M-dwarfs, also known as red dwarfs, are by far the most common stars in the universe. Laughlin et al. (1997) performed stellar evolution calculations for M-dwarfs with masses in the range 0.08 to 0.25 solar mass. Our Sun has a main-sequence lifespan of 10 billion years. In comparison, these M-dwarfs have main-sequence lifespans that are measured in trillions of years. The reason is because unlike our Sun, M-dwarfs have fully convective interiors and this prevents helium produced from the fusion of hydrogen to accumulate at the core, allowing M-dwarfs to burn a larger proportion of their hydrogen before leaving the main sequence. A 0.08 solar mass M-dwarf has a main sequence lifespan of 12 trillion years.
Figure 1: Artist’s depiction of the planetary system around a 0.13 solar mass M-dwarf known as Kepler-42. Credit: NASA/JPL-Caltech.
Figure 2: Evolution in the Hertzsprung-Russell diagram for stars with masses in the range 0.06 to 0.25 solar mass. Stars of less than 0.25 solar mass are not massive enough to evolve into red giants. The inset diagram shows the corresponding main-sequence lifetimes as a function of stellar mass. Note that a 0.08 solar mass M-dwarf has a remarkable main-sequence lifetime that exceeds 10 trillion years. (F. C. Adams, P. Bodenheimer, G. Laughlin, 1997)
The current age of the universe is 13.8 billion years. Since M-dwarfs have main-sequence lifespans that are many times longer than the current age of the universe, the post-main-sequence evolution of these stars can only be predicted based on theoretical models. Stars become more luminous as they age and increasingly massive stars will produce progressively larger luminosity increases. Calculations by Laughlin et al. (1997) show that during the course of evolution, a 0.08 solar mass star will increase in luminosity by ~15 folds, a 0.16 solar mass star will increase in luminosity by ~140 folds and a 0.25 solar mass star will increase in luminosity by close to a factor of a thousand. This increase in luminosity is compensated in one of two ways: (1) the star can grow bigger in size and become a “red giant”; (2) or the star can remain at its usual size but increase its temperature and become a “blue dwarf”.
As a star begins to exhaust most of its hydrogen fuel towards the end of its main-sequence life, its luminosity will increase many folds. M-dwarfs of less than 0.25 solar mass do not become red giants in their post-main-sequence phases. Instead, they remain small and grow hotter to become blue dwarfs. Only stars of more than 0.25 solar mass evolve into red giants. This is because for an M-dwarf of less than 0.25 solar mass, its outer layers do not become significantly more opaque with increasing temperature as the star’s luminosity increases. As a consequence, the star does not expand, but increases its radiative rate, causing its surface temperature to increase. The star appears “bluer” and becomes a blue dwarf. In the present-day universe, a blue dwarf is a hypothetical object whose existence is predicted based on theoretical models because the current universe is far too young for any blue dwarfs to have formed.
A 0.1 solar mass M-dwarf has a main-sequence lifespan of more than 6 trillion years. During this stupendously long period of time, the star fuses hydrogen into helium. Slowly but surely, increasing its helium mass fraction. Initially, the star has a surface temperature of 2230 K and 1/2400 of the Sun’s luminosity. After 5.74 trillion years, its surface temperature will increase to 3450 K and its luminosity increasing to 1/350 of the Sun’s luminosity. At this point, the star has burnt most of its hydrogen and it begins to develop a radiative core. Now, the star’s seemingly eternal youth draws to an end. Its evolutionary timescale accelerates and its luminosity increases more quickly. The increasing luminosity does not cause the star to expand physically in size. Instead, it raises the star’s surface temperature, turning it into a blue dwarf. At about 400 billion years after developing a radiative core, the star’s surface temperature will reach a maximum of 5810 K.
Being a blue dwarf does not mean the star will actually appear blue. It is simply the result of a significant increase in the star’s surface temperature, causing a large shift in the star’s light towards the bluer side of the electromagnetic spectrum. In fact, at its maximum surface temperature of 5810 K, the star’s colour will be somewhat similar to the present-day Sun. After those billions of years shinning as a blue dwarf, fusion eventually comes to a halt as the star runs out of hydrogen fuel. As the foregoing life story of a 0.1 solar mass star comes to an end, the star will continue to cool until it eventually becomes a black dwarf.
F. C. Adams, P. Bodenheimer, G. Laughlin (1997), “The End of the Main Sequence”, The Astrophysical Journal 482: 420-432, 1997 June 10