Labrosse, N.

Li, B.

Li, X.

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The Lyman <span class='mathrm'>α</span> and Lyman <span class='mathrm'>β</span> lines in solar coronal streamers

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       Labrosse, N. and Li, X. and Li, B. (2006) The Lyman α and Lyman β lines in solar coronal streamers. In: Lacoste, H. (ed.) Proceedings of SOHO-17 10 years of SOHO and Beyond 7 - 12 May 2006, Giardini Naxos, Sicily, Italy. ESA Special Publication (617). ESA Publications Division, Noordwijk, The Netherlands. ISBN 9789290929284  http://eprints.gla.ac.uk/24809/  Deposited on: 28 January 2010   Enlighten – Research publications by members of the University of Glasgow http://eprints.gla.ac.uk THE LYMAN α AND LYMAN β LINES IN SOLAR CORONAL STREAMERSN. Labrosse, X. Li, and B. LiInstitute of Mathematical and Physical Sciences, University of Wales Aberystwyth, Ceredigion SY23 3BZ, UK, Email:nll@aber.ac.uk, xxl@aber.ac.uk, bbl@aber.ac.ukABSTRACTWe use the plasma parameters derived from a new global2.5D three uid model of the solar wind to compute theLyman-α and Lyman-β line proles. The emergent hy-drogen radiation is calculated by solving the statisticalequilibrium equations for a 10 level hydrogen atom +continuum along a one-dimensional line of sight. Wedo not make any assumption about the formation mech-anisms of the lines. We study the effect of Doppler dim-ming. We nd that the width of the Lyman-β line moreaccurately reects the plasma temperature than that of theLyman-α line. Thus inferred temperatures from Lyman-α observations should be considered as lower limits forthe plasma temperature. We also present calculations ofthe relative contribution of resonant scattering and colli-sional excitation in the Lyman line intensities.1. INTRODUCTIONWe perform radiative transfer calculations in non localthermodynamic equilibrium (NLTE) to predict the prop-erties of the hydrogen lines in the corona. A large amountof our knowledge of the solar extreme ultraviolet (EUV)corona comes from the observations of the rst two H ILyman lines at 1215.67 	A and 1025.72 	A. To infer thecoronal plasma properties from observations it is neces-sary to get the line proles with enough spectral reso-lution. From the knowledge of the line width one canderive the temperature of the hydrogen atoms. If the cou-pling due to charge exchange between hydrogen atomsand ions is strong enough, then the proton temperature isequal to the hydrogen temperature. In our case, this cou-pling is strong enough at densities above 106 cm−3, i.e.within the whole streamer.2. CORONAL RADIATIONThe coronal model is obtained from a 2.5-D global threeuid solar wind model with electrons, protons, and α par-ticles (Li et al., 2006). A hot coronal boundary, electronheat ux and Coulomb coupling lead to a non-isothermalstreamer in which all three species have the same temper-ature. The plasma properties in the streamer are shown inFig. 1 for two heights of the line-of-sight (LOS).We solve the radiative transfer (RT) equations and thestatistical equilibrium (SE) equations in NLTE for a 10level + continuum hydrogen atom. The velocity depen-dent boundary conditions for the RT equations are deter-mined by the radiation coming from the disk. The emer-gent intensity Iν(µ) at an angle θ = cos−1 µ between thenormal to the surface and the LOS is given by:Iν(µ) =∫ τν0Sν(t)e−t/µ dt/µ , (1)with τν the optical depth at frequency ν. Using the for-mulation of the equivalent two-level atom, the line sourcefunction is:Slν = ε∗B∗ + (1− ε∗)J˜ν . (2)ε∗ andB∗ account for all the processes that can affect thecreation and the destruction of photons in the transition atfrequency ν, introducing a non-local and non-linear cou-pling between the radiation and the plasma. The scatter-ing term J˜ν is expressed as:J˜ν =1ϕν∫ ∞0R(ν′, ν)Jν′dν′. (3)The incident radiation is given by:Jν =14pi∮I0(ν +ν0cV · n′,n′)dn′ , (4)with I0(ν,n) the specic intensity of the incident radia-tion, n′ the direction of the incident photon, and V theradial velocity. Jν is calculated at a given height, tak-ing into account the center-to-limb variations of the in-cident radiation. In Eq. 3, ϕν is the normalized absorp-tion prole of the line, andR(ν ′, ν) is the angle-averagedfrequency redistribution function. To compute the fre-quency redistribution function for all Lyman lines up to Proc. SOHO 17 – 10 Years of SOHO and Beyond, Giardini Naxos, Sicily, Italy 7 – 12 May 2006 (ESA SP-617, July 2006)  Figure 1. From top to bottom: np, Te, and vp at a dis-tance of 0.05 RS (left) and 0.88 RS (right) above thelimb, plotted against the location along the line-of-sightin units of the solar radius RS , where the origin is at thecentre of the LOS.Ly-9, we use partial redistribution in frequency (PRD):a linear combination of RII (well suited to describe thescattering of radiation in the Lyman resonance lines) andRIII (close to complete redistribution (CRD); also usedfor all other lines). We assume isotropic scattering. Theredistribution function RIII is taken to be equal to thecomplete redistribution function.A detailed study of the emergent radiation of hydrogenin the Lyman lines is presented in Labrosse et al. (2006)without taking into account the Doppler effect due to theradial motion of the plasma. The results presented in thefollowing section include the Doppler effect. Howeverthe conclusions are the same as in Labrosse et al. (2006).3. RESULTSFig. 2 shows that the decrease of the intensity with al-titude is more pronounced for Lyβ than for Lyα, a rstindication that they relate to the plasma parameters indifferent ways. We observe a strong coupling betweenLyβ and Hα: the ratio of intensities in these two lines isconstant with height. Hα photons can be absorbed andsubsequently lead to the emission of Lyβ photons.We t the computed line proles with a gaussian to obtainthe width and thus a temperature TH . As is clearly seenon Fig. 3, the width of the Lyβ line is a good indicatorof the plasma temperature. On the contrary, the temper-ature derived from the Lyα line signicantly underesti-Figure 2. Integrated intensities of Lyα, Lyβ, and Hα vs.heliocentric distance. Dotted lines: no Doppler effect(V=0).mates the mean plasma temperature and the temperatureat the centre of the LOS within the streamer base (below2 RS).From Eq. (2) we identify the rst term of the right-hand side with the collisional component and the secondterm with the radiative component of the source function.Fig. 4 shows that Lyβ is mostly formed by collisionalexcitation in the streamer. Note that the collisional com-ponent of Lyα is not negligible in the streamer base.4. CONCLUSIONThe width of the Lyβ line is a better indicator of thestreamer temperature than the width of the Lyα line. Itis due to the formation mechanisms of the lines, and thecoupling of Lyβ with Hα.From our NLTE radiative transfer calculations, we obtainnew estimates of the radiative and collisional contribu-tions of the Lyman line intensities in a non-isothermalstreamer. These new values may have some importancein the derivation of element abundances.REFERENCESLabrosse, N., Li, X., & Li, B. 2006, A&A, submittedLi, B., Li, X., & Labrosse, N. 2006, J. Geophys. Res.,111, in press, doi:10.1029/2005JA011303Figure 3. Temperature derived from the width of Lyα, Lyβ, temperature at centre of LOS (solid line), and mean tempera-ture (dashed line), vs. heliocentric distance. Dotted lines: no Doppler effect (V=0).Figure 4. Relative contribution of the scattered (solid line) and collisional (dotted line) components for Lyα and Lyβ vs.heliocentric distance.

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The Lyman <span class='mathrm'>α</span> and Lyman <span class='mathrm'>β</span> lines in solar coronal streamers

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