In a new paper published by The Astrophysical Journal today, a team led by PhD candidate Nicole Crumpler has detected a long-theorized but very subtle effect in the White Dwarf “mass-radius relation.”
When a star has burned up all of its fuel and no longer generates much energy, it sheds its outer layers. What remains is a super dense core known as a White Dwarf star. Young White Dwarfs can be as hot as 100,000 degrees Celsius (180,000° Fahrenheit) or more. Since they have no source of energy, the dying core of the star will gradually cool over billions of years. Although only the size of the Earth, White Dwarfs have an average mass similar to our sun, making them so dense that just a teaspoon of material from the typical White Dwarf would weigh several tons on Earth. This incredible density has fascinating effects on the structure of these stars, summed up in a theory that dates back to the 1930s and the Nobel Prize-winning astrophysicist Subrahmanyan Chandrasekhar. The theory is the “mass-radius relation,” which suggests that more massive White Dwarfs are actually smaller in size due to quantum mechanical effects.
The radius of White Dwarf stars depends not only on the star’s mass but also on its temperature. This temperature dependence spawns from the nature of the gases in the outermost layers of White Dwarfs, which behave like an “ideal gas.” Ideal gas is the theoretically perfect balance of a gas’s volume, pressure, temperature, and number of atoms so that it’s stable. Think of it like a balanced scale, on one end of the scale is pressure and volume (size), on the other is temperature and number of atoms (mass). If the mass and pressure remain the same, then, if the gas’s temperature increases, its size must also increase for the gas to stay balanced. So a hotter White Dwarf is larger because the outer envelope puffs up just a little bit to remain stable.
This “puffiness” due to high temperatures is a very small effect, meaning the team had to measure the properties of White Dwarf stars very precisely. Actually, more precisely than is typically possible with the type of observations the team had access to. The trick? Focusing on the gravitational redshift, an effect observable in very dense stellar objects such as White Dwarfs. Gravitational redshift was first predicted by Albert Einstein in 1907 as part of his groundbreaking theory of general relativity. Light has a certain color depending on its energy; when light travels away from a high-mass object, like a White Dwarf, the gravitational pull of that object “steals” some of the energy from the light. As a result, the light’s wavelength becomes longer, shifting toward the red end of the spectrum, hence, “redshift.” The stronger the gravity, which depends on the mass and the size of the object, the more the light gets gravitationally redshifted.
The team’s previous 2020 study, led by Vedant Chandra (B.S. ’21), who is now a PhD student at Harvard University, used gravitational redshift measurements to find that White Dwarfs with greater masses have smaller radii on average, a direct confirmation of the hundred-year-old theory by Chandrasekhar. But there were too few White Dwarfs observed at the time to unveil the effect from stars’ temperatures, and that was left for future data sets. That future is now, and with many new observations of White Dwarf stars from the latest generations of data releases from the Sloan Digital Sky Survey and the Gaia Space Observatory, the team has assembled the largest White Dwarf catalog of its kind. The catalog contains more than 26,000 White Dwarf stars, analyzed with newly refined measurement procedures.
“It’s fascinating to finally see the temperature-dependence of the mass-radius relation so clearly with these new datasets, and also to think about what’s next,” said team-member Vedant Chandra. “Spectroscopic samples of White Dwarfs could grow tenfold over the next decade.”
To prove that temperature affects the mass-radius relation of White Dwarfs, the team split their large catalog into two groups; hot and cold stars. They measured the gravitational redshifts of each group and detected that warmer White Dwarfs, on average, have greater gravitational redshifts than cooler ones at a given radius. This means that warmer White Dwarfs of a particular size are typically more massive than their cooler counterparts. Due to the vast size of the new and improved catalog; the team has determined these results to be statistically significant. This means these astrophysicists can say, with confidence, that their findings have confirmed the long-theorized temperature dependence of the structure of White Dwarf stars and refined our understanding of the universe.
“Detecting this subtle temperature dependence is just one example of the amazing things astronomers can accomplish with large data sets like SDSS-V,” said Nicole Crumpler. “Already we are using this catalog of White Dwarfs to investigate new signals of dark matter hidden in the structure of these stars.”
The findings from this study are a leap forward in our understanding of White Dwarfs, but this is only the beginning. With many more observations planned in the future, scientists are poised to unlock even more secrets of these fascinating stars, bringing us closer to solving some of the universe’s most profound mysteries.
– Liam Roy