Bolometric correction

In astronomy, the bolometric correction is the correction made to the absolute magnitude of an object in order to convert its visible magnitude to its bolometric magnitude. It is large for stars which radiate much of their energy outside of the visible range. A uniform scale for the correction has not yet been standardized.

Description

Mathematically, such a calculation can be expressed:

The bolometric correction for a range of stars with different spectral type and groups is shown in the following table:[1][2][3]

Spectral type Main Sequence Giants Supergiants
O3 -4.3 -4.2 -4.0
G0 -0.10 -0.13 -0.1
G5 -0.14 -0.34 -0.20
K0 -0.24 -0.42 -0.38
K5 -0.66 -1.19 -1.00
M0 -1.21 -1.28 -1.3

The bolometric correction is large both for early type (hot) stars and for late type (cool) stars. The former because a substantial part of the produced radiation is in the ultraviolet, the latter because a large part is in the infrared. For a star like our Sun, the correction is only marginal because the Sun radiates most of its energy in the visual wavelength range. Bolometric correction is the correction made to the absolute magnitude of an object in order to convert an object's visible magnitude to its bolometric magnitude.

Alternatively, the bolometric correction can be made to absolute magnitudes based on other wavelength bands beyond the visible electromagnetic spectrum.[4] For example, and somewhat more commonly for those cooler stars where most of the energy is emitted in the infrared wavelength range, sometimes a different value set of bolometric corrections is applied to the absolute infrared magnitude, instead of the absolute visual magnitude.

Mathematically, such a calculation could be expressed:

[5]

Where MK is the absolute magnitude value and BCK is the bolometric correction value in the K-band.[6]

Setting the correction scale

The bolometric correction scale is set by the absolute magnitude of the Sun and an adopted (arbitrary) absolute bolometric magnitude for the Sun. Hence, while the absolute magnitude of the Sun in different filters is a physical and not arbitrary quantity, the absolute bolometric magnitude of the Sun is arbitrary, and so the zero-point of the bolometric correction scale that follows from it. This explain why classic references have tabulated apparently mutually incompatible values for these quantities.[7] The bolometric scale historically had varied somewhat in the literature, with the Sun's bolometric correction in V-band varying from -0.19 to -0.07 magnitude. It follows that any value for the absolute bolometric magnitude of the Sun is legitimate, on the condition that once chosen all bolometric corrections are rescaled accordingly. If not, this will induce systematic errors in the determination of stellar luminosities.[7][8]

The XXIXth International Astronomical Union (IAU) General Assembly in Honolulu adopted in August 2015 Resolution B2 on recommended zero points for the absolute and apparent bolometric magnitude scales.[9][10]

Although bolometric magnitudes have been in use for over eight decades, there have been systematic differences in the absolute magnitude-luminosity scales presented in various astronomical references with no international standardization. This has led to systematic differences in bolometric correction scales. When combined with incorrect assumed absolute bolometric magnitudes for the Sun this can lead to systematic errors in estimated stellar luminosities. Many stellar properties are calculated based on stellar luminosity, such as radii, ages, etc.

IAU 2015 Resolution B2 proposed an absolute bolometric magnitude scale where corresponds to luminosity 3.0128×1028 W, with the zero point luminosity chosen such that the Sun (with nominal luminosity 3.828×1026 W) corresponds to absolute bolometric magnitude . Placing a radiation source (e.g. star) at the standard distance of 10 parsecs, it follows that the zero point of the apparent bolometric magnitude scale corresponds to irradiance , where the nominal total solar irradiance measured at 1 astronomical unit (1361 W/m2) corresponds to an apparent bolometric magnitude of the Sun of .

A similar IAU proposal in 1999 (with a slightly different zero point, tied to an obsolete solar luminosity estimate) was adopted by IAU Commissions 25 and 36. However it never reached a General Assembly vote, and subsequently was only adopted sporadically by astronomers in the literature.

See also

External links

References

  1. ^ Popper, Daniel M. (1980-09-01). "Stellar Masses". Annual Review of Astronomy and Astrophysics. 18 (1): 115–164. Bibcode:1980ARA&A..18..115P. doi:10.1146/annurev.aa.18.090180.000555. ISSN 0066-4146.
  2. ^ Humphreys, R. M.; McElroy, D. B. (1984). "The initial mass function for massive stars in the Galaxy and the Magellanic Clouds". The Astrophysical Journal. 284: 565–577. Bibcode:1984ApJ...284..565H. doi:10.1086/162439. ISSN 0004-637X.
  3. ^ B., Kaler, James (1989). Stars and their spectra : an introduction to the spectral sequence. Cambridge [Cambridgeshire]: Cambridge University Press. ISBN 978-0521304948. OCLC 17731797.
  4. ^ Bessell, M. S.; et al. (May 1998). "Model atmospheres broad-band colors, bolometric corrections and temperature calibrations for O - M stars". Astronomy and Astrophysics. 333: 231–250. Bibcode:1998A&A...333..231B.
  5. ^ Salaris, Maurizio; et al. (November 2002). "Population effects on the red giant clump absolute magnitude: the K band". Monthly Notices of the Royal Astronomical Society. 337 (1): 332–340. arXiv:astro-ph/0208057. Bibcode:2002MNRAS.337..332S. doi:10.1046/j.1365-8711.2002.05917.x. Lower effective temperatures correspond to higher values of ; since , cooler RC stars tend to be brighter.
  6. ^ Buzzoni, A.; et al. (April 2010). "Bolometric correction and spectral energy distribution of cool stars in Galactic clusters". Monthly Notices of the Royal Astronomical Society. 403 (3): 1592–1610. arXiv:1002.1972. Bibcode:2010MNRAS.403.1592B. doi:10.1111/j.1365-2966.2009.16223.x. Retrieved 23 August 2015.
  7. ^ a b c Casagrande, Luca; VandenBerg, Don A. (October 2014), "Synthetic stellar photometry: general considerations and new transformations for broad-band systems", Monthly Notices of the Royal Astronomical Society, 444 (1): 392, arXiv:1407.6095, Bibcode:2014MNRAS.444..392C, doi:10.1093/mnras/stu1476 with up-to-date interpolation codes https://github.com/casaluca/bolometric-corrections
  8. ^ a b Casagrande, L; VandenBerg, Don A (2018-01-18). "Synthetic Stellar Photometry – II. Testing the bolometric flux scale and tables of bolometric corrections for the Hipparcos/Tycho, Pan-STARRS1, SkyMapper, and JWST systems". Monthly Notices of the Royal Astronomical Society. 475 (4): 5023–5040. arXiv:1801.05508. Bibcode:2018MNRAS.475.5023C. doi:10.1093/mnras/sty149. ISSN 0035-8711.
  9. ^ IAU XXIX General Assembly Draft Resolutions Announced, retrieved 2015-07-08
  10. ^ Mamajek, E. E.; et al. (2015). "IAU 2015 Resolution B2 on Recommended Zero Points for the Absolute and Apparent Bolometric Magnitude Scales". arXiv:1510.06262v2 [astro-ph.SR].
  11. ^ Flower, Phillip J. (September 1996), "Transformations from Theoretical Hertzsprung-Russell Diagrams to Color-Magnitude Diagrams: Effective Temperatures, B-V Colors, and Bolometric Corrections", The Astrophysical Journal, 469: 355, Bibcode:1996ApJ...469..355F, doi:10.1086/177785
  12. ^ a b Torres, Guillermo (November 2010). "On the Use of Empirical Bolometric Corrections for Stars". The Astronomical Journal. 140 (5): 1158–1162. arXiv:1008.3913. Bibcode:2010AJ....140.1158T. doi:10.1088/0004-6256/140/5/1158. Lay summary.
AB7

AB7, also known as SMC WR7, is a binary star in the Small Magellanic Cloud. A Wolf-Rayet star and a supergiant companion of spectral type O orbit in a period of 19.56 days. The system is surrounded by a ring-shaped nebula known as a bubble nebula.

Absolute magnitude

Absolute magnitude is a measure of the luminosity of a celestial object, on a logarithmic astronomical magnitude scale. An object's absolute magnitude is defined to be equal to the apparent magnitude that the object would have if it were viewed from a distance of exactly 10 parsecs (32.6 light-years), with no extinction (or dimming) of its light due to absorption by interstellar dust particles. By hypothetically placing all objects at a standard reference distance from the observer, their luminosities can be directly compared on a magnitude scale. As with all astronomical magnitudes, the absolute magnitude can be specified for different wavelength ranges corresponding to specified filter bands or passbands; for stars a commonly quoted absolute magnitude is the absolute visual magnitude, which uses the visual (V) band of the spectrum (in the UBV photometric system). Absolute magnitudes are denoted by a capital M, with a subscript representing the filter band used for measurement, such as MV for absolute magnitude in the V band.

The more luminous an object, the smaller the numerical value of its absolute magnitude. A difference of 5 magnitudes between the absolute magnitudes of two objects corresponds to a ratio of 100 in their luminosities, and a difference of n magnitudes in absolute magnitude corresponds to a luminosity ratio of 100(n/5). For example, a star of absolute magnitude MV=3 would be 100 times more luminous than a star of absolute magnitude MV=8 as measured in the V filter band. The Sun has absolute magnitude MV=+4.83. Highly luminous objects can have negative absolute magnitudes: for example, the Milky Way galaxy has an absolute B magnitude of about −20.8.An object's absolute bolometric magnitude represents its total luminosity over all wavelengths, rather than in a single filter band, as expressed on a logarithmic magnitude scale. To convert from an absolute magnitude in a specific filter band to absolute bolometric magnitude, a bolometric correction is applied.

For Solar System bodies that shine in reflected light, a different definition of absolute magnitude (H) is used, based on a standard reference distance of one astronomical unit.

Chi Centauri

Chi Centauri (χ Cen, χ Centauri) is a star in the constellation Centaurus.

χ Centauri is a blue-white B-type main sequence dwarf with a mean apparent magnitude of +4.36. It is approximately 510 light years from Earth. It is classified as a Beta Cephei type variable star and its brightness varies by 0.02 magnitudes with a period of 50.40 minutes.

This star is a proper motion member of the Upper-Centaurus Lupus sub-group in the

Scorpius-Centaurus OB association,

the nearest such co-moving association of massive stars to the Sun.

DY Centauri

DY Centauri is a variable star in the constellation Centaurus. From its brightness, it is estimated to be 7000 parsecs (23000 light-years) away from Earth.DY Centauri is classified as a R Coronae Borealis variable (RCB), a rare class of supergiant stars which show rapid and irregular decreases in brightness due to the formation of dust clouds on the stellar surface. However, DY Centauri is not an active RCB star anymore, and the last registered obscuration event was in 1934. This seems to be related to evolutionary changes in the star, represented by a very fast horizontal movement across the top of the HR diagram. Spectroscopic and photometric evidence show DY Centuari has increased its effective temperature from 5800 K in 1906 to 24800 K in 2010, while maintaining constant luminosity. As consequence, its visual apparent magnitude has faded from about 11.75 in the beginning of the 20th century to 13.2 in 2010 (due to changes in the bolometric correction), while its radius is calculated to have decreased from 100 R☉ to 8 R☉. There are only three other known stars with this behavior, called hot RCB stars.Periodic changes in the radial velocity of DY Centauri have been detected, indicating that the star in a single-lined spectroscopic binary in an eccentric orbit (e = 0.44) with a period of 39.67 days. The companion star has an estimated minimum mass of 0.2 M☉, so it can be a low mass white dwarf or main sequence star. With an estimated separation of only 10 R☉ at periastron, the system must have interacted in the past when the primary had larger dimensions, forming a common envelope.DY Centauri has a peculiar chemical composition and is poor in hydrogen and rich in helium and carbon, being identified as an extreme helium star (EHe). In comparison to other RCB and EHe stars, however, its hydrogen content is relatively high. Stars of this type are believed to be the product of the merger of two white dwarfs, therefore being single stars, which is inconsistent with the identification of DY Centauri as a close binary. Thus, the origin and evolutionary state of the DY Centauri system remain uncertain. In the future, it is likely that the primary will evolve to a B subdwarf, a class of stars frequently found in binary systems.The spectrum of DY Centauri indicates the presence of a low density expanding nebula around it, formed by gas ionized by ultraviolet radiation from the star. The nebula has an estimated dimension of 1.2 arcseconds and, from its expansion velocity, was probably created about a thousand years ago.

Gliese 581

Gliese 581 () is a star of spectral type M3V (a red dwarf) at the center of the Gliese 581 planetary system, about 20 light years away from Earth in the Libra constellation. Its estimated mass is about a third of that of the Sun, and it is the 89th closest known star to the Sun.

Gliese 832

Gliese 832 (Gl 832 or GJ 832) is a red dwarf of spectral type M2V in the southern constellation Grus. The apparent visual magnitude of 8.66 means that it is too faint to be seen with the naked eye. It is located relatively close to the Sun, at a distance of 16.2 light years and has a high proper motion of 818.93 milliarcseconds per year. Gliese 832 has just under half the mass and radius of the Sun. Its estimated rotation period is a relatively leisurely 46 days. The star is roughly 9.5 billion years old.In 2014, Gliese 832 was announced to be hosting the closest potentially habitable Earth-mass-range exoplanet to the Solar System. This star achieved perihelion some 52,920 years ago when it came within an estimated 15.71 ly (4.817 pc) of the Sun.

Hertzsprung–Russell diagram

The Hertzsprung–Russell diagram, abbreviated as H–R diagram, HR diagram or HRD, is a scatter plot of stars showing the relationship between the stars' absolute magnitudes or luminosities versus their stellar classifications or effective temperatures. More simply, it plots each star on a graph plotting the star's brightness against its temperature (color).

The diagram was created circa 1910 by Ejnar Hertzsprung and Henry Norris Russell and represents a major step towards an understanding of stellar evolution.

The related color–magnitude diagram (CMD) plots the apparent magnitudes of stars against their color, usually for a cluster so that the stars are all at the same distance.

Index of physics articles (B)

The index of physics articles is split into multiple pages due to its size.

To navigate by individual letter use the table of contents below.

Lambda Leporis

Lambda Leporis (λ Leporis) is a solitary, blue-white hued star in the southern constellation of Lepus. It is visible to the naked eye with an apparent visual magnitude of +4.29. Based upon an annual parallax shift of 3.83 mas, it is estimated to lie roughly 850 light years from the Sun. Relative to its neighbors, this star has a peculiar velocity of 16.3±2.8 km/s.This is a massive, B-type main-sequence star with a corrected stellar classification of B0.5 V. It has around 15 times the mass of the Sun and 4.5 times the Sun's radius. The star is radiating 15,488 times the Sun's luminosity from its photosphere at an effective temperature of 30,400 K.

List of photonics equations

This article summarizes equations in the theory of photonics, including geometric optics, physical optics, radiometry, diffraction, and interferometry.

Luminosity

In astronomy, luminosity is the total amount of energy emitted per unit of time by a star, galaxy, or other astronomical object. As a term for energy emitted per unit time, luminosity is synonymous with power.In SI units luminosity is measured in joules per second or watts. Values for luminosity are often given in the terms of the luminosity of the Sun, L⊙. 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.

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.

Nu Eridani

Nu Eridani (ν Eri) is a star in the constellation Eridanus. It is visible to the naked eye with an apparent visual magnitude of 3.93. The distance to this star is roughly 520 light years, based upon an annual parallax shift of 0.00625 arcseconds. If the star were 33 ly (10 pc) from the Sun, it would be the brightest star in the night sky with an apparent magnitude of −2.84. (Currently, the brightest star is Sirius at magnitude −1.46.)

This is a B-type subgiant star with a stellar classification of B1.5 IV. It is a hybrid pulsator variable, lying as it does on the overlapping instability strips for Beta Cephei variables and slowly pulsating B-type stars. The star shows at least fourteen pulsations frequencies, with nine that also display radial velocity variations. It has about nine times the mass of the Sun and six times the Sun's radius. Nu Eridani shines with 7,943 times the solar luminosity from its outer atmosphere at an effective temperature of 22,000 K.

Omicron Tauri

Omicron Tauri (ο Tau, ο Tauri) is a star in the constellation Taurus. Omicron Tauri is a yellow G-type giant with an apparent magnitude of +3.61. This star has three times the mass of the Sun and fifteen to eighteen times the Sun's radius. Based on the latter, interferometry-measured radius, it is rotating once every 533 days. It is approximately 212 light years from Earth and is radiating 155 times the luminosity of the Sun.This is a single-lined spectroscopic binary system with the two components orbiting each other over a period of 1,655 days with an eccentricity of 0.263.

R136a1

RMC 136a1 (usually abbreviated to R136a1) is a Wolf–Rayet star located at the center of R136, the central concentration of stars of the large NGC 2070 open cluster in the Tarantula Nebula. It lies at a distance of about 49.97 kiloparsecs (163,000 light-years) in a neighbouring galaxy known as the Large Magellanic Cloud. It has the highest mass and luminosity of any known star, at 315 M☉ and 8.7 million L☉, and is also one of the hottest, at around 53,000 K.

SMC AB8

AB8, also known as SMC WR8, is a binary star in the Small Magellanic Cloud (SMC). A Wolf-Rayet star and a main sequence companion of spectral type O orbit in a period of 16.638 days. It is one of only nine known WO stars, the only Wolf-Rayet star in the SMC not on the nitrogen sequence, and the only Wolf-Rayet star in the SMC outside the main bar.

Supergiant star

Supergiants are among the most massive and most luminous stars. Supergiant stars occupy the top region of the Hertzsprung–Russell diagram with absolute visual magnitudes between about −3 and −8. The temperature range of supergiant stars spans from about 3,450 K to over 20,000 K.

Upsilon Orionis

Upsilon Orionis (υ Ori, υ Orionis) is a star in the constellation Orion. It has the traditional name Thabit (ﺛﺎﺑﺖ, Arabic for "the endurer"). It is a blue-white main sequence star of apparent magnitude 4.62 located over 3000 light-years distant from the Solar System. It is a suspected Beta Cephei variable.

Xi Ursae Majoris

Xi Ursae Majoris (ξ Ursae Majoris, abbreviated Xi UMa, ξ UMa), also named Alula Australis, is a star system in the constellation of Ursa Major. On May 2, 1780, Sir William Herschel discovered that this was a binary star system, making it the first such system ever discovered. It was the first visual double star for which an orbit was calculated, when it was computed by Félix Savary in 1828. It is also a variable star with a small amplitude. Xi Ursae Majoris is found in the left hind paw of the Great Bear.

Zero Point (photometry)

In astronomy, the Zero Point in a photometric system is defined to be the detector count when the apparent magnitude is 0. The zero point is used to calibrate a system to the standard magnitude system, as the flux detected from stars will vary from detector to detector. Traditionally, Vega is used as the calibration star for the zero point magnitude in specific pass bands (U, B, and V), although often, an average of multiple stars is used for higher accuracy. It is not often practical to find Vega in the sky to calibrate the detector, so for general purposes, any star may be used in the sky that has a known apparent magnitude.

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