Are magnetically-powered phenomena on brown dwarfs similar to or very different from M dwarfs? Jeffrey L. Linsky JILA/University of Colorado and NIST The EVLA Vision: Stars on and off the Main Sequence Socorro NM May 2009

Outline for this “tale of thermonuclear failure and its many consequences” Low mass “objects” do not have stable thermonuclear reactions to heat their cores and halt the gravitational contraction → rapid rotation and degenerate convective cores → secular cooling of the atmosphere. Cool atmospheres have very low ionization → decoupling of turbulent flows and magnetic fields until very deep in the atmosphere → photospheric magnetic fields with very little free energy. Very small Rossby numbers predict saturated activity if brown dwarfs are like M dwarfs, but L X is weak. Why? Weak coronal heating (due to small convective speeds and near potential magnetic fields) → low density coronae → gyrosynchrotron radio emission (L R ~n rel B 2 E 2 ) but weak X-ray emission (L x ~n e 2 f(T)).

Spectra (not mass) determine star types (Burgasser in Physics Today June 2008)

Evolutionary tracks (age and mass) (Burrows et al. ApJ 491,856 (1997))

Theoretical BD models from Burrows et al. (Rev. Mod. Phys. 73, 719 (2001)). With time: T c and ρ c increase. Blue: H burning stars ( M sun ). Green: BDs that burned D and now have electron degenerate cores and cool. Red: BDs that did not burn D ( M J ). Dots mark ages when 50% of D and Li burned in core. Cores are convective metallic H/He mixtures

The interior structure of a star changes with decreasing mass Central temperatures (Tc) decrease with lower mass Central densities (ρ c ) increase then decrease Cores degenerate when (ψ=kT/kT F <0.1) Core fully convective for M<0.35M sun (M3 V) Uncertainties: EOS, convection in molecular atmosphere, opacities. Jupiter: M=0.001M sun ChabrierChabrier Solid lines (t=5Gyr), dashed lines (t=10 8 yr) (Chabrier & Baraffe ARAA 38, 337 (2000)

From M dwarfs to brown dwarfs: T C as function of mass and age Dashed lines indicate temperatures for burning H, Li, & D. Minimum mass for burning H is 0.075M sun (about M8 but depends on age) Chabrier & Baraffe (2000)

Brown dwarf photosphere models There are nonLTE radiative/convective equilibrium models for M, L, T dwarfs and gas giant planets by Allard, Hauschildt, Tsuji, etc. Major issues include: completeness of molecular opacities, convection (ML or 3D hydro), dust formation and opacity, initial conditions for young (t<few Myr) BDs. Photospheres are neutral and the depth where ionization becomes important increases to later spectral type. With decreasing T eff, the magnetic field and convective motions are uncoupled deeper into the star. This will be important for MHD coronal heating and structure. Very different from the Sun and M dwarfs. H 2 dissociation produces small (dT/dh) ad and low v conv

Saturation at small Rossby numbers (Reiners et al. ApJ 692, 538 (2009)) Rossby number = R 0 =P rot /τ conv For M dwarfs and hotter stars, saturation of Bf, L x /L bol, and L Hα /L bol at R 0 <0.1 For R 0 >0.1, activity indicators depend on rotation (and age). All seven M3.5-M6 rapid rotators (vsini>5) are in saturation regime. Saturation behavior for both fully convective stars and stars with radiative cores.

All L dwarfs are rapid rotators and in the saturation regime (Reiners & Basri ApJ 684, 1390 (2008))

Rotational evolution of M and BDs: observations and theory (Reiners & Basri (2008)) Blue = young stars; red = old stars Solid lines: rotation models for stars of mass 0.06 – 0.10 Msun Dashed lines: isochrones for 2, 5, 10 Myr (upper left to lower right) Theory: gravitation contraction and a magnetic-wind breaking law depending on mass and T eff (lower convective speed → decreased coronal heating and lower mass loss and angular momentum loss).

Change in properties from M stars to BDs (Berger et al. ApJ 676, 1307 (2008)) ParameterEarly MVB 10LSR1835 Sp. TypeM0-M6M8M8.5 Log(L x /L bol )Up to to -5<-5.7 Flares?yes ? Log(L Hα /L bol )Up to to -5 UV(2600Å)/photoLarge10xphot~photo Log(νL R /L X ) >-11.3 vsin i (km/s)3-56.5~50 Mass/Sun ?0.06? H burning core?YesYes?No?

Late M-BD stars are in saturation regime (log R 0 <0.1) but L X /L bol below hotter stars

Violation of the radio vs. X-ray luminosity law of Guedel & Benz (2003) (cf. Berger et al. 2008)

Failure of acoustic heating

BD atmospheres have very low ionization and high resistivity Fractional ionization very small except deep in the atmosphere High diffusion rate means that the magnetic field has lowest energy (potential) and no twist.

Magnetic Reynolds number and coupling of B to convective motions R m =vL v /η d ~B T /B 0 (advection/diffusion) For T eff <1700 K, photospheric motions completely decoupled from B except deep in photosphere. Untwisted fields have no free energy and cannot heat a chromosphere or corona by reconnection. With decreasing T eff, dynamos can operate deeper in the star.

A modest proposal for explaining the violation of the radio vs. X-ray luminosity law BDs have cool neutral atmospheres → magnetic fields have little free energy in the photosphere → low heating rate for the corona. Coronae are cooler with small pressure scale heights and low densities. Coronal magnetic field reconnections likely occur where density very low. (Extremely low β.) L X ~n e 2 f(T). More sensitive to density than T. L R ~n rel B 2 (ε/m 0 c 2 ) 2 (if gyrosynchrotron emission). Electron energy distribution (power law) is critical. What mechanisms could stress coronal magnetic fields? (1) stellar differential rotation, (2) interactions with magnetic fields or winds of a “roaster”, (3) emergence of new fields from below, etc.

Possible scenarios for heating BD chromospheres (H α, UV) and coronae (X-rays, radio, flares) Important papers: Mohanty et al. (ApJ 571, 469 (2002)); Meyer & Meyer-Hofmeister (A&A 341, L23 (1999)). Acoustic wave fluxes (F ac ~v 8 conv ) fail to explain Hα emission of L dwarfs by 3-5 orders of magnitude. Energy not from photospheric turbulent flows twisting the magnetic fields because little coupling to magnetic fields. Differential rotation could be the energy source for winding the field lines in the corona and eventual dissipation.

How are flares possible in BDs? Intermittent events are possible. Mohanty et al. (2002) suggest that some emerging twisted flux ropes may be thick enough to emerge through the photosphere without being diffused. Consider a bootstrap scenario in which emerging twisted flux ropes heat and ionize the surrounding atmosphere and reduce the neutrality. (Perhaps by current dissipation.) Flares on BDs may have different properties from M dwarfs because the surrounding gas is low density (e.g., strong nonthermal radio emission with little thermal X-ray emission).

L Hα /L bol as a function of vsini and spectral type (Reiners & Basri (2008)) Filled circles: near M9; open circles: M9-L1; filled squares: L1.5-L3; open squares: L3.5 and later. Late M dwarfs saturated or rotation-activity (at low vsini). BDs far below M dwarfs at all vsini due to lower heating rates. No rotation-activity as previously found by Mohanty & Basri (2003).

Evolution of stellar effective temperatures as function of mass For M<0.075M sun,T eff decreases with age. An ambriguity: at a given T eff, there are young low mass stars and old higher mass stars. As T eff decreases the atmospheres become far less ionized and poor electrical conductors. Chabrier & Baraffe (2000)