Editing Absolute magnitude (section)

=== Bolometric magnitude ===
{{See also|Apparent bolometric magnitude}}

The absolute [[Bolometer|bolometric]] magnitude ({{math|''M''<sub>bol</sub>}}) takes into account [[electromagnetic radiation]] at all [[wavelengths]]. It includes those unobserved due to instrumental [[passband]], the Earth's atmospheric absorption, and [[Extinction (astronomy)|extinction by interstellar dust]]. It is defined based on the [[luminosity]] of the stars. In the case of stars with few observations, it must be computed assuming an [[effective temperature]].

Classically, the difference in bolometric magnitude is related to the luminosity ratio according to:<ref name="Carroll"/>
<math display="block">M_\mathrm{bol,\star} - M_\mathrm{bol,\odot} = -2.5 \log_{10} \left(\frac{L_\star}{L_\odot}\right)</math>
which makes by inversion:
<math display="block">\frac{L_\star}{L_\odot} = 10^{0.4\left(M_\mathrm{bol,\odot} - M_\mathrm{bol,\star}\right)}</math>
where
*{{math|''L''<sub>⊙</sub>}} is the Sun's luminosity (bolometric luminosity)
*{{math|''L''<sub>★</sub>}} is the star's luminosity (bolometric luminosity)
*{{math|''M''<sub>bol,⊙</sub>}} is the bolometric magnitude of the Sun
*{{math|''M''<sub>bol,★</sub>}} is the bolometric magnitude of the star.

In August 2015, the [[International Astronomical Union]] passed Resolution B2<ref name="IAU_XXIX"/> defining the [[Zero Point (photometry)|zero points]] of the absolute and apparent [[bolometric magnitude]] scales in SI units for power ([[watt]]s) and irradiance (W/m<sup>2</sup>), respectively. Although bolometric magnitudes had been used by astronomers for many decades, there had been systematic differences in the absolute magnitude-luminosity scales presented in various astronomical references, and no international standardization. This led to systematic differences in bolometric corrections scales.<ref name="IAU2015B2"/> Combined with incorrect assumed absolute bolometric magnitudes for the Sun, this could lead to systematic errors in estimated stellar luminosities (and other stellar properties, such as radii or ages, which rely on stellar luminosity to be calculated).

Resolution B2 defines an absolute bolometric magnitude scale where {{math|1=''M''<sub>bol</sub> = 0}} corresponds to luminosity {{math|1=''L''<sub>0</sub> = {{val|3.0128|e=28|u=W}}}}, with the zero point [[luminosity]] {{math|''L''<sub>0</sub>}} set such that the Sun (with nominal luminosity {{val|3.828|e=26|u=W}}) corresponds to absolute [[bolometric magnitude]] {{math|1=''M''<sub>bol,⊙</sub> = 4.74}}. 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 {{math|''m''<sub>bol</sub> {{=}} 0}} corresponds to [[irradiance]] {{math|1=''f''<sub>0</sub> = {{val|2.518021002|e=-8|u=W/m<sup>2</sup>}}}}. Using the IAU 2015 scale, the nominal total [[solar irradiance]] ("[[solar constant]]") measured at 1 [[astronomical unit]] ({{val|1361|u=W/m<sup>2</sup>}}) corresponds to an apparent bolometric magnitude of the [[Sun]] of {{math|1=''m''<sub>bol,⊙</sub> = −26.832}}.<ref name="IAU2015B2" />

Following Resolution B2, the relation between a star's absolute bolometric magnitude and its luminosity is no longer directly tied to the Sun's (variable) luminosity:
<math display="block">M_\mathrm{bol} = -2.5 \log_{10} \frac{L_\star}{L_0} \approx -2.5 \log_{10} L_\star + 71.197425</math>
where
*{{math|''L''<sub>★</sub>}} is the star's luminosity (bolometric luminosity) in [[watt]]s
*{{math|''L''<sub>0</sub>}} is the zero point luminosity {{val|3.0128|e=28|u=W}}
*{{math|''M''<sub>bol</sub>}} is the bolometric magnitude of the star

The new IAU absolute magnitude scale permanently disconnects the scale from the variable Sun. However, on this SI power scale, the nominal [[solar luminosity]] corresponds closely to {{math|1=''M''<sub>bol</sub> = 4.74}}, a value that was commonly adopted by astronomers before the 2015 IAU resolution.<ref name="IAU2015B2" />

The luminosity of the star in watts can be calculated as a function of its absolute bolometric magnitude {{math|''M''<sub>bol</sub>}} as:
<math display="block">L_\star = L_0 10^{-0.4 M_\mathrm{bol}}</math>
using the variables as defined previously.

{{anchor|Solar System|Solar system|Solar System bodies|Solar system bodies}}