1、Spectral Diagnostics of Solar Atmosphere (2),Cheng Fang Department of Astronomy Nanjing University, China,CONTENTS,Semi-empirical modelingDiagnostics of non-thermal particlesDynamic modelsSummary,Solar spectral observations,THEMIS,VTT,Meudon tower,Kitt peak NOAO,Hinode,Solar Tower of Nanjing Univers
2、ity,Multi-line 2D spectral observations H CaII 8542 HeI 10830,2D line profiles,4D data set x-dimension y-dimension wavelength time,What can we obtain by analyzing solar spectra?,Semi-empirical modeling Velocity diagnostics Non-thermal particle diagnostics Dynamic process diagnostics Magnetic field m
3、easurement (by use of Stokes line profiles) etc.,Semi-empirical modeling,Basic equations radiative transfer: statistical equilibrium: hydrostatic equilibrium:,Semi-empirical modeling,Method,Flare models (Machado et al. 1980),A higher temperature in the chromosphereA lower transition region,Compariso
4、n of some models,Quiet-Sun: VALCSmall flare: F1Big flare: F2White-light flare: F1*，F3,A time-varying model (Gan & Fang 1987),Observed H line profiles (Gan, Rieger & Fang, 1993),Line asymmetries: blue vs. redImplying mass motions in the flare atmosphere,H line asymmetry (Ichimoto & Kurokawa 1984),H r
5、ed asymmetries caused by downward motionsLine bisector method at far wingsMomentum balance between upflowing and downflowing plasma,H line asymmetry,1980年6月23日flare X-ray（upper）and H line profiles with that of pre-flare subtracted。It can be seen that the red asymmetry of line profiles appears mainly
6、 at the impulsive phase of flares, so it closely relates to the heating and non-thermal particle bombardment.,(Canfield et al., BAAS, 1985),Flare models with velocity fields (Gan et al. 1993),Blue asymmetry,Flare models with velocity fields (Gan et al. 1993),Red asymmetry,Flare semi-empirical models
7、 with velocity field (Falchi & Mauas 2002),Left: before (full-line, dotted-line) and at the beginning (dashed-line) of the first HXR spikeRight: after the HXR spike (full-line and dotted-line),Full-line: VALCDashed-line: Ding & Fang,Flare semi-empirical models with velocity fields (Falchi & Mauas 20
8、02),Before a HXR spike After the spike,H,CaII K,Si,Thick line: ComputedThin line: Observed,Diagnostics of non-thermal particles in solar flares,radiative transfer: statistical equilibrium: hydrostatic equilibrium:,How can we compute the non-thermal excitation and ionization rates?,Non-thermal partic
9、le excitation and ionization probabilities (Fang et al. 1993; Henoux et al. 1993),When an electron beam bombards on an atmosphere with neutral hydrogen atoms, the energy deposit can be written as,Where Fc is the total flux above the energy cut-off Ec , is the power index. The energy deposit mainly r
10、elates to the non-thermal excitation probability and ionization probability from the ground level,Is the excitation and ionization potentials respectively,Non-thermal particle excitation and ionization probabilities,Considering that the secondary electrons produced by ionization can also make hydrog
11、en atoms excitation and ionization, Dalgarno & Griffing (Proc.Roy.Soc.London, 1958) obtained that after the bombardment of the electron beam each ion will have an average energy of 36 eV, i.e.,So we can get the non-thermal ionization probability as,If we only consider the first 4 levels of hydrogen
12、atoms, then,non-thermal particles excitation and ionization probabilities,If we assume that the excitation cross section varies not much with energy, then,So we can get,Example of the Effects of the non-thermal electron beam (Xu, Fang, Gan, ChJAA, 2005),H、Ly and Ly line profiles with non-thermal eff
13、ect included. We take = 4，Ec = 20 keV。The flux of electron beam is taken as 1012（solid line）、51011（dotted dashed）、1011（dashed）and 1010（three dotted-dashed）erg/cm2/s。,By fitting the observed line profiles, we can get the flux and power index of non-thermal particles (electrons),Effects of the non-the
14、rmal electron beam and velocity fields on the H profiles (Ding & Fang 1997),Both blue and red asymmetries can be produced by downward motions, depending on the strength of the electron beam,An electron beam bombards on the model F1= 3 solid line= 4 dashed line= 5 dotted line,Effects of the non-therm
15、al electron beam on the Ni I 676.8nm line (Ding et al. 2002),Two requirements for producing an emission Ni I profile: a cool atmosphere & a non-thermal electron beam,Model F1,Penumbra model Ding & Fang,An atmosphere bombarded by an electron beam with Flux= 0 solid line Flux=109 dashed line Flux=1010
16、 dotted line Flux=1011 dash-dotted line,Role of the non-thermal electron beam in producing white-light flares (Ding et al. 2003),Energy deposit of an electron beamRadiative cooling rateEnergy balance,White-light flares: numerical results (Ding et al. 2003),Continuum Contrast at 8500,Temperature dist
17、ributionDotted-line: flux=1011 Dashed-line: flux=1010,Dynamic models,Basic assumptions:loop geometryone-dimensionalthermal conduction and/orelectron (proton) beam heating,Dynamic models,Basic equations mass conservation: momentum conservation: energy conservation: where,Electron-heated model (Fisher
18、 et al. 1985),Confirming chromospheric evaporation and condensation,Electron-heated model (Mariska 1995),A lower coronal pressure: evaporation velocity is too large,Electron-heated model (Mariska 1995),A higher coronal pressure: line width is too small,Proton-heated model (Emslie et al. 1998),Unifor
19、m coronal heatingSmaller evaporation velocityDifferential emission measure inconsistent with observations,Radiation hydrodynamic model (Abbett & Hawley 1999),mass conservation: momentum conservation: energy conservation: level population equation: radiative transfer equation: where,Radiation hydrody
20、namic model (Allred et al. 2005),Improved soft X-ray and EUV irradiation heating codes（CHIANTI，ATOMDB）Double power-law electron beams as observed（Holman et al. 2003）H: 6 levels + continuum, He I: 9 levels + continuum, Ca II: 6 levels + continuumGrids: depth 191, angle 5, transition 100,Dynamics for
21、the F10 Model electron beam with flux=1010 ergs cm -2 s-1,00.3 s: The chromosphere is rapidly heated to 104 K by the electron beam.0.33 s: Pressure increase produces an upward shock. Radiative cooling roughly balances the heating so that the evolution is slow.3 s: Hydrogen is completely ionized, the
22、refore the temperature rises quickly.350 s: He I becomes ionized to He II. Radiative cooling balances the heating, resulting a gentle phase again.,PFS: preflare stateQe: electron beam heating rate,Dynamics for the F10 Model,Dynamics for the F10 Model,73 s: He II is completely ionized. Heating exceed
23、s the radiative cooling again. Temperature explosively increases, producing a low-density high-temperature bubble.85221 s: The bubble expands until it reaches the boundary. A hotter, denser corona and a lower transition region are formed.,Line profiles: Ly H He II 304 Ca II K,Continuum enhancement:
24、white-light flaresContinuum dip: black-light flares,Flare elementary bursts: observations (Wang et al. 2000),Kernel K1 shows fluctuations of a much larger amplitude than pure noises.,Flare elementary bursts: simulations (Ding et al. 2001),Rate eq.,Energy eq.,Intensity,Flare elementary bursts: simula
25、tions (Ding et al. 2001),Dynamic response to small-scale injection of nonthermal electrons,Summary,Semi-empirical models of solar flares have been widely used, which can fully account for most of the observed spectra. The disadvantage is the assumption of a static atmosphere.Radiation dynamic models are still to be developed. The computed spectra do not match well the observed ones.Nonthermal electrons are shown to play a significant role in not only increasing the line intensity, but also changing the line asymmetry, and producing WLFs etc.Spectral diagnostics is a powerful tool.,Thank you,
