Magnetic reconnection in stars: fast and slow

D. J. Mullan

University of Delaware, Newark DE USA

Flares in stars

•Flare: a transient increase in brightness•In the Sun, flares occur in magnetic regions.•Flare stars are known to have strong surface fields.•Flares derive their energy from magnetic fields,•Magnetic energy accumulates slowly, is released rapidly•How to release magnetic energy? Magnetic reconnection (M.R.)•Stars: is there a progression in the properties of M.R. along the main sequence?

Berger et al (2010): LHα /Lbol vs. Spec. type

•

• Notation fl. qus. up.lt Fl.; Qu.;U.L.

Berger et al (2010): LX /Lbol vs. Spec. type

Berger et al (2010): L(radio) vs L(X-ray)

Why is LX proportional to Lrad in F-(early)M stars?

• Guedel and Benz (1993): “common origin scenario”

• X-ray emission and radio emission rely on the same (or closely related) populations of electrons

• Electrons are relativistic (at least mildly so)

• First they interact with B synch radio

• Then thermalize in ambient gas X-rays

Towards later spectral types: ≥M7-8

• Hα emission diminishes rel. to Lbol : reduced deposition of mechanical energy in the chromosphere

• X-ray emission diminishes rel. to Lbol : reduced deposition of mechanical energy in the corona

• But L(rad) increases rel. to Lbol : an electron population survives which emits radio but not X-rays

Magnetic reconnection

• Berger et al: a decrease occurs in the efficiency of chromospheric and coronal heating at M6-M8

• An increase occurs in the efficiency of radio emission also at M6-M8

• What could cause main sequence stars to undergo systematic changes in chr/cor/radio as the spectral type increases?

Magnetic Reconnection (1): resistivity is dominant

Transverse thickness δ of plasma sheet where reconnection occurs

δ = δSP = √(ηc2 Δ /4πVA)

η=electrical resistivity; outflow VA=Alfven sp.

δSP = fn(T, Ne, L, B)

(SP = Sweet and Parker,1958)

Ohm’s law

• E + v x B / c = ηJ + J x B /(nec)• Convection resistance Hall effect• Two regimes:• If Convection=resistance Sweet-Parker

reconnection (resistivity dominates)• If Convection = Hall effect Hall reconnection

dominates: two fluids are involved, with particles M1 /M2 >> 1

•

Reconnection: two regimes

• (1) Sweet-Parker reconnection: dominant wave mode = Alfven in the ions: speed of the wave VA is the same at all length scales

• Measured VA in solar active regions: CoMStOC (1988-1994) no larger than a few tens of Mm/sec

• Elec. energy at v=30 Mm/sec is ≈ 3 keV

Reconnection: regime (2)

• (2) Hall reconnection: dominant wave mode = Whistlers:

• Wave speed increases at shorter length scales

• This difference makes Hall reconnection faster than S-P: models yield factor of 106 enhancement in reconnection rate

• Electrons escape at Vae Ee > 300 keV

Reconnection: 2 length-scales

• S-P reconnection occurs on diffusive length scale δSP = √(ηc2 Δ /4πVA)

• Hall reconnection occurs on ion inertial length scale : di = c/ωpi (ωpi =

plasma frequency in the ions)

Electrons are magnetized, ions are not

The Hall hypothesis for flares

• Transition from slow to fast reconnection is predicted to occur when a reconnection site evolves to a condition where δSP = di

• Onset of a flare occurs when this conditions is first satisfied in an A.R.

• Theoretical basis of the Hall hypothesis: computer modeling

• Observational basis?

Conditions in stellar flares

• Data base: EUVE• Observe stars at

energies from 25 eV to 200 eV

• Good for observing flares: non-flaring stars (kT= few eV) emit little

• Flares: kT = 1 keV

Flare light curve analysis

• Observe: (i) τd (decay time-scale)

• (ii) EM (Emiss. meas. at peak of flare)

• Assume: radiative cooling time is comparable to conductive cooling time

• Derive N, T, L (loop length)

• Calculate B from B2 = 16πN kT• (Mullan et al. 2006)

• 140 flares: N, L, B, T: wide ranges (103,103, 60, 15)

Stellar flare data: two length scales

• 140 stellar flares• Single instrument

• Knowing T, Ne, B, L

• Evaluate δSP, di

• Plot!

• Flare conditions are consistent with

δSP = di

i.e. when the Hall effect sets in

Flares in stars

• Hall effect onset brings significant ordering to the properties of stellar flares

• Flare build-up: Sweet-Parker slow reconnection

• Flare onset: when the SP diffusion region becomes as thin as the ion inertial length, Hall reconnection sets in

• Reconnection becomes rapid: FLARE

The Hall effect triggers a flare

• Reconnection occurs in two phases:

• (1) Sweet-Parker (slow): δSP > di

• (2) Hall effect (106 times faster): δSP < di

• Some active regions never flare: why not?

• Conditions never lead to δSP as small as di

• But slow reconnection leads to some enhanced coronal heating. T(A.R.) > T(diff. cor. =1.7-1.8 MK)

Further testing stars for fast (Hall) reconnection

• Two length scales: δSP and di

• Both depend on local parameters:

N, T, L, B:

Evaluate δSP and di in parameter space

Limit T: (i) “hot” (corona) (ii) “cool atmos.”

Resistivity: (i) Spitzer (ii) Kopecky (1958)

Hall reconnection onset: in parameter space: hot corona

Stars with hot coronae

• 150 representative pts in parameter space

• 90% of pts in “phase space” lie below the line δSP = di

• Reconnection in 90% of “coronal stars” is fast Ee > 300 keV (“common origin hypothesis”)

• Flares in stars with spectral types G, K, and early M have L(rad) and LX

Hall reconnection onset in parameter space: cool atmos.

Stars with cool atmospheres

• 90% of points in “parameter space” lie above the line δSP = di

• Reconnection in 90% of “stars” is slow

• Flares are rare in stars later than M6-M7

• No (nearly-)relativistic electrons to emit synch radio or heat ambient gas to X-ray emitting temps. But….

Radio emission: electron cyclotron maser (ECM)

• Melrose and Dulk (1982): maser is driven by a loss-cone distribution

• Condition: ωpe << Ωe

• Electron beam with speed v/c=0.1, density 107 cm-3 has ECM growth rate = 108 sec-1 : saturates in 100re (< 1 km)

• v/c = 0.1 v = 30 Mm/sec (E = 3 keV: non-relativistic!)

ECM growth rates

• Treumann (2006): shell distribution: even faster growth rates for ECM emission

• Tang & Wu (2009): for E= 10’s of keV, ECM growth rates = 109 sec-1

• TW: for E<3 keV, ECM growth rate decreases rapidly

ECM Radio emission in stellar atmospheres

• Electrons moving at speeds V of ≥30 Mm/sec are capable of significant ECM emission

• At a slow reconnection site (S-P): charged particles emerge at speed VA

• Where, in the n,B,L plane, does VA have values ≥30 Mm/sec ?

Hall reconnection onset: in the n,B,L plane: cool atmos.

Slow reconnection: an effective source of ECM

• Even if reconnection is slow in >M7 stars (i.e. no bona fide flares), in 70% of stars electrons can be ejected at speeds of ≥30 Mm/sec

• Effective source of ECM radio emission

• Coolest dwarfs are only rarely (10%) sites of flares (i.e. fast reconnection) but can be effective (70%) sites of coherent radio emission (ECM)