Matsushima, Satoshi

Miyamoto, Shotaro

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RIGHT:URL:CITATION:AUTHOR(S):ISSUE DATE:TITLE:On the Ultraviolet Radiation fromthe Solar Corona (II)Miyamoto, Shotaro; Matsushima, SatoshiMiyamoto, Shotaro ...[et al]. On the Ultraviolet Radiation from the Solar Corona (II).Memoirs of the College of Science, University of Kyoto. Series A 1949, 25(2): 63-671949-10-30http://hdl.handle.net/2433/257316                                             '                                   '        Memoirs of t•he College of SLeience, Univers{.ty of Xyoto, Series A,                  Vo}. XXV, No. 2, Artiele M, 1949.            On the Ultraviolet Radiation from                   the Solar Corolla. IIz•                       • By         $hetare Miyamoto aRd Satoshi Matsushima.de                      (R-eeeived April le, 1947)                                     'g 5. fonis'cttion of JXeL Denote by Bic the absorption coefficientfrom the grouRd level 1 of HeJto thecontinuous level c. We assunieit to be equal to the vaiue at the series limit with the effective rangedv. Then we can• write'i                                "n                      '5'ie :7]#c9,"iti" ,f' (5,Din whichf== 1.55 ancl U, == 9.75Å~10Z5. '    Let .tlci ancl .B,i be the Ei.nstein coefficients for the transition c ---> 1.eTqli ueSi'b;ltfi]3aVe) by the well"rknown consideration of therniodynamical                                                   '       iliif = 4(21' W]iK,"rl7)31fi ,.=1,, =: o,B,,d, , 6, =:2Ze',V,3, ' (s,.g)where T means the electron temperature of the chromosphere. We8?3oitiosSS eelge'.aSsume it to be equai to the effective temperatufe of    Let Ne, N and N" be tke particle density Qf electron, He 1 andHe 21 respectively, and Jv, the meaR intexxsity of the coronai v-radiation.Then, th'e eguation of ionization is g{ven by      ' a\eN"9Aci =: NBiet71vdv, ' (•5,3)where'we have introduced the factor g in order to include the captureto the excited levels. This becomes, by using (5,9"),                     -ZVZN" nd 4(27r7nkT)S12' '''' N- ghC'a, Jl"' (5,4)    As for J•,, it changes with the clepth, since the chromosphere' isnot transparent to the coronal radiation. We shall- first calculate theoptical depth of the chroinosphere. The optical depth at the height gis, by eefinition,               - ee•rept.                     s '-64 Sltotaro llityamoto a7?d Satoshi 2ifatsushima.                           co -                      T == S4'lll BicAr (-") a.c '. ' (s, s)                           x•                     ptti . •    Following A. Uns61d"', assume the density distribution of the lowerchro:nosphere to be of the form: .              xN(fi) == A' (O) (O.982e""ctZ + O.O18e-'di'Z) , (5,6)            a -' 5.9 Å~ 10-"Scm-i , a' =:2.6 Å~ lo-Scm-i.    We shal1 first consider A'(fi) to be the particle clensity of the totalgas, or practically that of hydrogen. It is not known exactly. In thefollowing, we shall treat three cases: logN(O) :16, 15 and 14. -HTeabundance is also not known accurately. Using Payne's estimatione,from the steilar data, we take for the !ogarithm of the reiative abttn-dance of He to H to be -2.7. Thus, we shall consider for .EITe thefollowing three cases: logAT(O) == 13.3, 12.3 and 11.3.' '    As wlli be seen iater, EIe ionization is weak throu.crhout the chronio-sphere, so that we can consider (5,6) as the distribution of He 1.The optical depth ,(5,5), is then expressed by this a.nd (5,1) as foHows:              r == til,:,,l21;;j`A'(o)(O'9.. 82e-att + O'2,i&e-th'")• (s,7)VVrith this foymula we find for the opticai thickness n. :1500, 150, 15,corresponding to Iog .ZST(O) x 13.3, 12.3 and 11.3 respectivelJr.    Coronai radiation .wi11 be absorbed or scattered in the claromosphere.Ift place of the exact treatment of the probiem, we shail consider twoextreme cases : Ramely, the case of pure absorption and of pure scat--tering. As is easil•y seexx by the rough estimation, the probability ofde--excitation from the excited level of Hel by the electron collisionis la:rger thaR that of ionization anf3 capture. Therefore, the actuaicondition in the chromosphere-may be neai' to the case of pure absorption.    Xn the case of pure absorption, we have at once                                                     '                          ,1,1=,]r,*e"r, (s,s)      'while in the case of pure scattering, it can easily be shown that                                         '                      ,J,1 == ,T,*(5 -. 2e-r), (5,9)     'where we have denoted by Jv* the mean intensity of incident coronal  g 6. The ionization formula (5,)3) coniblned with (5,8) becomes                       '                                tt                                    '                    tt                     Ai'AA.'" :3.1Å~lo5e-'. (6Jl)I•+E(.) decreases withrv(s), while at the deeperlayers,.it again decreases,since the coronal radia-tio.R is weakened rapidlyby the absorption. E(.")thus takes a maximum atcertain height.    Inte.crrating E(Åí) tethe line of sight, we ob-tain the guantity directlycomparable to the. inten-sity of the flash. Thelieavy curves itt Fig.1represent the result ofintegration. The height ofthe maximum is shift--ed scarcely, but thereremains a considerableorder of intensity evenat the base .t -- O.    A. ?annekoek andM.Minnaert7 have ob-served that the He inten--             Z>'lt7•aviolet Radiattio7z fro7n thee golar aorena. 65I'n the numerical caiculation we have taken g = 2 and Te = 10('. Assumethat the distribution of the free electron foilo"rs the law (5,6), withCillie' ancl Menzei's estimatioR2 A',(O) -ww4Å~ 10iicm`'3 at the'base.Then, for .Ak .v 109cm'-e and e-'Nl near s• =: 10eOkm we have.zsgr+/N :3 >< lo"4. . .    Population N' ef the excited levels are connected wlth tke ienizedievel by the usual Saha formula: •                                                     '                        bleN"                              me .lrNT(7T). • (6,2)                          .LNt .            'Observed He spectra are emitted by the scattering of the photospliericr'adiation. They are thus proportionai to 2V' and hence to -ZNrJry, ac-cording to (6,2). Three Iight curves in Fig.I i'epresent the quantity                                .LNT (x) -. '                                    e, (6,3)                        E (,c) =                               .LTYT (O)for logN(O) ==13.3,12.3 and 11.3 respectively. At the great height,fi.S,geeleeereeotfiici:kv  le"k•ss2ae"(o]eb?l.e eFig. 1          e.rJ 1.0 Jibnyht Curves : E(Ner1)o,-ijcale unlt 2.x JO-G, 10--3 andheavyeurves : Integrated quaqtity, seaie unit 10km, 100kma and leeOkTn, eaeh for logN(o)=13.3, IE .3 and 11S respectively.66 Shotaro 21fi•yr a7ngoto and Satoshi le31atszt,shima                                                              t/             'sity in' c' reases with helght and first above "v 1000km it begins to decrease.Appearance of the maximun} is also observed by E.J. ?erepelkin andO.A. MeinikovS in Dt}-Iine. Theoretically, the maximum place' is afunction of Åíhe chromospheric density. It occurs near 1000km for1..cr N• (O)=12•3• ,''  So far, we have negtected tlie absorption due te the neutral                                                               'h}rdrogen. It must be taken into account for the lower chromosphere.The absorption decreases rapidly with increaslng hei.crht, since thehydrogen begins to ionize. Consicleration of this effect will not chanty.eour cenclusion.    In the case of pure scatterin'g, coronal radiation takes a constantintensity throughout the chromgsphere. ConseguentlJr, there appearsno maximum. VV'hen the hydrogen absorption is effe'ctive, coronalracliation will be weakened in the lower chromosphere .and again wecan expectamaxlmunL . .  g 7. Cro)zeent-},cetion of tlt,e exz`eltecg ctto?n. We shall make some estimation•about the absolute clenslty of the excitecl He atoms, whicl} can becompared with those deducecl from the fiash observation. At t-heheight -v iOQO I<ni ancl for lo.cr .LV'(O) -- l2.3, we have, as 'before,log -.?lt""/-,N' == -fi5. il)NIext, by (6,.O,) with Z == 4.74el•' for the ionlzationpotential from the e.xcited level, we have log A?V""/ATV'i = 6.5. Therefore,log A7- '/A' =: -10 ane with log ..ly' -ww 10, we have N' .v 1 cm-3. .Thesefigures are in acc,ord with observation in their oi"der of magnitudes.  g 8. Io?ii.recdio)b of ffe]L Ionization forniula for -Elle Jlcan be writtenas                                      '                   27X71,N++cl +A,1 = x"ir+tZE/el,,7',d, , (8, 1)where J," is the mean intensity at the liknit of llelJ ionizationZ= o"4.14el•r and other notations are parailel to (5,3). . .    The probabi!ity of absorption per sec per atoni is g{vexx by     ac•fvdv == !iB, i,(v)J.dy, B,,(v) = 3.?;.7;."3 "},Zh;.e,,ie•(z :2)                                                   t.                                        . (8,2)Coronal intensity ,f, is given by (4,1). Introducing it into (8,2), we                                           oo ,•             .B,,.]-,d,==2",7.rlll)If{{ii";,IOfii,(ki'I,)3!fi3.llgd•a: . (s,3)                                          hVefKTe             Ultraviolet Ra(liation tlj-om the /SfolaT Corona. 67For the capture probability, we have                                                 '                              '           Aci == (6`9"lllilil//i,i ..ii31'7I,E3 (lil}.Z)"i:" Z`ic•S'ilV i,i,"Ei (f,?lili.LIV,) ' (8,4)    Using these expressions.and tak'ing g" == .9., Te tr= 10e, IZi = 5600,we get for (8,1),                     Nepai>'."" ,,,. 2.1Å~ le". (8,5)    Owing to its small concentration, lle7fis transparent to thecoronal radiation near 54.14eV, but it wiil be weakened in the lowerchronaosphere by the absorption due to IIe J and Ile ll.    )t4-686 of -li(.ell is emitted by the capture. Its inteRsity ma>r beproportional to Ai,AT'", which, in turn, is proportional to N" b>" (8,5).According to (6,1), xTV'" is preportional to N/zV, at great height.Thus, a 61ow decrease of )L 4686 with increasing height can be expected,in accord with observation.    In g4, it has been shown that the contact temperature raises toT == 16500 at X -- 54.14eV. If we make the formal application ofSaha's formula, we intist take Åë(54.14eV) -- Z5040/T == 16.5. Thisis in agreement with the estiniation 4? == 15.67 derived by A. Uns61clfrom other directions.9    lnstitt{te of Ast"'opliysies,    Uni•ve?•.s-ity oJ' Jfyoto, Jlcepaan.    9 A.7)"r'il- 1947.         - Referencesa• 3, P. Vinti, Phys. Rev. 44, 52• `1 (1933).5• A. Vns61d, Physi}< der Sternatrnosphttre, (193S) Kap. XVII, 98.6. C. H. ?ayne, Stellar Atrnospliere, (18"215),7. A. PanneX-oek and M. Minnaert, Verh. Akad. W'etensch. An}sterd. (Sect. 1) 13, Nr• 5  (1928). Cf. also, A. Uns6}di, ?hysik der Sternatn}osphttre (1938) I<ap. XVII, 98.8• E. J. Perepe}k'in and O. A. Me]nikov, Pulkovo Bull. 14, Nr. I22 (19.,",-5). Cf. a]so, A.  Vns6Id, loc. eit.9L• A. Uns6Id, Physik der Sternatrposphi're, (19i S) K{ p. .XVII, 97..

On the Ultraviolet Radiation from the Solar Corona (II)

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On the Ultraviolet Radiation from the Solar Corona (II)

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