Luminosity
Luminosity is an absolute measure of radiated
In
In contrast, the term brightness in astronomy is generally used to refer to an object's apparent brightness: that is, how bright an object appears to an observer. Apparent brightness depends on both the luminosity of the object and the distance between the object and observer, and also on any absorption of light along the path from object to observer. Apparent magnitude is a logarithmic measure of apparent brightness. The distance determined by luminosity measures can be somewhat ambiguous, and is thus sometimes called the luminosity distance.
Measurement
When not qualified, the term "luminosity" means bolometric luminosity, which is measured either in the
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. In practice bolometric magnitudes are measured by taking measurements at certain wavelengths and constructing a model of the total spectrum that is most likely to match those measurements. In some cases, the process of estimation is extreme, with luminosities being calculated when less than 1% of the energy output is observed, for example with a hot
The term luminosity is also used in relation to particular passbands such as a visual luminosity of K-band luminosity.[9] These are not generally luminosities in the strict sense of an absolute measure of radiated power, but absolute magnitudes defined for a given filter in a photometric system. Several different photometric systems exist. Some such as the UBV or Johnson system are defined against photometric standard stars, while others such as the AB system are defined in terms of a spectral flux density.[10]
Stellar luminosity
A star's luminosity can be determined from two stellar characteristics: size and
An alternative way to measure stellar luminosity is to measure the star's apparent brightness and distance. A third component needed to derive the luminosity is the degree of
In the current system of
Blue and white supergiants are high luminosity stars somewhat cooler than the most luminous main sequence stars. 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⊙. For example, R136a1 has a temperature over 46,000 K and a luminosity of more than 6,100,000 L⊙[14] (mostly in the UV), it is only 39 R☉ (2.7×1010 m).
Radio luminosity
The luminosity of a
For example, consider a 10 W transmitter at a distance of 1 million metres, radiating over a bandwidth of 1 MHz. By the time that power has reached the observer, the power is spread over the surface of a sphere with area 4πr2 or about 1.26×1013 m2, so its flux density is 10 / 106 / (1.26×1013) W m−2 Hz−1 = 8×107 Jy.
More generally, for sources at cosmological distances, a
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 = 2×1026 m giving a radio luminosity of 10−26 × 4π(2×1026)2 / (1 + 1)(1 + 2) = 6×1026 W Hz−1.
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 4×1027 × 1.4×109 = 5.7×1036 W. This is sometimes expressed in terms of the total (i.e. integrated over all wavelengths) luminosity of the Sun which is 3.86×1026 W, giving a radio power of 1.5×1010 L⊙.
Luminosity formulae
This section needs additional citations for verification. (July 2023) |
The Stefan–Boltzmann equation applied to a black body gives the value for luminosity for a black body, an idealized object which is perfectly opaque and non-reflecting:[11]
Imagine a point source of light of luminosity 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.
- is the area of the illuminated surface.
- is the flux densityof the illuminated surface.
The surface area of a sphere with radius r is , so for stars and other point sources of light:
For stars on the main sequence, luminosity is also related to mass approximately as below:
If we define as the mass of the star in terms of solar masses, the above relationship can be simplified as follows:
Relationship to magnitude
Luminosity is an intrinsic measurable property of a star independent of distance. The concept of magnitude, on the other hand, incorporates distance. The
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.
In measuring star brightnesses, absolute magnitude, apparent magnitude, and distance are interrelated parameters—if two are known, the third can be determined. 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
The difference in bolometric magnitude between two objects is related to their luminosity ratio according to:[19]
where:
- is the bolometric magnitude of the first object
- is the bolometric magnitude of the second object.
- is the first object's bolometric luminosity
- is the second object's bolometric luminosity
The zero point of the absolute magnitude scale is actually defined as a fixed luminosity of 3.0128×1028 W. Therefore, the absolute magnitude can be calculated from a luminosity in watts:
and the luminosity in watts can be calculated from an absolute magnitude (although absolute magnitudes are often not measured relative to an absolute flux):
See also
- Glossary of astronomy
- List of brightest stars
- List of most luminous stars
- Orders of magnitude (power)
- Solar luminosity
References
- ^ "Luminosity | astronomy". Encyclopedia Britannica. Retrieved 24 June 2018.
- ^ "* Luminosity (Astronomy) - Definition, meaning - Online Encyclopedia". en.mimi.hu. Retrieved 24 June 2018.
- ISBN 978-0-226-35171-1.
- ISBN 978-1-118-68152-7.
- ^ Bahcall, John. "Solar Neutrino Viewgraphs". Institute for Advanced Study School of Natural Science. Retrieved 3 July 2012.
- arXiv:1510.07674 [astro-ph.SR].
- S2CID 119275940.
- S2CID 119181086.
- ^ "ASTR 5610, Majewski [SPRING 2016]. Lecture Notes". www.faculty.virginia.edu. Archived from the original on 24 April 2021. Retrieved 3 February 2019.
- Bibcode:2000A&A...364..217D
- ^ a b "Luminosity of Stars". Australia Telescope National Facility. 12 July 2004. Archived from the original on 9 August 2014.
- ISBN 978-3-540-00179-9.
- Bibcode:2001JRASC..95...32L. Retrieved 2 July 2012.
- S2CID 118510909.
- S2CID 10579880.
- ^ "2022 CODATA Value: Stefan–Boltzmann constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. May 2024. Retrieved 18 May 2024.
- ^ Joshua E. Barnes (18 February 2003). "The Inverse-Square Law". Institute for Astronomy - University of Hawaii. Retrieved 26 September 2012.
- ^ "Magnitude System". Astronomy Notes. 2 November 2010. Retrieved 2 July 2012.
- ^ "Absolute Magnitude". csep10.phys.utk.edu. Retrieved 2 February 2019.
Further reading
- Böhm-Vitense, Erika (1989). "Chapter 6. The luminosities of the stars". Introduction to Stellar Astrophysics: Volume 1, Basic Stellar Observations and Data. ISBN 978-0-521-34869-0.
External links
- Luminosity calculator
- Ned Wright's cosmology calculator
- University of Southampton radio luminosity calculator at the Wayback Machine (archived 8 May 2015)