The vast majority of stars in the universe, including the sun that we rely on for survival, will eventually evolve into white dwarfs. The mass of white dwarfs is mainly distributed between 0.5-0.7 M ⊙. However, observations indicate that a small portion of white dwarfs have very low masses, even less than 0.3 M ⊙. We refer to helium core white dwarfs with masses less than 0.3 solar masses as Extremely Low Mass White Dwarfs (ELM WDs). They are located between main sequence stars and white dwarfs in the color magnitude map, with effective temperatures generally ranging from 8000 to 22000 K and surface gravitational accelerations typically in the range of 105 to 107 cm/s2
Figure 1: On the left is a very low mass white dwarf, and on the right is a companion star with a smaller radius and greater mass. Image source: CfA/David A. Aguilar
Observational ELM WDs (including ELM WDs in the prototype stage, commonly abbreviated as pre ELM WD, proto He WD, or pre He WD) are typically located in binary systems with orbital periods ranging from a few minutes to several hundred days. Companions mainly include white dwarfs, neutron stars, and A/F dwarf stars (see Figure 2). The ELM WDs+white dwarf binary system was mainly discovered through the Extreme Low Mass Survey project. In 2009, the Warren Brown team at the Harvard Smithsonian Center for Astrophysics launched the ELM survey project using a 6.5-meter multi mirror telescope. The ELM survey is a time-domain spectroscopic survey project that has currently measured the orbital and atmospheric physical parameters of 148 double white dwarfs, of which approximately 80% of the systems contain ELM WDs. They are basically single line spectral binary stars, whose luminosity is mainly dominated by ELM WDs sub stars. This is partly because ELM WDs have a thick hydrogen rich envelope (0.01-0.05M ⊙) at the time of their birth, and the hydrogen in the envelope burns through p-p chains, maintaining the high luminosity of the white dwarf for a long time. This evolutionary stage is called the near constant luminosity state, with a typical time scale of 0.5-2 Gyr. On the other hand, white dwarfs mainly rely on electron degeneracy pressure to resist their gravitational collapse, and their radius is inversely proportional to their mass. When entering the cooling phase, compared to massive white dwarfs such as CO WD, ONe WD, etc., ELM WDs have a larger radius and higher luminosity at the same effective temperature, making their electromagnetic radiation signals easier to detect. Therefore, ELM WDs have important value in determining the orbital parameters of twin white dwarfs, the basic physical parameters of each sub star, and determining the gravitational wave signal characteristics of twin white dwarfs. Existing observational data shows that approximately 10 double white dwarfs containing ELM WDs are strong sources of gravitational wave radiation, and they are used as verifiable binary stars for future space gravitational wave detectors (LISA and Tianqin).
Figure 2: Mass orbital period diagram of a small mass white dwarf. The solid gray line represents the relationship between the mass and orbital period of the companion star of a white dwarf formed by a stable material transfer channel. Image source: Khurana et al.（2023）
EL CVn type binary stars are a type of occultation binary consisting of an A/F dwarf and an ELM WDs. Their light curves exhibit a box shaped primary minimum and a slightly shallow secondary minimum (see Figure 3). This special light curve shape makes it easy to distinguish EL CVn binary stars in photometry. Thanks to the new observational opportunities provided by large-scale time-domain photometric surveys such as WASP, Kepler, and TESS, astronomers have discovered approximately 80 EL CVn type binary stars from massive light curve data. In addition, observations of millisecond pulsars have also discovered over 10 ELM WDs.
Figure 3: Phased light curve of EL CVn binary WASP1814+48. The primary minimum corresponds to ELM WDs with smaller radii but higher temperatures being completely obscured by larger companion stars, while the secondary minimum corresponds to smaller ELM WDs passing in front of larger companion stars. Image source: Lee et al.（2022）
Some ELM WDs have been found to be pulsating, typically exhibiting non radial g-mode pulsations with periods ranging from approximately 1000 to 6000 seconds. Excitingly, researchers have detected for the first time two p-type pulsating signals with periods of P1=134.275 s and P2=107.56 s on a pulsating very low mass white dwarf SDSS J111215.82+111745.0 through high-speed photometry observations. For massive white dwarfs, their p-mode pulsation period is only a few seconds, making it difficult to detect under current observation conditions. Therefore, the observation of p-mode pulsations on small mass white dwarfs is an important progress in the study of white dwarf star seismology. This provides us with a rare opportunity to explore the internal structure and formation channels of white dwarfs using asteroseismology.
In general, ELM WDs are products of binary star evolution. These precursor stars of white dwarfs undergo significant material transfer before a helium flash, transferring most of their envelope material to companion stars or directly ejecting it into space, leaving behind a small mass helium nucleus and a thicker hydrogen rich envelope. The specific formation channels include stable Roche lobe material exchange and common envelope ejection. The ELM WDs and EL CVn binary stars in millisecond pulsars are formed through stable material exchange. Double white dwarfs containing ELM WDs may evolve into AM CVn type binary stars, or merge to form low luminosity supernovae and R CrB stars. Although single star ELM WDs have not been observed yet, theoretical calculations suggest that during Type Ia supernova explosions, the hydrogen rich outer shell of red giants may be stripped off by supernova ejecta to form single star ELM WDs.
Figure 4: Low resolution LAMOST spectra of extremely low mass white dwarfs. The solid lines in black, red, and gray represent observed data, theoretical spectra, and fitting residuals, respectively.
In recent years, domestic researchers have discovered a batch of reliable candidates for ELM WDs based on the LAMOST spectral data from the national scientific facility, and determined the orbital parameters of several binary star systems containing ELM WDs. This fully demonstrates the potential of LAMOST in the study of extremely low mass white dwarfs. With the accumulation of LAMOST survey spectral data and subsequent time-domain spectroscopic and photometric observations, we look forward to discovering more ELM WDs and distinguishable binary white dwarf gravitational wave source candidates, providing more comprehensive data support for further revealing the properties of such special stars and tracing the evolution of star formation and other cutting-edge topics.