How Well Do We Understand M Dwarfs?

S. Dieterich (sdieterich[at]stsci.edu)

Close your eyes, reach into our galaxy, and pick a random star. Chances are that star will be small, not much bigger than Jupiter, will shine with a dim orange-red color, and be about the temperature of a stove flame—pretty cold as far as stars go. Now open your eyes and stare into the clear dark sky. You will not see a single one of these stars, even though they are the nearest stars to our solar system; they are just too faint for the naked eye. That is the realm of the M dwarfs. The spectral type is defined by the presence of strong titanium oxide absorption bands in the red end of the optical region. Their masses range from about 0.08 to 0.6 solar masses. With such a wide range in masses and corresponding parameters, the M dwarfs have often been called a main sequence within the main sequence.

These stars comprise about seventy percent of the stars in our galaxy (Henry et al. 2006, 2018), and yet they are arguably the least understood type of star. Their still mysterious aspects stem mostly from two reasons. First, they are faint and were difficult to study before red-sensitive CCDs and infrared arrays replaced blue-sensitive photographic film. The 2 Micron All Sky Survey (2MASS) survey in the early 2000s was a particular watershed moment, especially for population properties. Second, they are intrinsically complex objects when compared to hotter stars. The cooler temperatures of red dwarfs allow for the formation of simple molecules such as water, methane, and titanium oxide, among many others. Figure 1 compares the molecular line-dominated spectrum of a typical M dwarf to that of the hot star Vega. An additional complication is the treatment of convective interiors. Early M dwarfs are thought to be partly convective, and mid-to-late M dwarfs are fully convective objects. Theoretical troubles in dealing with convective heat transfer deepen the difficulty.

Despite their small size and faint glow, we cannot ignore the M dwarfs. Doing so would be setting aside seventy percent of our galaxy, and conceivably other galaxies as well, as uninteresting. What is more, it has recently become clear that M dwarfs preferentially harbor rocky planets much like Earth (e.g., TRAPPIST-1; Gillon et al. 2017). Could these planets sustain life? The habitability of planets around M dwarfs is one of the most hotly debated issues in astronomy, and we simply cannot answer that question unless we understand these tiny stars in detail.

What does it mean to actually understand a star? Even for the chemically complex red dwarfs, theorists are able to create sophisticated models to predict what observable quantities should look like based on a star's most fundamental quantity—its mass. A good theoretical model thus should be able to predict what an astronomer will see at the telescope for stars of a given mass. More specifically, we want theory to be able to reproduce the star's spectrum (Figure 1) given the initial mass. This connection from mass to emerging spectrum is at the heart of stellar structure and evolution, and testing it is where our Hubble Space Telescope story begins.

two chartes with spectra
Figure 1: A segment of the spectrum of the hot star Vega (top) compared to the spectrum of the cool M dwarf GJ 1245 A (bottom). Both spectra cover the wavelength region where visible red light gradually becomes infrared. The red dwarf spectrum shows complex structure due to light absorption by many molecular species, whereas the spectrum of Vega is smooth except for a few atomic absorption lines. TiO absorption gives the M dwarf spectrum its sawtooth like appearance. At a temperature of about 2,200 Celsius (4,000 F) the spectrum of GJ 1245 is significantly more difficult to model. Both spectra were taken with HST/STIS. The Vega spectrum is part of HST's fundamental spectral library for calibrations (Calspec) and the spectrum of GJ 1245 A was observed as part of the author's research.

A star's mass may be its most fundamental property, but measuring stellar masses is an extremely tricky business. Dynamical masses can only be measured in binary star systems, and those with amenable periods are also too close together to study individually. For M dwarfs, the sweet spot lies at periods of about five to 15 years, with the upper limit depending on one’s patience and funding. Fortunately for those of us who study red dwarfs, Hubble's exquisite angular resolution came to the rescue, both as an astrometric observatory capable of detecting minute motions of celestial bodies and as a spectroscopic observatory.

In a multi-decade effort that began early in Hubble's life in the 1990s, a team led by my collaborators Fritz Benedict and Todd Henry started mapping the orbital motions of several red dwarf binaries using HST's Fine Guidance Sensors (FGS). The three FGSs are interferometers that can detect when Hubble's pointing is precisely aligned with the line of sight to a given star. It does that by measuring when light reflecting off of different sides of Hubble's field of view is traveling exactly the same distance from the star, down to uncertainties comparable to the wavelength of light itself. FGS is primarily a spacecraft guidance instrument, but, in a clever feat of optical design, it also has a science use. For guidance purposes, FGS relies on a star being a single unresolved point of light. Pointing FGS at a binary star will generate an anomalous interference pattern. That pattern carries information about the binary's separation, orientation, and brightness ratio.

Like other astronomical interferometers, FGS is a binary star machine. What is more, it can do something no other instrument on Earth or in space can do: It can ascertain the locations of closely separated binary stars not only in terms of their positions relative to each other, but with respect to the background of distant stars. That means that whereas other instruments measure the relative motion of the secondary star of a binary around the primary star, FGS can measure what is really happening: both components are orbiting a common center of mass. Figure 2 explains the difference.

2 charts showing orbits
Figure 2: The figure on the left shows the orbits of the red dwarfs GJ 1005 A and B, mapped with FGS. We can see the orbits of both components around a common center of mass, which allows for the measurement of individual masses. The figure on the right shows the relative orbit of GJ 65 AB. In this relative orbit what is plotted is the motion of the secondary component around the primary component, assumed to be at the origin of the plot. This relative orbit can only tell us the total mass of the system. Note also how FGS measurements fit the orbit much more precisely than ground-based measurements (from Benedict et al. 2016).

Whereas the relative motions can yield only the sum of the masses of the two stars in a binary, FGS can determine their individual masses. In an amazing technical feat (handling FGS data is not for the faint of heart), not to mention considerable long-term scientific vision, the team led by Fritz Benedict and Todd Henry was able to determine the masses for 30 individual red dwarf stars using FGS. Their results were published in 2016 in what is known as the red dwarf Mass-Luminosity Relation (Benedict et al. 2016).

The mass-luminosity relation helps our understanding of red dwarfs a great deal, but it is not as global a test of theory as we would like. It connects masses to a star's white light brightness, whereas we would really like to see a spectrum. We had the masses and orbits from FGS, but the stars were still too close together to get unblended spectra through conventional means. It then occurred to me that if we could align Hubble's roll angle precisely, we could observe both stars in a binary system simultaneously with STIS, Hubble's workhorse spectrograph.

The observations would be challenging. The alignment required rotating the entire spacecraft along its long axis. Such "orient constraints" are not unusual, but calculating it required a high level of confidence that the FGS orbits were correct, down to only a few degrees of uncertainty. My team and I were fortunate to be awarded 12 orbits of HST time to try for six binary systems, and we were able to get the procedure to work for five of those. After almost 20 years of HST observations and using two of Hubble's instruments, we now had the Holy Grail we were after: high-quality spectra for M dwarfs with precisely known masses.

How well did the models match the observations? Figure 3 shows a section of the STIS spectra for the M dwarf GJ 22 A in red over-plotted with the best-fitting model spectrum in blue. The agreement is remarkably good, down to the fine structure of the molecular lines. That is very good indication that the surface temperature of GJ 22 A is indeed the temperature corresponding to that spectrum, about 3,200 Celsius (5,800 F). However, we know the mass of GJ 22 A to be 0.403 solar masses, and when we use the models to calculate the temperature of GJ 22 A based on its mass, we get a variety of values within uncertainties of the accepted value. Out of the five mass models we tested, four of them gave predictions that were too cold, as cold as 2,500 Celsius (4,500 F) and one of them predicted a temperature that was a bit too hot.

spectrum of the M dwarf GJ 22
Figure 3: A section of the spectrum of the M dwarf GJ 22 A, observed with STIS. The best-fit model spectrum (Allard et al. 2013) is over-plotted in blue. The agreement indicates that G 22 A has a surface temperature of about 3,200 Celsius (5,800 F) and a chemical composition similar to our Sun. The overall agreement between the two plots is remarkable, with the few differences in the fine structure being mostly due to the noise in our observations.

The implications for our understanding of planetary habitability around M dwarfs are profound. While we can take some consolation that we can at least model the light that shines on the planet, not being able to determine the star's mass from observing that light means we cannot know the planet's mass, and that means we really don't know much at all about the planet. In our submitted publication, our team stressed that we believe the true value of this data set is not so much as a test of past theory, but rather as a guide to future efforts. Now, for the first time, we have a data set that shows the connection between a star's mass, its most fundamental parameter, and the details of the light we actually observe emerging from that star. When theorists finally understand that connection we will have a real shot at imagining what life may be like in the planets surrounding these tiny stars.

The paper is Dieterich et al. 2020: "The Solar Neighborhood XLVI: Testing M Dwarf Models with Hubble Space Telescope Dynamical Masses and Spectroscopy," now undergoing peer review.

References

Allard, F., et al. 2013, Memorie della Societa Astronomica Italiana Supplement, 24, 128

Benedict, G. F., et al. 2016, The Astronomical Journal, 152, 141

Gillon, M., et al. 2017, Nature, 542, 456

Henry, T. J., et al. 2006, The Astronomical Journal, 132, 2360

Henry, T. J., et al. 2018, The Astronomical Journal, 155, 265