Luminosity
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.
[1][2] In astronomy, luminosity is the total amount of electromagnetic energy emitted per unit of time by a star, galaxy, or other astronomical objects.
Luminosity can also be given in terms of the astronomical magnitude system: the absolute bolometric magnitude (Mbol) 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.
[6] While bolometers do exist, they cannot be used to measure even the apparent brightness of a star because they are insufficiently sensitive across the electromagnetic spectrum and because most wavelengths do not reach the surface of the Earth.
[10] A star's luminosity can be determined from two stellar characteristics: size and effective temperature.
Both can be measured with great accuracy in certain cases, with cool supergiants often having large angular diameters, and some cool evolved stars having masers in their atmospheres that can be used to measure the parallax using VLBI.
However, for most stars the angular diameter or parallax, or both, are far below our ability to measure with any certainty.
A third component needed to derive the luminosity is the degree of interstellar extinction that is present, a condition that usually arises because of gas and dust present in the interstellar medium (ISM), the Earth's atmosphere, and circumstellar matter.
A star like Deneb, for example, has a luminosity around 200,000 L⊙, a spectral type of A2, and an effective temperature around 8,500 K, meaning it has a radius around 203 R☉ (1.41×1011 m).
For comparison, the red supergiant Betelgeuse has a luminosity around 100,000 L⊙, a spectral type of M2, and a temperature around 3,500 K, meaning its radius is about 1,000 R☉ (7.0×1011 m).
Red supergiants are the largest type of star, but the most luminous are much smaller and hotter, with temperatures up to 50,000 K and more and luminosities of several million L⊙, meaning their radii are just a few tens of R⊙.
The observed strength, or flux density, of a radio source is measured in Jansky where 1 Jy = 10−26 W m−2 Hz−1.
For example, consider a 10 W transmitter at a distance of 1 million metres, radiating over a bandwidth of 1 MHz.
More generally, for sources at cosmological distances, a k-correction must be made for the spectral index α of the source, and a relativistic correction must be made for the fact that the frequency scale in the emitted rest frame is different from that in the observer's rest frame.
So the full expression for radio luminosity, assuming isotropic emission, is
, and in radio astronomy, assuming thermal emission the spectral index is typically equal to 2.
)[15] For example, consider a 1 Jy signal from a radio source at a redshift of 1, at a frequency of 1.4 GHz.
To calculate the total radio power, this luminosity must be integrated over the bandwidth of the emission.
where A is the surface area, T is the temperature (in kelvins) and σ is the Stefan–Boltzmann constant, with a value of 5.670374419...×10−8 W⋅m−2⋅K−4.
A hollow sphere centered on the point would have its entire interior surface illuminated.
For stars on the main sequence, luminosity is also related to mass approximately as below:
Luminosity is an intrinsic measurable property of a star independent of distance.
The apparent magnitude is a measure of the diminishing flux of light as a result of distance according to the inverse-square law.
[17] The Pogson logarithmic scale is used to measure both apparent and absolute magnitudes, the latter corresponding to the brightness of a star or other celestial body as seen if it would be located at an interstellar distance of 10 parsecs (3.1×1017 metres).
[18] By measuring the width of certain absorption lines in the stellar spectrum, it is often possible to assign a certain luminosity class to a star without knowing its distance.
Thus a fair measure of its absolute magnitude can be determined without knowing its distance nor the interstellar extinction.
Since the Sun's luminosity is the standard, comparing these parameters with the Sun's apparent magnitude and distance is the easiest way to remember how to convert between them, although officially, zero point values are defined by the IAU.
The magnitude of a star, a unitless measure, is a logarithmic scale of observed visible brightness.
The apparent magnitude is the observed visible brightness from Earth which depends on the distance of the object.
The difference in bolometric magnitude between two objects is related to their luminosity ratio according to:[19]
