Estrelas anãs brancas e subanãs no sloan digital sky survey

White dwarf stars are the final observable evolutionary state of over 95% of stars and also a common outcome in binary evolution. Therefore, studying white dwarfs is a powerful tool to understand both single and binary stellar evolution, local initial mass function, and post-main sequence mass loss, leading us to a better comprehension of the history of stellar formation and evolution of different stellar populations. In order to make this type of studies possible, a large and preferably complete sample of white dwarf stars, covering the whole range of physical parameters, is required. The simplest way to achieve that is to take advantage of data provided by large surveys. The Sloan Digital Sky Survey has already allowed the increase of the number of known white dwarf stars fivefold up to its data release 10. In this work, we extended the search for white dwarfs to the new objects in the data release 12, discovering 3 157 new white dwarfs and 1 349 new subdwarfs. For the first time, we have extended this search to log g < 6.5, corresponding to M < 0.3 M⊙. White dwarfs below this mass limit cannot be formed through single evolution within a Hubble time; however, if the star is part of a close binary system, the mass loss of the system may be so intense that the resulting white dwarf has mass below the single evolution limit. These objects are known as extremely-low mass white dwarfs (ELMs) They show Teff < 20 000 K and 5.0 . log g . 6.5 and spectra very similar to main sequence A stars. Less than a hundred of them are known, and most objects were discovered relying on biased selection criteria, that excluded cool (Teff < 9 000 K), lowermass (M . 0.15 M⊙) ELMs, making it difficult to validate the models and comprehend the properties of the ELMs as a class. We have identified thousands of objects whose physical properties, effective temperature and surface gravity, place them in the range of by-products of binary interaction such as the ELMs. We have called them sdAs, referring to their sub-main sequence log g and hydrogen dominated spectra. They seem to be composed of overlapping stellar populations, and we found that at least 7% are more likely ELMs or their precursors, the pre-ELMs, than main sequence stars. Obtaining time-resolved spectroscopy for 26 objects, we could confirm 15 to be in close binaries. One of them is also an eclipsing system, while another is a pulsator — the eighth member of the pulsating ELM class. Other six new pulsators were found as part of our follow-up, five of them in the vicinity of the ELM instability strip. With these results, we increase the population of ELMs by 20%, raising the fraction of cool ELMs from 4 to 20%, which is consistent with the predictions from the evolutionary models.Estrelas anãs brancas são o último estágio evolutivo observável de mais de 95% das estrelas e também um resultado comum na evolução de estrelas binárias. O estudo de anãs brancas é, portanto, uma ferramenta poderosa na compreensão da evolução de estrelas simples e binárias, da função de massa inicial local, e da perda de massa após a sequência principal, levando-nos a uma melhor compreensão do histórico de formação e evolução estelar de diferentes populações. Para que esses estudos sejam possíveis, é necessária uma amostra grande e preferencialmente completa de anãs brancas, cobrindo todo o intervalo de parâmetros físicos. A maneira mais simples de obter isso é utilizando dados de grandes projetos de mapeamento. O Sloan Digital Sky Survey já permitiu o aumento do número de anãs brancas conhecidas em cinco vezes até o data release 10. Neste trabalho, estendemos a busca por anãs brancas aos novos objetos no data release 12, descobrindo 3 157 novas anãs brancas e 1 349 novas subanãs. Pela primeira vez, estendemos essa busca para log g < 6.5, correspondente a M < 0.3 M⊙. Anãs brancas abaixo desse limite de massa não podem formar-se em um tempo de Hubble; contudo, se a estrela é parte de um sistema de binárias próximas, a perda de massa pode ser tão intensa que a anã branca resultante tem massa inferior ao limite por evolução simples. Esses objetos são chamados anãs brancas de massa extremamente-baixa (ELMs, do inglês extremely-low mass white dwarfs) Elas têm Teff < 20 000 K e 5.0 . log g . 6.5 e espectros muito similares a estrelas A de sequência principal. Menos de cem são conhecidas, e a maioria dos objetos foi descoberta tendo em conta um critério de seleção tendencioso, que excluiu ELMs frias (Teff < 9 000 K) e com mais baixa massa (M . 0.15 M⊙), tornando difícil verificar modelos e compreender as propriedades das ELMs como classe. Nós identificamos milhares de objetos cujas propriedades físicas, temperatura efetiva e log g, estão no intervalo de produtos de evolução binária, como as ELMs. Nós os chamamos de sdAs, referindo-nos ao seu log g que as coloca abaixo da sequência principal e seu espectro dominado por hidrogênio. As sdAs parecem conter populações estelares sobrepostas, e encontramos que 7% são mais compatíveis com (pre-)ELMs do que com objetos de sequência principal. Obtivemos espectroscopia resolvida temporalmente para 26 objetos e pudemos confirmar que 15 estão em binárias. Um objeto faz parte de um sistema eclipsante, enquanto outro é pulsante — o oitavo membro da classe de ELMs pulsantes. Outros seis objetos também apresentaram pulsações em nossas observações, cinco desses estão na vizinhança da faixa de instabilidade das ELMs. Com estes resultados, aumentamos a população de ELMs por um fator de 20%, elevando a fração de ELMs de 4 para 20%, um valor que é consistente com as previsões de modelos evolucionários

The sdA problem : III. New extremely low-mass white dwarfs and their precursors from Gaia astrometry

The physical nature of the sdA stars – cool hydrogen-rich objects with spectroscopic surface gravities intermediate between main-sequence and canonical-mass white dwarfs – has been elusive since they were found in Sloan Digital Sky Survey Data Release 12 spectra. The population is likely dominated by metal-poor A/F stars in the halo with overestimated surface gravities, with a small contribution of extremely low-mass white dwarfs and their precursors, i.e. ELMs and pre-ELMs. In this work, we seek to identify (pre-)ELMs with radii smaller than what is possible for main-sequence stars, allowing even for very low metallicity. We analyse 3891 sdAs previously identified in the Sloan Digital Sky Survey using Gaia DR2 data. Our Monte Carlo analysis supports that 90 of these are inconsistent with the main sequence. 37 lie close to or within the canonical white dwarf cooling sequence, while the remaining 53 lie between the canonical white dwarfs and main sequence, which we interpret as likely (pre-)ELMs given their spectral class. Of these, 30 pass more conservative criteria that allow for higher systematic uncertainties on the parallax, as well as an approximate treatment of extinction. Our identifications increase the number of known (pre-)ELMs by up to 50 per cent, demonstrating how Gaia astrometry can reveal members of the compact (pre-)ELM subpopulation of the sdA spectral class

White dwarf and subdwarf stars in the Sloan Digital Sky Survey Data Release 16

White dwarfs are the end state of the evolution of more than 97 per cent of all stars, and therefore carry information on the structure and evolution of the Galaxy through their luminosity function and initial-to-final mass relation. Examining the new spectra of all white or blue stars in the Sloan Digital Sky Survey Data Release 16, we report the spectral classification of 2410 stars, down to our identification cut-off of signal-to-noise ratio equal to three. We newly identify 1404 DAs, 189 DZs, 103 DCs, 12 DBs, and nine CVs. The remaining objects are a mix of carbon or L stars (dC/L), narrow-lined hydrogen-dominated stars (sdA), dwarf F stars, and P Cyg objects. As white dwarf stars were not targeted by SDSS DR16, the number of new discoveries is much smaller than in previous releases. We also report atmospheric parameters and masses for a subset consisting of 555 new DAs, 10 new DBs, and 85 DZs for spectra with signal-to-noise ratio larger than 10

Mysterious, variable, and extremely hot : white dwarfs showing ultra-high excitation lines : I. Photometric variability

Context. About 10% of all stars exhibit absorption lines of ultra-highly excited (UHE) metals (e.g., O viii) in their optical spectra when entering the white dwarf cooling sequence. This is something that has never been observed in any other astrophysical object, and poses a decades-long mystery in our understanding of the late stages of stellar evolution. The recent discovery of a UHE white dwarf that is both spectroscopically and photometrically variable led to the speculation that the UHE lines might be created in a shock-heated circumstellar magnetosphere. Aims. We aim to gain a better understanding of these mysterious objects by studying the photometric variability of the whole popula tion of UHE white dwarfs, and white dwarfs showing only the He ii line problem, as both phenomena are believed to be connected. Methods. We investigate (multi-band) light curves from several ground- and space-based surveys of all 16 currently known UHE white dwarfs (including one newly discovered) and eight white dwarfs that show only the He ii line problem. Results. We find that 75+8 −13% of the UHE white dwarfs, and 75+9 −19% of the He ii line problem white dwarfs are significantly photo metrically variable, with periods ranging from 0.22 d to 2.93 d and amplitudes from a few tenths to a few hundredths of a magnitude. The high variability rate is in stark contrast to the variability rate amongst normal hot white dwarfs (we find 9+4 −2%), marking UHE and He ii line problem white dwarfs as a new class of variable stars. The period distribution of our sample agrees with both the orbital period distribution of post-common-envelope binaries and the rotational period distribution of magnetic white dwarfs if we assume that the objects in our sample will spin-up as a consequence of further contraction. Conclusions. We find further evidence that UHE and He ii line problem white dwarfs are indeed related, as concluded from their overlap in the Gaia HRD, similar photometric variability rates, light-curve shapes and amplitudes, and period distributions. The lack of increasing photometric amplitudes towards longer wavelengths, as well as the nondetection of optical emission lines arising from the highly irradiated face of a hypothetical secondary in the optical spectra of our stars, makes it seem unlikely that an irradiated late-type companion is the origin of the photometric variability. Instead, we believe that spots on the surfaces of these stars and/or geometrical effects of circumstellar material might be responsible

The frequency of gaseous debris discs around white dwarfs

A total of 1–3 per cent of white dwarfs are orbited by planetary dusty debris detectable as infrared emission in excess above the white dwarf flux. In a rare subset of these systems, a gaseous disc component is also detected via emission lines of the Ca ii 8600 Å triplet, broadened by the Keplerian velocity of the disc. We present the first statistical study of the fraction of debris discs containing detectable amounts of gas in emission at white dwarfs within a magnitude and signal-to-noise ratio limited sample. We select 7705 single white dwarfs spectroscopically observed by the Sloan Digital Sky Survey (SDSS) and Gaia with magnitudes g ≤ 19. We identify five gaseous disc hosts, all of which have been previously discovered. We calculate the occurrence rate of a white dwarf hosting a debris disc detectable via Ca ii emission lines as 0.067±0.0420.025 per cent. This corresponds to an occurrence rate for a dusty debris disc to have an observable gaseous component in emission as 4 ± 42 per cent. Given that variability is a common feature of the emission profiles of gaseous debris discs, and the recent detection of a planetesimal orbiting within the disc of SDSS J122859.93+104032.9, we propose that gaseous components are tracers for the presence of planetesimals embedded in the discs and outline a qualitative model. We also present spectroscopy of the Ca ii triplet 8600 Å region for 20 white dwarfs hosting dusty debris discs in an attempt to identify gaseous emission. We do not detect any gaseous components in these 20 systems, consistent with the occurrence rate that we calculated

Ground-based observation of ZZ Ceti stars and the discovery of four new variables

We perform ground-based photometric observations of 22 DA white dwarf stars, 10 already known ZZ Cetis and 12 candidates with atmospheric parameters inside the classical instability strip. We report on the discovery of four new variable DA white dwarf stars. Two objects are near the middle of the instability strip, SDSS J082804.63+094956.6 and SDSS J094929.09+101918.8, and two red edge pulsators, GD 195 and L495−82. In addition, we classified four objects as possible variables, since evidence of variability was detected in the light curve, but the signal-to-noise ratio was not sufficient to establish a definite detection. Follow-up observations were performed for 10 known ZZ Ceti stars to verify period stability and search for new periodicities. For each confirmed variable, we perform a detailed asteroseismological fit and compare the structural parameters obtained from the best-fitting models with those obtained from spectroscopy and photometry from Gaia. Finally we present a study of the asteroseismological properties of a sample of 91 ZZ Ceti stars

The McDonald Observatory search for pulsating sdA stars : asteroseismic support for multiple populations

Context. The nature of the recently identified “sdA” spectroscopic class of stars is not well understood. The thousands of known sdAs have H-dominated spectra, spectroscopic surface gravity values between main sequence stars and isolated white dwarfs, and effective temperatures below the lower limit for He-burning subdwarfs. Most are likely products of binary stellar evolution, whether extremely low-mass white dwarfs and their precursors or blue stragglers in the halo. Aims. Stellar eigenfrequencies revealed through time series photometry of pulsating stars sensitively probe stellar structural properties. The properties of pulsations exhibited by sdA stars would contribute substantially to our developing understanding of this class. Methods. We extend our photometric campaign to discover pulsating extremely low-mass white dwarfs from the McDonald Observatory to target sdA stars classified from SDSS spectra. We also obtain follow-up time series spectroscopy to search for binary signatures from four new pulsators. Results. Out of 23 sdA stars observed, we clearly detect stellar pulsations in 7. Dominant pulsation periods range from 4.6 min to 12.3 h, with most on timescales of approximately one hour. We argue specific classifications for some of the new variables, identifying both compact and likely main sequence dwarf pulsators, along with a candidate low-mass RR Lyrae star. Conclusions. With dominant pulsation periods spanning orders of magnitude, the pulsational evidence supports the emerging narrative that the sdA class consists of multiple stellar populations. Since multiple types of sdA exhibit stellar pulsations, follow-up asteroseismic analysis can be used to probe the precise evolutionary natures and stellar structures of these individual subpopulations

Discovery of 74 new bright ZZ Ceti stars in the first three years of TESS

We report the discovery of 74 new pulsating DA white dwarf stars, or ZZ Cetis, from the data obtained by the Transiting Exoplanet Survey Satellite mission, from Sectors 1 to 39, corresponding to the first 3 cycles. This includes objects from the Southern hemisphere (Sectors 1–13 and 27–39) and the Northern hemisphere (Sectors 14–26), observed with 120 s- and 20 s-cadence. Our sample likely includes 13 low-mass and one extremely low-mass white dwarf candidate, considering the mass determinations from fitting Gaia magnitudes and parallax. In addition, we present follow-up time series photometry from ground-based telescopes for 11 objects, which allowed us to detect a larger number of periods. For each object, we analysed the period spectra and performed an asteroseismological analysis, and we estimate the structure parameters of the sample, i.e. stellar mass, effective temperature, and hydrogen envelope mass. We estimate a mean asteroseismological mass of 〈Msis〉 = 0.635 ± 0.015 M⊙, excluding the candidate low or extremely low-mass objects. This value is in agreement with the mean mass using estimates from Gaia data, which is 〈Mphot〉 = 0.631 ± 0.040 M⊙, and with the mean mass of previously known ZZ Cetis of 〈M*〉 = 0.644 ± 0.034 M⊙. Our sample of 74 new bright ZZ Cetis increases the number of known ZZ Cetis by ∼20 per cent

Linhas-satélite no espectro de hidrogênio perturbado por prótons

Quando um átomo colide com outras partículas durante um processo de emissão ou absorção de fótons, seu espectro é afetado por essa interação. Esse efeito é conhecido por alargamento colisional ou alargamento por pressão e é um dos diversos mecanismos de alargamento que pode afetar uma linha espectral. A diferença entre esse mecanismo e os demais é a possibilidade de formação de um estado ligado transiente entre partícula radiadora e perturbadores durante a colisão. Esse estado é chamado quase-molécula e tem um espectro de energia distinto daquele das partículas isoladas. Assim sendo, além do alargamento, há a possibilidade de formação de linhas em comprimentos de onda que não podem ser explicados se considerado o espectro das partículas isoladas. Essas linhas são chamadas satélites, e sua presença também induz assimetrias no perfil e mudança na opacidade do gás, o que, no caso de atmosferas estelares, altera a cor das estrelas. Satélites já foram detectadas no espectro ultravioleta de estrelas anãs brancas com temperaturas próximas a 15000K. Apesar dessas identificações preliminares, ocorridas nos anos 1980, modelos de atmosfera que incluam consistentemente os efeitos quasemoleculares ainda não existem. Com o advento de grandes projetos de mapeamento do céu, como o Sloan Digital Sky Survey (SDSS), o número de anãs brancas conhecidas está crescendo significativamente. No data release 7 do SDSS, encontramos 19712 (Kleinman et al. , 2013), duplicando o número de anãs brancas conhecidas. Com os data releases 9 e 10, descobrimos outras 8800 (Kepler et al. , 2014). A boa determinação da temperatura e da massa dessas estrelas, que é importante para o entendimento do histórico de formação estelar na nossa Galáxia, depende do conhecimento da forma das linhas de Balmer, que são as mais fortes em cerca de 80% das anãs brancas. Como elas são afetadas pelas colisões com os prótons livres da atmosfera parcialmente ionizada das anãs brancas, é importante que esse efeito seja considerado. Por isso, desenvolvemos um código que permite o cálculo das contribuições quasemoleculares do H+2 ao espectro do átomo de hidrogênio. O método escolhido foi a teoria unificada em seu desenvolvimento quântico, conforme proposto por Allard et al. (1999), pois ela permite determinar a forma completa da linha. Utilizamos os dados disponibilizados por Santos & Kepler (2012) para calcular as contribuições do H+2 à série de Lyman até Lyman-δ e à série de Balmer até Balmer-10. Em seu trabalho, eles também obtiveram os perfis para todas essas linhas na aproximação quase-estática, mas tal método, devido à suposição de velocidade nula, não é válido para o centro da linha. Obtivemos os perfis em densidades de perturbadores e temperaturas que podem descrever bem a atmosfera de estrelas anãs brancas. Todos os satélites já observados foram identificados, juntamente com outros ainda não detectados. Além disso, o código foi escrito de forma que leia quaisquer potencial e momento de dipolo dados, de modo que ele pode ser utilizado para avaliar contribuições devido a outras partículas. Esperamos que os perfis obtidos possam ser incluídos em modelos de atmosfera para estrelas anãs brancas e que este estudo possa ser estendido para incluir as contribuições importantes de outros perturbadores.When an atom collides with particles during a process of emission or absorption of a photon, its spectrum is affected by this interaction. Such effect is known as collisional broadening or pressure broadening and it’s one of many broadening mechanisms that can affect a spectral line. The difference between such mechanism and others is the possibility of formation of a transient bound state between radiating particle and perturbers during the collision. Such state is known as quasi-molecule, and it has an energy spectra different than the one by isolated particles. So, besides the broadening, there is also the possibility of lines forming at wavelengths that can not be explained in terms of the spectra of the isolated particles. Those lines are called satellites, and its presence also induces asymmetries in the profile and changes in the gas opacity, what, in the case of stellar atmospheres, alters the color of the stars. Satellites were already detected in the ultraviolet spectra of white dwarf stars with temperatures around 15000K. In spite of those early identifications, done in the 1980s, atmosphere models that take quasi-molecular effects fully in account still do not exist. With the advent of large projects of sky mapping, such as Sloan Digital Sky Survey (SDSS), the number of known white dwarfs is significantly growing. In the data release 7 of SDSS, we found 19712 (Kleinman et al. , 2013), doubling the number of known white dwarfs. With data releases 9 and 10, we discovered another 8800 (Kepler et al. , 2014). The good determination of temperature and mass for those stars, which is important to the understanding of the history of star formation in our Galaxy, depends on the knowledge of the shape of the Balmer lines, that are the strongest ones in around 80% of white dwarfs. As they are affected by collisions with free protons of the partially ionized atmosphere of the white dwarfs, it is important that such effect be considered. Thus, we developed a code that allows the calculation of quasi-molecular H+2 contributions to the spectrum of the hydrogen atom. The chosen approach was the unified theory in its quantum-mechanical development, as proposed by Allard et al. (1999), because it allows the determination of the shape of the whole line. We used data provided by Santos & Kepler (2012) to evaluate H+2 contributions to the Lyman series up to Lyman-δ and to the Balmer series up to Balmer-10. In their work, they also obtained the profiles for all those lines in the quasistatic approach, but that method, due to its assumption of zero velocity, is not valid for the line center. We obtained the profiles at perturber densities and temperatures that can describe well the atmosphere of white dwarfs stars. All the satellites already observed are identified, together with others not yet detected. Besides that, the code was written in a way that it reads any given potential energy and dipole moment data, so it can be used to evaluate contributions due to other particles. We hope that the obtained profiles can be included in atmosphere models for white dwarf stars and that this study can be extended to include contributions due to other important perturbers

Estudo do efeito de colisões H-H+ no espectro do átomo de hidrogênio

Neste trabalho, estudamos o efeito de colisões sobre o espectro de um átomo de hidrogênio. A teoria de alargamento espectral foi revisada, com ênfase no alargamento por colisões. Para esse tipo de alargamento, existem três modelos: a Aproximação Quasi-estática, que desconsidera a velocidade das partículas perturbadoras, o Modelo Quântico, que considera o emissor e os perturbadores como uma quasimolécula gigante e resolve o equação de Schrödinger para esse sistema, e as Teorias Unificadas. Dentre as Teorias Unificadas, adotamos o Modelo de Anderson-Talman, o qual inclui todas as características dos outros modelos, mas assume que o emissor e o perturbador interagem fracamente, de modo que a perturbação é adiabática e a trajetória do perturbador pode ser aproximada como retilínea e com velocidade constante. Além disso, desconsidera-se a interação entre os perturbadores. Utilizando esse modelo, nos concentramos no efeito das colisões com prótons no espectro do átomo de hidrogênio. Tal efeito é observado, por exemplo, no espectro ultravioleta de anãs brancas, especialmente na forma de linhas-satélite. Para modelar essa interação, utilizamos primeiramente um potencial de poço-quadrado com profundidade e alcance ajustados a um potencial realista. Com o potencial do tipo poço, que permite o cálculo analítico da função de autocorrelação, pudemos descrever o efeito de variações na densidade, e na temperatura, sobre a linha espectral. A densidade afeta apenas a amplitude das linhas e sua largura à meia altura. Já a temperatura afeta também a posição das linhas e pode, ainda, tornar os satélites assimétricos. Também utilizamos outros potenciais para verificar sua adequação em descrever a interação entre perturbador e emissor. Verificamos que um potencial da forma de uma meia gaussiana invertida ´e inadequado, já que tem um alcance exageradamente longo e uma parte confinante também muito larga. Além disso, ele não vai a infinito conforme se aproximam as partículas, o que é esperado em razão da repulsão coulombiana. Isso é resolvido com o uso de um potencial de Lennard-Jones, com o qual foi possível obter uma linha espectral em concordância com o que se tem na literatura, apresentando alargamento coerente com o observado e, ainda, alguns satélites. Esperamos que, com os conhecimentos adquiridos nesse trabalho, seja possível obter um perfil de linha a partir de potenciais realistas calculados numericamente e levando em conta, além disso, os momentos de dipolo que descrevem a probabilidade entre transições. Com isso, pode-se incorporar o efeito de colisões com prótons como uma fonte de opacidade em modelos de atmosfera, obtendo-se modelos mais precisos que permitirão melhor determinação de propriedades físicas de estrelas que contenham hidrogênio em sua atmosfera.We studied the effect of colisions in the spectrumof a hydrogen atom. The theory of spectral broadening was reviewed, with emphasis on collisional broadening. There are three models for this type of broadening: the Quasi-static Approximation, which disregards the motion of the perturber particles, the Quantum Model, which treats the radiator and the perturbers as a giant quasimolecule and solves the Schr¨odinger equation to the system, and the Unified Theories. For the Unified Theory, we adopted the Anderson-Talman model, which includes all other models, but assumes that the radiator and the perturbers interact weakly, so that the perturbation is adiabatic and the perturber trajectory may be treated as rectilineal and with constant speed. In addition, it desconsiders the interaction between the perturbers. Using this model, we focused on the effect of collisions with protons in the spectrum of the hydrogen atom. Such effect is observed on the ultraviolet spectrum of white dwarf stars, especially by means of satellite lines. To model this interaction, we used initially a square-well potential with depth and range fitted to a realistic potential. With the square-well potential, which gives an analytical autocorrelation function, we could describe the effect of changes in the density of the perturbers, and of the temperature, on the spectral line. The density affects only the amplitude and the full width at half maximum of the lines. The temperature has effect on the position of the lines as well and can also make the satellites asymetrical. We checked whether other simple potentials could describe the interaction between perturber and radiator. We verified that a potential written as a half-gaussian upside down is inappropriate, because it has a range which is exceedingly large and a confining-well too wide. Besides, it doesn’t diverges when R→0, which is expected due to the couloumbian repulsion. That is solved by the use of a Lennard-Jonnes potential, with which it was possible to obtain an spectral line in agreement with the literature, showing a broadening consistent with the observed and, also, some satellites. We hope that, with the knowledge acquired in this work, it will be possible to obtain a spectral profile from realistic potentials evaluated numerically and also taking in account the dipole moment which describes the probability between transitions. Therewith, one can add the effect of collisions with protons as a source of opacity in atmosphere models, obtaining better models which are going to provide more accurately the physical properties of stars whose atmosphere contains hydrogen