Solar radiation and plasma diagnostics
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Solar radiation and plasma diagnostics

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Lecture given at the 2011 STFC Advanced Summer School in Solar Physics

Lecture given at the 2011 STFC Advanced Summer School in Solar Physics

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Solar radiation and plasma diagnostics Solar radiation and plasma diagnostics Presentation Transcript

  • Solar radiation and plasma diagnostics Nicolas Labrosse School of Physics and Astronomy, University of Glasgow 0
  • OutlineI – Solar radiationII – Plasma diagnosticsIII – Arbitrary selection of research papers Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 1
  • I. Solar radiationI.1 OverviewI.2 Radiation basicsI.3 Radiative transferI.4 How is it formed?I.5 How do we detect it? 2
  • I.1 Overview• Basic facts– Too many photons for your naked eyes!– Optical telescopes show the visible surface (photosphere) Has particular features such as sunspots (appear dark)– Spectroscopy (late 1800s) allowed the chromosphere to be studied– Although the corona can be observed during eclipses, most of ourknowledge come from Radio observations: patchy microwave emission Soft X-rays: diffuse emission over solar disk except in coronal holes Hard X-rays: bright in localised areas (active regions) Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 3
  • I.2 Radiation basics• Radiation field in the solar atmosphere– Amount of radiant energy flowing through unit area per unit timeper unit frequency and per unit solid angle: intensity Iν– If radiation field is in thermal equilibrium with surroundings (aclosed cavity at temperature T): blackbody radiation 2πhν 3 1Planck function Iν = ≡ Bν (T ) erg s-1 cm-2 sr-1 Hz-1 c2 e kT − 1 hν– Deep in the solar atmosphere, local thermodynamic equilibriumholds, and mean free path of photons is short (a few km): photonswithin a small volume can be considered to be contained in a cavitywhere the temperature is ~ constant. Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 4
  • I.2 Radiation basics• Radiation field in the solar atmosphere From Rutten’s notes Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 5
  • I.3 Radiative transfer• The interaction of the radiation field with the plasma is described by the Radiative Transfer Equation– Medium emits radiant energy at rate λ erg cm s sr Å -3 -1 -1 -1– and absorbs radiant energykλ is the linear absorptioncoefficient in cm-1– If a beam of radiation withintensity Iλ(0) enters a uniform slab of linearthickness x, the emergent radiation is thenIλ(x)=Iλ(0) e-τ , where τ=kλ x is the optical dh = dl cos Ψdepth of a uniform slab at wavelength λ. cos Ψ = µE.g. kλ=10-6 cm-1 around 5000 Å Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 6
  • I.3 Radiative transfer• The interaction of the radiation field with the plasma is described by the Radiative Transfer Equation– More generally we have τ = kλ dx– Radiation propagating through theslab along OA varies between h andh+dh due to absorption and emission:Iλ (h + dh, Ψ) − Iλ (h, Ψ) = λ (h)dh sec Ψ − Iλ (h, Ψ)kλ dh sec Ψ– In the limit where dh→ 0, we get dh = dl cos Ψ dIλ cos Ψ = µ µ = λ − kλ Iλ dh Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 7
  • I.3 Radiative transfer• The interaction of the radiation field with the plasma is described by the Radiative Transfer Equation dIλ µ = λ − kλ Iλ dh– Finally, in the solar atmosphere,the optical depth at height h is h τλ (h ) = kλ dh ∞– The radiative transfer equation is then dIλ dh = dl cos Ψ µ = Iλ − Sλ RTE dτλ cos Ψ = µwith the source function Sλ = λ /kλ Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 8
  • I.3 Radiative transfer dIλ• Solutions to the Radiative Transfer Equation µ = Iλ − S λ dτλ– The intensity of radiation flowing through the upper atmosphere (relativeto the point where the optical depth is τ) is given by τ τ /µ S(t) −t/µI(τ, µ+) = −e e dt ∞ µ– If τ→ 0 then ∞ S(t) −t/µI(0, µ+) = e dt 0 µ If S is constant at all depths: I(0, µ+) = S If S is constant in only a small slab of optical thickness τ : I(0, µ+) = S(1 − e−τ /µ ) emergent intensity not as large as S; reduced by optical depth term. If τ is very small, then I(0, µ+) = Sτ /µIn the case of constant source function, the emergent intensity from a slab cannot be greater than S, but may be much smaller than S if the optical depth is small. Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 9
  • I.3 Radiative transfer• Solutions to the Radiative Transfer Equation If S is not constant at all depths: taking S(τ ) = a + bτ one finds I(0, µ+) = a + bµThis solution matches the limb darkening of the Sun! This particular form of the source function is actually a natural consequence of the assumption of a Gray atmosphere, where the opacity is independent of wavelength. This results in the Eddington-Barbier relationship: the intensity observed at any value of µ equals the source function at the level where the local optical depth has the value τ = µ. It means that you see deeper in the atmosphere as you look towards the centre (µ=1) than towards the limb (µ→ 0). Limb darkening and EB also imply that T increases with τ Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 10
  • I.4 How is it formed?• From Rob Rutten’s notes Simple absorption line Simple emission line Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 11
  • I.4 How is it formed?• From Rob Rutten’s notes Simple absorption edge Simple emission edge Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 12
  • I.4 How is it formed?• From Rob Rutten’s notes Self-reversed absorption line Doubly-reversed absorption line Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 13
  • I.5 How do we detect it?• The photosphere (in short)– Take advantage of photons that haveoptical depth unity at the surface of the Sun– This happens in the visible around 5000 Å– Many absorption lines (dark) superimposed on the continuumsignal presence of atoms / ions in the solar atmosphere absorbingradiation coming from below.– The line strengths depend on the column densities of these atoms/ ions which contain electrons in the lower state of the transition Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 14
  • I.5 How do we detect it?• The photosphere (in short)– The continuum... Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 15
  • I.5 How do we detect it?• The chromosphere (in short)– Don’t wait for an eclipse!– Tune your instrumentto detect photons for whichτ∼1 about 1000-2000 km above the photosphere– This means looking at the core of lines such as Hα or Ca II K– No limb darkening: rather, limb brightening!So T decreases with τ. Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 16
  • I.5 How do we detect it?• The corona (in short)– Optical forbidden lines tell you that it’s hot ~ 1-2 MK and tenuous(less than 109 cm-3)See Edlen (1945) on Fe X 6375 Å and Fe XIV 5303 Å – Soft X-ray spectrum shows Parkinson (1973) strong emission lines and no obvious sign of continuum Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 17
  • II. Plasma diagnosticsII.1 OverviewII.2 Direct spectral inversionII.3 Imaging vs spectroscopy 18
  • II.1 Overview• What do we (I) mean by plasma diagnostics? An empirical derivation of:– Temperatures– Densities– Mass flow velocities– Pressure– Chemical abundancesin a specific (observed) region of the solar atmosphere at a certain time.• What for?– Energy and momentum balance and transport Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 19
  • II.1 Overview• Direct inversion of spectral data– For optically thin plasma (all emitted photons leave freely withoutinteraction)– Yields spatially averaged values• Forward approach– Necessary for optically thick plasma– Semi-empirical models Start with given spatial distribution of T, p, n Solve excitation and ionisation balance for all species Determines opacities and emissivities Solve RTE to get the emergent spectrum Compare with observed spectrum ... and adjust model to start over again Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 20
  • II.2 Direct spectral inversion• Optically thin plasma emitting Gaussian-shaped line– Line width yields ion temperature T and non-thermal (ormicroturbulent) velocity ξ– Observations of different lines give an idea of variation of T and ξ,and so of distribution of energy in different layers– See e.g. Chae et al (1998) analysis ofSOHO/SUMER observations.“The isotropic and small-scale nature of the nonthermal motions appear to be suited for MHD turbulence.” Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 21
  • II.2 Direct spectral inversion• Optically thin plasma emitting Gaussian-shaped line– Electron density estimated by Stark broadening (generally yields upper limits) Collisional depolarization Thompson scattering measurements Emission measure methods– Neutral and ion densities; abundances Line strengths, or absorption of radiation Often requires good photometric calibration and accurate atomic data– Gas pressure Derived from density and temperature measurements Using pressure-sensitive lines (or line intensity ratios) Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 22
  • II.2 Direct spectral inversion• Application to XUV / EUV / UV lines– A lot of data: SOHO/SUMER, SOHO/CDS, SOHO, UVCS,Hinode/EIS, and then IRIS (?)– Techniques described now applicable to plasma with ne < 1013 cm-3in ionization equilibrium– See work of Feldman et al (1977), Mariska (1992), Mason andMonsignori Fossi (1994), Phillips et al (2008), ... Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 23
  • II.2 Direct spectral inversion• Line emission from optically thin plasma– Emissivity of b-b transition– Under the coronal approximation, only the ground level (g) andexcited level (j) are responsible for the emitted radiation. Thestatistical equilibrium reduces to:– Now only have to balance excitation from ground level withspontaneous radiative decay, which yields– Now the population of the g level can be written as: Abundance of element with respect to H ~1 ~ 0.8 Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 24
  • II.2 Direct spectral inversion Carole Jordan’s workSolar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 25
  • II.2 Direct spectral inversion• Line emission from optically thin plasma– Collisional excitation coef:(assuming Maxwellianvelocity distribution) Statistical weight Collision strength– Finally...where we have introduced the contribution function G(T) Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 26
  • II.2 Direct spectral inversion http://www.chianti.rl.ac.uk/Contribution functions for lines belonging to O III – O VI ions, CHIANTI v.5.1 Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 27
  • II.2 Direct spectral inversion• Electron temperature– Emission measure: yields amount of plasma emissivity along LOS Use the fact that contribution function is peaked to write , with EM can be directly inferred from the observation of spectral lines It may be defined also as EM = n2 Vc [cm-3], with Vc the coronal volume e emitting the line EM also yields the electron density Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 28
  • II.2 Direct spectral inversion• Electron temperature– Differential Emission measure: yields distribution in temperature ofplasma along LOS and thus The DEM contains information on the processes at the origin of the temperature distribution, BUT The inversion is tricky, using observed line intensities, through calculating G(T), assuming elemental abundances, and is sensitive to uncertain atomic data Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 29
  • II.2 Direct spectral inversion• Electron density from line ratios– Allowed transitions have I ∝ n2 e– Forbidden and intersystem transitions, with a metastable (longlifetime) upper state m, can be collisionally de-excited towards level k– For such a pair of lines from the same ion: , soThis is because of the density dependence ofthe population of level m– Intensity ratio yields ne averaged along LOS at line formationtemperature Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 30
  • II.2 Direct spectral inversion• What is the volume filling factor?– Measures the fraction of the volume filled by material fV ∼ EM/n2 e Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 31
  • II.3 Imaging vs spectroscopy• Line profiles give us key information on plasma parameters– Line width: thermal and non-thermal processes– Line position: Doppler shifts, mass flows– Line intensity: densities, temperature– Line profile shape: optical thickness• Issues– It takes time to acquire spectra on rather limited field of views– Data analysis relies on complex atomic data with highuncertainties– Line identification and blends can cause headaches! Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 32
  • II.3 Imaging vs spectroscopy• Spectra are still useful even without detailed profiles– Integrated intensities should not be affected by instrumental profile• Imaging– No detailed line profile, no Doppler shifts– High cadence, high temporal resolution– Narrow-band imaging getting close to spectroscopic imaging Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 33
  • III. Arbitrary selection of researchpapers 34
  • III. Arbitrary selection of research papers• Plasma diagnostics in the solar wind acceleration region– Uses ratio of collisional and radiative components of pairs ofstrong resonance lines (e.g., O VI 1032/1037; Ne VIII 770/780; Mg X610/625; Si XII 499/521; Fe XVI 335/361)– Kinetic temperatures and deviations from Maxwellian distributionscan be determined from line shapes and widths (mass or charge-to-mass dependent processes)– Mass-independent broadening can also be produced by bulkmotions of coronal plasma– Measurements provide key tests for models See Kohl & Withbroe (1982); Withbroe et al. (1982); UVCS papers Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 35
  • III. Arbitrary selection of research papers• Plasma diagnostics in the solar wind acceleration region– Solar wind velocities by the Doppler dimming effect (Hyder & Lites1970) Intensity of resonantly scattered component of spectral line depends on ∞ ∫ J φ (ν −ν )dν −∞ ν w Doppler shift introduced by wind velocity mean intensity of disk radiation normalised absorption profile Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 36
  • III. Arbitrary selection of research papers Kohl & Withbroe 1982Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 37
  • III. Arbitrary selection of research papersLabrosse et al (2007, 2008) Labrosse et al (2006) Ly-β Ly-α Ly-α (SOHO/UVCS) Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 38
  • III. Arbitrary selection of research papers• The TR and coronal downflows– Net redshift in all TR emission lines, peaking at log T=5, explainedby material draining down on both sides of TR loops towardsfootpoints (Brekke et al., 1997; Dammash et al., 2008).– Similar observations in coronal lines (e.g. EIS: del Zanna 2008,Tripathi et al 2009)– Also observed in optically thick Lyman lines by SOHO/SUMER(see Curdt et al., 2011) Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 39
  • III. Arbitrary selection of research papers• Lyman-α is one of the most important lines– 1216 Å– Transition between atomic levels 1 and 2 of hydrogen– Key role in radiative energy transport in solar atmosphere Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 40
  • III. Arbitrary selection of research papersCorrespondence between asymmetry and downflows Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 41
  • Correspondence between line reversals and magnetic field Flatter profiles (reduced opacity) cluster along the network lane Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 42
  • III. Arbitrary selection of research papers• Plasma diagnostics in the flaring solar chromosphere (Graham et al., 2011)– Combined EIS, RHESSI, XRT and TRACE data covering a widerange of temperatures– Evidence for T~7 MK in footpoints from XRT– and ne~a few 1010 cm-3 at T~1.5-2 MK– Small downflows at T<1.6MK; upflows up to 140 km s-1 above Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 43
  • III. Arbitrary selection of research papers• Graham et al., 2011 Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 44
  • III. Arbitrary selection of research papers• Graham et al., 2011 Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 45
  • III. Arbitrary selection of research papers• Graham et al., 2011 Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 46
  • III. Arbitrary selection of research papers• Solar prominence diagnostics with Hinode (Labrosse et al., 2011)– Used EIS data covering a wide range of temperatures– Evidence for absorption and volume blocking– Used optically thick He II 256 Å line and non-LTE models– Infer H column density of 1020 cm-2 Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 47
  • III. Arbitrary selection of research papers• Labrosse et al., 2011 EIS field of view SOT XRT Prominence observed on 26 April 2007 by Hinode Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 48
  • III. Arbitrary selection of research papers• Labrosse et al., 2011 Line formed in the PCTR Line formed in the corona Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 49
  • III. Arbitrary selection of research papers• Labrosse et al., 2011 τ 195 = 0.3 − 0.6 Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 50
  • III. Arbitrary selection of research papers• Labrosse et al., 2011– Prominence plasma parameters obtained by comparison betweeninferred intensities and computed intensity at 256 Å Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 51
  • Further reading• Where can I look to learn more about solar radiation and plasma diagnostics?– ADS– Nuggets (UKSP, EIS, RHESSI, ...)– Rob Rutten’s lectures: http://www.astro.uu.nl/~rutten/Lectures.html– Physics of the Sun: A first course, by D. Mullan, CRC Press– Solar Astrophysics, by Foukal, Wiley-vch Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 52