Observational Cosmology Journal Club 07/09/2018 Shijie Wang 1. Heller, R. (2018). Formation of hot Jupiters through disk migration and evolving stellar tides. Retrieved from arxiv.1806.06601 2. Rey, J., et al. A 4.6-year period brown-dwarf companion interacting with the hot-jupiter CoRoT-20 b. Retrieved from arxiv. 1807.01229
[P1]Background: Hot Jupiters Definitions and up-tonow discoveries Mysterious origins formation channels In-situ via core accretion? Disk Migration(e.g. Lin et al. 1996) Scattering, Kozai-effect, tidal circularisation(e.g. Nagasawa et al. 2008) Problems: stopping mechanism & fine-tuning dissipation Fig. 1. Normalised histogram of the observed semimajor axis distribution of exoplanets with masses > 0.1M J around stars with masses 0.75 to 1.25
Methods: Overview Two stages investigation: (I.)disk migration (II.)tides I. Disk + Tidal torques -> type II migration until II. Disk disappear -> tidal dissipation only -> survive & pile up Highlights: Stellar evolution model STAREVOL code (Amard et al. 2016) Initial spin: 1.4 day -> spin up for first 100 Myr to 0.25 day Two layer model: radiative core + convective envelope contraction -> stellar radius -> Love number Q corotational radius -> tidal torque & tidal dissipation Important Improvement: previous studies use fixed Q
Methods: Disk Profile Temperature Viscosity α = 10 3 Surface density Fig.2. Midplane temperature of the disk, assuming viscous heating dominates
Methods: Torques at disk phase Disk Migration Torque viscosity ν = αc s 2 Ω p is a function of distance and couples with sound velocity and midplane temperature Tidal Torque k 2, :2 nd degree tidal Love number (Bolmont & Mathis 2016) Γ t is positive when a > r co, where r co = [ G M +M P Ω 2 Frequency averaged ] 1/3 = 0.02AU star transfer its angular momentum to the planet s orbital angular momentum. And Vice versa.
Methods: Tidal Dissipation Stage Tidal Dissipation function (Eggleton et al. 1998) Compare Pure Equilibrium Tidal Model (application only when e is small) β = 1 e 2 n σ σ p
Results Balance of torques A Monte Carlo simulation of 1 000 realizations 28.4% of HJs that form around sun-like stars survive their inwards migration
Results (a) Frequency-averaged tidal dissipation factor (b) rotation period of the star during the first 10 Myr of stellar evolution. (c) Tidally-driven orbital evolution of a single planet on a grid of 100 equally-spaced initial orbits. Orbital decay is calculated via Eq. (7) (assuming e = 0) according to the dynamical tide model with stellar evolution as per (a) and (b). (d) Stellar dissipation factor (e) stellar rotation period over the first 1 Gyr of stellar evolution. (f) Comparison of the planetary orbital evolution in the dynamical tide model (blue lines) and in the equilibrium tide model (orange lines, Q = 10 5 ). Fig. 4. Evolution of the spin and orbital properties of a Sun-like star (initial rotation period 1.4 d, metallicity Z = 0.0134) as per Amard et al. (2016) and Bolmont & Mathis (2016) and orbital evolution of a hot Jupiter population
Results Fig.5. Normalized histograms of 911 orbital integrations of a Jupiter-mass planet around a Sun-like star as per Fig. 4(f). (a) assumes the equilibrium tide model and a fixed Q* = 105, (b) is based on the dynamical tide model with stellar evolution of a sun-like star (metallicity Z = 0.0134) (c) sub-solar (Z = 0.004), solar (Z = 0.0134), and super-solar (Z = 0.0255) metallicities after 1000 Myr
Summary Discussion: Possible Improvements? Disk Profile Uncertainties Conventional Type II Migration -> flow is forbidden Tidal migration only valid for small eccentricity and spin-orbit misalignment Conclusion 4.2% planets around Sun-like star initially gives birth to a HJ, 28.4 % HJS ultimately survives > explain HJ occurrence rate 1.2% naturally produce a pile-up of planets near 0.05AU
[P2]: Discovery of CoRoT-20c CoRoT-20c: An additional substellar companion in the CoRoT-20 system based on six years of HARPS and SOPHIE radial velocity follow-up CoRoT-20 System: Discovered by the CoRoT space mission(baglin et al. 2009) Composed of a 14.7-magnitude G-type star hosting a very high density transiting HJ, CoRoT-20b is the first identified system with an eccentric hot Jupiter (e 0.2) Data from exoplanets.org Rey, J., et al. A 4.6-year period brown-dwarf companion interacting with the hot-jupiter CoRoT-20 b.
Spectroscopic follow-up A long-term radial velocity monitoring of CoRoT-20 was done: HARPS spectrograph (Mayor et al. 2003) from November 2011 to September 2013 SOPHIE spectrograph (Per- ruchot et al. 2008; Bouchy et al. 2009a) from October 2013 to November 2017. A total of 33 new RV measurements spanning six years were obtained Rey, J., et al. A 4.6-year period brown-dwarf companion interacting with the hot-jupiter CoRoT-20 b.
Analysis: Orbital Parameters Orbit fitting with DACE fit a two-keplerian model to the SOPHIE, HARPS and FIES data Eccentricities and periastron arguments are very similar Rey, J., et al. A 4.6-year period brown-dwarf companion interacting with the hot-jupiter CoRoT-20 b.
Analysis Best fit line reveals the presence CoRoT-20c with a minimum mass of m sin i = 17M J, orbiting the star in an eccentric orbit of 4.6 years No correlation between star activity and the RV. Quiet star. No additional signals were found in the RV residuals. Rey, J., et al. A 4.6-year period brown-dwarf companion interacting with the hot-jupiter CoRoT-20 b.
Dynamical Analysis: GENGA Numerical simulations using the GENGA integrator Initial conditions: best-fit values No constraint on i c survey between 5 175 Total 1600 simulations Red: Largest L-K oscillns. White: Unstable Rey, J., et al. A 4.6-year period brown-dwarf companion interacting with the hot-jupiter CoRoT-20 b.
Discussions High eccentricity of CoRoT-20b is expected to be entirely due to the presence of CoRoT-20c Three mechanism to explain: Lidov-Kozai, Gravitational Scattering, Secular migration Complementary observational techniques -> more constrain on the mass of CoRoT-20c If coplanar-> probabilities for CoRoT-20c to transit on mid- November 2020 but with an uncertainty of about 1 month Rey, J., et al. A 4.6-year period brown-dwarf companion interacting with the hot-jupiter CoRoT-20 b.