Jitse Niesen: /* Example of a Nonstandard Finite Difference Model */ typo in equation

2012-03-01T14:13:46Z

Example of a Nonstandard Finite Difference Model: typo in equation

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In [[astronomy]], a '''bolometric correction''' is a correction that must be made to the absolute [[Magnitude (astronomy)|magnitude]] of an object in order to convert an object's [[visible magnitude]] to its [[Bolometric_magnitude#Bolometric_magnitude|bolometric magnitude]]. Mathematically, such a calculation can be expressed:
:<math> BC = M_b - M_v\!\,</math>

The following is subset of a table from Kaler<ref name="kalerpaper"/> (p. 263) listing the bolometric correction for a range of stars. For the full table, see the referenced work.

{| class="wikitable" border="1"
|-
! Class
! 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.

The bolometric correction scale is set by the absolute magnitude of the Sun and an adopted [[bolometric magnitude]] for the [[Sun]]. The choice of adopted solar absolute magnitude, bolometric correction, and absolute bolometric magnitude are not arbitrary, although some classic references have tabulated mutually incompatible values for these quantities
.<ref name=tableprovisoBC/> 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. Since the Sun is also a variable star, and there are minor differences in adopted solar luminosity values (albeit at a subtle level), in 1999 two [[IAU]] commissions
(Commissions 25: Stellar Photometry and Polarimetry, and Commission 36: Theory
of Stellar Atmospheres) agreed to separate the definition of bolometric correction and magnitude from the variable Sun. The 1999 [[IAU]] statements define that absolute bolometric magnitude zero correlates to a bolometric luminosity of 3.055e28 [[Watt]]s. This particular luminosity was selected as the zero-point for the absolute bolometric magnitude scale so that the Sun's luminosity (3.842e26 Watts) would correspond to absolute bolometric magnitude 4.75
(the value that was most commonly used by most astronomers). As the Sun has an apparent V magnitude of -26.75, and absolute V magnitude of 4.82, then the IAU bolometric magnitude scale implies that the bolometric correction for the Sun (with effective temperature of 5778 K) is -0.07 magnitude.<ref name=mamajeksun /> The new IAU definition means that theoretical evolutionary models for stars can define brightnesses in terms of bolometric and absolute magnitudes on a scale that is tied to a physical quantity (the luminosity zero-point of 3.055e28 [[Watt]]s) rather than to the Sun (which is intrinsically variable, and there are systematic uncertainties in the value of the solar flux constant as measured at 1 AU).

==See also==
*[[absolute magnitude]]

==External links==
*http://www.peripatus.gen.nz/Astronomy/SteMag.html - contains table of bolometric corrections
*http://articles.adsabs.harvard.edu//full/1996ApJ...469..355F/0000360.000.html - contains detailed tables<ref name=tablesof_bolometric_correction/> of bolometric corrections (note that these second set of tables are consistent with a bolometric magnitude of 4.73<ref name=tableprovisoBC/> for the Sun and also be aware that there are misprint<ref name=tableprovisoBC/> errors for a few of the figures in the tables)

==References==
{{reflist|30em|refs=

<ref name=kalerpaper>{{cite journal | title = Stars and their spectra: An Introduction to the Spectral Sequence | author = Kaler, James B. | year = 1989 | pages = 300}}</ref>

<ref name=tablesof_bolometric_correction>{{citation | display-authors=1 | last1=Flower | first1=Phillip J.| title=Transformations from Theoretical Hertzsprung-Russell Diagrams to Color-Magnitude Diagrams: Effective Temperatures, B-V Colors, and Bolometric Corrections | url=http://articles.adsabs.harvard.edu//full/1996ApJ...469..355F/0000360.000.html | journal=[[The Astrophysical Journal]] | volume=469 | page=355 |date=September 1996 | doi=10.1086/177785| bibcode=1996ApJ...469..355F }}</ref>

<ref name=tableprovisoBC>{{cite journal | author=Torres, Guillermo | title=On the Use of Empirical Bolometric Corrections for Stars | url=http://iopscience.iop.org/1538-3881/140/5/1158/fulltext/ | journal=[[The Astronomical Journal]] |date=November 2010 | volume=140 | issue=5 | pages=1158–1162 | layurl=http://iopscience.iop.org/1538-3881/140/5/1158/fulltext/aj363350t3_ascii.txt | doi=10.1088/0004-6256/140/5/1158 | bibcode=2010AJ....140.1158T |arxiv = 1008.3913 }}</ref>

<ref name=mamajeksun>{{cite web |url=http://www.pas.rochester.edu/~emamajek/sun.txt |title=Basic Astronomical Data for the Sun (BADS)|author=Eric Mamajek |date=April 12, 2012|work= |publisher= |accessdate=6 May 2012}}</ref>

}}

[[Category:Observational astronomy]]

Nonstandard finite difference scheme - Revision history

Jitse Niesen: /* Example of a Nonstandard Finite Difference Model */ typo in equation