Hubble deep field 30th magnitude

Spectroscopic Parallax: Useful Astrophysics Basics, Magnitude, Apparent, Absolute, Theory

Spectroscopic parallax is an astronomical method for measuring the distances to stars. Despite its name, it does not rely on the geometric parallax effect.

This technique can be applied to any main sequence stars for which a spectrum can be recorded. This method is derived from the spectroscopic studies of sunspots and stars by Walter Sydney Adams and Ernst Arnold Kohlschutter.

white Dwarf

The method depends on the star being sufficiently bright to provide a measurable spectrum, which as of 2013 limits its range to about 10,000 parsecs. To apply this method, one must measure the apparent magnitude of the star and know the spectral type of the star.

The spectral type can be determined by observing the star’s spectrum. If the star lies in the main sequence, as determined by its luminosity class, the spectral type of the star provides a good estimate of the star’s absolute magnitude.

Visible Astronomy: Some Useful Basics to Make You Curious.

Hubble Space Telescope can see as distant as 30th magnitude objects.
Hubble Space Telescope can see as distant as 30th magnitude objects.

For any cluster for which we plot an HR diagram, we only know the apparent magnitudes, not the absolute magnitudes. If we know the absolute magnitude for one spectral type, then we can find the distance modulus for stars of that spectral type in the cluster. The distance modulus is the same for all the stars in the cluster, so we can calibrate the whole HR diagram in terms of absolute magnitudes. To obtain a reliable calibration, we would like to carry it out for many stars.

For any given star, we measure m, the apparent magnitude. We take a spectrum of the star to determine its spectral type. From the spectral type, we know the absolute magnitude, M. Knowing the apparent magnitude (m) and the absolute magnitude (M) of the star, one can calculate the distance (d) of the star using the equation

The true distance to the star may be different than the one calculated due to interstellar extinction.

Also see Betelgeuse is Surprisingly Smaller, Closer to Us.

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