Binary Stars and Apparent Magnitudes

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SUMMARY

The discussion centers on calculating the apparent magnitude of a single star in a binary star system with two stars of equal luminosity observed as a single image. Given the combined apparent magnitude of 10.7 and the distance of 85 parsecs, participants emphasize the need to utilize the logarithmic relationship between luminosity and magnitude. The formula m = -2.5 log(L) is crucial for this calculation, along with the logarithmic base of approximately 2.512 for combining magnitudes. The approach involves manipulating logarithmic values to derive the individual star's magnitude.

PREREQUISITES
  • Understanding of astronomical magnitudes and luminosity
  • Familiarity with logarithmic functions and their properties
  • Knowledge of the distance modulus formula (m - M = 5 log(d) - 5)
  • Basic concepts of binary star systems
NEXT STEPS
  • Study the application of the distance modulus in stellar astronomy
  • Learn about the logarithmic scale in astronomy, specifically the base 2.512
  • Explore methods for calculating individual star magnitudes in binary systems
  • Investigate the effects of distance on apparent and absolute magnitudes
USEFUL FOR

Astronomy students, astrophysicists, and anyone interested in understanding binary star systems and the calculation of stellar magnitudes.

LavaLynne
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Homework Statement


A binary star system at a distance of 85pc consists of two stars of equal luminosity that are so close together that they are observed in a telescope as a single image. If the apparent magnitude of the two stars combined is 10.7 what would be the apparent magnitude of just one of the component stars?[/B]

Homework Equations


m= -2.5 log(L)

m-M=5log(d)-5

[/B]

The Attempt at a Solution


I think I need to figure out what the two luminosities are added together?
 
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Hi LavaLynne, Welcome to Physics Forums.

You should be able to work directly with the magnitudes if the sources are very close together (inseparable when imaged). You may have to do some fancy footwork with logarithms though.

Magnitudes are based on a logarithmic scale, but the actual logarithmic base is the (approximate) value 2.512.

A "linear" way to add values x1 and x2 that are based on a logarithmic scale of some base b would be:
$$b^{-x_{sum}} = b^{-x1} + b^{-x2}$$

That should be enough information for you to find a way to determine the magnitudes of your two identical stars.
 
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