It is therefore necessary to combine interferometric measurements with the color or spectral types of stars and to establish empirical formulas for calculating effective temperatures. Boyajian et al. Based on these stellar parameters, they obtained the empirical equations of spectral-type— T eff and color— T eff for these stars. In the same way, Boyajian et al. These empirical equations can be used to calculate the effective temperature of the stars in other samples.
Second, effective temperatures can be indirectly measured using the stellar spectral lines. The more common methods are the excitation equilibrium of the Fe lines, or fitting Balmer lines.
The advantage of these two methods is that they are not affected by reddening, and the disadvantage is that they strongly depend on the model assumptions. In addition to directly measuring radius or indirectly using spectral lines, a so-called semi-direct method has often been used, called infrared flux method IRFM , to calculate the effective temperature. The advantage of the this method is that it can simultaenously measure the angular diameter and the effective temperature of the star.
The relations in these works are in the form of Eq. Equation A. In general, there are many ways to measure the effective temperature. Even if photometry alone is available, using the empirical color— T eff relation can also help to calculate effective temperature.
The greatest advantage in estimating stellar mass using the MLR is that a large sample of stars can be computed fast, and the methods we described above are all applicable to the rapid computing of large samples of stars, so that the addition of a temperature modifier does not affect the practicability of estimating the stellar masses. Data correspond to usage on the plateform after The current usage metrics is available hours after online publication and is updated daily on week days. Introduction 2.
General structure 4. UK versus US spelling and grammar 5. Punctuation and style concerns regarding equations, figures, tables, and footnotes 6. Verb tenses 7. General hyphenation guide 8. Common editing issues 9. Measurements and their descriptions Free Access. Top Abstract 1. Data selection 3. Modified estimation Alonso, A. Rucinski, G. A resulting MLR for the mass range 1. The stars discussed in Section 2 are shown together with their observational errors and are indicated by different symbols see the caption to the figure.
MLR of A—F stars. For comparison, components of close detached main-sequence double-lined eclipsing binaries i. Their typical uncertainty does not exceed 0. As can be seen from Fig. The resulting MLR and other relations of rapid rotators for the mass range 2. From top to bottom: MLR, mass—temperature and mass—radius relations of B stars. Symbols are as in Fig. HR diagram of B stars. A group of late B rapid rotators 4. Their radii slightly exceed those of the shorter period stars, and the temperatures of slow and rapid rotators do not differ.
It can be seen from Fig. It should be noted that according to Bennett et al. However, evolved main-sequence stars tend to be cooler, but no sign of this is seen in Fig 4. Our results are also in agreement with theoretical calculations. It should be reminded see Section 1 that here the luminosities for the slow rotators were derived from calibrations based on rapid rotators. However, as the reviewer Anthony Brown points out, the effect goes in the right-hand direction. If a correct calibration were available for slow rotators, they would be assigned lower luminosities, making the discrepancy with the late B stars worse.
It should be mentioned that there are other effects with an increasing observational bias such an age and metallicity dispersions. However, our two samples, slow and rapid rotators, apparently do not differ systematically from each other either in ages or in metallicities. More massive stars do not exhibit significant differences in luminosity, temperature and radius between slow and rapid rotators. In a previous study Malkov found a notable difference between the parameters of B0V—G0V components of eclipsing binaries and those of single stars of the corresponding spectral type.
In the present work data were collected on fundamental parameters mass, radius, luminosity, temperature of 52 intermediate-mass 1. Those stars are presumably not synchronized with the orbital periods. They are, consequently, rapid rotators and evolve similarly with single stars.
A weighted least-squares polynomial fit was performed to approximate the observational data by a spline for MLR, mass—radius and mass—temperature relations. For the mass range 1. Late B rapid rotators 4. There is no way to estimate the degree to which the effect on the IMF may be important for higher masses. Knowledge of the MLR of isolated stars should come from dynamical mass determinations of visual binaries combined with spatially resolved precise photometry.
The fact cannot be ignored that evolution within the main sequence confuses the rotation consequences for stellar parameters to the point where the two effects can only be separated with difficulty because there is a continuum of evolutionary states. A good possibility would be to select stars that are exactly on the ZAMS, but this is not practical as there would not be enough stars to do the analysis. In stellar ensembles of the same age and chemical composition such as open clusters one can hope to do this, because there the main sequence defined by all other stars serves as a reference.
However, very few stars in open clusters have dynamical mass determinations. I thank Annemarie Bridges for her careful reading of and constructive comments on the paper. Abt H. Levy S. Morrell N.
Africano J. Evans D. Fekel F. Smith B. Morgan C. Ahn Y. Armstrong J. Mozurkewich D. Vivekanand M. Baize P. Balega I. Balega Yu. Bennett P. Harper G. Brown A. Hummel C. Verschueren W. Baade R. Kirsch Th. Reimers D. Hatze A.
Kurster M. Clausen J. Helt B. Vaz L. Garcia J. Olsen E. Southworth J. Code A. Bless R. Davis J. Brown R. Collins G. II Sonneborn G. Couteau P. De Mey K. Aerts C. Waelkens C. Van Winckel H.
Delfosse X. Fortveille T. Beuzit J. Urdy S. Perrier C. Mayor M. Eaton J. Google Scholar. Google Preview. An 80 solar mass star is not that much bigger than the Sun, but its luminosity is 10 6 times greater. The radiation passing through each square meter of photosphere is perhaps 10 4 times greater than for the Sun.
Radiation can apply a pressure force per unit area when it interacts with matter because photons of light can act as particles. In collisions with atoms, the atoms can be kicked away from the star. At the upper mass limit of main sequence stars, the addition of a bit more mass would increase the luminosity and radiative flux and simply blow away what has been added.
Stable stars in a main sequence state with more than about 80 solar masses simply cannot exist. The lower mass limit on stars seems to be about 0. Below this mass limit, internal temperatures and pressures are too low to sustain thermonuclear conversion of hydrogen to helium.
The condition of hydrostatic equilibrium is that the pressure is balancing gravity. Since higher mass means a larger gravitational force, higher mass must also mean that higher pressure is required to maintain equilibrium. If you increase the pressure inside a star, the temperature will also increase. So, the cores of massive stars have significantly higher temperatures than the cores of Sun-like stars.
At higher temperatures, the nuclear fusion reactions generate energy much faster, so the hotter the core, the more luminous the star. If you actually look at the equations that govern stellar structure, you can derive from those equations that:. Below is a plot that obeys this relationship and gives the theoretical calculations of a star's luminosity given its initial mass on the Main Sequence.
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