Post on 22-Dec-2015
PPARC, Adv. Summer School, Palma 2006
N+N+N International Meeting for Young Scientists
(a British Council initiative)
From our star to far stars: variation and variability
Budapest (Hungary)
15-18 January, 2007
…details to follow soon (check the forthcoming issues of UK Solar Newsletter; if you are not subscribed, speak to Robertus ASAP)
…for more info see http://astro.elte.hu/nnn2007
PPARC, Adv. Summer School, Palma 2006
Coronal heating: a Coronal heating: a theoretical approachtheoretical approach
Istvan BallaiSPARG, University of Sheffield
PPARC, Adv. Summer School, Palma 2006
IntroductionIntroduction
•The eclipse of 1869 revealed emission line in the green part of the corona- was named coronium.•Grotrian in 1939 finally showed that this emission line to be due to Fe XIV at 5303Å.•This demonstrated that the corona has a temperature > 1MK, and so the coronal heating problem began….
PPARC, Adv. Summer School, Palma 2006
Publications/year (ADS for coronal heating)(more than 4,600 publications)
0
50
100
150
200
250
300
350
1960 1964 1968 1972 1976 1989 1984 1988 1992 1996 2000 2004
TRACE
SoHO
Yohkoh
Skylab
PPARC, Adv. Summer School, Palma 2006
• Problem: very high temperature of the upper atmosphere
• Question: what heating mechanism(s) do operate?
IntroductionIntroduction
PPARC, Adv. Summer School, Palma 2006
Multi-temperature vision of the Sun
Blue: EIT 171 A (0.95 MK)
Green: EIT 195 A (1.5MK)
Red: EIT 284 A (2MK)
PPARC, Adv. Summer School, Palma 2006
“The literature of coronal heating is primarily theoretical. Observations are often cited in support of a proposed theory or another, ..but…neither existing observations nor the current generation of models are sufficiently detailed to test any mechanism critically.” (Zirker, 1993)
• We now have an explosion of high resolution space datasets (Yohkoh, SOHO, TRACE, RHESSI and more to come) – that are providing constraints on theory and distinguishing between possible models.
The coronal heating is still an unsolved problem in the solar and stellar physics
IntroductionIntroduction
PPARC, Adv. Summer School, Palma 2006
Observational factsObservational facts
• Highly inhomogeneous
• Rôle of magnetic field
PPARC, Adv. Summer School, Palma 2006
• Highly inhomogeneous
• Role of magnetic field
Observational factsObservational facts
PPARC, Adv. Summer School, Palma 2006
• Consists of myriads of coronal loops
Observational factsObservational facts
PPARC, Adv. Summer School, Palma 2006
• length scale: from resolution up to 700 Mm
• radius: from resolution up to 10 Mm
• temperature: from 1-2x104 K to 2x106 K
• magnetic field strength: 1- 104 G
• equilibrium bulk motion
Flux tubes
Observational factsObservational facts
PPARC, Adv. Summer School, Palma 2006
The complex problem of coronal heatingThe complex problem of coronal heating
Energy sourceConversion mechanism
Heating
Plasma response
Radiation
Observables
Klimchuk, 2006
PPARC, Adv. Summer School, Palma 2006
The energy requirementParameter(erg cm-2s-1)
Coronalhole(open)
Activeregion(closed)
Chromosphericradiation loss
4 106 2 107
Radiation 104 < 106
Conduction 5 104 105 – 106
Solar wind (5-10) 105 ( < 105 )
× ×
×
×
PPARC, Adv. Summer School, Palma 2006
The energy source
Widely accepted: mechanical motions in and below the photosphereFootpoint motions can generate stresses (DC currents) and waves (AC currents) depending on the time-scale of the motion compared to the Alfven time
EUV, UV, X-ray coronal images and magnetograms firmly established that coronal heating is a magnetic phenomenon (e.g. Vaiana and Rosner 1978)
Heating models DC models
AC models
Hybrid AC/DC models
tdr>tA
tdr<tA
(Kinetic, turbulences)
PPARC, Adv. Summer School, Palma 2006
The energy source – DC heating
• Footpoint motions perform work on the coronal magnetic field and increase its free energy at a rate given by the Poynting flux through the base
• Magnetic field concentrated in small tubes (~kG) which expand out in the chromosphere and transition region
• Small loops form a low-laying “magnetic carpet” and they do not penetrate into the corona
• Part of the inter-network flux extends above the carpet and spreads out in the corona the magnetic field in the quiet Sun is a mixture of network field and surviving inter-network field.
• Bv~100 G (AR), 5-10 G (QS), Vh~105 cm/s, assume Bh~Bv:
hh VB vB1
F
F≈108 erg/cm2 s
PPARC, Adv. Summer School, Palma 2006
Thin tubes merge into corona
Peter (2001)
Tu et al. (2005)
PPARC, Adv. Summer School, Palma 2006
Heating by DC currentsHeating by DC currents
2D reconnection theories2D reconnection theories¤ 2D reconnection: X-point collapses to a singular sheet
¤ Magnetic energy heat+K.E.+ fast particles
¤ Well understood
¤ Source of heating and of many dynamic processes (flares, EEs, TRBs)
PPARC, Adv. Summer School, Palma 2006
2D reconnection theories2D reconnection theories
¤ In 2D well-developed
Slow Sweet-Parker reconnection (1958); rec. rate ≈R-1/2
Fast Petschek reconnection (1964)rec. rate ≈1/ln R
Many other fast regimes (depend on B.C.’s)
Almost uniform (Priest &Forbes, 1986)
Non-uniform (Priest & Lee, 1992)
Excellent review by Priest and Forbes (Magnetic reconnection, CUP, 2000)
PPARC, Adv. Summer School, Palma 2006
3D reconnection theories3D reconnection theories
Key question: structure of null-point
¤ Simplest: B=(x,y,-2z)
¤ Two families of field lines through null-point:
Spine field lines
Fan surface
PPARC, Adv. Summer School, Palma 2006
3D reconnection theories3D reconnection theories
Three types of reconnection at Null
¤ Spine reconnection
¤ Fan reconnection
¤ Separator reconnection
Double 3D null-point topology
(courtesy of K. Garlsgaard)
PPARC, Adv. Summer School, Palma 2006
3D reconnection theories3D reconnection theories
Spine reconnection Fan reconnection
PPARC, Adv. Summer School, Palma 2006
3D reconnection theories3D reconnection theories
¤ So, can reconnection heat the corona?
¤ Yes, possibly, in different ways…but observations are needed to see which way!
Examples:
Reconnection at null-point, e.g., XBP interpreted as converging flux
(Parnell et al. 1993, Priest et al. 1994)
PPARC, Adv. Summer School, Palma 2006
The energy source – AC heatingThe energy source – AC heating
• The turbulent convection that stresses the coronal magnetic field generates a large flux of upwardly propagating waves (acoustic, Alfvén, slow and fast magnetosonic)
• Mode coupling and other processes transfer energy between different types of waves, so the mix of waves changes as a function of height.
• Theoretical and observational estimates suggest energy fluxes at the top of
convection zone of several 107 erg/cm2s (Narain & Ulmschneider,1996) more than adequate to heat the corona
• Only a small fraction of the flux is able to pass through the very steep density and temperature gradients in the chromosphere and transition region.
• Acoustic and slow waves steepen into shock waves and are strongly damped, while fast waves are strongly refracted and reflected, only Alfvén waves are able to penetrate into the corona. The do not form shocks since they are transversal and their energy is ducted along the magnetic field rather than being refracted across it.
PPARC, Adv. Summer School, Palma 2006
Behaviour of acoustic wavesBehaviour of acoustic waves
Chromospheric heating by acoustic waves
• Convection generates acoustic waves propagating upwards, steepens into shock waves or are reflected by the density gradients in the TR
2vCF SM KmHe Hh
160,0 22 Av
Hh
eA 2
22
22
hA
v kv
k 02vk
evanescent
waves
so
PPARC, Adv. Summer School, Palma 2006
Behaviour of AlfvBehaviour of Alfvéén wavesn waves
• Significant transmission of Alfvén waves is possible only within narrow frequency bands centered on discrete values where loop resonance conditions are satisfied (Hollweg, 1981)
• Enough flux may pass through the base of long (>100 Mm) active regions loops to provide their heating (Hollweg, 1985); in the case of short loops this does not apply.
• Waves can be generated in the corona itself by, e.g. magnetic reconnection and change of the equilibrium (AC/DC heating mechanism)
PPARC, Adv. Summer School, Palma 2006
Heating by AC currentsHeating by AC currents• Recent high resolution observations show undoubtful evidence for
waves in the corona• Prominences• Plumes• Corona (EIT/SoHO, TRACE)
– Flare excited waves in loops-fast kink modes (Aschwanden et al. 1999, Nakariakov and Ofman 1999)
– Feet of long loops-slow waves (De Moortel et al. 2002ab, Aschwanden et al. 2002 )
– CME/flare excited global waves (EIT waves) –fast waves (Thompson et al. 1999, Ballai and Erdélyi 2003a,b, Ballai et al. 2005)
For an effective damping these waves require small scales
PPARC, Adv. Summer School, Palma 2006
Resonant absorptionResonant absorption
Ideal MHD equations singular dissipation heating
Concept of Connection Formulae
ωdriver = ωlocal
(Ionson 1978, Rae & Roberts 1982, Hollweg 1984, Poedts et al. 1989, Goossens 1991, Ruderman et al 1997ab, Ballai et al. 1998ab, Ballai and Erdélyi 1998,2000ab, etc,etc)
PPARC, Adv. Summer School, Palma 2006
Why resonant absorption ?Why resonant absorption ?
• Inhomogeneous plasmas: natural behaviour
• Easy wave energy transfer resulting in heating
• Condition to occur: ωdriver = ωlocal
• Could/may/viable to explain:
- local/atmospheric heating
- power loss of acoustic waves in sunspots
- damping of helioseismic (p/f/g) eigenmodes
- energisation of MHD waves in magneto/heliosphere
PPARC, Adv. Summer School, Palma 2006
Resonant absorptionResonant absorption
• High frequency Alfvén waves are able to reach corona
• They are incompressible and transversal subject to damping due to ohmic and/or shear viscosity
• In the corona ν/µ≈1011 and η0/η1≈105 , so they have a very weak damping.
• For effective damping small trasversal scales are requiredresonant absorption
))()((
)(
222222
1131
121
CAA
r
rr
vcD
PCCdr
dPD
rPCrCdr
rdD
PPARC, Adv. Summer School, Palma 2006
• Driven problem ω is prescribed• Eigenvalue problem ω is searched for
constC
B
TCBiP
B
Cgi
A
A
Az
ABr
sgn2
sgn
21
2
Jumps are independent of dissipative coefficient
Concept of connection formulaeConcept of connection formulae
PPARC, Adv. Summer School, Palma 2006
Resonant a
bsorption is
working!
Resonant absorptionResonant absorption
PPARC, Adv. Summer School, Palma 2006
Internal background motionInternal background motion
•Steady large-scale flows (e.g., Doyle et al. 1997)•Flow has a major influence on resonant absorption
5-6% vA
PPARC, Adv. Summer School, Palma 2006
But…
• ε– the dimensionless amplitude of the perturbations; R– total Reynolds number; f—any large variable
• linear theory
• nonlinear theory
• Suppose
32
2
2 R
rf
zff
1
1
32
32
1010
11
R
R
for
Resonant absorption is a nonlinear phenomena
(Ruderman et al.1997, Ballai et al. 1998,1999, 2000, Ballai and Erdélyi 1998)
PPARC, Adv. Summer School, Palma 2006
But…
• Nonlinearity gives just a small correction to the net absorption coefficientlinear theories give acceptable solutions (Ruderman 2000)
• Nonlinearity in dissipative layers generate a mean flow outside the layer
• The mean (turbulent) flow can locally enhance the dissipative coefficients
• The observation of the generated mean flow could be a first evidence of the resonant absorption
PPARC, Adv. Summer School, Palma 2006
(Ofman and Davila 1995)
PPARC, Adv. Summer School, Palma 2006
Resonant absorption/phase mixingResonant absorption/phase mixing
• To have a heating for the entire loop, we have to suppose that waves are not monochromatic or stochastic processes have to be taken into account (Tsiklauri and Nakariakov 2002, Ruderman 2003)
• Dissipative layer the oscillations are in phase as long as ω and kvA are in phase
• If they start to be out of phase phase mixing (Heyvaerts and Priest 1983, Browning and Priest 1984, Hood et al 1997, Nakariakov et al 1997, Ruderman et al. 1998, De Moortel et al. 2000, Tsiklauri et al. 2003, etc.)
PPARC, Adv. Summer School, Palma 2006
Energy conversion-conclusionEnergy conversion-conclusion
• Through energy conversion, the magnetic stress energy and wave energy is transformed into heat.
• Since classical dissipation coefficients are small in the corona, significant heating requires the formation of steep gradients and small length scales.
Magnetic gradients heating by reconnection and Ohmic dissipation
Velocity gradients heating by viscous dissipation
• Gradients are formed through slow quasi-static evolution and through dynamical processes
• Possible scenarios: instabilities, turbulences, loss of equilibrium, simple and complex flow patterns at the base of complex coronal magnetic fields (DC) and resonant absorption, phase mixing (AC)
PPARC, Adv. Summer School, Palma 2006
Energy conversion and microphysicsEnergy conversion and microphysics
• Microphysics is likely to play a key role in the energy conversion process, e.g. anomalously large (nonclassical) transport coefficients are required for significant heating even in the presence of steep gradients.
• Coronal transport coefficients are not known with precision but indirect techniques are used to infer values for, e.g. viscosity, thermal and electrical conduction, etc. CORONAL SEISMOLOGY (Nakariakov et al. 1999, Ofman and Aschwanden 2002, Klimchuk et al. 2004, Ballai and Erdélyi 2005)
• Collisionality of the coronal plasma: the collisionless effects are extremely important for reconnection (Bhattacharjee 2004) and wave propagation (Ballai et al. 2002)
• Hybrid codes developed to take into account both the MHD and particle aspects of the plasma
PPARC, Adv. Summer School, Palma 2006
Plasma responsePlasma response
• The fundamental principle: the close thermal and dynamic connection between the corona and the lower atmosphere (coupled system)
• In the case of static equilibrium, thermal conduction transports more than a half of the coronal heating energy down to the transition region, where it is more efficiently radiated
• When heating is time-dependent, an increase in the heating rate causes the coronal temperature to rise, producing an increase of the downward heat flux. The TR is unable to radiate the additional energy, so heated plasma flows into corona through “chromospheric evaporation”
• If the upflow is fast, it can be explosive causing shocks, if the heating rate then decreases, an inverse-like process occurs in which the plasma drains from the loop and “condenses” back into the chromosphere.
PPARC, Adv. Summer School, Palma 2006
RadiationRadiation
• We determine the radiation spectrum emitted by the heated corona• If the plasma is in ionisation equilibrium, this task is relative simple
(see the CHIANTI software, Dere et al. 1997).
• If the plasma is not in ionisation equilibrium the problem is much more complicated. The equilibrium can be destroyed by, e.g.
– Rapid evolution of an impulsive heating– Rapid cooling– Flow through a steep temperature gradient
In this case we have solve the ionisation rate equation in order to determine the radiation spectrum
)(2 TGnemissivity e
PPARC, Adv. Summer School, Palma 2006
Observation of heating eventsObservation of heating events
• Even the present high resolution satellites provide a minimum information about the heating and the findings are often the result of averaging over space, time and wavelength.
• The best resolution at the moment is ≈ 350 km. In order to see heating at work we would need 10-103 m (!!!)
• Small-scale events have different names but they may turn out to belong to identical physical processes.
- ephemeral regions - nanoflares
- emerging flux events - microflares
- flux cancellation - soft X-ray jets
- events, blinkers - AR transient brightening
- soft X-ray bright points
PPARC, Adv. Summer School, Palma 2006
Small-scale phenomena and their occurrence domain (QS- quiet Sun, AR-active region, Ph–photosphere, TR–transition region, C–corona)
Phenomenon Horizontal domain
Vertical domain Wavelength
Ephemeral regions
QS Ph Optical
Emerging flux events
QS, AR Ph Optical
Flux cancellation QS, AR Ph OpticalExplosive events QS TR EUVBlinkers QS, AR TR EUVNano- and microflares
QS, AR C EUV, SXR
X-ray brightpoints
QS C SXR
Soft X-ray jets QS, AR C SXRAR brightenings AR C SXR
PPARC, Adv. Summer School, Palma 2006
Physical parameters of coronal small-scale phenomena (L-
spatial scale, T-electron temperature, n-electron density) Phenomenon L [Mm] T [MK] n [x108 cm-3]
Nanoflares 2.8-7.9 1-1.4 2.9-4.4
QS transient brightening
3.2-14.1 1.3-1.7 …..
QS heating event 4.5-7.9 1.2-1.5 7-20
AR transient brightening
5-40 4-8 20-200
SXR jets 15-100 3-8 7-40
PPARC, Adv. Summer School, Palma 2006
Open questions in the coronal heating Open questions in the coronal heating problemproblem
• Are distinct coronal loops heated differently from the diffuse corona?
• Are there different classes of loops that are heated in different ways?
• Is quiet Sun heating similar to active regions heating?
• How the AC/DC mechanisms work together?
• Are stellar coronae heated in the same way as the solar corona?
PPARC, Adv. Summer School, Palma 2006
UVCS results: solar minimum (1996-1997 )UVCS results: solar minimum (1996-1997 )
On-disk profiles: T = 1–3 million K Off-limb profiles: T > 200 million K !
• The fastest solar wind flow is expected to come from dim “coronal holes.”
• In June 1996, the first measurements of heavy ion (e.g., O+5) line emission in the extended corona revealed surprisingly wide line profiles . . .
PPARC, Adv. Summer School, Palma 2006
Heating of the open coronal structuresHeating of the open coronal structures
Very strong perp. heating of the oxygen (Cranmer et
al. 1998)
(Xing et al. 2002)
PPARC, Adv. Summer School, Palma 2006
The impact of UVCSThe impact of UVCSUVCS has led to new views of the collisionless nature of solar wind acceleration.Key results include:
• The fast solar wind becomes supersonic much closer to the Sun (~2 Rs) than previously believed.
• In coronal holes, heavy ions (e.g., O+5) both flow faster and are heated hundreds of times more strongly than protons and electrons, and have anisotropic temperatures. (e.g., Kohl et al. 1997,1998)
PPARC, Adv. Summer School, Palma 2006
• SUMER and UVCS (SoHO) have provided very strict constraints on heating of coronal holes
• H+ are mildly anisotropic (Tperp>Tparallel); O 5+ are strongly anisotropic (Tperp/Tparallel=10-200) above 2-3 RSun
• At r=3RSun, Tperp for O5+ is 2x108K (vth=450 km/s), while H+ have Tperp=3x106K (vth=225 km/s)
• At r=3.5 RSun the outflow speed of O5+ is twice the outflow speed of H+
• These properties can be explained by the resonant interaction of coronal ions with ion-cyclotron waves, i.e. by ion-cyclotron resonance
• Ion cyclotron waves (10-104 Hz) have not yet been observed in the solar wind or corona (Cranmer et al. 1999)
• Some attempts to describe waves in collisionless plasmas (Nakariakov and Oraevski 1995, Ballai et al. 2002)
Ion-cyclotron resonanceIon-cyclotron resonance
PPARC, Adv. Summer School, Palma 2006
Ion-cyclotron resonanceIon-cyclotron resonance
• The condition of resonance
• This mass-dependent mechanism is a wave-particle interaction
• Ωi decreases with distance more and more energy injected at lower k is swept into the high frequency domain, where is dissipated by the ions
• Dissipation of ion-cyclotron waves produces diffusion in velocity space, along contours of constant energy
• Ions are accelerated along the field lines
cmBqvkk
i
iii ,||||||
PPARC, Adv. Summer School, Palma 2006
Where do cyclotron waves come from?Where do cyclotron waves come from?
(1) Base generation by, e.g., “microflare” reconnection in the lanes that border convection cells (e.g., Axford & McKenzie 1997).
Both scenarios have problems . . .
(2) Secondary generation: low-frequency Alfven waves may be converted into cyclotron waves gradually in the corona.
PPARC, Adv. Summer School, Palma 2006
How the ion-cyclotron waves are How the ion-cyclotron waves are generated?generated?
• Alfvén waves with frequencies > 10 Hz have not been observed in the corona or solar wind
• Base generation: by, e.g. “microflare” reconnection in the lines that border convection cells.
• Problem: Low Z/A ions consume base-generated wave energy before it can be absorbed
• Secondary generation: The Sun is suspected to emit low-frequency (<10 mHz) Alfvén waves. This source of “free energy” may be converted into ion cyclotron waves gradually throughout the corona (MHD turbulent cascade, instabilities seeded by non-Maxwellian distributions)
• Problem: Turbulence produces mainly high-kperp fluctuations (i.e. still low frequency). Ion-cyclotron waves propagating parallel to B0 may compromise only a small fraction of the total fluctuation power
PPARC, Adv. Summer School, Palma 2006
Heating mechanismsHeating mechanisms
• A surplus of proposed ideas? (Mandrini et al. 2000; Aschwanden et al. 2001)
PPARC, Adv. Summer School, Palma 2006
Conclusions: What do weConclusions: What do we need?need?
• Data analysis
• Direct observations
• Direct or indirect evidence for heating, e.g. mean flow for resonant heating
• Observe reconnection driven resonant MHD waves
• Use the newly developed coronal seismology for plasma and field parameters
PPARC, Adv. Summer School, Palma 2006
Conclusions Conclusions
• MHD heating occurs across S-STP
• Theories (waves, reconnection, turbulence) progressed
• “Candidates” are all natural for plasma heating/acceleration
• MHD heating is sensitive to flows
• Various structures may be heated by different mechanisms
• More observations are needed (Solar B, STEREO, SDO, etc…) to establish the effects of magnetic carpet, and of zoo of transients!