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At least 235 records · Page 13

Mergers Matter: Gravothermal Collapse in Dwarf Halos with Self-Interacting Dark Matter

Self-Interacting Dark Matter (SIDM) models with large cross sections at relative velocities below $\sim100\,{\rm km \, s}^{-1}$ can be tested with dwarf galaxy observations. We analyze six dark-matter-only zoom-in $\sim10^{10}\,{\rm M}_\odot$ halos with diverse assembly histories, adopting a cross section over mass of $σ/m = 70\,cm^2 \, g^{-1}$. We find that mergers inject orbital kinetic energy into the halo, altering the heat transport and the gravothermal evolution of the core. Three of the six halos -- those with the most quiescent merger histories -- show clear signs of core collapse in these simulations. Halos with sustained mergers do not collapse. Furthermore, merger-induced heat transport drives two non-collapsing halos to central densities well below the predictions of the gravothermal fluid model. These findings suggest a novel mechanism for producing dark-matter-deficient galaxies and expanding the diversity of rotation curves beyond what halo concentration alone predicts. Merger histories are thus essential for understanding central density distributions of dwarf galaxy halos in SIDM.

Silverman, Maya [UC, Irvine; Bohr Inst.] (ORCID:00↗

The Sonora Brown Dwarf Atmosphere and Evolution Models. I. Model Description and Application to Cloudless Atmospheres in Rainout Chemical Equilibrium

Here we present a new generation of substellar atmosphere and evolution models, appropriate for application to studies of L-, T-, and Y-type brown dwarfs and self-luminous extrasolar planets. The models describe the expected temperature-pressure profiles and emergent spectra of atmospheres in radiative-convective equilibrium with effective temperatures and gravities within the ranges 200 ≤ T eff ≤ 2400 K and $2.5\leqslant \mathrm{log}g\leqslant 5.5$. These ranges encompass masses from about 0.5 to 85 Jupiter masses for a set of metallicities ([M/H] = – 0.5 to + 0.5), C/O ratios (from 0.5 to 1.5 times that of solar), and ages. These models expand the diversity of model atmospheres currently available, notably to cooler effective temperatures and greater ranges in C/O. Notable improvements from past such models include updated opacities and atmospheric chemistry. Here we describe our modeling approach and present our initial tranche of models for cloudless, chemical equilibrium atmospheres. We compare the modeled spectra, photometry, and evolution to various data sets.

79 ASTRONOMY AND ASTROPHYSICS↗

The Dark Matter Content of Milky Way Dwarf Spheroidal Galaxies: Draco, Sextans, and Ursa Minor

The Milky Way Survey of the Dark Energy Spectroscopic Instrument (DESI) has so far observed three classical dwarf spheroidal galaxies (dSphs): Draco, Sextans, and Ursa Minor. Based on the observed line-of-sight velocities and metallicities of their member stars, we apply the axisymmetric Jeans Anisotropic Multi-Gaussian Expansion modeling (JAM) approach to recover their inner dark matter distributions. In particular, both the traditional single-population Jeans model and the multiple population chemodynamical model are adopted. With the chemodynamical model, we divide member stars of each dSph into metal-rich and metal-poor populations. The metal-rich populations are more centrally concentrated and dynamically colder, featuring lower velocity dispersion profiles than the metal-poor populations. We find a diversity of the inner density slopes γ of dark matter halos, with the best constraints by the single-population or chemodynamical models consistent with each other. The inner density slopes are $0.7{1}_{-0.35}^{+0.34}$, $0.2{6}_{-0.12}^{+0.22}$, and $0.3{3}_{-0.16}^{+0.20}$ for Draco, Sextans, and Ursa Minor, respectively. We also present the measured astrophysical J and D factors of the three dSphs. Our results indicate that the study of the dark matter content of dSphs through stellar kinematics is still subject to uncertainties behind both the methodology and the observed data, through comparisons with previous measurements and datasets.

Dark matter↗

The Draco Dwarf Spheroidal Galaxy in the First Year of Dark Energy Spectroscopic Instrument Data

We investigate the spatial distribution, kinematics, and metallicity of stars in the Draco dwarf spheroidal galaxy using data from the Dark Energy Spectroscopic Instrument (DESI). We identify 155 high-probability members of Draco using line-of-sight velocity and metallicity information derived from DESI spectroscopy along with Gaia Data Release 3 proper motions. We find a mean line-of-sight velocity of −290.62 ± 0.80 km s −1 with dispersion = $9.57$$^{+0.66}_{–0.62}$ km s −1 and mean metallicity [Fe/H] = −2.10 ± 0.04, consistent with previous results. We also find that Draco has a steep metallicity gradient within the half-light radius, and a metallicity gradient that flattens beyond the half-light radius. We identify eight high-probability members outside the King tidal radius, four of which we identify for the first time. These extratidal stars are not preferentially aligned along the orbit of Draco. We compute an average surface brightness of 34.02 mag arsec –2 within an elliptical annulus from the King tidal radius of 48'.1–81′.

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Magellan/M2FS and MMT/Hectochelle Spectroscopy of Dwarf Galaxies and Faint Star Clusters within the Galactic Halo*

We present spectroscopic data for 16,369 stellar targets within and/or toward 38 dwarf spheroidal galaxies and faint star clusters within the Milky Way halo environment. All spectra come from observations with the multiobject, fiber-fed echelle spectrographs M2FS at the Magellan/Clay telescope or Hectochelle at the MMT, reaching a typical limiting magnitude G ≲ 21. Data products include processed spectra from all observations and catalogs listing estimates—derived from template model fitting—of line-of-sight velocity (median uncertainty 1.4 km s –1 ) effective temperature (255 K), (base-10 logarithm of) surface gravity (0.59 dex in cgs units), [Fe/H] (0.4 dex) and [Mg/Fe] (0.27 dex) abundance ratios. The sample contains multiepoch measurements for 3720 sources, with up to 15 epochs per source, enabling studies of intrinsic spectroscopic variability. The sample contains 6087 likely red giant stars (based on surface gravity), and 4492 likely members (based on line-of-sight velocity and Gaia-measured proper motion) of the target systems. The number of member stars per individual target system ranges from a few, for the faintest systems, to ~850 for the most luminous. For most systems, our new samples extend over wider fields than have previously been observed; of the likely members in our samples, 820 lie beyond 2 times the projected half-light radius of their host system, and 42 lie beyond 5 R half .

79 ASTRONOMY AND ASTROPHYSICS↗

The metallicity distribution in the core of the Sagittarius dwarf spheroidal: Minimising the metallicity biases

We present the metallicity and radial velocity for 450 bona fide members of the Sagittarius dwarf spheroidal (Sgr dSph) galaxy, measured from high-resolution spectra (R ≃ 18 000) obtained with FLAMES at the VLT. The targets were carefully selected (a) to sample the core of the main body of Sgr dSph while avoiding contamination from the central stellar nucleus, and (b) to prevent any bias on the metallicity distribution by selecting targets based on their Gaia parallax and proper motions. All the targets selected in this way were confirmed as radial velocity members. We used this sample to derive the first metallicity distribution of the core of Sgr dSph, which is virtually unaffected by metallicity biases. The observed distribution ranges from [Fe/H] ≃ -2.3 to [Fe/H] ≃ 0.0, with a strong, symmetric, and relatively narrow peak around [Fe/H] ≃ -0.5 and a weak and extended metal-poor tail, in which only 13.8 ± 1.9% of the stars have [Fe/H] < -1.0. We confirm previous evidence of correlations between chemical and kinematical properties of stars in the core of Sgr. In our sample, stars with [Fe/H] ≥ -0.6 display a lower velocity dispersion and a higher rotation amplitude than those with [Fe/H] < - 0.6, confirming previous suggestions of disk/halo structure for the progenitor of the system.

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Lyman continuum leaker candidates among highly ionised, low-redshift dwarf galaxies selected from He II

Contemporary research suggests that the reionisation of the intergalactic medium (IGM) in the early Universe was predominantly realised by star-forming (proto-)galaxies (SFGs). Due to observational constraints, our knowledge on the origins of sufficient amounts of ionising Lyman continuum (LyC) photons and the mechanisms facilitating their transport into the IGM remains sparse. Recent efforts have thus focussed on the study of local analogues to these high-redshift objects. We aim to acquire a set of very low-redshift SFGs that exhibit signs of a hard radiation field being present. A subsequent analysis of their emission line properties is intended to shed light on how the conditions prevalent in these objects compare to those predicted to be present in early SFGs that are thought to be LyC emitters (LCEs). We used archival spectroscopic SDSS DR12 data to select a sample of low-redshift He II 4686 emitters and restricted it to a set of SFGs with an emission line diagnostic sensitive to the presence of an active galactic nucleus, which serves as our only selection criterion. We performed a population spectral synthesis with FADO to reconstruct these galaxies’ star-formation histories (SFHs). Utilising the spectroscopic information at hand, we constrained the predominant ionisation mechanisms in these galaxies and inferred information on interstellar medium (ISM) conditions relevant for the escape of LyC radiation. Our final sample consists of eighteen ionised, metal-poor galaxies (IMPs). These low-mass (6.2 ≤ log(M * /M ⊙ ) ≤ 8.8), low-metallicity (7.54 ≤log(O/H) + 12 ≤ 8.13) dwarf galaxies appear to be predominantly ionised by stellar sources. We find large [OIII] 5007/[OII] 3727 ratios and [SII] 6717,6731/Hα deficiencies, which provide strong indications for these galaxies to be LCEs. At least 40% of these objects are candidates for featuring cosmologically significant LyC escape fractions ≳10%. The IMPs’ SFHs exhibit strong similarities and almost all galaxies appear to contain an old (> 1 Gyr) stellar component, while also harbouring a young, two-stage (~10 Myr and < 1 Myr) starburst, which we speculate might be related to LyC escape. The properties of the compact emission line galaxies presented here align well with those observed in many local LCEs. In fact, our sample may prove as an extension to the rather small catalogue of local LCEs, as the extreme ISM conditions we find are assumed to facilitate LyC leakage. Notably, all of our eighteen candidates are significantly closer (z < 0.1) than most established LCEs. If the inferred LyC photon loss is genuine, this demonstrates that selecting SFGs from He II 4686 is a powerful selection criterion in the search for LCEs.

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Can local white dwarfs constrain dark matter interactions?

We investigate whether nearby white dwarfs (WDs) can constrain dark matter (DM) interactions with ordinary matter. As experimental sensitivity improves, driven by the Gaia mission, the sample volume of nearby WDs has been increasing over recent years. We carefully select a sample of ten cold, isolated, non-magnetic WDs within 13 pc of the Sun. We model their carbon-oxygen interior using a finite temperature relativistic equation of state and model atmospheres to infer their core temperatures. This enables us to perform a thorough estimation of the DM capture rate and evaporation mass using actual astrophysical observations. Given the low local DM density, we focus on DM that annihilates into long-lived mediators, which escape the WD and later decay into photons. While Fermi-LAT data shows no significant gamma-ray excess, future telescopes, CTA North & South, LHAASO, SWGO, could probe DM-nucleon cross sections down to ∼ 10 -41 cm 2 for DM masses above the TeV scale. Our results are competitive with current direct detection bounds (e.g., LZ) in the multi-TeV regime. This work underscores the importance of systematic WD studies in the broader landscape of DM detection and demonstrates the synergy between astrophysical and terrestrial searches in exploring DM interactions.

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Combined dark matter search towards dwarf spheroidal galaxies with Fermi -LAT, HAWC, H.E.S.S., MAGIC, and VERITAS

Dwarf spheroidal galaxies (dSphs) are excellent targets for indirect dark matter (DM) searches using gamma-ray telescopes because they are thought to have high DM content and a low astrophysical background. The sensitivity of these searches is improved by combining the observations of dSphs made by different gamma-ray telescopes. We present the results of a combined search by the most sensitive currently operating gamma-ray telescopes, namely: the satellite-borne Fermi -LAT telescope; the ground-based imaging atmospheric Cherenkov telescope arrays H.E.S.S., MAGIC, and VERITAS; and the HAWC water Cherenkov detector. Individual datasets were analyzed using a common statistical approach. Results were subsequently combined via a global joint likelihood analysis. We obtain constraints on the velocity-weighted cross section 〈σv〉 for DM self-annihilation as a function of the DM particle mass. This five-instrument combination allows the derivation of up to 2-3 times more constraining upper limits on 〈σv〉 than the individual results over a wide mass range spanning from 5 GeV to 100 TeV. Depending on the DM content modeling, the 95% confidence level observed limits reach 1.5×10 -24 cm 3 s -1 and 3.2×10 -25 cm 3 s -1 , respectively, in the τ + τ - annihilation channel for a DM mass of 2 TeV.

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A comprehensive chemical abundance analysis of the extremely metal poor Leoncino Dwarf galaxy (AGC 198691)

ABSTRACT We re-examine the extremely metal-poor dwarf galaxy AGC 198691 using a high quality spectrum obtained by the LBT’s MODS instrument. Previous spectral observations obtained from KOSMOS on the Mayall 4-m and the Blue channel spectrograph on the MMT 6.5-m telescope did not allow for the determination of sulfur, argon, or helium abundances. We report an updated and full chemical abundance analysis for AGC 198691, including confirmation of the extremely low “direct” oxygen abundance with a value of 12 + log (O/H) = 7.06 ± 0.03. AGC 198691’s low metallicity potentially makes it a high value target for helping determine the primordial helium abundance (Yp). Though complicated by a Na i night sky line partially overlaying the He i λ5876 emission line, the LBT/MODS spectrum proved adequate for determining AGC 198691’s helium abundance. We employ the recently expanded and improved model of Aver et al., incorporating higher Balmer and Paschen lines, augmented by the observation of the infrared helium emission line He i λ10830 obtained by Hsyu et al. Applying our full model produced a reliable helium abundance determination, consistent with the expectation for its metallicity. Although this is the lowest metallicity object with a detailed helium abundance, unfortunately, due to its faintness [EW(Hβ) < 100 Å] and the compromised He i λ5876, the resultant uncertainty on the helium abundance is too large to allow a significant improvement on the measurement of Yp.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Jets from main sequence and white dwarf companions during common envelope evolution

ABSTRACT It has long been speculated that jet feedback from accretion on to the companion during a common envelope (CE) event could affect the orbital evolution and envelope unbinding process. We present global 3D hydrodynamical simulations of CE evolution (CEE) that include a jet subgrid model and compare them with an otherwise identical model without a jet. Our binary consists of a 2-M⊙ red giant branch primary and a 1- or 0.5-M⊙ main sequence (MS) or white dwarf (WD) secondary companion modelled as a point particle. We run the simulations for 10 orbits (40 d). Our jet model adds mass at a constant rate $\dot{M}_\mathrm{j}$ of the order of the Eddington rate, with maximum velocity vj of the order of the escape speed, to two spherical sectors with the jet axis perpendicular to the orbital plane. We explore the influence of the jet on orbital evolution, envelope morphology and envelope unbinding, and assess the dependence of the results on the jet mass-loss rate, launch speed, companion mass, opening angle, and accretion rate. In line with our theoretical estimates, jets are choked around the time of first periastron passage and remain choked thereafter. Subsequent to choking, but not before, jets efficiently transfer energy to bound envelope material. This leads to increases in unbound mass of up to $\sim 10{{\ \rm per\ cent}}$, as compared to the simulations without jets. We also estimate the cumulative effects of jets over a full CE phase, finding that jets launched by MS and WD companions are unlikely to dominate envelope unbinding.

79 ASTRONOMY AND ASTROPHYSICS↗

GMRT H I mapping of mid-infrared bright blue compact dwarf galaxies W1016+3754 and W2326+0608

We present the results from deep 21 cm H i mapping of two nearby Blue Compact Dwarf Galaxies (BCDGs), W1016+3754 and W2326+0608, using the Giant Metrewave Radio Telescope (GMRT). These BCDGs are bright in mid-infrared data and undergoing active star formation. With the GMRT observations, we investigate the role of cold neutral gas as the fuel resource of the current intensive star formation activity. Star formation in these galaxies is likely to be due to the infall of H I gas triggered by gravitational perturbation from nearby galaxies. The BCDG W2326+0608 and nearby galaxy SDSS J232603.86+060835.8 share a common H I envelope. We find star formation takes place in the high H I column density gas (≳10 21 cm −2 ) regions for both BCDGs. The recent starburst and infall of metal-free gas have kept the metallicity low for the BCDG W1016+3754. The metallicity for W2326+0608 is higher, possibly due to tidal interaction with the nearby galaxy SDSS J232603.86+060835.8.

79 ASTRONOMY AND ASTROPHYSICS↗

DAmodel: hierarchical Bayesian modelling of DA white dwarfs for spectrophotometric calibration

We use hierarchical Bayesian modelling to calibrate a network of 32 all-sky faint DA white dwarf (DA WD) spectrophotometric standards (⁠16.5 < V , 19.5⁠) alongside three CALSPEC standards, from 912 Å to 32 μm. The framework is the first of its kind to jointly infer photometric zero points and WD parameters (surface gravity log g⁠, effective temperature T eff ⁠, extinction A V ⁠, dust relation parameter R V ) by simultaneously modelling both photometric and spectroscopic data. We model panchromatic Hubble Space Telescope Wide Field Camera 3 (HST/WFC3) UVIS and IR photometry, HST/STIS UV spectroscopy, and ground-based optical spectroscopy to sub-per cent precision. Photometric residuals for the sample are the lowest yet yielding < 0.004 mag RMS on average from the UV to the NIR, achieved by jointly inferring time-dependent changes in system sensitivity and WFC3/IR count-rate nonlinearity. Our GPU-accelerated implementation enables efficient sampling via Hamiltonian Monte Carlo, critical for exploring the high-dimensional posterior space. The hierarchical nature of the model enables population analysis of intrinsic WD and dust parameters. Inferred spectral energy distributions from this model will be essential for calibrating the James Webb Space Telescope as well as next-generation surveys, including Vera Rubin Observatory’s Legacy Survey of Space and Time and the Nancy Grace Roman Space Telescope.

methods: statistical↗

Collapse of magnetized white dwarfs as site of heavy-element formation and kilonova signal

We present the first end-to-end calculation connecting the accretion-induced collapse (AIC) of a magnetized, rapidly rotating white dwarf to observable kilonova signatures, combining two-dimensional (2D) general-relativistic neutrino-magnetohydrodynamic simulations, followed by radiation hydrodynamics with in-situ nuclear network and 2D Monte Carlo radiative transfer with spatially resolved heating rates. Unlike all previous unmagnetized AIC models – which predicted proton-rich, $^{56}$Ni-dominated ejecta – strong magnetic fields eject ${\approx }\, 0.2\, \mathrm{ M}_\odot$ of neutron-rich material ($\langle Y_e \rangle \sim 0.24$) on dynamical time-scales, before neutrino irradiation can raise the electron fraction, enabling strong r-process nucleosynthesis up to and beyond the third peak. The resulting kilonova is lanthanide-rich ($X_{\rm lan} \approx 8~{{\ \rm per\ cent}}$) and dominated by near-infrared emission. We compute synthetic light curves in the Large Synoptic Survey Telescope and J ames Webb Space Telescope bands and find striking agreement, without parameter tuning, between the observations of AT 2023vfi/GRB 230307A and our broadband light curves for polar viewing angles. These results establish magnetized AIC as a viable channel for heavy r-process element production and a compelling progenitor candidate for long-duration gamma-ray bursts with kilonova signatures.

MHD↗

High-resolution Spectroscopic Study of Dwarf Stars in the Northern Sky: Lithium, Carbon, and Oxygen Abundances

Abundances of lithium, carbon, and oxygen have been derived using spectral synthesis for a sample of 249 bright F, G, and K Northern Hemisphere dwarf stars from the high-resolution spectra acquired with the VUES spectrograph at the $Mol\dot{e}tai$ Astronomical Observatory of Vilnius University. The sample stars have metallicities, effective temperatures, and ages between (–0.7 ÷ 0.4) dex, (5000 ÷ 6900) K, (1 ÷ 12) Gyr, accordingly. We confirm a so far unexplained lithium abundance decrease at supersolar metallicities—A(Li) in our sample stars, which drop by 0.7 dex in the [Fe/H] range from +0.10 to +0.55 dex. Furthermore, we identified stars with similar ages, atmospheric parameters, and rotational velocities, but with significantly different lithium abundances, which suggests that additional specific evolutionary factors should be taken into account while interpreting the stellar lithium content. Nine stars with predominantly supersolar metallicities, i.e., about 12% among 78 stars with C and O abundances determined, have the C/O number ratios larger than 0.65, thus may form carbon-rich rocky planets. Ten planet-hosting stars, available in our sample, do not show a discernible difference from the stars with no planets detected regarding their lithium content.

79 ASTRONOMY AND ASTROPHYSICS↗

Candidate Brown-dwarf Microlensing Events with Very Short Timescales and Small Angular Einstein Radii

Short-timescale microlensing events are likely to be produced by substellar brown dwarfs (BDs), but it is difficult to securely identify BD lenses based on only event timescales t{sub E} because short-timescale events can also be produced by stellar lenses with high relative lens-source proper motions. In this paper, we report three strong candidate BD-lens events found from the search for lensing events not only with short timescales (t{sub E}≲6 days) but also with very small angular Einstein radii (θ{sub E}≲0.05 mas) among the events that have been found in the 2016–2019 observing seasons. These events include MOA-2017-BLG-147, MOA-2017-BLG-241, and MOA-2019-BLG-256, in which the first two events are produced by single lenses and the last event is produced by a binary lens. From the Monte Carlo simulations of Galactic events conducted with the combined t{sub E} and θ{sub E} constraint, it is estimated that the lens masses of the individual events are 0.051{sub −0.027}{sup +0.100} M{sub ⊙}, 0.044{sub −0.023}{sup +0.090} M{sub ⊙}, and 0.046{sub −0.023}{sup +0.067} M{sub ⊙}/0.038{sub −0.019}{sup +0.056} M{sub ⊙} and the probability of the lens mass smaller than the lower limit of stars is ∼80% for all events. We point out that routine lens mass measurements of short-timescale lensing events require survey-mode space-based observations.

79 ASTRONOMY AND ASTROPHYSICS↗

TOI-503: The First Known Brown-dwarf Am-star Binary from the TESS Mission

We report the discovery of an intermediate-mass transiting brown dwarf (BD), TOI-503b, from the TESS mission. TOI-503b is the first BD discovered by TESS, and it has circular orbit around a metallic-line A-type star with a period of P = 3.6772 ± 0.0001 days. The light curve from TESS indicates that TOI-503b transits its host star in a grazing manner, which limits the precision with which we measure the BD’s radius (R{sub b}=1.34{sub −0.15}{sup +0.26}R{sub J}). We obtained high-resolution spectroscopic observations with the FIES, Ondřejov, PARAS, Tautenburg, and TRES spectrographs, and measured the mass of TOI-503b to be M {sub b} = 53.7 ± 1.2 M{sub J}. The host star has a mass of M {sub ⋆} = 1.80 ± 0.06 M {sub ⊙}, a radius of R {sub ⋆} = 1.70 ± 0.05R {sub ⊙}, an effective temperature of T {sub eff} = 7650 ± 160 K, and a relatively high metallicity of 0.61 ± 0.07 dex. We used stellar isochrones to derive the age of the system to be ∼180 Myr, which places its age between that of RIK 72b (a ∼10 Myr old BD in the Upper Scorpius stellar association) and AD 3116b (a ∼600 Myr old BD in the Praesepe cluster). Given the difficulty in measuring the tidal interactions between BDs and their host stars, we cannot precisely say whether this BD formed in situ or has had its orbit circularized by its host star over the relatively short age of the system. Instead, we offer an examination of plausible values for the tidal quality factor for the star and BD. TOI-503b joins a growing number of known short-period, intermediate-mass BDs orbiting main-sequence stars, and is the second such BD known to transit an A star, after HATS-70b. With the growth in the population in this regime, the driest region in the BD desert (35--55M{sub J}sin i) is reforesting.

79 ASTRONOMY AND ASTROPHYSICS↗

Intrinsic Color Indices of Early-type Dwarf Stars

Early-type stars are short lived and scarce in comparison with other types. Based on the recently released catalogs of early-type stars from the largest Large Sky Area Multi-Object Fiber Spectroscopic Telescope spectroscopic survey, the intrinsic colors of the stars with effective temperature up to 32,000 K are determined for the bands from ultraviolet to infrared using the blue-edge method. Analytic relations are derived for the intrinsic color index with the effective temperature for the Wide-field Infrared Survey Explorer, Two Micron All Sky Survey, Gaia, AAVSO Photometric All-Sky Survey, Sloan Digital Sky Survey, the Panoramic Survey Telescope and Rapid Response System 1, and Galaxy Evolution Explorer bands. The results are generally consistent with previous works. In addition, the intrinsic colors of O-type dwarfs and OB supergiants are roughly estimated.

79 ASTRONOMY AND ASTROPHYSICS↗