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How does spectroscopic parallax estimate the distance to a star?

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Diagram illustrating how astronomers calculate the distance to a star using parallax: Earth is shown in two positions on opposite sides of its orbit around the Sun, with lines extending to a nearby star X and further to distant background stars. The apparent shift in star X's position, measured as angle A, is used to determine its distance, with the baseline labeled as 186,000,000 miles. — Parallax Calculating stellar distances.

Spectroscopic parallax is an indirect method used to estimate the distance to a star by determining its absolute magnitude from its spectrum.12

The process relies on the fact that a star's spectral features—specifically the relative intensities of certain lines—reveal its intrinsic luminosity. By analyzing these spectral lines, astronomers can classify the star according to the MK system, which categorizes stars into specific spectral and luminosity classes (such as supergiants, giants, or main-sequence dwarfs).12

Once the star's luminosity class is identified, its absolute magnitude ( $M$ ) can be estimated. By comparing this absolute magnitude to the star's observed apparent magnitude ( $m$ ), astronomers can calculate the distance using the relationship between these two values and the inverse square law of light. This method is particularly useful for stars too distant for accurate direct trigonometric parallax measurements. The accuracy of these estimates has been significantly improved through the use of two-dimensional classification systems and calibrated standard stars.2