Bolometric correction

In

bolometric magnitude

. It is large for stars which radiate most 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:

BC=M_{\text{bol}}-M_{v}

The bolometric correction for a range of stars with different spectral types 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 and negative 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 the 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]

BC_{K}=M_{\text{bol}}-M_{k}

Where M_K is the absolute magnitude value and BC_K 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 explains 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.

bolometric magnitude

scale where

M_{\text{bol}}=0

corresponds to luminosity 3.0128×10²⁸

bolometric magnitude

M_{{\text{bol}}_{\rm {Sun}}}=4.74

. Placing a

bolometric magnitude

scale

m_{\text{bol}}=0

corresponds to irradiance

f_{o}=2.518021002...\times 10^{-8}\mathrm {W/m^{2}}

, where the nominal total

bolometric magnitude of the Sun

of

m_{{\text{bol}}_{\rm {Sun}}}=-26.832

.

A similar

IAU

Commissions 25 and 36. However it never reached a General Assembly vote, and subsequently was only adopted sporadically by astronomers in the literature.

External links

https://github.com/casaluca/bolometric-corrections - most up to date tables of bolometric corrections across the HR diagram and interpolation routines in different photometric filters^[7]^[8]
https://web.archive.org/web/20080312151621/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^[11] of bolometric corrections (note that these second set of tables are consistent with a bolometric magnitude of 4.73^[12] for the Sun and also be aware that there are misprint^[12] errors for a few of the figures in the tables)

References

ISSN 0066-4146
.

ISSN 0004-637X
.

OCLC 17731797.{{cite book}}: CS1 maint: multiple names: authors list (link
)

Bibcode:1998A&A...333..231B
.

S2CID 17930469
. Lower effective temperatures correspond to higher values of $BC_{K}$ ; since $M_{K}=M_{bol}-BC_{K}\!\,$ , cooler RC stars tend to be brighter.

S2CID 119181086
.

^
doi:10.1093/mnras/stu1476 with up-to-date interpolation codes https://github.com/casaluca/bolometric-corrections

^
ISSN 0035-8711
.

^ IAU XXIX General Assembly Draft Resolutions Announced, retrieved 2015-07-08

arXiv:1510.06262v2 [astro-ph.SR
].

doi:10.1086/177785

^
S2CID 119219274
.