Tidally Delayed Spin-Down of Very Low Mass Stars

TL;DR

This work tackles the problem of anomalous spin evolution in very low-mass stars by introducing a self-consistent model that couples magnetized wind spin-down to tides from close substellar companions. The approach links X-ray luminosity, magnetic field strength, mass loss, and tidal torques within a dynamical framework, using equilibrium tides for circular BD/M-dwarf orbits and a Parker-wind driven angular-momentum loss with dynamo saturation. The key finding is that brown-dwarf companions can significantly delay spin-down of old, late-type M dwarfs, producing a bimodal fast/slow rotator distribution and a dearth of intermediate rotators; partially convective stars exhibit different responses, with Jupiter-mass companions capable of spinning up hosts and enhancing X-ray activity. These results offer a mechanism to explain observed rotation-period gaps and provide a pathway to constrain the population distribution of companion orbital separations from spin and activity evolution, with implications for gyrochronology and exoplanet demographics. $\frac{d\omega_*}{d\tau}=\gamma_W+\gamma_T(1-2H(a_{crit}-a))$ and $l_{x,*}\propto b_{r,*}^{\frac{4}{1-\lambda}}$ (with $\lambda=\tfrac{1}{3}$) are central to the coupling between magnetic braking, tides, and observable activity in the model.$

Abstract

Very low-mass main-sequence stars reveal some curious trends in observed rotation period distributions that require abating the spin-down that standard rotational evolution models would otherwise imply. By dynamically coupling magnetically mediated spin-down to tidally induced spin-up from close orbiting substellar companions, we show that tides from sub-stellar companions may explain these trends. In particular, brown dwarf companions can delay the spin-down and explain the dearth of field, late-type M dwarfs with intermediate rotation periods. We find that tidal forces also strongly influence stellar X-ray activity evolution, so that methods of gyrochronological aging must be generalized for stars with even sub-stellar companions. We also discuss how the theoretical predictions of the spin evolution model can be used with future data to constrain the population distribution of companion orbital separations.

Figures (8)

• Figure 1: Evolution of rotation and orbital separation for System 1. We use a $0.2M_\odot$ mass M-dwarf with $0.1$ days initial period, $100 \rm G$ magnetic field and companion BD at $a_{\rm i}=6 R_{\rm co}$ initial orbital separation. Different colors represent varying BD companion masses between $15-75M_{\rm J}$. Top panel: spin evolution due only to magnetic braking (grey) and coupled to tides (colored). Cusps represent engulfment points. The thickness of the grey and colored curves is determined by the highest and lowest $\epsilon$ values (see text). Black dots represent fully convective M dwarfs with measured rotation periods and estimated ages from Galactic kinematics irwin2011Angular. The vertical grey dashed lines separate M-dwarfs in the thin, intermediate and thick disk populations with corresponding age ranges of $0.5-3$ Gyr, $3-7$ Gyr and $7-13$ Gyr. The x-axis and y-axis are normalized to 1 Gyr and a 1-day rotation period, respectively. Bottom panel: orbital separation for solutions without tides (dashed) and coupled to tides (solid) analgous to the top panel. The x-axis is normalized to 1 Gyr, and the y-axis is normalized to the stellar radius $R_\star$.
• Figure 2: Evolution of rotation for System 2. We use an M-dwarf with the same stellar and companion BD mass ranges as in Fig. \ref{['fig:0.1']}, but with initial stellar rotation period of $0.3$ days, $50\rm G$ magnetic field, and orbital separation at $a_{\rm i}=2.9 R_{\rm co}$. colors and axes are same as Fig. \ref{['fig:0.1']}.
• Figure 3: Evolution of rotation and orbital separation for System 3A. We use an M-dwarf with initial period of $6$ days, $200 \rm G$ magnetic field, and orbital separation at $a_{\rm i}=0.5 R_{\rm co}$. This causes earlier inward migration of all the companions compared to Fig. \ref{['fig:0.3']} but also eventual engulfment. Top panel: black circles qualitatively illustrate the bimodal behavior of the M-dwarf rotation period during certain ages. colors and axes are same as Fig. \ref{['fig:0.1']}.
• Figure 4: Evolution of rotation and orbital separation for System 3B. We use an M-dwarf with the same stellar properties as in Fig. \ref{['fig:5']} and a $m=75M_{\rm J}$ companion BD. Here different colors represent different initial orbital separations varying between $0.5-0.95 R_{\rm co}$. colors and axes are same as Fig. \ref{['fig:0.1']}.
• Figure 5: Evolution of rotation period and X-ray luminosity $l_x$ for System 4. We use a $0.6M_\odot$ mass K-dwarf with a $10$ day initial period, $5 \rm G$ magnetic field and an initial orbital separation $a_{\rm i}=0.5 R_{\rm co}$. Different colors in each panel represent different companion masses between $2-16M_{\rm J}$. Top panel: colors and axes are the same as Fig. \ref{['fig:0.1']}. Bottom panel: The x-axis is normalized to 1 Gyr, and the y-axis is normalized to the solar X-ray luminosity $\mathcal{L}_{{\rm x}\odot}.$