The distance modulus { displaystyle mu=m-M} is the apparent magnitude of a celestial body And absolute magnitude It is derived from the definition of flux measured by celestial luminosity observation through logarithmic relationship: The relationship between the observed brightness of the light source and the distance is the inverse square law - if the distance of the light source is doubled, the brightness will be reduced to a quarter. For a single object or two objects with the same luminosity, Can be used Replace, therefore: The absolute magnitude is defined as the apparent magnitude of a celestial body at a distance of 10 seconds, so the luminosity equation can be written as Rearrange the logarithmic relationship into Then, give the distance module , the distance unit given is the second difference The uncertain value (δ d) in the distance can be calculated from the uncertain distance modulus (δ μ) using the following formula Here is the application of standard error analysis.
The difference between apparent magnitude and absolute magnitude is not the method to determine the distance. Absorption spectrum is another important factor, and even has advantages in some special cases (for example, in the direction of the center of the Milky Way). Since the distance module cannot correct the interstellar absorption (if it is used innocently, the distance will be overestimated), it is necessary to use the absorption correction module.
The first term is called apparent distance module, and the representation is , the second term is called true distance modulus, and the representation is 。 The apparent distance module is the difference between the observed apparent magnitude and some theoretically estimated absolute magnitude. The true distance modulus needs further theoretical steps, and the interstellar absorption coefficient needs to be estimated.
The distance module is most commonly used to represent the distance between neighboring galaxies in the universe, such as Large Magellanic Cloud The distance modulus of is 18.5, Andromeda galaxy The distance modulus of is 24.4, and Virgo Galaxy Cluster Galaxies of NGC 4548 The distance modulus is 31.0. In the case of the Big Magellanic Cloud, this means Supernova SN 1987A The peak apparent magnitude of is 2.8, and the absolute magnitude obtained is - 15.7, which is lower than the standard luminosity of supernovae. Distance modulus is also the preferred distance expression for many observers. Because the actual effect of increasing distance is to dim the luminosity of celestial bodies, for example, the apparent magnitude of sun like stars (M=5) in the galaxies of the Virgo Galaxy Cluster is 36, which can be quickly calculated in your own brain. Because the apparent magnitude of celestial bodies can be accurately measured through telescopes, this approach aims to highlight the fact that many studies on distance in astronomy are inferred or derived from the absolute magnitude of celestial bodies whose real distance has been determined.
