Coronal Heating and Energetics

Coronal heating and X-ray corona energetics

• Global structure of the solar corona • Coronal heating, what does it mean? • Dissipation processes in the corona • Observations of MHD waves in loops • Dynamics of the magnetic network

• Flares and coronal heating Yohkoh SXT 3-5 Million K

Coronal heating, what does it mean?

Mechanical and magnetic energy:

• Magnetoconvection, • Generation/release restructuring of fields an magnetic reconnection • Transport/propagation • Magnetohydrodynamic + plasma waves, shocks • Ohmic + microturbulen • Conversion/dissipation heating, radiative cooling Active corona in three EUV colours resonance absorption

Corona in late May 2002 Energetics of the solar corona 20000001.3 MK K 1300000 K Parameter Coronal Active (erg cm-2s-1) hole region (open) (closed) Chromospheric 4 106 2 107 radiation loss

Radiation 104 < 106 Conduction 5 104 105 – 106 Solar wind (5-10) 105 ( < 105 )

5 -2 -1 SOHO EIT Fe Fe IX,X IX,X 17.1 17,1 nm nm Photosphere: 6.3 1010 erg cm-2 s-1 10 erg cm s Fe IX,X 17.1 nm = 100 W m-2

1 Multiply ionized atoms North coronal hole in various lines indicate temperature gradient 1400000 K FeXII 1242 Å

1100000 K MgX 624.9 Å

230000 K OV 629.7 Å

180000 K NV 1238.8 Å

10000 K cont. 1240 Å Peter, 2002 Forsyth & Marsch, Space Sci. Rev., 89, 7, 1999 SUMER/SOHO 10 August 1996

How is the solar corona heated? Collisional heating rates

10 -3 Chromosphere: N = 10 cm hG = 400 km Perturbation scales: ∆L = 200 km, ∆B = 1 G, ∆V = 1 km/s, ∆T = 1000 K

2 -8 Viscosity: HV = η (∆V/∆L) = 2 10 2 -7 Conduction: HC = κ ∆T/(∆L) = 3 10 2 2 2 -7 Joule: HJ = j /σ = (c/4π) (∆B/∆L) /σ = 7 10

2 -1 -3 -1 Radiative cooling: CR = N Λ(T) = 10 erg cm s

Walsh, 2002 Smaller scale, ∆L ≈ 200 m, required λColl ≈ 1 km

Electrons and Coulomb Perpendicular filamentary structure collisions in fine loops and coronal emission Parameter Chromo Corona Solar Solar wind, -sphere (1.3RS) wind Helios (1AU) 1. Filamentary nature of -3 10 7 ne /cm 10 10 10 loops is consequence of fine solar surface fields.... 3 6 5 Te /K 2 10 1-2 10 10 2. Transient localised λ /km 1 1000 107 heating with threshold..... 3. Non-classical diffusive perpendicular transport by turbulence too slow.... • Non-Maxwellian 4. Field line stochasticity? • Heat flux tail • Relative rarity of loops, high contrast

Pilipp et al., JGR, • Temperature anisotropy Litwin & Rosner, ApJ • Well-defined transverse dimension 92, 1075, 1987 412, 375, 1993

2 Requirements on coronal transport Coronal heating - an unsolved problem Coronal plasma beta is low, β ≈ 0.1 - 001, --> strongly magnetized particles, which move „freely“ parallel to B. Why?

Coulomb collisional transport, then diffusion coefficient: Incomplete and insufficient diagnostics: D = ( )2 1 m2s-1 c ρe νe ≈ • Only remote-sensing through photons (X-rays,

with electron Larmor radius, ρe ≈ 25 cm, and collision extreme ultraviolet (EUV), visible, infrared) and -1 8 -3 frequency, νe ≈ 10 s ; ρp ≈ 10 m, B ≈ 1 G, ne ≈ 10 cm . electromagnetic waves (radio, plasma), and corpuscular radiation (solar wind, energetic Enhanced transport only by „anomalous“ processes: Waves, particles) turbulence, drifts, flows, stochastic fields, hyperresistivity..... • No coronal in-situ measurements, such as possible in other solar system plasmas (Earth‘s Loop switch-on time: τ ≈ 1-10 s. Is the current channel magnetosphere, solar wind,...... ) Litwin & Rosner, scale comparable to transverse loop dimension, ApJ 412, 375, 2 12 1993 a ≈ 1000 km? Cross diffusion time: tD = a /D ≈ 10 s.

Corona and magnetic network Magnetic network loops and funnels 80000 K 1996

Structure of transition region Magnetic field of coronal funnel

FB = AB FM = AρV A(z) = flux tube cross section

Dowdy et al., Solar Phys., Hackenberg, Marsch and Mann, SOHO EIT He II 30.4 nm 105, 35, 1986 Space Sci. Rev., 87, 207, 1999

Dynamic network and magnetic EUV jets and reconnection in furnace by reconnection the magnetic network

Evolution of a jet in Si IV 1393 Å visible as blue and Static red shifts in SUMER spectra field Waves out Gabriel • E-W step size 1" , ∆t = 5 s (1976) Loops Picoflare? down

Jet head moves New flux fed in at sides by 1" in 60 s convection (t ~ 20 minutes)

Axford and McKenzie, 1992, and 7 -2 -1 FE = 10 erg cm s Space Science Reviews, 87, 25, 1999 Innes at el., Nature, 386, 811, 1997

3 Solar oscillations 1/day Loops, loops and more TRACE velocity spectrum loops

5-minutes P-modes oscillations, 0.0033 Hz

10-6 10-2 Cortes, 1998

Characteristic time scales for Oscillations of magnetic flux tube the evolution of loops

• Dynamic time scale for restoration of pressure equilibrium:

t = L/c = 1.1 L /T 1/2 [minutes] 2 2 -1/2 1/2 dyn s 9 6 CT = CSVA(CS +VA ) VA = B/(4πρ) • Conductive time scale for exchange of thermal energy:

2 7/2 2 5/2 2 B tcon = 3nkBT l /(2κcT ) = 30 n10l9 /T6 ≈ 7(l9/L9) tdyn • Radiative time scale for cooling by radiation losses: ρ 5/3 1/6 trad = 3nekBT/(nenHΛ(T) ≈ 5 T6 /n10 = 35 T6 tdyn compressible incompressible

Legend: L, loop length; l, gradient scale length; cs, sound speed; T, 9 Magnetic Magnetic loop temperature; Λ(T), radiative loss function; L9 = 10 cm = 10 000 km; 6 10 -3 and curvature T6 = 10 K; n10 = 10 cm ; κc = thermal conductivity. thermal force Schrijver et al., Solar Phys. 187, 261, 1999 pressure (tension)

MHD wave heating Wave spectrum generation by turbulent shaking of flux tubes

Process Period/s Here α is the Alfvèn/fast < 5 mixing length, λ= α H, with magnetosonic barometric Sound/slow < 200 scale height H. magnetosonic Photosphere: Coronal magnetic field rooted H=300 km. down in turbulent photosphere Gravity 40 => Waves! Conduction 600 Thin flux tube oscillations -> • Generation of MHD waves Radiation 3000 torsional driven by magneto-convection Convection > 300 Alfvén waves • Phase mixing due to gradients • Absorption at small scales Musielak & Ulmschneider, A&A, 386, 606, 2002

4 Coronal mass ejections Active flare loops Coronal mass ejections

- longitudinal spreads? - origin and directions? - global distribution? The stormy Sun

Prominence Light bulb Schwenn et al., 1998, 2000 LASCO on SOHO, helical CME

Coronal heating: a buzzword Coronal heating - an unsolved problem

Coronal heating? Why?

closed magnetic Small brightenings loops are at a range of Facing complexity and variability: observed at a wavelenths wide range of temperatures • Solar corona is non-uniform and highly structured polar plumes are observed at “coronal” • Corona varies in time (magnetic activity cycle) “diffuse” temperatures in open corona magnetic structure, • Temporal and spatial changes occur on all scales radiating at 2 the coronal holes MK is not confined to special energy requirements • Corona is far from thermal (collisional) equilibrium “bright” loops in cool (104 K) prominence • Coronal processes are dynamic and often nonlinear Time and space dependence!

The elusive coronal magnetic field MHD model of coronal magnetic field

Future: High-resolution imaging and closed spectroscopy (35 km pixels) of the corona

open Modelling by extrapolation: • Loops (magnetic carpet) • Open coronal funnels Linker et al., JGR, 104, 9809, 1999 „Elephants trunk“ coronal hole • Closed network

5 Coronal cooling, what does it mean? Fast solar wind parameters

Heating and cooling • Energy flux at 1 R : F = 5 105 erg cm-2 s-1 varies spatially and S E -1 • Speed beyond 10 RS: Vp = (700 - 800) km s temporally! 8 -2 -1 • Proton flux at 1 AU: np Vp = 2 10 cm s • Dense plasma • Density at 1 AU: n = 3 cm-3 ; n /n = 0.04 • Radiative cooling: quiet in magnetic + p α p emissions, flares, blinkers, gravitational • Temperatures at 1 AU: 5 6 5 brightenings, in UV, EUV, confinement Tp = 3 10 K ; Tα = 10 K ; Te = 1.5 10 K and X-rays • Heavy ions: T m / m T ; V - V = V • Dilute plasma i ≅ i p p i p A • Cooling through particles: escaping on solar wind, energetic ions Schwenn and Marsch, 1990, 1991 and electrons open field lines

Corona of the active sun Thermodynamics of the corona

1998 Entropy balance (advective change equals other entropy productions): ∂s/∂t + V•∇s =

Energy fluxes (in steady state the total flux is free of divergence):

∇ • (FK + FG + FR + FJ + FV + FC + FM ) = 0

Kinetic + gravitational + radiative + ohmic + viscous + conductive + mechanical EIT - LASCO C1/C2

Electron temperature in the corona Temperature profiles in the corona and fast solar wind SP Streamer SO belt, closed

( Si 7+) Ti ~ mi/mp Tp Coronal hole, ( He open 2+) magnetically Corona

Solar wind David et al., A&A, Heliocentric distance SUMER/CDS SOHO 336, L90, 1998 Cranmer et al., Ap.J., 2000; Marsch, 1991

6 Pitch-angle diffusion of solar wind protons Energy balance in the corona

VDF contours are Coronal loops: segments of circles Energy balance mainly between radiative cooling and centered in the mechanical heating

wave frame (< VA ) V •∇s = ds/dt|R + ds/dt|M + ds/dt|C

Helios Velocity-space resonant Coronal holes: diffusion caused by the Energy balance mainly between solar-wind losses and cyclotron-wave field! mechanical heating

∇ • (FK + FG + FM ) = 0

Marsch and Tu, JGR, 2 2 106, 8357, 2001 FM = ρVsw (V sw + V ∞)/2 V∞ = 618 km/s

Magnetic loops on the Sun Empirical scaling laws for loops

TRACE L(T) ~ T HXR n(T) ~ T2 SXR EUV p(T) ~ T3 E(T) ~ T6

• Thin strands, intrinsically dymnamic and continously evolving, • Intermittent heating (in minutes), primarily within 10-20 Mm, • Meandering of hot strings through coronal volume, • Pulsed injection of cool material from chromosphere below, Scale height for loop footpoints: h (T) ~ T-1/2 • Variable brightenings, by braiding-induced current dissipation? eq Aschwanden, Solar 24 Phys. 190, 233, 1999 Lower cutoff: Lmin = 5 Mm, Emin = 20 erg

Coronal heating mechanisms I Coronal heating mechanisms II

Wave (AC) mechanisms (generation, propagation, non-uniformity) Resonant absoption of magnetoacoustic • Sound waves, shocks (barometric stratification), turbulence surface waves on a field gradient Phase mixing leads to current sheets and small • Magnetoacoustic (body, surface), Alfvén (resonance absorption) scale gradients -> • Plasma (dispersive) waves (Landau damping), ion-cyclotron waves dissipation

Current sheet (DC) mechanism (formation of sheets, flux emergence) • Quasistatic current sheet formation in force-free fields

• Dynamic formation driven by flux emergence Generation of small scales • Field-aligned currents (ohmic and anomalous resistivity) by wave front tilting

Heating by micro/nano/pico flares (magnetic field reconnection) • Thermalization of energetic particles (Bremsstrahlung: radio to X-rays)

• Reconnection driven by colliding magnetic flux Ulmschneider, 1998

7 Coronal heating mechanisms III Coronal heating mechanisms IV

Heating by kinetic plasma waves Pressure equilibrium: Anisotropic 2 pe = pi + Bi /8π Absorption of high-frequency waves protons in solar wind Wave generation and transport? 2 Gas pressure: pe ≈ 1 dyn/cm Equipartition field: B ≈ 1 kG i Damping rate: γ/ω ∼ ∂f/∂v electrons with suprathermal • Generation by turbulence tails • Landau damping: ω - k • v = 0 • Wave mode couplings • Cyclotron damping: ω - k • v ± Ω = 0

Advantage: Processes occur at small scales, Turbulent heating near the ion inertial length or gyroperiod,

Shearing motion Decay into smaller = VA/Ω , τ = 2π/Ω vortices or flux tubes Problem: Velocity distribution are unknown; in-situ evidence for non-thermal features -> Heyvaerts & Priest, 1983

Measuring thermal structure of loops Conclusions on thermal structure

• Thermal loop structure is a possible heating diagnostic. • But one must be careful on the interpretation of hydrostatic and LTE models.

Possible observational “solutions” • Follow T(s) evolving in time, not just snapshots • Yohkoh/SXT observations • Spectrometer and imager working together (more in the future) • Spatially uniform heating • Keep spectrometer slit at one position -> temporal variations only • Velocity and density tracking as indicators of dynamics needed Priest12-Nov-02 et al., 2000 45

Ubiquitous magnetic reconnection Solar flare in the corona

Parker’s (1988) nanoflare concept

Power-law of flare frequency f against energy E Flare f(E) = f E-α 0 Active loops Spectral index, α < -2, for nanoflare dominated heating Self-organised criticality :

• Corona is modeled as an externally driven, dissipative dynamical system SOHO • Larger catastrophes are triggered by a chain reaction EIT of many smaller events

8 Flare energy Exponent α Number Plethora of Brightenings

) spectra 2.02-2.42 4497 (P) Active region transient brightenings (SXT), Explosive events -1 (SUMER), 2.53-2.50 11150 (K) erg (power laws) -2 EUV brightenings (EIT, TRACE), Blinkers (CDS)…. 1.79 (0.08) 281 (A) cm -1 1.74 291 (S) s

-50 1.54 2878 (C)

Sun‘s luminosity 3.38 1033 erg/s Explosive events (Innes et al., 1997) Blinkers (Harrison, 1997)

5 5

Flare frequency (10 • 2 x 10 K • 2 x 10 K f = E-α • 60 s • 1000 s

-1 -1 Aschwanden • 160 kms • 20 kms et al., 2000 Flare energy E (erg) • 2 arcsec (1500 km) • 10 arcsec (7500 km)

Impulsively driven oscillations Detection of longitudinal waves

Intensity (density) variation: TRACE Slow magnetoacoustic waves • Period/s 136-649 TRACE • Decay time/s Loop images 200-1200 in Fe 171 Å at 15 s cadence • Amplitude/km 100-9000

Schrijver et al. (2002) and Aschwanden et al. (2002) provide extensive overview and analysis of 17 cases of De Moortel flare-excited transversal oscillations of coronal loops. et al., 2000

Loop oscillation properties Loop oscillations in the solar corona

Parameter Range Fe XIX 1118 Å Fe XIX radiance Footpoint length 10.2 - 49.4 Mm Doppler shift Footpoint width 3.9 - 14.1 Mm Transit period 1.3 - 6.3 s Propagation speed 65 - 205 km s-1 Relative amplitude 0.7 - 14.6 % Damping length 2.9 - 18.9 Mm Energy flux 195 - 705 mW m-2

Distance along slit (110000Distance along slit km) 50 arcsec Oscillations: Statistical overview of the ranges of the physical above limb 2000/09/29 properties of 38 longitudinal oscillations detected blue <--> red De Moortel, Ireland at the base of large coronal loops (1 RS = 700 Mm). and Walsh, 2002 Wang et al., 2002 Time (240 minutes) Time ->

9 Coronal heating: Summary

• Corona, a restless, complex non- uniform plasma environment dominated by magnetic field

• Evidence for quasi-periodic oscillations through the solar atmosphere and in loops

• Small-scale brightenings in a range of wavelengths and with power-law distribution in energy

Heating mechanisms remain unknown!