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For example, according to Google, the apparent magnitude of the sun is $-26.74^m$.

Is this the apparent magnitude viewed through Earth's atmosphere when the object is at zenith?

(Assuming most favorable conditions, sea level, zenith extinction is about $19\%$ or $0.23^m$, at least according to the IAO table of constants)

Might it be an extra-atmospheric value instead, i.e. corrected for any form of extinction?

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The IAU has a conventional value for solar luminosity of 3.828×1026 W. (see Prša et al. 2016). This corresponds to an absolute bolometric magnitude of 4.74 (this includes all the light, including infrared and ultraviolet), and at a distance of 1 AU, that corresponds to an apparent bolometric magnitude of -26.84.

The value was derived from space observations, averaged over a solar cycle, These measure a solar irradiance of 1361 Wm-2, to within instrumental accuracy. This can be combined with the value of the AU to give the above value for luminosity.

Applying a bolometric correction of 0.10 (for a G2V star like the sun) gives the Wikipedia (sourced from NASA) value of -26.74. There does not appear to be any atmospheric extinction applied to this value, which should therefore be considered to be the value at the top of the atmosphere. Actual brightness will be somewhat lower.

There is physical variation in the brightness of the sun, most notably in the 11 year sunspot cycle. And the distance to the sun varies with the Earth's elliptical orbit, so on any given day the apparent magnitude of the sun may be more or less than the quoted value.

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  • $\begingroup$ "Actual brightness will be somewhat lower": did you mean higher (than the - 26.74 value)? $\endgroup$ Sep 26, 2022 at 11:16
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Apparent magnitudes in standard photometric systems are defined above the atmosphere. i.e. They should have been corrected for atmospheric extinction unless otherwise specified.

As the Wikipedia article on "apparent magnitude" states. Apparent magnitude is measured by comparison with calibration stars

Such calibration obtains the brightness as would be observed from above the atmosphere, where apparent magnitude is defined.

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  • $\begingroup$ Can you add a reference that states that? $\endgroup$ Sep 26, 2022 at 22:03
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Photometry is a mature subfield, and has been taken to greater and greater significant digits by now. Certainly, the pursuit of exoplanets by the transit method has spurred the subfield to mind-boggling (to the layman) precision.

At a minimum, reference stars have been taken to (off the top of my head- not Googling yet) millimag precision. Given that zenith angle results in a dimming of 2x or more, it’s safe to say millimag precision involves taking our atmosphere into account.

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  • $\begingroup$ So it's an the apparent magnitude is extra-atmospheric? $\endgroup$
    – Cheng
    Sep 26, 2022 at 0:37

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