulence and metallicities

For a detailed analysis of stellar chemical abundances, high-resolution spectra in the optical have mainly been used, while the development of near-infrared (NIR) spectrograph has opened new wavelength windows. Red giants have a large number of resolved absorption lines in both the optical and NIR wavelengths, but the characteristics of the lines in different wave passbands are not necessarily the same. We present a selection of FeI lines in the $z^{\prime}$, $Y$, and $J$ bands (0.91-1.33 $μ$m). On the basis of two different lists of lines in this range, the Vienna Atomic Line Database (VALD) and the catalog published by Meléndez & Barbuy in 1999 (MB99), we selected sufficiently strong lines that are not severely blended and compiled lists with 107 FeI lines in total (97 and 75 lines from VALD and MB99, respectively). Combining our lists with high-resolution ($λ/Δλ= 28,000$) and high signal-to-noise ($>500$) spectra taken with a NIR spectrograph, WINERED, we present measurements of the iron abundances of two prototype red giants: Arcturus and $μ$ Leo. A bootstrap method for determining the microturbulence and abundance together with their errors is demonstrated. The standard deviations of $\logε_{\rm Fe}$ values from individual FeI lines are significantly smaller when we use the lines from MB99 instead of those from VALD. With the MB99 list, we obtained $ξ=1.20\pm0.11\ {\rm km~s^{-1}}$ and $\logε_{\rm Fe}=7.01\pm0.05$ dex for Arcturus, and $ξ=1.54\pm0.17\ {\rm km~s^{-1}}$ and $\logε_{\rm Fe}=7.73\pm0.07$ dex for $μ$ Leo. These final values show better agreements with previous values in the literature than the corresponding values we obtained with VALD.

astro-ph.SR↗

arXiv2018

Luminosity Function of Faint Sporadic Meteors measured with a Wide-Field CMOS mosaic camera Tomo-e PM

Imaging observations of faint meteors were carried out on April 11 and 14, 2016 with a wide-field CMOS mosaic camera, Tomo-e PM, mounted on the 105-cm Schmidt telescope at Kiso Observatory, the University of Tokyo. Tomo-e PM, which is a prototype model of Tomo-e Gozen, can monitor a sky of ${\sim}1.98\,\mathrm{deg^2}$ at 2\,Hz. The numbers of detected meteors are 1514 and 706 on April 11 and 14, respectively. The detected meteors are attributed to sporadic meteors. Their absolute magnitudes range from $+4$ to $+10\,\mathrm{mag}$ in the $V$-band, corresponding to about $8.3{\times}10^{-2}$ to $3.3{\times}10^{-4}\,\mathrm{g}$ in mass. The present magnitude distributions we obtained are well explained by a single power-law luminosity function with a slope parameter $r = 3.1{\pm}0.4$ and a meteor rate $\log_{10}N_0 = -5.5{\pm}0.5$. The results demonstrate a high performance of telescopic observations with a wide-field video camera to constrain the luminosity function of faint meteors. The performance of Tomo-e Gozen is about two times higher than that of Tomo-e PM. A survey with Tomo-e Gozen will provide a more robust measurement of the luminosity function.

astro-ph.EP↗

arXiv2018

A newly-identified emission-line region around P Cygni

We present a high-resolution ($R \simeq 20,000$) near-infrared (9,100-13,500 $Å$) long-slit spectrum of P Cygni obtained with the newly commissioned WINERED spectrograph in Japan. In the obtained spectrum, we have found that the velocity profiles of the [Fe II] emission lines are resolved into two peaks at a velocity of $\simeq220$ km s$^{-1}$ with a moderate dip in between and with additional sub-peaks at $\simeq\pm100$~km~s$^{-1}$. The sub-peak component is confirmed with the long-slit echellogram to originate in the known shell with a radius of $\simeq10^{\prime\prime}$, which was originally created by the outburst in 1600 AD. On the other hand, the $\simeq220$ km s$^{-1}$ component, which dominates the [Fe II] flux from P Cygni, is found to be concentrated closer to the central star with an apparent spatial extent of $\simeq3^{\prime\prime}$. The extent is much larger than the compact ($<0^{\prime\prime}.1$) regions traced with hydrogen, helium, and metal permitted lines. The velocity, estimated mass, and dynamical time of the extended emission-line region suggest that the region is an outer part of the stellar wind region. We suggest that the newly-identified emission-line region may trace a reverse shock due to the stellar wind overtaking the outburst shell.

astro-ph.SR↗

arXiv2018

Correction of near-infrared high-resolution spectra for telluric absorption at 0.90-1.35 microns

We report a method of correcting a near-infrared (0.90-1.35 $μ$m) high-resolution ($λ/Δλ\sim28,000$) spectrum for telluric absorption using the corresponding spectrum of a telluric standard star. The proposed method uses an A0\,V star or its analog as a standard star from which on the order of 100 intrinsic stellar lines are carefully removed with the help of a reference synthetic telluric spectrum. We find that this method can also be applied to feature-rich objects having spectra with heavily blended intrinsic stellar and telluric lines and present an application to a G-type giant using this approach. We also develop a new diagnostic method for evaluating the accuracy of telluric correction and use it to demonstrate that our method achieves an accuracy better than 2\% for spectral parts for which the atmospheric transmittance is as low as $\sim$20\% if telluric standard stars are observed under the following conditions: (1) the difference in airmass between the target and the standard is $\lesssim 0.05$; and (2) that in time is less than 1 h. In particular, the time variability of water vapor has a large impact on the accuracy of telluric correction and minimizing the difference in time from that of the telluric standard star is important especially in near-infrared high-resolution spectroscopic observation.

astro-ph.IM↗

arXiv2017

Star formation activity beyond the outer Arm I: WISE-selected candidate star-forming regions

The outer Galaxy beyond the Outer Arm provides a good opportunity to study star formation in an environment significantly different from that in the solar neighborhood. However, star-forming regions in the outer Galaxy have never been comprehensively studied or cataloged because of the difficulties in detecting them at such large distances. We studied 33 known young star-forming regions associated with 13 molecular clouds at $R_{\rm G}$ $\ge$ 13.5 kpc in the outer Galaxy with data from the Wide-field Infrared Survey Explorer (WISE) mid-infrared all-sky survey. From their color distribution, we developed a simple identification criterion of star-forming regions in the outer Galaxy with the WISE color. We applied the criterion to all the WISE sources in the molecular clouds in the outer Galaxy at $R_{\rm G}$ $\ge$ 13.5 kpc detected with the Five College Radio Astronomy Observatory (FCRAO) $^{12}$CO survey of the outer Galaxy, of which the survey region is 102$^\circ$.49 $\le$ $l$ $\le$ 141$^\circ$.54, $-$3$^\circ$.03 $\le$ $b$ $\le$ 5$^\circ$.41, and successfully identified 711 new candidate star-forming regions in 240 molecular clouds. The large number of samples enables us to perform the statistical study of star-formation properties in the outer Galaxy for the first time. This study is crucial to investigate the fundamental star-formation properties, including star-formation rate, star-formation efficiency, and initial mass function, in a primordial environment such as the early phase of the Galaxy formation.

astro-ph.GA↗