A new mechanism for heating the solar corona Gaetano Zimbardo Universita’ della Calabria Rende, Italy SAIt, Pisa, 6 maggio 2009

More than mass proportional heavy ion heating observed in solar corona Soho/UVCS observations have shown that heavy ions in polar corona are heated more than protons: Heavy ion heating is more than mass proportional; Perpendicular temperature much larger than parallel temperature (Kohl et al., 1997, 1998) Mg(+9) heating faster than minutes (Esser et al., 1999)

What are the possible heating mechanisms? Ion cyclotron heating is a possibility, but some details are not yet fully understood. Shock waves are common in the corona (e.g., Aschwanden, 2005) Shibata suggests that shocks are formed in connection with reconnection jets (Shibata, 1992; Yokoyama and Shibata, 1996)

Fast shocks considered by Lee and Wu, ApJ (2000), Ryutova and Tarbell, PRL (2003), Ballai et al., ApJ (2005); shocks in chromosphere considered by Vecchio et al., A&A (2009) We assume that small scale shocks and plasma jets are formed at the reconnection region. Larger scale shocks are associated with flares and CMEs.

We consider a quasi-perpendicular supercritical (M A > 2.7) collisionless shock These shocks are characterized by ion reflection (e.g., Phillips and Robson, 1972; Scudder et al., 1986): From Krasnoselskikh et al., 2002

Ion reflection and the shock foot is observed both in laboratory, in space, and at the solar wind termination shock: Burlaga et al., Nature, 2008Phillips and Robson, PRL, 1972

Nonadiabatic heating of reflected ions: We adopt the Normal Incidence Frame (NIF); V 1 = (V x, 0, 0) V x = - V sh B 1 = (B x, 0, B z ) B z >> B x (  Bn almost 90° ) W k = q i E y  y E y = V x B z /c  y = 2  i ramp x y Reflected ion B1B1 B2B2 VxVx EyEy

Energy gain for reflected ions in a single shock encounter Energy gain mass proportional! Let us define the efficiency,  for protons: For a shock with M S = 5, we obtain a factor 100 increase in energy. Heating essentially perpendicular!

ramp x y B1B1 B2B2 VxVx EyEy B3B3 H+H+ foot O +5 For heavy ions …

A more detailed calculation, taking into account the fact that the true orbit is a trochoid, and that for protons motion is mostly in the foot magnetic field B foot, yields For typical values of b = where Heating more than mass proportional!

Comparison with observations: For b = 0.5 – 1 we obtain for O 5 + : In agreement with SOHO/UVCS observations, which yield (Esser et al., ApJ, 1999) Assuming b = o.5 for He 2+ we obtain: Kasper et al., PRL 2008

Reflected protons can excite ion cyclotron waves AMPTE-IRM data from the Earth’s bow shock (Czaykowska et al., Ann. Geo., 2001)

Open Question 1: Are there enough supercritical collisionless shocks in the transition region / corona ? STEREO, SOHO and future missions can give invaluable information: Look for fast collisionless shocks with M A > 3 These can be associated with coronal hole jets, magnetic reconnection, type II radio bursts, etc. Need to determine the physical parameters upstream and downstream of the shock: Shock speed, magnetic field, plasma density.

Open Question 2: Heavy ion reflection Ions reflected if kinetic energy less than potential barrier ?? The potential  is strongly spiky and fluctuating … Waves and/or turbulence can perturb the incoming ion orbit … Magnetic deflection also important … Quasi-perpendicular shocks also exhibit cyclic reformation … Experimental evidence of He 2+ reflection off Earth’s bow shock (Scholer et al., JGR, 1981).

Cross shock electric field measured by Polar at Earth’s bow shock (Bale and Mozer, PRL, 2007).  = Volts

Conclusions Coronal heavy ion heating by Q perp shock waves has many attractive features: i) more than mass proportional ii) essentially perpendicular to the magnetic field iii) very fast (a single shock encounter is considered) iv) temperature anisotropy can feed cyclotron emission, which later heats solar wind plasma Points which need to be further investigated: 1. Heavy ion reflection needs strong fluctuations in potential barrier and magnetic overshoot, to be studied by numerical simulation; 2. STEREO and SOHO unique observing capabilities will help to understand whether enough collisionless shocks are present in the solar corona.

Alpha particle reflection observed by Scholer et al., JGR, 1981 Scholer et al. argue that “if the potential is highly turbulent in space and time […] protons as well as alpha particles could be reflected”

Experimental evidence of cyclic reformation from Cluster data (Lobzin, Krasnoselskikh et al., GRL 2007) Numerical simulations also show that ion reflection rate varies from 0 – 100 % (Quest, 1986)

Fuselier et al. JGR (1995) report observations of suprathermal He 2+ in the foreshock, which has a nongyrotropic distribution consistent with specular reflection Louarn et al., Ann. Geophys. (2003) show that 30 keV protons can be explained by Fermi acceleration due to multiple reflections at quasi-perpendicular shock

Problem of heavy ion reflection: Specular ion reflection is due to an electrostatic potential barrier  : Ions reflected if kinetic energy less than potential barrier: i.e., which is never found; however …