Tidal Dissipation in WASP-12 The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. Citation Weinberg, Nevin N. et al. “Tidal Dissipation in WASP-12.” The Astrophysical Journal 849, 1 (October 2017): L11 © 2017 The American Astronomical Society As Published http://dx.doi.org/10.3847/2041-8213/AA9113 Publisher American Astronomical Society Version Final published version Citable link http://hdl.handle.net/1721.1/114967 Terms of Use Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. The Astrophysical Journal Letters, 849:L11 (6pp), 2017 November 1 https://doi.org/10.3847/2041-8213/aa9113 © 2017. The American Astronomical Society. All rights reserved. Tidal Dissipation in WASP-12 Nevin N. Weinberg1 , Meng Sun2, Phil Arras2 , and Reed Essick1 1 Department of Physics, and Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology, Cambridge, MA 02139, USA 2 Department of Astronomy, University of Virginia, P.O. Box 400325, Charlottesville, VA 22904-4325, USA Received 2017 August 31; revised 2017 September 22; accepted 2017 October 1; published 2017 October 24 Abstract WASP-12 is a hot Jupiter system with an orbital period of P=1.1 days, making it one of the shortest-period giant planets known. Recent transit timing observations by Maciejewski et al. and Patra et al. founda decreasing period with PP∣ ˙∣=3.2 Myr. This has been interpreted as evidence of either orbital decay due to tidal dissipation or a long-term oscillation of the apparent period due to apsidal precession. Here, we consider the possibility that it is orbital decay. We show that the parameters of the host star are consistent with either a M*;1.3 Me main sequence star or a M*;1.2 Me subgiant. We find that if the star is on the main sequence, the tidal dissipation is too inefficient to explain the observed P˙. However, if it is a subgiant, the tidal dissipation is significantly enhanced due to nonlinear wave-breaking of the dynamical tide near the star’s center. The subgiant models have a tidal 5 ˙ quality factor Q¢´* 210and an orbital decay rate that agrees well with the observed P. It would also explain why the planet survived for ;3 Gyr while the star was on the main sequence and yet is now inspiraling on a 3 Myr timescale. Although this suggests that we are witnessing the last ∼0.1% of the planet’s life, the probability of such a detection is a few percent given the observed sample of ;30 hot Jupiters in P<3-day orbits around M*>1.2 Me hosts. Key words: binaries: close – planet–star interactions – planets and satellites: individual (WASP-12b) – stars: oscillations 1. Introduction With a few more years of monitoring it should be possible to distinguish unequivocally between orbital decay and precession The orbits of hot Jupiters are expected to decay due to tidal (Patra et al. 2017). In this paper, we consider whether the decay dissipation within their host stars (Rasio et al. 1996). While explanation is plausible. In Section 2, we construct stellar there is considerable indirect evidence of orbital decay in the fi ( models that t the observed properties of WASP-12. In ensemble properties of hot Jupiter systems Jackson et al. 2008, Section 3, we describe the relevant tidal processes and then use 2009; Hansen 2010; Penev et al. 2012; Schlaufman & ) the stellar models to calculate the expected rate of tidal Winn 2013; Teitler & Königl 2014 , the recent transit timing dissipation. We conclude in Section 4. observations of WASP-12 by Maciejewski et al. (2016) and Patra et al. (2017) could be the first direct evidence of the orbital decay of an individual system. They detect a decrease in 2. Stellar Models of WASP-12 the orbital period at a rate P˙=−29±3msyr−1. This = ˙ = The WASP-12 host star has an effective temperature Teff corresponds to an inspiral timescale of just PP∣ ∣ 3.2 Myr 3 5 6300±150 K and a mean density ρ*≡3M*/4pR = and a stellar tidal quality factor Q*¢ »´210. −3 * fi 0.475±0.038 g cm (Hebb et al. 2009;Chanetal.2011; As both studies note, it is dif cult to tell whether the ) observed P˙ is due to orbital decay or is instead a portion of a here and below we adopt the values from the latter reference . Note that ρ is measured solely from the transit parameters of long-term (≈14 yr) oscillation of the apparent period. The latter * the light curve (see Seager & Mallén-Ornelas 2003) and is not could be due to apsidal precession if the eccentricity is derived from a fit to stellar evolution models, unlike the stellar e≈0.002. However, it is not clear how to maintain such an e ( ) mass M* and radius R*. The spectrum of WASP-12 is consistent in the face of rapid tidal circularization. Patra et al. 2017 with a supersolar metallicity ([Fe/H]=0.30± 0.10) and a spin mention gravitational perturbations from the star’s convective ( < ± −1) ( ) that is slow v sin i 2.2 1.5 km s and likely misaligned eddies, a mechanism Phinney 1992 proposed to explain the with the planet’s orbital plane (Schlaufman 2010;Albrecht small but nonzero eccentricities of pulsars orbiting white et al. 2012).Byfitting stellar models to T , ρ , and the ( ; ) eff * dwarfs. However, the host star M* 1.3 Me has a very low- metallicity, Chan et al. (2011; see also Hebb et al. 2009;Enoch (; −3 ) mass convective envelope 10 Me and we estimate that et al. 2010; Fossati et al. 2010; Maciejewski et al. 2011) find ∼ −3 there is too little energy in the eddies to maintain an e 10 . M*=1.36±0.14 Me, R*=1.595±0.071 Re,andasurface Another mechanism that can cause decade-long oscillations of gravity log g*=4.164± 0.029 (in cgs units). Based on three the period that Patra et al. mention is the Applegate (1992) separate age-dating techniques (lithium abundance, isochrone effect, which invokes variations in the quadrupole moment of analysis, and gyrochronology) Hebb et al. (2009) find that the star over a magnetic activity cycle. However, Watson & WASP-12 is likely to be several Gyr old, implying an age Marsh (2010) estimate that for WASP-12b, this effect shifts the comparable to its main sequence lifetime. transit arrival times by ΔT10 s after T≈10 yr. This We construct stellar models using the MESA stellar − corresponds to an average ∣P˙∣;2PΔT/T2<1msyr 1 evolution code (Paxton et al. 2011, 2013, 2015), version (Birkby et al. 2014), more than an order of magnitude smaller 9575. We assume a solar abundance scale based on Asplund than the measured value. et al. (2009; solar metallicity Z=Ze=0.0142) and follow the 1 The Astrophysical Journal Letters, 849:L11 (6pp), 2017 November 1 Weinberg et al. Figure 2. Effective temperature T and mean density ρ* at the moment when Figure 1. Evolution of the effective temperature T and mean density ρ* for eff eff the core ceases to be convective and the star enters the subgiant phase. The six stellar models. Each model is labeled by (M*/Me, Z, αMLT). The evolution labels indicate M*/Me with points spaced by 0.01 Me (connected by straight goes from right to left, starting from when the star is 1 Gyr old. The squares ) mark when the core ceases to be convective. Observations of WASP-12 lines for clarity . The blue solid curves assume solar metallicity ρ Z=Ze=0.0142 and the black dashed–dotted curves assume Z=0.02. The constrain its Teff and * to lie within the region indicated by the gray box. The α = ( ) three curves for each Z assume, from bottom to top, MLT 1.9, 2.1, and 2.3. blue solid red dashed curves are models that match the observations when on ρ the subgiant branch (main sequence). Observations of WASP-12 constrain its Teff and * to lie within the region indicated by the gray box. ( ) MESA prescriptions given in Choi et al. 2016 for calculating As we describe in Section 3, the efficiency of tidal the abundances, equation of state, opacity, and reaction rates. dissipation is significantly enhanced if WASP-12 has a As we show below, the properties of WASP-12 are ; radiative core. The only models with radiative cores that we consistent with both M* 1.3 Me main sequence models and fi T ρ ; nd are consistent with the measured eff and * are the M* 1.2 Me subgiant models. The range of subgiant models subgiant models. Torres et al. (2012) estimate a somewhat that fits the observations is sensitive to how convection and lower Teff=6118±64 K, which could match the Teff of main mixing in radiative zones is implemented in MESA. In sequence models with fully radiative cores (i.e., fi particular, we nd it is sensitive to the values of the parameters M*1.1 Me). However, we find that such models have too α of mixing length theory MLT, overshooting fov, semiconvec- high a ρ*. α tion sc, and diffusive mixing. Although recent studies are In Figure 2 we show Teff as a function of ρ* at the moment the starting to place interesting constraints on some of these core ceases to be convective and the star enters the subgiant ( parameters Silva Aguirre et al.