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Theoretical isochrones for near-solar metallicity and a range of ages. In stellar evolution, an isochrone is a curve on the Hertzsprung-Russell diagram, representing a population of stars of the same age but with different mass. [1] The Hertzsprung-Russell diagram plots a star's luminosity against its temperature, or equivalently, its color ...
Thus, from the Stefan–Boltzmann law, the luminosity is related to the surface temperature T S, and through it to the color of the star, by = where σ B is Stefan–Boltzmann constant, 5.67 × 10 −8 W m −2 K −4. The luminosity is equal to the total energy produced by the star per unit time.
In massive stars (greater than about 1.5 M ☉), the core temperature is above about 1.8×10 7 K, so hydrogen-to-helium fusion occurs primarily via the CNO cycle. In the CNO cycle, the energy generation rate scales as the temperature to the 15th power, whereas the rate scales as the temperature to the 4th power in the proton-proton chains. [2]
where G is the gravitational constant, M is the mass of the star, R is the radius of the star, and L is the star's luminosity. As an example, the Sun 's thermal time scale is approximately 15.7 million years.
A star also radiates neutrinos, which carry off some energy (about 2% in the case of the Sun), contributing to the star's total luminosity. [5] The IAU has defined a nominal solar luminosity of 3.828 × 10 26 W to promote publication of consistent and comparable values in units of the solar luminosity. [6]
By measuring the peak wavelength of a star, the surface temperature can be determined. [17] For example, if the peak wavelength of a star is 502 nm the corresponding temperature will be 5772 kelvins. The luminosity of a star is a measure of the electromagnetic energy output in a given amount of time. [25]
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Along with this abundance information, a reasonable guess at the zero-age luminosity (such as the present-day Sun's luminosity) is then converted by an iterative procedure into the correct value for the model, and the temperature, pressure and density throughout the model calculated by solving the equations of stellar structure numerically ...