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Concept
Distance modulus
Summary
The distance modulus is a way of expressing distances that is often used in astronomy. It describes distances on a logarithmic scale based on the astronomical magnitude system.
The distance modulus is the difference between the apparent magnitude (ideally, corrected from the effects of interstellar absorption) and the absolute magnitude of an astronomical object. It is related to the distance in parsecs by:
This definition is convenient because the observed brightness of a light source is related to its distance by the inverse square law (a source twice as far away appears one quarter as bright) and because brightnesses are usually expressed not directly, but in magnitudes.
Absolute magnitude is defined as the apparent magnitude of an object when seen at a distance of 10 parsecs. If a light source has luminosity L(d) when observed from a distance of parsecs, and luminosity L(10) when observed from a distance of 10 parsecs, the inverse-square law is then written like:
The magnitudes and flux are related by:
Substituting and rearranging, we get:
which means that the apparent magnitude is the absolute magnitude plus the distance modulus.
Isolating from the equation , finds that the distance (or, the luminosity distance) in parsecs is given by
The uncertainty in the distance in parsecs (δd) can be computed from the uncertainty in the distance modulus (δμ) using
which is derived using standard error analysis.
Distance is not the only quantity relevant in determining the difference between absolute and apparent magnitude. Absorption is another important factor, and it may even be a dominant one in particular cases (e.g., in the direction of the Galactic Center). Thus a distinction is made between distance moduli uncorrected for interstellar absorption, the values of which would overestimate distances if used naively, and absorption-corrected moduli.
The first ones are termed visual distance moduli and are denoted by , while the second ones are called true distance moduli and denoted by .
Official source
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