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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]
At a stellar core temperature of 18 million kelvin, the PP process and CNO cycle are equally efficient, and each type generates half of the star's net luminosity. As this is the core temperature of a star with about 1.5 M ☉, the upper main sequence consists of stars above this mass.
However, some stars are nearly identical to the Sun and are considered solar twins. An exact solar twin would be a G2V star with a 5,778 K temperature, be 4.6 billion years old, with the correct metallicity and a 0.1% solar luminosity variation. [153] Stars with an age of 4.6 billion years are at the most stable state.