PPARC/Mallorca September 2006 1 Solar Flares Lyndsay Fletcher University of Glasgow Introduction...

PPARC/Mallorca September 2006 1

Solar Flares

Lyndsay FletcherUniversity of Glasgow

Introduction

Part 1: Observationsenergy build-upimpulsive phase atmospheric response

Part 2: Theorynature of reconnectionparticle acceleration


RHESSI and TRACE flare observations

Bremsstrahlung emission: 12-25keV – Red

25-50keV – Blue

Thermal emission at ~ 1.5MK and ~25MK, green


Flare Questions

• What is the source of the flare energy?

• How is energy stored and how/why is it released?

• How is energy converted into heat, particles, radiation, bulk kinetic energy?

• How does the solar atmosphere respond?


Introduction




Source of Flare Energy

Energy is imparted to the coronal magnetic field at or below photosphere - photosphere is a high beta plasma so gas pressure forces dominate.

magnetic field evolution from SOHO/MDI


Dt

DvgρBjp

Assume ~ steady state, with negligible gravitational forces and pressure gradients (low beta corona). Then

0Bj

Energy storage in the corona

MHD Force balance equation

MHD version of Ampère’s Law

BαB

0BB

So , meaning

Force-free condition, i. e. field and current are aligned

constant along field lines

Twisting the field produces ‘free energy’ in the form of current.

j = B/


When does energy build-up occur?

Result:

AR twists are too large to be generated by the photospheric flows.

So the field emerges from the convection zone already carrying current.

Does the magnetic field emerge already bearing free energy?

From vector magnetic field measurements, Leka et al. (1996) determined the curl of the magnetic field in an emerging active region

They also measured the photospheric flows during and after emergence.


Location of free energy - observations

Shear is concentrated close to magnetic neutral line


Can flares be predicted?

Folk Knowledge:

A complex, rapidly-evolving, large active region has highest probability of producing a flare, within a few days of its emergence.

More accurate predictions?

Prediction based on past X-ray activity (Bayesian statistics)

Moderately successful (Wheatland 2004)

Statistics of magnetic field parameters and their variations

Rather unsuccessful (Leka and Barnes 2006)

Neural Net ‘learning’ of appearance of ARs about to flare

Underway


Preflare Activity

What are the signs that a flare is going to happen?

Most Reliable - The rise/darkening/expansion of an AR H filament minutes to hours before flare (Svestka 1976, Martin 1980)


The slow filament rise probably indicates the onset of an MHD instability.

polar crown filament

active region filament

Filaments are dense, cool gas suspended in the corona.

movie

movie


Preflare Activity

• Small UV/EUV ‘twinkles’ (Moore & Sterling, Warren & Warshall)• Small GOES events and preheating • “Sigmoid” magnetic configuration (Hudson & Sterling)• Early hard X-ray coronal sources (Lin et al.)• Moving blueshifted H events (Des Jardins & Canfield 2003)

But none of these is unique to flares

Are there any other signs that a flare is going to happen?

Other pre-flare phenomena include:


• Magnetic energy for the flare is stored as field-aligned currents.

• Most of the energy is concentrated close to a neutral line, probably low in the atmosphere (~10,000km).

• The flare is related to the onset of an MHD instability, probably followed by fast magnetic reconnection.

• The conditions leading to a flare cannot easily be identified – flare prediction is still not possible.

Energy storage and flare trigger - overview


Introduction




Flare X-ray Time ProfilesImpulsive phase - energy release• Hard X-rays (10s of keV)• Duration ~ 5 minutes to 1 hour• Bursty time profile (tacc ~ seconds)

Gradual phase - response• thermal emission (~0.1-1 keV)• rise time ~ minutes

GOES flare classification scheme

Flux in the 1-8 Å band

C: more than 10-6 W m-2 at Earth (e.g. C4.2 flare => 4.2x10-6 Wm-2) M: more than 10-5 W m-2 at EarthX: more than 10-4 W m-2 at Earth


Impulsive Phase X-ray Spectrum

Gamma-ray lines

hot thermal emission

Non-thermal electron bremsstrahlung: I() ~ -


X-Rays

X-rays observed by e.g. RHESSI are electron-proton bremsstrahlung from energetic electrons (> 15keV)

• Thermal bremsstrahlung: Eelectron ~ E target and spectrum F()~ e-/kt

- Primarily coronal.

• Non-thermal bremsstrahlung: Eelectron >> E target and spectrum F()~

- Primarily chromospheric ‘thick target’ (electron slows as it radiates)

- Very inefficient: ~ 10-5 of the electron energy radiated as X-rays.


RHESSI X-ray imaging

• 2” imaging at ~ 20-50 keV, ~ 4s resolution (if sufficient counts)

• Spectroscopy with 1 keV energy resolution

20” =15,000km

Orange = 25-50keV

Blue = TRACE white light

RHESSI imaging


X-Ray spectrum

• In impulsive phase, HXR spectrum can be fitted by a hot (20MK) or superhot (~60MK) thermal component plus a power-law F(E)=FoE.

• Parameters of fit are correlated and vary during flare.

• Microflares also show thermal + power-law spectrum.

10 100E (keV)

Typical spectral fit, Holman et al (2003) Variation of fit parameters during a flare, Grigis & Benz (2005)

electron spectral index


HXR spectral inversion

Photon spectrum I() is related to source-averaged electron spectrum EF

If Q is known, the integral can be inverted (i.e. differentiated) to recover source-averaged spectrum (Kontar et al. ’03, ’06)

No photospheric albedo correction

With albedo correction

Collisional thick target interpretation

Beam number ~ 1036-37 e- s-1 above 20keV Combining with observed HXR footpoint areas < 10” x 10” Beam flux > 1018-19 e- cm-2 s-1 above 20keV


Other Impulsive Phase Emission

During the impulsive phase bursts of -rays hard X-rays, UV/EUV, H and

(sometimes) optical emission show where fast particles hit the low atmosphere

Optical/UV/EUV emission from heat deposition /ionisation / collisional / radiative excitation

White light luminosity increase confirms total energy input deduced from HXRs

HXR contours on 195A emission

1600 A broadband emission

White light footpoints


What is significant about footpoint locations?

Metcalf et al. (2003)

Separatrix intersections Time evolution of HXRfootpoint positions

Radiation from non-thermal particles appears at the photospheric intersection of separatrix surfaces (eg Demoulin, Aulanier).

Motion of footpoints across magnetic field can be used to deduce a coronal magnetic reconnection rate.


Separatrices (2-D and 3-D)

(Priest and Schrijver 1999) (Priest and Schrijver 1999)

Separatrices are (curves)/surfaces separating domains of different magnetic connectivity in (2D)/3D

Radiation produced at predicted separatrix locations shows the importance of reconnection processes happening at domain boundaries


Flare Impulsive Phase Energy Spectrum

Gamma-raylines

hot thermal emission

Non-thermal electron bremsstrahlung: I() ~ -


Gamma-rays

• Continuum -rays by bremsstrahlung (~ 10MeV)

• Nuclear de-excitation lines caused by proton bombardment; - ‘prompt’ radiation provides a diagnostic of protons above 30MeV

• The positron annihilation line at 511keV

• The neutron capture line at 2.23 MeV - n(p,)D - this is a delayed line, as neutrons must slow down before reacting.

formed low in the atmosphere, and after other emissions.

Production of nuclear de-excitation lines


Neutrons produced by energetic ions (10s of MeV/nucleon).

The capture line is predicted to form within 500km of neutron production site.

But observed to be systematically offset from HXRs (electrons) by ~ 10,000km (15”).

Location of -ray sources

Similar time profiles for HXRs and de-excitation lines imply related acceleration.

However, radiation produced by ions is in a different location from electron bremsstrahlung

Hurford et al. 2006


Flare Energy Budget

Estimates made by Emslie et al. (2004, 2005) confirm that a significant fraction of total flare energy appears in fast particles

above 20 -40keV


Coronal radio emission

Metric and decimetric Type III bursts are plasma radiation produced by electron beams (mode-conversion of Langmuir waves).

Upward and downward-going beams observed

Occur at peak time of HXR emission. Detailed radio/HXR burst-to-burst time-correlations improve at higher starting frequency (Benz et al ‘05)

Non-linear coherent emission electron number estimates difficult.

Microwave gyro-synchrotron emission from fast electrons in coronal loops is also significant.

Electron numbers can be made to agree with numbers from HXR.

Also info on angular distribution


Coronal Hard X-ray Sources

First observed by SMM/HXIS, then at better resolution by Yohkoh/HXT. Now in many RHESSI flares (inc. occulted)

Flares seen without HXR footpoints – only coronal HXR loops. Emission up to 50keV implies ne ~ 1011cm-3 (Veronig & Brown 2004)

Occulted sources present up to at least 50 keV (Bone et al. 2006)

20-30 keV 30-50 keV 50-100 keV

Coronal energy deposition between 1030 and 1031 erg

In situ electron measurements

Some hard X-ray events are also observed by particle detectors in space (e.g. 14 Apr 2002, Krucker et al, 2003)

10 100

1E-5

1E-4

1E-3

0.01

0.1

1

10 14-April-2002, 22:25 UT

WIND/3DP, =2.6

<F(E)>, RHESSI, =2.5

F0(E), RHESSI, =4.5

Ele

ctro

n F

lux

Energy, keV

In situ electron fluxes do not agree with thick-target fluxes deduced from RHESSI


• During the impulsive phase, most of the flare energy is released.

• Energetic particles receive up to 50% of the total energy (rest goes to CME and heating).

• Most of the impulsive phase energy is focused into a few small sources.

• These sources are closely related to magnetic separatrices.

• Up to 1037 electrons accelerated per second (i.e. all the electrons in (10,000km)3 at 1010 cm-3.

• Similar number of ions accelerated, but in a different place or following a different path.

Impulsive phase – main points


Introduction




Flare leads to brightening coronal loops, producing high fluxes of soft X-ray emission (0.1-1 keV).

loops then cool through EUV temperatures

Atmospheric response – soft X-ray and EUV


Atmospheric response - chromospheric upflows

Energy input in the form of a beam heats the chromosphere rapidly and – if heating is strong enough - it expands upwards.

Blueshifts on outer part of arcadeare evaporation

Redshifts on inner part of arcadeare material cooling and draining.

Chromospheric ‘evaporation’ has beenobserved spectroscopically in H (e.g. Antonucci et al 1984)

Also in UV/EUV using SoHO/CDS post-flare observations (e.g. Czaykowska et al 1999)


Latest numerical simulations disagree with evaporation scenario

Coronal density increases, but temperature does not: increasing ionisation, radiative losses and gas expansion absorb the energy

Allred et al 2006.

T

ne


Introduction




Magnetic reconnection allows the coronal field to reconfigure, liberating magnetic energy

Reconnection is the process whereby two field lines, being frozen inand carried along by the fluid, break and rejoin in a different way.

Reconnection results from the local breakdown of flux conservation.

So a particle that was on fieldline A can end up on fieldline B

A B

Liberation of stored energy


Bη)Bv(t

B 2

Breakdown of Flux Conservation

The induction equation – describes advection and dissipation of field

Define associated timescales :

a = L/v and d = L2/

where L is the typical length scale for variation in the magnetic field.The ratio of d to a is called the Magnetic Reynolds number, RM

η

vL

τ

τR

A

DM

Normally in the corona, dissipation is much slower than advection (low collisional resistivity , large v and L); so the field is frozen.


Magnetic Field Dissipation

d in the corona is about 106 years. How do we speed up dissipation?

d = L2/so must decrease the length scale L, or increase resistivity.

As field is advected by flow, it generates steep gradients - current sheets

V

Field lines are advected in to the current sheet, reconnect, and plasma is advected out at the upstream Alfvén speed - Sweet-Parker reconnection.

Sweet-Parker reconnection is rather inefficient: the rate scales as Rm-1/2

It is too slow (by ~ 5 orders of mag) to explain flare energy release.


Petschek Reconnection

The Petschek model reduces the size of the diffusion region.

Outflow at~ Alfvèn speed

• The reconnection rate is determined by the external conditions• At slow shocks, energy conversion can occur• May be fast enough to explain flare release if a high ‘anomalous resistivity’ is invoked.

Reconnection rate increases as plasma is ‘slingshotted’ out


Most solar reconnection theory is done in the MHD framework.

MHD Ohm’s law jBvE

This only includes a resistivity term due to classical (Ohmic) dissipation.

Non-MHD regimes of reconnection

Generalised Ohm’s law

ei ppBj

n

j1 jBvE ieei

ei mmmmte

nmme

e.g. the Hall term arises since protons and electrons follow different orbits in a magnetic field

• Decoupling of e, p leads to whistler wave generation

• Dissipation occurs by wave-particle interaction


2-D versus 3-D reconnection

Simple models are 2D. The corona is certainly 3D

(Priest and Schrijver 1999)

(Priest and Schrijver 1999)


Introduction




Mechanisms of Particle Acceleration

Accelerating coronal charged particles requires electric fields.

There are three mechanisms most often discussed in the context of acceleration of solar flare particles

•DC field acceleration - E large-scale and organised

•Stochastic resonant acceleration – E small-scale and random

•Diffusive Shock Acceleration – Both large and small-scale fields

The last of these three is generally thought of as a ‘secondary’ accelerator of particles, in the presence of a shock associated with a coronal mass ejection. We shall concentrate on the DC and stochastic models.


Field-aligned DC electric fields

• For example, a local increase in resistivity in a current loop leads to large potential drop (since huge inductance of circuit prevents rapid change in current)

• Electrons accelerated if this DC field is greater than the Dreicer field, Ed

The Dreicer field is the value of the DC field such that the force exerted on the electrons exceeds drag force from e-e Coulomb collisions

• Ed typically 10-4 V/cm

• Electrons with speeds greater than a critical speed =vTe (Ed/E)1/2 are freely accelerated ‘runaway’ electrons

FE FDRAG

electron beam B


DC electric fields in a current sheet

Observations suggest that super-Dreicer fields occur in reconnection regions.

Inferred values of reconnection electric field are ~ 1 V/cm

In a model with symmetry in the plane perpendicular to the loop, this field is• parallel to solar surface and• normal to loops in post-flare arcade

Problem: E B almost everywhere, somostly particles EB drift.

However, near X-line, there may be anunmagnetised region (B(x,y) 0)

- or a component of B parallel to E

So some efficient particle acceleration can occur – how much?total potential drop = 1010 V!

L~109cm

E


Stochastic Resonant Acceleration

Frequency matching condition:

k|| v|| - l = 0

However, as soon as a particle picks up some energy from a monochromaticwave, its gyration frequency changes and resonance is lost.

But particles resonating with a wave spectrum can ‘hop’ stochastically from one resonance to another as their energy increases or decreases (e.g. Miller & Vinas 1993, Miller 1998)

Particles gyrating in a magnetic field pick up energy from plasma wavesif their gyration frequency is resonant with (multiples of) the wave frequency

, = wave and cyclotron frequenciesk|| = parallel wave number v|| = parallel particle speedl = integer


Energy vs. time for a single proton in isotropic, high frequency turbulence

Miller & Viñas (1993)

Energy lost or gained in each interaction, but overall, the energy of the particle increases

Protons and ions (mostly) resonate with high-frequency Alfvenic waves

Electrons resonate with electron cyclotron waves


Closing ThoughtsClosing Thoughts

Observations of solar flares in the X-ray and EUV, from the last 15 years or so, have demonstrated a great variety and complexity

To a great extent, they still support the overall picture of reconnection in thecorona resulting in the acceleration of a vast number of particles, which leadto heating and mass-motion in the lower atmosphere.

However, the study of solar flares involves some formidable theoretical problems, such as: • What is the microphysics of coronal reconnection? • How do we extend our understanding of 2-D reconnection to 3-D?• How do we tie together the MHD, plasma and kinetic aspects of theory?

We must also not ignore the physics which has been painfully learned in otherfields, such as lab devices and magnetospheric reconnection


11:04 11:06 11:08 11:10 11:12 11:14

RHESSI often observes X-raysat ~ 10-20 keV, several minutes before the impulsive phase.

RHESSI preflare sources


Coronal Sigmoids

So-called for their ‘S’ shape (in the Northern Hemisphere)

Visible in soft X-rays (e.g. by Yohkoh/SXT and now GOES SXI)

pre-flare sigmoid observed by Yohkoh Soft X-ray Telescope

post-flare configuration – cusp shows that an eruption has happened.


RHESSI Imaging

RHESSI uses ‘collimating optics’ - slits and slats

Only X-rays from certain directions can be detected

Rotation axis

Germanium detector


How RHESSI makes an image

Slats rotate pastsource

Detector Illumination

Modulation patterns

Modulated brightness patterns from all 9 grid pairs are combined to calculate the most likely source intensity distribution

Technique is similar to radio interferometry


= 0: ‘potential’ field. There are no currents (no free energy)

= const: linear force-free field. j= B

const: non-linear FFF

By)α(x,B

MDI/SXT potential nonlinear FF

field ‘twist’ ‘free energy’ in the form of current: j = B/

Coronal ‘Free Energy’


Nov 18, 2003: GOES M4, Krucker

night

nightUpwards motion ~5-40 km/s

Coronal HXR sources

> 20keV emission faint, fast time variations

gradual variations below 10 keV

Coronal energy deposition between 1030 and 1031 erg (depending on model)

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PPARC/Mallorca September 2006 1 Solar Flares Lyndsay Fletcher University of Glasgow Introduction...

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