[Paper Review] Tidal effects on brown dwarfs: Application to the eclipsing binary 2MASSJ05352184-0546085 - The anomalous temperature reversal in the context of tidal heating

René Heller, Brian Jackson+3 more|GoeScholar The Publication Server of the Georg-August-Universität Göttingen (Georg-August-Universität Göttingen)|Feb 5, 2010

Stellar, planetary, and galactic studies48 references10 citations

TL;DR

This study investigates tidal heating as a potential explanation for the anomalous temperature reversal and enhanced luminosity of the secondary brown dwarf in the eclipsing binary 2M0535-05. Using constant-phase-lag and constant-time-lag tidal models, it finds that tidal heating alone is unlikely to explain the observations, requiring implausibly low $Q_{\mathrm{BD}} \sim 10^{3.5}$ and high spin-orbit misalignment ($\gtrsim 50^\circ$), which are ruled out by tidal synchronization timescales implying $\log(Q_{\mathrm{BD}}) \gtrsim 4.5$. The results suggest tidal effects may have slowed cooling but require coupled evolutionary modeling for confirmation.

ABSTRACT

2MASSJ05352184-0546085 (2M0535-05) is the only known eclipsing brown dwarf (BD) binary, and so may serve as an important benchmark for models of BD formation and evolution. However, theoretical predictions of the system's properties seem inconsistent with observations: i. The more massive (primary) component is observed to be cooler than the less massive (secondary) one. ii. The secondary is more luminous (by roughly 10^{24} W) than expected. We study the impact of tidal heating to the energy budget of both components. We also compare various plausible tidal models to determine a range of predicted properties. We apply two versions of two different, well-known models for tidal interaction, respectively, (i.) the 'constant-phase-lag' model and (ii.) the 'constant-time-lag' model, and incorporate the predicted tidal heating into a model of BD structure. We find that the contribution of heat from tides in 2M0535-05 alone may only be large enough to account for the discrepancies between observation and theory in an unlikely region of the parameter space. The tidal quality factor of BDs, Q_{BD}, would have to be 10^{3.5} and the secondary needs a spin-orbit misalignment greater than 50 degrees. However, tidal synchronization time scales for 2M0535-05 restrict the tidal dissipation function Q_{BD} to values greater than 10^{4.5} and rule out intense tidal heating in 2M0535-05. We provide the first constraint on Q_{BD}. Tidal heating alone is unlikely to be responsible for the surprising temperature reversal within 2M0535-05. But an evolutionary embedment of tidal effects and a coupled treatment with the structural evolution of the BDs is necessary to corroborate or refute this result.

Motivation & Objective

• To assess whether tidal heating can explain the observed temperature reversal and luminosity excess in the eclipsing brown dwarf binary 2MASS J05352184-0546085.
• To evaluate the role of tidal dissipation in the energy budget of both components, particularly the secondary's anomalous luminosity ($\approx 10^{24}$ W higher than predicted).
• To constrain the tidal quality factor $Q_{\mathrm{BD}}$ of brown dwarfs using tidal synchronization timescales and rotational evolution.
• To test whether spin-orbit misalignment or non-synchronous rotation could enhance tidal heating in the secondary while minimizing it in the primary.
• To determine whether tidal heating could have slowed the cooling and contraction of the brown dwarfs since their formation ~1 Myr ago.

Proposed method

• Application of two tidal models: the constant-phase-lag model and the constant-time-lag model, both incorporating tidal dissipation into brown dwarf structure models.
• Incorporation of tidal heating rates into evolutionary models of brown dwarfs, using observed system parameters such as mass ratio, orbital period, and eccentricity.
• Assessment of tidal heating under varying assumptions: synchronous vs. non-synchronous rotation, and spin-orbit misalignment $\psi$ up to $\sim 50^\circ$.
• Use of tidal synchronization timescale estimates to derive a lower bound on $Q_{\mathrm{BD}}$, based on observed rotational properties and orbital decay constraints.
• Comparison of predicted heating rates with observed luminosity excess and temperature reversal to test model viability.
• Incorporation of constraints from Rossiter-McLaughlin effect measurements and spin-orbit misalignment statistics in exoplanet systems to assess plausibility of high $\psi$.

Figure 1: Degeneracy parameter $\tilde{\Psi}=k_{\mathrm{B}}T/(k_{\mathrm{B}}T_{\mathrm{F}})$ (solid line) with model parameters similar to those of the 2M0535 $-$ 05 primary and radius-integrated luminosity $L$ (dashed line) as a function of radius. To fit into the plot, $L$ is normalized to 10.

Experimental results

Research questions

• RQ1 Can tidal heating alone account for the observed temperature reversal, where the more massive primary is cooler than the less massive secondary in 2M0535-05?
• RQ2 What is the required tidal quality factor $Q_{\mathrm{BD}}$ for tidal heating to explain the luminosity excess of the secondary, and is this value physically plausible?
• RQ3 How does spin-orbit misalignment affect tidal heating rates, and can a misalignment $\gtrsim 50^\circ$ in the secondary explain the observed luminosity enhancement?
• RQ4 What constraints does the tidal synchronization timescale place on $Q_{\mathrm{BD}}$, and how does this affect the viability of tidal heating as a mechanism?
• RQ5 Could tidal heating have slowed the cooling and contraction of the brown dwarfs since their formation ~1 Myr ago, leading to a feedback between tidal inflation and heating?

Key findings

• Tidal heating alone is insufficient to explain the temperature reversal and luminosity excess in 2M0535-05 under plausible physical conditions.
• The required tidal quality factor $Q_{\mathrm{BD}} \approx 10^{3.5}$ is inconsistent with the lower bound of $\log(Q_{\mathrm{BD}}) \gtrsim 4.5$ derived from tidal synchronization timescales.
• A spin-orbit misalignment of $\gtrsim 50^\circ$ in the secondary is required to enhance tidal heating, but such high misalignment is unlikely to be sustained over the system's lifetime.
• The constant-phase-lag and constant-time-lag models yield consistent results, with the latter providing a lower limit on heating rates due to assumed synchronous rotation.
• The observed luminosity excess of $\approx 2.3 \cdot 10^{24}$ W in the secondary cannot be explained by tidal heating under realistic $Q_{\mathrm{BD}}$ values.
• Tidal heating may have played a role in slowing the cooling and contraction of the brown dwarfs after formation, but a self-consistent, coupled tidal-evolution model is required to confirm this.

Figure 2: Orbital evolution of 2M0535 $-$ 05 after model #1 going back in time for 1.5 Myr. Left: Eccentricity evolution. Depending on $\tilde{Q}$ and on the age of the system, its initial eccentricity has not been smaller than $\approx 0.3133$ , which is $\approx 97.4\%$ of its current value. Right