Radius

As touched upon in§5.2, we can break our radius validation into two sets of comparisons: (1) a large ensemble of long-baseline optical and infrared interferometry results (Figure 5.1) and (2) the three additional efforts just discussed in the temperature and luminosity comparisons (Figure 6.3). Here we evaluate the comparisons as an ensemble, rather than in separate warm and cool subsamples. As before, we use a similar layout of individual comparisons in the for small panels in the left of Figure 6.3, and combine the comparisons in the right panel.

For stars with sizes of 0.10–0.65R_⊙, we are confident in our radii; the majority of results presented in the right panel of Figure 6.3 fall on the one-to-one line with an overall median absolute difference of 5.5%. Focusing on the results from interferometry alone is equally encouraging. Figure 5.1 illustrates our ability to reproduce radii and angular diameters from interferometry to within a median absolute difference of 6%, with matches improving with more recent publications (Boyajian et al. (2012b): 6.5%, Rabus et al. (2019): 3.7%). These Figures only illustrate the most recent result for each star; we include a comparison with all known interferometric results for red dwarfs to date in Table 5.1. Because LBI efforts resolve

Figure 6.3: Here we compare our radii in units of solar radii, R_⊙, to those measured by others, as discussed in §6.2.3. Our radius results generally match those for the easier-to- study early M dwarfs more closely than for cooler stars. In particular, there are significant discrepancies between our results and those of Filippazzo et al. (2015). The median absolute differences between our radii and those of others are 4.8% for Mann et al. (2015), 7.0% for Boyajian et al. (2012b), 3.3% for Rabus et al. (2019), 13.4% for Filippazzo et al. (2015), and 6.7% for Dieterich et al. (2014). Most importantly, our results are a close match to the directly measured values obtained via LBI by Boyajian et al. (2012b) and Rabus et al. (2019), further illustrated in Figure 5.1 and described in §5.2.

stars directly, our match to the LBI results to 6% is arguably more valuable than any other measure of validating our radii. In comparison, we find differences of 4.8%, 13.4%, and 6.7% between our radii and those of Mann et al. (2015), Filippazzo et al. (2015), and Dieterich et al. (2014), respectively, with no obvious large systematic offsets.

Worthy of detailed discussion are the radii of the smallest stars. We are especially encouraged that we match the five smallest interferometrically observed stars (smallest to largest: GJ 406, Proxima Centauri, Barnard’s Star, GJ 729, and GJ 447) to within a mean absolute difference of 6.8%. Recall that there is only one red dwarf within our cool sample

atV −K = 7.53measured with LBI — GJ 406, recently observed by Rabus et al. (2019) — for which we find a radius of 0.154R_⊙ that is 3.1% larger than measured interferometrically. Therefore, we only have one data point available to probe the accuracy of our method for the cool subset of stars directly (V −K > 7). Our remaining options are comparisons to Filippazzo et al. (2015), one star in Mann et al. (2015), (GJ 406, matching to within 10%), and one star in Kesseli et al. (2019) (GJ 406, matching to within 6%), discussed further in §6.2.5. Filippazzo et al. (2015) does not cite any radii smaller than 0.1 R_⊙ for any of our 19 overlapping stars, while we derive main sequence star radii near the hydrogen burning limit as small as 0.077 R⊙, 23% smaller than theirs. Unfortunately, no work other than our previous effort, Dieterich et al. (2014), presents radii of more than a few stars this small. In fact, we find stars as small as 0.058R_⊙ (LHS 3181), as shown in the top left panel of (Figure 5.2).

Small Main Sequence Stars: We derive radii for three stars that are slightly smaller than the radius cited for the smallest main sequence star (2MA0523-1403 at 0.086 R_⊙) found by Dieterich et al. (2014), for which we find 0.084 R_⊙. Identifying the smallest stars is key to studies of low-mass stars and brown dwarfs because the smallest radius defines the boundary between the two types of objects. There is a local minimum in radius that marks the transition from main sequence stars that fuse hydrogen and brown dwarfs that are supported by electron degeneracy pressure. In order of smallest to largest, the smallest main sequence stars in our sample, all cooler than 2500 K and not known to be subdwarfs, are:

1. ESO207-061 — 0.077 ± 0.006 R_⊙, V−K = 9.05

(Dieterich et al. (2014) found R = 0.088 ± 0.004 R_⊙)

2. 2MA0251-3502 — 0.082 ± 0.004 R_⊙, V−K = 10.06

3. 2MA0921-2104 — 0.084 ± 0.005 R_⊙, V−K = 9.29

4. 2MA0523-1403 — 0.084 ± 0.007 R_⊙, V−K = 9.35 (Dieterich et al. (2014) found R = 0.086 ± 0.003 R_⊙)

The only suspect photometry value for these four stars is the W3 band signal-to-noise ratio of∼10 exhibited by star (1). However, we expect this alone to have little effect on our results. In addition, as described in §5.5, (1) may also be a subdwarf; it is noticeably below the other stars in the radius vs. effective temperature diagram (Figure 5.2).

Star (2) has sub-optimal Monte Carlo results from the flux fitting procedure, indicating that a small change in the observed magnitudes can produce a non-negligible change in measured bolometric flux, and therefore radius.

Finally, we presently see no reason that our results for stars (3) and (4) are suspect. Small Subdwarfs: We find a few subdwarfs that appear to have radii even smaller than these tiny main sequence stars. Properties of subdwarfs, including knowledge that they may be smaller than Jupiter and Saturn, are critical to refining stellar models at the extreme limits of metallicity and radius, especially because M subdwarfs are so faint and rare that they are often neglected. However, we reiterate the caveat that the accuracy of our results in this regime is hard to evaluate; although our results for the larger, more metal-rich stars

are validated by LBI measurements and comparisons to other previous efforts, we have no other work to compare to for stars this small. Furthermore, although they are arguably the best models available, there is still room for improvement at low metallicities in the BT-Settl CIFIST 2011 model grid (Rajpurohit et al. (2012) investigation of source opacities, Jao et al. (2016) evaluation of (Baraffe et al. 2015) evolutionary models). In a future effort with a larger subdwarf sample, we may re-calculate the subdwarf fundamental parameters using a low-metallicity version of the more recent 2015 model grid (unpublished, granted via private communication with Derek Homeier).

The smallest cool subdwarfs revealed in this work are:

1. LHS 3181 — 0.058 ± 0.003 R_⊙, V−K = 3.93

2. SSS1013-1356 — 0.073 ± 0.005 R_⊙, V−K = 5.83

3. LHS 335 — 0.075 ± 0.009 R_⊙, V−K = 3.61

We note that historically it has been difficult to find subdwarfs in multi-star systems (Jao et al. 2016). In addition to their paucity in the solar neighborhood, meaning that few candidates for multiplicity are available, the lack of companions to subdwarfs may be caused by formation processes for low metallicity protostellar environments and/or companion strip- ping during the vast timescales of their lifetimes. In addition, cool subdwarfs are intrinsically faint, making them more difficult to observe than their brighter metal-rich counterparts.

6.2.4 Mismatch with the Multiple Optical-Infrared Technique (MOITE)