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How to Weigh a Star by Its Pulse ✛

Original: "A Seismic Technique for Obtaining White Dwarf Fundamental Parameters from Mean Period Spacings and Astrometry"
· Keaton J. Bell, Agnès Bischoff-Kim
arXiv:2608.25026v1 · 2026-08-25 · CC BY 4.0 · 1 min
Stellar
Astronomers measured the mass and temperature of a white dwarf by listening to its oscillations and watching its brightness.

The star WD 0158−160 pulsates: its brightness changes every 38 seconds. These oscillations are like heartbeats, but inside a star. Astronomers have learned to use this rhythm and the star's brightness to determine how heavy it is and how hot it is.

Previously, the mass of a white dwarf was measured from its spectrum — the rainbow into which light is split. But the lines in this rainbow are blurred, and different models give different answers. The new method works differently. The rhythm of pulsations depends on the star's internal structure: the denser and hotter it is, the faster or slower the beats. But the rhythm alone is not enough — several configurations give the same tempo.

A white dwarf is the remnant of a star like the Sun: it has about half the Sun's mass but is the size of Earth. A teaspoon of its material weighs a ton.

The second key is brightness. The Gaia telescope measured the distance to the star precisely: 223 light-years. Knowing the distance and apparent brightness, astronomers calculate how much light the star actually emits. This luminosity depends on the star's size, and the size is related to its mass and temperature. When the rhythm and brightness were combined, they pointed to a unique solution: a mass of 0.608 solar masses and a temperature of 24,600 degrees. Now this method can be applied to other pulsating white dwarfs to check whether older methods were wrong.

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The average period spacing of the white dwarf WD 0158−160 is 38.1 seconds — about the same duration as one brightness oscillation caused by a gravity wave inside a star the size of Earth. The star's mass is 0.6 solar masses, meaning its matter is compressed to a density of about a ton per cubic centimeter.

M_G = M_{G,\mathrm{Bergeron}} - 2.5 \log\left(\frac{R_{\mathrm{WDEC}}}{R_{\mathrm{Bergeron}}}\right)^2
The absolute magnitude scales with the square of the radius, since luminosity is proportional to surface area.
L_{ij} \propto \frac{1}{\sqrt{\sigma_{\Delta\Pi,ij}^2+\sigma_{\Delta\Pi,obs}^2}} \exp\left[-\frac{(\Delta\Pi_{obs}-\Delta\Pi_{ij})^2}{2(\sigma_{\Delta\Pi,ij}^2+\sigma_{\Delta\Pi,obs}^2)}\right] \times \frac{1}{\sqrt{\sigma_{M_G,ij}^2+\sigma_{M_G,obs}^2}} \exp\left[-\frac{(M_{G,obs}-M_{Gij})^2}{2(\sigma_{M_G,ij}^2+\sigma_{M_G,obs}^2)}\right]
Product of two Gaussian likelihoods for period spacing and absolute magnitude.
P(M_{\star,i}, T_{\mathrm{eff},j}) = \frac{L_{ij}}{\sum L_{ij} \Delta M_{\star} \Delta T_{\mathrm{eff}}}
The probability of parameters equals the normalized likelihood on the grid.
Scientists
Subrahmanyan ChandrasekharCecilia Payne-GaposchkinRalph Fowler
Concepts
cataclysmic variable astrometry white dwarf asteroseismology stellar pulsation sdss stellar model tess magnetic white dwarf cosmic chronometry statistical method OISST v2.1 thermal property measurement symplectic geometry