Table 5. Mass Estimates for the Four Stars in TIC 121088959/60

Parameter	Star Ca	Star Cb	Star A	Star B
Mass \( \mathbf { M } _ { \odot } \))	0.190 \( ^ + \) 0.009	0.138 \( ^ + \) 0.005	0.430 \( ^ { + } \) 0.008	0.386 \( ^ + \) 0.008
Radius \( \mathbf { R } _ { \odot } \))	0.201 \( ^ + \) 0.007	0.160 \( ^ + \) 0.005	0.394 \( ^ + \) 0.005	0.358 \( ^ + \) 0.007
\( T _ { \mathrm { e f f } } \)(K)	3228 \( ^ + \) 25	3033 \( ^ + \) 30	3512 \( + \) 10	3468 \( ^ + \) 10
Luminosity \( \mathrm { L } _ { \odot } \))	0.0040 \( ^ + \) 0.0004	0.0020 \( \mathrm { ^ { + } } \) 0.0002	0.0213 \( ^ + \) 0.0007	0.0167 \( + \) 0.0007
a \( \mathbf { R } _ { \odot } \))	6.08 \( + \) 0.07	6.08 \( \mathrm { ~ \texttt ~ { ~ \, ~ \, ~ } ~ } \) 0.07	...	...

Figure 13. Allowed orbits in the \( P _ { \mathrm { A C } } - \omega _ { \mathrm { A C } } \) plane.

The results of acceptable AC orbits are shown in Figs. 12 and 13. In Figure 12 we show the orbits which satisfy all five constraints in the \( P _ { \mathrm { A C } } - e _ { \mathrm { A C } } \) plane. Since constraints (i)-(iii) are analytic functions of \( P _ { \mathrm { A C } } \) and \( e _ { \mathrm { A C } } , \) and a reasonable assumption about \( P _ { \mathrm { A B C } } \) (see above), we show those as solid limiting curves. The remainder of the constraints come from the RV and PM differences between stars A and B. It seems clear that inner orbital periods \( P _ { \mathrm { A C } } \) ranging from about a year to 1000 years are acceptable. All eccentricities seem possible. However, for nominal eccentricities in triple systems of∼0.2 − 0.7 (see Figure 9 of Borkovits et al. 2016) we more likely can expect to find \( P _ { \mathrm { A C } } \) in the range of 1 − 50 yr. In Figure 13 we show \( \omega _ { \mathrm { A C } } \) vs \( P _ { \mathrm { A C } } \). These two parameters are slightly correlated, with more allowed orbits having \( \omega _ { \Delta C } \simeq 9 0 ^ { \circ } \)◦and \( 2 7 0 ^ { \circ } \)◦and covering a more restricted range of \( P _ { \mathrm { A C } } \). The inclination angles \( i _ { \mathrm { A C } } \) (not shown in the plots) are uniformly distributed between a minimum of \( 6 8 ^ { \circ } \) and \( 9 0 ^ { \circ } \).

# 7 COMPARISON WITH OTHER LOW-MASS ECCENTRIC BINARIES

Similar to the case of the vast majority of close main-sequence bi-naries, it is clear that since the radii of the low-mass protostars were much larger than the present-day separation of its stars, the eccentric binary Cab cannot have been formed in its present orbital configu-ration (see, e.g. Kiseleva et al. 1998; Fabrycky & Tremaine 2007). Perhaps the most interesting question about this close pair is how it has managed to retain such a high eccentricity despite the requisite orbital shrinkage during its past history. Some possibilities are as follows: (i) the initial eccentricity of the originally wider orbit was much higher, and while there is ongoing tidal friction causing orbital shrinkage and circularization, the system is still sufficiently young that there has not been enough time to circularize the orbit; (ii) the shrinkage of the initial orbit, which was wide enough to accommo-date the protostars, was the result of some other mechanism(s) beside tidal dissipation such as, e.g., (a) escape of an additional stellar com-ponent or, (b) accretion-driven migration (see, e.g. Tokovinin & Moe 2020, and further references therein). Or, another possibility is, (iii) that the observed current high eccentricity is a consequence of on-going dynamical interactions with the more distant, third and fourth stellar components of the quadruple system.

We constructed a so-called “\( P - e \)” diagram showing the known cases of eccentric binaries in Figure 14 (upper panel). We plot-ted there the same datasets as in a previous paper by Zasche et al. (2021): small red dots are from the SB9 catalogue (Pourbaix et al. 2004); yellow dots show eclipsing binaries from the catalogue of eccentric binaries by Kim et al. (2018); blue dots show Kepler bina-ries by Kjurkchieva et al. (2017); black dots show those from ASAS published by Shivvers et al. (2014); cyan points are from Halbwachs et al. (2003); green points are from Triaud et al. (2017); and magenta points are from (Latham et al. 2002). All of these were studied as spectroscopic and/or eclipsing binaries. However, some of the most extreme points from the SB9 catalogue have very uncertain orbits and should not be considered as real eccentricities. Moreover, most of the data shown here represent much more massive stars, for which the circularization process is different due to their internal structure (as recently proven on real data, see e.g. Van Eylen et al. 2016).

For these reasons, we have tried to compare the comparable, i.e., plot our unique low-mass system with other stars having derived eccentricities and both components of the M spectral type. Specifi-cally, (i) the set of Kepler eclipsing binaries yielded 7 systems with GAIA photometric index (\( B _ { p } - R _ { p } ) \, > \, 1 . 8 \) mag; (ii) the spectro-scopic survey by Latham et al. (2002) contains only one system with effective temperature below 4000 K; and (iii) the survey Halbwachs et al. (2003) provided two binaries with masses below \( 0 . 6 \, M _ { \odot } . \) These are plotted in the bottom panel of Fig. 14. These data are then com-plemented with other M+M binaries taken from various dedicated studies (Stassun et al. 2006; Morales et al. 2009; Carter et al. 2011;Irwin et al. 2011; Gómez Maqueo Chew et al. 2012; Kraus et al. 2015; David et al. 2016; Gillen et al. 2017; Kraus et al. 2017; Lubin et al. 2017; Irwin et al. 2018; Murphy et al. 2020; Acton et al. 2020). The data for these low-mass binaries are plotted together in the bot-tom panel of Fig. 14 with curves representing the close pericenter approaches (i.e., \( 1 . 5 \times R _ { \star } \, = \, a \cdot ( 1 - e ) \)) when they likely collide with each other. The periastron separations are calculated for dif-ferent spectral types (from M0V to M6V) according to their typical radii and masses according to Pecaut & Mamajek (2013), assuming both components are similar to each other (same masses and radii). One can also ask whether some proximity effect near periastron pas-sage would also be visible on the light curve of the binary. However, we have calculated that such an effect is so small that it cannot be detected with the current precision of the available TESS data.