Bolometric brightness

In Astronomy is bolometric magnitude is a measure of the total luminosity of a celestial body , for example. B. a star or a galaxy . In contrast to visual or X-ray brightness, it describes the luminosity integrated over the entire electromagnetic spectrum .

Both the (visual) areas of the spectrum that are visible to our eyes and the invisible ones contribute to the bolometric brightness. The spectrum ranges from radio waves through infrared radiation and ultraviolet radiation to X-ray and gamma radiation .

The bolometric brightness is usually given in units of "magnitudes", but can also be given in watts , ergs per second or other units of power . It is denoted by the symbol or , depending on whether the absolute or the apparent bolometric brightness is meant. ${\displaystyle M_{\mathrm {bol} }}$ ${\displaystyle m_{\mathrm {bol} }}$

Bolometric correction

No detector available today is sensitive in all spectral ranges. In addition, the earth's atmosphere is opaque to large parts of the electromagnetic spectrum. Therefore the bolometric brightness cannot be determined directly from the ground.

In many cases, brightnesses are determined in visual (therefore visible to the eye) bands. The bolometric correction allows visual brightnesses to be converted into bolometric ones. It is defined as follows

${\displaystyle m_{\mathrm {bol} }=m_{\mathrm {v} }-BC}$

with the visual brightness , the bolometric brightness, and the bolometric correction . ${\displaystyle m_{\mathrm {v} }}$ ${\displaystyle m_{\mathrm {bol} }}$ ${\displaystyle BC}$

To determine the bolometric correction, the actual distribution of the radiated energy over the entire spectrum must be estimated. This can be done either through measurements on comparable objects or through theoretical models. The correction can be calculated according to Planck's law of radiation :

${\displaystyle BC=m_{\mathrm {v} }-m_{\mathrm {bol} }=2{,}5\cdot \log \left({\frac {F_{\mathrm {bol} }}{F_{550\,\mathrm {nm} }}}\right)}$

${\displaystyle BC=2{,}5\cdot \left(4\cdot \log \left({\frac {5770\,\mathrm {K} }{T}}\right)+\log \left({\frac {\exp {\left({\frac {h\cdot c}{k\cdot 5770\,\mathrm {K} \cdot 550\,\mathrm {nm} }}\right)}-1}{\exp {\left({\frac {h\cdot c}{kT\cdot 550\,\mathrm {nm} }}\right)}-1}}\right)\right)}$

${\displaystyle BC=2{,}5\cdot \left(4\cdot \log \left({\frac {5770}{T/\mathrm {K} }}\right)+\log \left({\frac {92{,}1}{\exp {\left({\frac {26160}{T/\mathrm {K} }}\right)}-1}}\right)\right)}$

In the case of main sequence stars , the radiation is described quite well by Planck's law of radiation and the bolometric correction can accordingly be calculated well. Numerical values ​​of the bolometric correction for stars of a number of spectral types and stages of development can be found in every major astronomical table.

Bolometric brightness and correction using the example of the sun

The absolute visual brightness of the sun is and the absolute bolometric brightness (instead of you can also write Mag). This means that for the sun the bolometric correction is. ${\displaystyle 4^{\mathrm {M} }{,}83}$ ${\displaystyle 4^{\mathrm {M} }{,}74}$ ${\displaystyle 4^{\mathrm {M} }{,}74}$ ${\displaystyle 4{,}74}$ ${\displaystyle BC=4^{\mathrm {M} }{,}83-4^{\mathrm {M} }{,}74=+0^{\mathrm {M} }{,}09}$

Relationship between bolometric brightness and luminosity

The bolometric brightness is directly related to the luminosity:

${\displaystyle M_{\mathrm {bol} }-M_{\mathrm {bol,\odot } }=-2{,}5\cdot \log \left({\frac {L}{L_{\odot }}}\right)}$

${\displaystyle \Rightarrow {\frac {L}{L_{\odot }}}=10^{0,4\cdot \left(M_{\mathrm {bol,\odot } }-M_{\mathrm {bol} }\right)}}$

literature

• Alfred Weigert , Heinrich Johannes Wendker : Astronomy and Astrophysics. A basic course. 3rd revised edition. VCH, Weinheim u. a. 1996, ISBN 3-527-29394-9
• Jeffrey Bennett, Megan Donahue , Nicholas Schneider, Mark Voith: Astronomy. The cosmic perspective. Edited by Harald Lesch . 5th updated edition. Pearson studies, Munich a. a. 2010, ISBN 978-3-8273-7360-1 ( Ph - Physics ).

Web links

• Representation of the Magnitudo system
• Calculation of the bolometric correction for 3,500 K.

Individual evidence

1. ↑ EE Mamajek, G. Torres, A. Prsa, P. Harmanec, M. Asplund: IAU 2015 Resolution B2 on Recommended Zero Points for the Absolute and Apparent Bolometric Magnitude Scales . In: arXiv . October 21, 2015, arxiv : 1510.06262 .