Luminosity

has an intrinsic luminosity of . In astronomy, this amount is equal to one solar luminosity, represented by the symbol L ☉ . A star with four times the radiative power of the Sun has a luminosity of . Luminosity is an absolute measure of radiated electromagnetic energy per unit time, and is synonymous with the radiant power emitted by a light-emitting object. In astronomy, luminosity is the total amount of electromagnetic energy emitted per unit of time by a star, galaxy, or other luminous astronomical object. In SI units, luminosity is measured in joules per second, or watts. In astronomy, the luminosity of the Sun, L ☉ is often used as a unit of luminosity. Luminosity can also be stated in the astronomical magnitude system: the absolute bolometric magnitude (M bol ) of an object is a logarithmic measure of its total energy emission rate, while absolute magnitude is a logarithmic measure of the luminosity within some specific wavelength range or filter band. In contrast, the term brightness in astronomy is generally used to refer to an object's apparent brightness to an observer. Apparent brightness depends on the luminosity of the object, the distance between the object and observer, and on any absorption of light along the path from object to observer. Apparent magnitude is a logarithmic measure of apparent brightness.…

has an intrinsic luminosity of . In astronomy, this amount is equal to one solar luminosity, represented by the symbol L ☉ . A star with four times the radiative power of the Sun has a luminosity of . Luminosity is an absolute measure of radiated electromagnetic energy per unit time, and is synonymous with the radiant power emitted by a light-emitting object. In astronomy, luminosity is the total amount of electromagnetic energy emitted per unit of time by a star, galaxy, or other luminous astronomical object. In SI units, luminosity is measured in joules per second, or watts. In astronomy, the luminosity of the Sun, L ☉ is often used as a unit of luminosity. Luminosity can also be stated in the astronomical magnitude system: the absolute bolometric magnitude (M bol ) of an object is a logarithmic measure of its total energy emission rate, while absolute magnitude is a logarithmic measure of the luminosity within some specific wavelength range or filter band. In contrast, the term brightness in astronomy is generally used to refer to an object's apparent brightness to an observer. Apparent brightness depends on the luminosity of the object, the distance between the object and observer, and on any absorption of light along the path from object to observer. Apparent magnitude is a logarithmic measure of apparent brightness. Distance can often be estimated as the luminosity distance if the luminosity is thought to be known, but this can be inaccurate. L_{\nu} = \frac{S_{\mathrm{obs}} 4 \pi {D_{L}}^{2}}{(1+z)^{1+\alpha}} where L ν is the luminosity in , S obs is the observed flux density in , D L is the luminosity distance in metres, z is the redshift, α is the spectral index (in the sense I \propto {\nu}^{\alpha} , and in radio astronomy, assuming thermal emission the spectral index is typically equal to 2.) For example, consider a 1 Jy signal from a radio source at a redshift of 1, at a frequency of 1.4 GHz. Ned Wright's cosmology calculator calculates a luminosity distance for a redshift of 1 to be 6701 Mpc = 2×10 26 m giving a radio luminosity of . To calculate the total radio power, this luminosity must be integrated over the bandwidth of the emission. A common assumption is to set the bandwidth to the observing frequency, which effectively assumes the power radiated has uniform intensity from zero frequency up to the observing frequency. In the case above, the total power is . This is sometimes expressed in terms of the total (i.e. integrated over all wavelengths) luminosity of the Sun which is , giving a radio power of . L = \sigma A T^4, where A is the surface area, T is the temperature (in kelvins) and is the Stefan–Boltzmann constant, with a value of Imagine a point source of light of luminosity L that radiates equally in all directions. A hollow sphere centered on the point would have its entire interior surface illuminated. As the radius increases, the surface area will also increase, and the constant luminosity has more surface area to illuminate, leading to a decrease in observed brightness. F = \frac{L}{A}, where A is the area of the illuminated surface. F is the flux density of the illuminated surface. The surface area of a sphere with radius r is A = 4\pi r^2 , so for stars and other point sources of light: F = \frac{L}{4\pi r^2} \,, where r is the distance from the observer to the light source. For stars on the main sequence, luminosity is also related to mass approximately as below: \frac{L}{L_{\odot}} \approx {\left ( \frac{M}{M_{\odot}} \right )}^{3.5}. M_\text{bol1} - M_\text{bol2} = -2.5 \log_{10}\frac{L_\text{1}}{L_\text{2}} where: M_{\text{bol1}} is the bolometric magnitude of the first object M_\text{bol2} is the bolometric magnitude of the second object. L_\text{1} is the first object's bolometric luminosity L_\text{2} is the second object's bolometric luminosity The zero point of the absolute magnitude scale is actually defined as a fixed luminosity of . Therefore, the absolute magnitude can be calculated from a luminosity in watts: M_\mathrm{bol} = -2.5 \log_{10} \frac{L_{*}}{L_0} \approx -2.5 \log_{10} L_{*} + 71.1974 where is the zero point luminosity and the luminosity in watts can be calculated from an absolute magnitude (although absolute magnitudes are often not measured relative to an absolute flux): L_{*} = L_0 \times 10^{-0.4 M_\mathrm{bol}} ==See also== Eddington luminosity Glossary of astronomy List of brightest stars List of most luminous stars Orders of magnitude (power) Solar luminosity ==References== ==Further reading== ==External links== Luminosity calculator Ned Wright's cosmology calculator

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