Forging the Vulcans: Forming Close-in Earths and Super-Earths around Low Mass Stars Subhanjoy Mohanty (Imperial College London) Jonathan Tan (University of Florida, Gainesville) VIEW FROM KEPLER-62F: artist’s impression Some Examples of Transiting Planets P=10.3d Kepler 62 bcdef: 5 planets around a Solar-type star, , M~4.3M R=1.97R♁ ♁ with 2 Super-Earths in the Habitable Zone M ≲ 9 M♁ BORUCKI et al. 2013 P=13.0d R=3.15R♁ , M~13.5M♁ M ≲ 4 M♁ P=22.7d R=3.43R♁ , M~6.1M♁ M ≲14 M♁ P=32.0d R=4.52R♁ , M~8.4M♁ M ≲ 36 M♁ P=46.7d R=2.61R♁ , M~2.3M♁ M ≲ 35 M♁ P=118.4d R=3.66R♁ , M <300M♁ Kepler 11 bcdefg: 6 Close-packed Low-mass, Low-density planets around a Solar-type star LISSAUER et al. 2011 Statistics around Solar-type Stars ~50% of Solar- type stars have close-in Earths & super-Earths ~50% of M dwarfs have PETIGURA et al. 2013 close-in Earths & super-Earths Statistics around Red Dwarfs (very low-mass stars) DRESSING et al. 2013 Formation Mechanisms Problem with normal MMSN: Not enough solid material at small radii to form multiple close-in super-Earths in situ 1. Formation at larger radii, followed by radial migration. But: produces planets trapped near mean motion resonances, while no such preference observed in close-in super-Earths 2. Planet-planet scattering, followed by tidal circularization. But: cannot explain low-dispersion in orbital inclinations 3. In-situ formation from disk with Σ > ΣMMSN . But: significant fraction of such disks would be grav. unstable 4. Preferential enrichment of inner disk in solids, followed by in-situ formation (Hansen & Murray ‘13; Chatterjee & Tan ‘14). MRI-driven Disk Accretion stellar X-ray ionization (Gammie 1996) (Chatterjee & Tan 2014) Current Treatment Only Qualitative treatment so far of location and strength of Pressure Barrier at Dead Zone Inner Boundary (DZIB): Assumes: (e.g., Chatterjee & Tan ‘14; Kretke et al. ‘09) 1. Ad hoc location of DZIB at T ~ 1200K 2. α-disk structure with some specified Mdot, with ad hoc α in MRI-active zone and a step change in α change across the DZIB BUT: Disk structure + B-field determines MRI-driven α, which In turn determines Mdot ! heating and disk structure ! COUPLED PROBLEM: for steady-state: Must solve disk structure and MRI eqns simultaneously Conditions for Ang. Mom. Transport by B-Fields 2 α = 1/(2β)= PB / 2Pg (where PB = B /4π) (Wardle 2007) (Mohanty, Ercolano & Turner 2013) Active Disk Equations STRUCTURE (Xiao et al in prep, adapted from CT14 and FKR, for α-disk model): (assume vertically isothermal) 0 0 1/2 1/2 Cs,vert = (kT / μmp) , zH = (2) (cs / Ω) 2 2 ρ = ρ0 exp[-(z/zH) ], P = P0 exp[-(z/zH) ] IONIZATION: Saha Equation at T for Na, K + dust + chemical network 2 α (B): Sol. to MRI eqns. for various B, for given structure and ionization (α = PB / 2Pg , PB = B /4π) 2 Mdot (B): Mdot = B h / 4Ω (~ 2π αPgh / Ω) α FLOOR Next Steps 1. Insert derived MRI-disk structure / α into hydro simulations (FARGO), to derive planet mass / gap opening (including vertical B-fields => smaller gap-opening mass) 2. Reinsert gap properties (width, height) into MRI calculations to derive Dead Zone retreat due to stellar X-rays, and location of new pressure boundary. 3. Reinsert into FARGO to calculate new planet mass / gap opening; repeat cycles 2 & 3 (until dust in disk runs out). 4. Repeat 1-3 including more accurate chemistry, for different Mdot and Mstar, to get planetary masses and separations as a function of Mdot and Mstar; compare statistically to Kepler (and later TESS etc) stats to validate. 5. Understand why Vulcans do NOT form around the 50% of low-mass stars. How to NOT Form Vulcans 1. HALL EFFECT: In the presence of an external field, can either enhance the MRI or quench it, depending on whether the field is aligned or anti-aligned with the spin-axis of the disk. Quenching the MRI in the inner disk removes the pressure trap (low-α continues in the mid-plane all the way to the disk inner truncation radius) and stops Vulcan formation. 2. Stellar magnetic fields are just such an external field in the inner disk. Generated in the stellar interior, so magnetic axis should be independent of spin-axis of the disk: 50% aligned, 50% anti-aligned: ⇒ Vulcans present around half the low-mass stars, absent in other half 3. Midplane in the inner disk is usually dominated by Ohmic resistivity, so Hall effect wouldn’t apply. BUT Hall dominates when the dust fraction becomes very small, so IS very important within dust sublimation radius. Conclusions 1. ~50% of all low mass stars: both solar-types and M dwarfs, have multiple Earth / super-Earth size planets at P < ~50-100d (Vulcans) 2. Inward migration of pebbles due to radial drift (gas-drag), followed by in-situ planet formation in an MRI-drive pressure trap at the DZIB, appears an excellent way to form the Vulcans. 3. Conversely, MRI-quenching by disk Hall effect due to stellar fields can explain why these planets are NOT formed in ~50% of low-mass stellar systems (e.g., in Solar System). 4. Detailed MRI calculations, coupled to hydrodynamic simulations, necessary to contruct a quantitative and testable model; underway.. 5. Comparisions to detailed data (Kepler, followed by TESS, CHEOPS) required to validate the model; will carry out… HST Spitzer Kepler Keck VLT PRESENT NEAR-FUTURE (5-10 yrs) JWST PLATO TESS GMT TMT ELT The End.