Key Properties of Solar Chromospheric Line Formation Process

Chin. J. Astron. Astropbys. Vol. 2 (2002). No. 1. 71-80Chinese Journal ofAstruoiny andAstrophysics .Key Propen:ties of Solar Chromospheric Line FormationProcessZhong-Quan Qu* and Zhi XuPI AY'unnan Observato:y, Chinese Acaderny of Sciences, Kunming 650011、ational Astronomical Observatories, Chinese Academy of Sciences, Beijing 100012Received 2001 June 23; accepted 2001 September I:Abstract T'he distribution or wavelength-dependence of the formation regions offrequently used solar lines, Ha, H3. CallH and Call8542, in quiet Sun, faint andbright flares is explored in the ipolarized case. We stress four aspects character-ising the property of line fornation process: 1) width of linc formation core; 2) lineformation region; 3) inAuence of the tempcrature minirnun region: and 4) wave-length ranges within which one can obtain pure chromospheric and photsphericfiltergrarus. It is shown that the above four aspects depend strongly on the atmo-spheric physiral condition and the lines used. The formation regions of all the wave-length points within a line may be contiruously distributed over one depth domainor discretely dlistributed because of no contribution coming from the temperatureminimum rcg on, an importanl domain in the solar atmosphere that deternines thedistribut ion fattcrn of escape photons. On the other hand, the formation region ofone wavelengl h point may cover only onc height rallge ur spread over two domainswhich are sep nrated again by the ternperature minimum region. Diferent lines mayform in diferent regions in the quiet Sun. However, these liue formation regions be-come closer in. solar faring regions. Finally, though the stratification of line-of-sight.velocity can ;.Iter the position of the line formation core within the line band andresult in the iasymmetry of the line formation core about the shifled line center. itcan only lead [o negligible changes in the line formation region or the line formnationcore width. All these results can be instructive to solar filt ering observations.Key words: line: formation - radiat ive transfer Sun: chromosphere1 INTRODUCTIONThe goal of investigating the line formation theory related to contribution functiou (CF) liesin the interpreting .nf the observed datia. T nfortunately; such an application was misled to thediagnostics o[ atunopheric physical parameters without a solid basis cstablished for identifsingthe line formation depth and the 'measurernent depth' for a special measurement (Ruiz Cobo. E mal: zqqu@cosmos ynao.ac.cn中国煤化工MHCNMHG72Z.Q.Qu&Z.Xu.et al. 1994; Sanchez Almneida et al. 1990: Qu & Gu 1999). However. this does not nuean thatthe theory has nothing to do with the observations. In fact, it tells us the place where theescape photons originate arnd thus supplies a useful tool to interpret the fitergrams oftcn usedin solar physics. In this paper, we emphasize this application and show what conclusioins cealnbe drawn fror1 the cxploration and try lo give al instruction to the solar filtering observntionswith frequent y used 'chromospheric lines'.In our two previous papers (Qu et al. 1999. Paper |: Qu et: al. 2001 Paper II: andhereafter), Wl introduced the concept of 'line fornalion core'. defined it as one wavelengthinterval containing the line center, within which all the escape photons come from such regionsthat are phys ically identical, and pointed out that this forrmation region can 1ost suitablyrepresent the line formation region because of the following features.1) Within the line formation corc. the energent line photons conne frorn the iomnain whichwe call the *li:te formalion region': It should be noted that this term does not mean that all thewavelength points within the line are formed in this region, it only means the formnation regionof all the wav:length points in the“line formation core" :2) The line formation region defined in this way is located in general at the highest al-mospheric layers that deviate farthest from the thermodynamir cquilibrium (TE). when themagnetic fielc is absent or has lttle infuence on the line formation process. Only if the linesplitting take: place at the line center due to the presence of magnetir field, can the linc for-mation core disappear and does the line-center formation region no longer contains the highestlevels (see Paper I):3) The de pth coverage of the line formation region deduced from the above definition isgenerally more sensitive to the variation of atmospheric thermodynamical condition than theformation reg ons of the other wavelengths within the line.4) Neither the width of the line formation core nor ilts formation region is serusitive t tlestratification >f the macroscopic line-of-sight velocity. but the formation regions of its 1leigh.boring wavelength points are often more influenced by velocity.In this paper, these features can also be found in the line formation process of four othersolar chromospheric lines. than the Mg15172.7 line observed in Paper I.Generally speaking, four aspects outline the property of line formation process for the solarchromnospheric lines. They are: 1) the width of the line fornation core; 2) the line formnationregion; 3) the inAuence of the temperature minimum region; and 4) the wavelength rangeswithin which one can obtain pure chromospheric and photospheric filtergrans, respetively. Inthis paper, we will focus on their dependence on different atmospheric conditions and try to givean answer to isues such as whether one can observe all the layers froni the line formation rcgionto the farthes1 wing formation region using the line-center and of-line-center filtergrams of oreline. As will be shown, this issuc is tightly linked to the contribution from the temperaturemininum region to the emergent line photons.2 CONTRIBUTION FUNCTION, MODEL ATMOSPHERES AND CALCULA-TION OF LINE PARAMETERSAccording to our previous work (Qu et al. 1999), the cmergent intensity can be expressedaI,(0)- Ek=CFn，(1)where the contribution function to the first-order derivative terin of the total source fiunetion中国煤化工MHCNMHGKer Proper! ies of Solar Chromospheric Line Formation Processs73with respect to the optical depth readsCF(n)=e-7-[(1-<←2n 1)S(n)-(1--57.- 0n-185(02] .drin the above cexpression k denotes the grid number. The definitions of the other symbols canbe found in Paper I.Equation (1) lugether with Equarion (2) suggest thal the contribution from each layer to theernergent intensity originates froun a weighted source function and its weighted depth variationalong the line of sight. The weighting functions consist of two factors. One is the attenuationfactor and the otler a modifying one due to the thickness of the layer. For cxamplc, t.heweighting function for the zero- order termise 7-1(1-e:-ATe-1). If the thickness△Tk-1 is verysrnall. it tends toe-Tk t△Tk- 1, and the term containing the factor becomes c-T 1SfOTk1 ≈e-T-1 S,dr.Three surface eatures of solar atmospheres are selected here. They are the average quictSun. a faint flare and a bright flare. The average quiet Sun model atmosphere comes fromModel C (with 52 grids) of Vernacca et al. (VAL-C,1981) but with a lttle modification of 47more grids interpolated and extrapolated by smoothing curves of each parameter. T he two flaremnodels originate fr om Model F1 (with 37 grids) and Model F2 (with 32 grids) of Machado ct al.(1980), but also with 62 more grids for Model F1 and 67 more grids for Model F2 interpolatedand extrapolated .u the same manner. Thus 99 grids in total (with grid number ‘n = 1'representing the u1pernost layer and 'n = 99' the lowest layer of the nodel atmosphere) areset fur each of the threc models, and the geomnetric height ranges are from (-75 km, 2543 km)to (-96.05 km, 2100.03 km) for the average quiet Sun model, and from (100km, 1459km) to (-38.12 kn.1461.76 km) for the Model F1 and from ( 75 kmn, 1120 km) to ( 69.29 kmn, 114.80 kin)for Mlodel F2.Figure 1 ilustr xtes the temperaturc and electron number density stratlification of the threcmodels. Comparing with VAL-C (solid line), F1 (dashed linc) and F2 (dotted line) have nar-rower low tempera .ure regions and low density region under the transition region. In contriastto the tenperature enhancernent at the top layers of the flarc model atmosphores, the electronderusity drops very rapidly at the transition regions after a lift in the uppermost levels of thechromosphere.We adopt Ha. H3, CallH and CalI8542 lines which are frequently used in the diagnostics ofthe chromospheric :structures. These lines are often called 'solar chromospheric lines'. However.one should remember that this term needs to be more delicately defined, because not all thewavelength points within these lines are formed in the chronosphere, and their line formationregions depend strc ngly on the thermodynamical conditions. For example, HB, as shown below,formed in quiet Sun is not a pure chromospheric line, because there is a significant cont ributionfrom the photosph:re to the emnergent photons of the line formation core and in the Aaringregions. its formati on region may contain a part of the lransition region.The calculatior. code of the line parameters, ie, damping constant a, Doppler width Oλp.line-center and cou inum absorption coficients xI and Xc, as well as lincenter and continuumemission cefficients jn and jc, is that proposed by Ding and Fang (1989). They consideredatomic structures including 12 energy levels plus onc continuun state for hydrogen and fivelevels plus one con ;inuum for once ionized calcium. The relative abundlance of Call is sct at2.14x 10-6 at eact depth grid.中国煤化工MYHCNMHG74Z.Q.Qu&Z.Xu16 p15 I5.595:F。13E4.5 tQuiet SunIFI12 EFQuiet Sun3.5-500 050010001500 2000 2500 -500) 500 1000 1500 2000 2500h (km)Fig.1 Su.mple stratifcation of teinpcraturc and electron number density of model atmo-spheres. The solid lincs indicate those of the model of the quiet Sun (\AL-C). the dashedincs the faint flare (F1) and the dotted the bright flare (F2).3 FORMATION REGIONS OF Ha, H3, CallH AND Call 8542In the following, the formation properties of Ha, H3, CaltH and Call 8542 are cxplorcd inhe quiet Sun, faint Aare and bright Aare model atmospheres respectively. According to thisschedule, the :ormatiou properties of difTerent liues in the sarne mnodel atinosphere are easilycompared. Ho.vever. we will also pay enough attention to the variation of formation regions ofcach line in th: three different atmospheric conditions. We give the detailed information aboutthese four lines in the following Table 1. The infuence of line-of-sight velocity is left to thelater part. of this sect ion.3.1Formation Regions in the Quiet SunThe distributions of formation regions of wavelengths within Ha, H3, CallH and Call 8542:an be found in the sample curves in Fig.2. One of the 1ost striking phenomena is that fewescaping Ha or H3 photons arc produced in the region (480 km, 600 km) containing the tenper-ature minimnul I levels, while fromn this region there are a great urnount of CallH photons withwavelengths near |O入| = 280 mA escaping into space, and a not negligible amount of Call 8542photons with wvavelengths ranging from 180 mA lo 250 mA. This indicates the difference be-tween the two lines and means that in the quict Sun, one cannot observe the temperatureminirnurn regicon via Ha and H3 filtrgrarms, no Inat ter how wide the bandpass is and where itscentra! wavelength is located. However, it can be seen clearly with filtergrans of CallH if thebandpass is pluced within the band from 180 mnA to 400 mA. When obscrving H3 formation inthis surface fea ture. an unusual phenomenon can be noticed that it is not a pure chrornosphericline. Even in he line formation core (|O入| ≤40mA). the photospheric layers just below thetemperature ninimun region contribute sorne escape photons (see the solid and dashed linesin the H3 patel of Fig.2). This mcans that the filtcring observation using H3 line cannot中国煤化工MHCNMHGKey Properties of Solar Chronosplheric l.ine Forrnation Process75vield pure chromospheric images, though the photospheric ingredient is relatively faint whenobserving within the line forrmation core. That also tells us. as an ilustration, that it is notsuitable to assign a formation depth to a line when the formnation region contains two separatoddomains. This is the reason why we do not generally xssin a formnation depth to a line.3E-0061.8E 006(a) Hu . Quiet Sun(b) H - Quiet Sun1.6E-0062:5E-0061.4E-00610002E-0061.2E-006661E-0061.5E 0065 8E.007056E-0074E-007805E-0074202E-007-5E 007-2E-007-500 0~ 50010015002002500-500500 1000 1500 2000 2500h (km)2.5E-0063E-007(d) Call 8542-Quiet Sun(C) Call H-Quiel Sun25E-00716101.5E-0061.5E-00760占1E:0061E.007100/i 1405E-00830-5E-007-SE-008-500 0 500 1000 1500 2000 2500-500 05001000150020002500Fig.2 Furmation region distributions of sarmple wavelength points within the lines IIa (a), .H3 (b). CallH .c) and Ca118542 (d) in the quict Sun. The labels for each curve indicate thedistance from line center in mA. and the same are uscd for the following figures. All the CF'sare drawn on the geometric depth scale, the unit is ergcm -2s -↓sr -1 Hz一, and hereafter. Thegreatest umbe" labelling the curve in each panel gives the adopted farthest distance from theline center. Sane for the following figures.3.2 Formation Regions in the Faint FlareIn solar faring; region, the concavity of temperature curve lends to be narrower. Approach-ing the transition zonc, the temperature gradient becomes very great. Mealw hile, the electrondensity variation turns out to be stccper in the middle and lower layers of the chronnosphere andit rapidly decreases in the thin transition region (see Fig. 1). Corresponding to the atmospheric中国煤化工MYHCNMHG76Z.Q.Qu&Z.Xu.variation, the I nes bccorue emmission lines (cf. fig. 26 of VAI. and fig. 4 of Machado ct al. 1980).The most striking difference in the line formation regions in the solar Aare is that they'beconne very narrow (see all the panels in Fig.3). For example, the line formation regionl ofHa is markedly compressed from 993 krm to 11 km. This signifes that the filtering observationwithin the line formation core will give an imagc of very thin layers which can never be acquiredin the quiet Sum regions. Comparing with the formation regions of the other wavelength points.the depth cover age of the line fornation region is the imnost sensitive to the variation comnparingwith other wavelength bands, as we point out in Scction 1. The line formation regions of thefour lines arc c oser to each other. a pattern very different from t.he quiet Sun.3.5E-0062.5E-006Hu-F182011B.「13E-0062E-00625E-006| I 15000.1201.5E.00628台1.5E-0065 1E:0061E-0065E 0075E-00760525)0F-5E-007_-200 0 200 400 600 800 1000120014001600-200 0 200 400 600 800 1002001001600h (km)4.5E-0061.8E-006CallH- FI4E-006(all8S42 .FI1.6E-00635E-0061.4E-0063E.0062001.2E-0062.5E.0061314片2E-068E-007、201.5E-00606E-0074E-007、562E-007:00/610:2E-007200 0 200 400 600 800 1000120014001600h (hm)Fig.3 (F c Irves of sample wavelength points within Har, H3, CallH and ('a118542 lines inthe solar fainl. flare case. It is very marked that the line fornuation regions uf the four lincsare much clo:er to each other than in the quiet Sun. Note that the distribution pattern offormation reg ons of wavelength points within the two ionized calcium lines is critically chaugedwhen conpar:d with t.he quict Sun case.中国煤化工MYHCNMHGKey P'ropertics of Solar Chrounospleric Line Fornation Processs73.3 Formatiorl Regions in the Bright FlareFew critical changcs takc place in the bright faring atmosphere conupared with the faintAlare case. though much more energy is released in the latter (see Fig. 4). The most outstandingvariation occurs i1 the line formation cores of Ha, H3. and Call 8542 lines which arc simultanc-ously broadened due to their increased Doppler widths. Table 1 shows that their formation corewidths are broadened almost by a factor of two in the bright Aare than in the faint flare case.The line formatio 1 regions of these four lines are further compressed into several kiloreters. andtheir locations as well as depth coverage become further closer to each other. This indicates thalthe filtering observations with bandpass within the line formation cores of these four lincs willgive almost the sime features of the thin layers of trausition region. In the line-center filteriugobservation. the flare looks like a thin cloud over the background of other surface features. Notonly are the line formnation regions compressed, but also the formation regions of some otherwavelength points. For instance, see |Oλ| = 660 mA curve of Ha, |△λ| = 280mA curve of IH3,|A\| = 140mA curve of CallH, and |△入| = 130 mA curve of Call 8542, and conupare with theircounterparts in Figure 3. .1.4E-0051.2E-005Hx-12.Hβ-F21E-0058E-006840^6E-006台台6E-06444E-0063000080.2E-0062E-006 F 2000006∞15220200083080100000-2E-006-200 0 200 400 600 800 1000 1200h (hm)18E 0057E-006CallH F21.6E.005 Call 8542-125E-0061 2E-005片14占8E-00630|3E:0002E 0062804E 0061E-006601000)-2E-006 E0 0 200 400 600 800 1000 1200h (km)Fig.4 CF cur\es of sanple wavelength points witlin Ha, H3, Call and Call 8542 lines formingin bright flarc. Note that the line formation rcgions of the four lines approach cach other closerthan in the fuint case.中国煤化工MYHCNMHG"82.Q.Qu&Z.Xu3.4 Summary'll'e diseuss in detail the forniation properties of the four lincs annd uarize the abuveresults in Table l where the 7 columns list the spectral line. nodlel ai losphere. line fornationcore width in urit of mA: linc formation region in unit of *km。wavelength range in unit ofmA lused to obt.in the diferent filtergrams of the to'mperature uininum region (labelled byRange 1). imagc: of the pure chronosphere (abelled by Range 2) aund pictures of the pure: pho-tosphere (labelle i by Range 3) respectively. In Table 1, "QS, F1. F2' denote the quier Su21. faintHare and bright Harc. respectively, and "none' indicates that there is n0 wavelength points sial-isfying the obser vational requirement within the line band aulopted. The latter live paranetorsrefAect the most umportant line fornation properties in the sample model atnospheres.Table 1 Form ation Property of Ha. H3, CallH alld Call 8542 in the Sample Model AtnospherrsLineMode Fornation CoreFiornationWavelengthWavelength WavclengthI'sed Atmosplere Width (mA)Region (km)Range 1 (m八)" Rangc 2 (mA) Range 3 (mA)QS210(1107. 2100)|1X|< 240J入之66(HaF1(1426. 1437)none1o11F2720(1097. 1100)one9008(223. 444)(617. 2091)380H3(1378. 1437)nfome280locul320(1095. 1100)440nong6(1473. 2098)(180. 400)120nondC'aitH4((1419. 1433)(610. 1000)nonc6((830、1000)8((1050. 1945)Calu854260(1319. 1431)(280. 580)220[1090. 1098)(360. 1000)112* in this colunn. the symmctric wnvelength intrval to the listrd in the bluc wing also belongs to the ralnge[t should be pointed ount that the values in Table 1 are only drluced from the acceptedmodel atmosphe:e. They are merely reference values alld furthermore only refer to the staticat mosphere.In the above situations, we do not consider the stratification of the macroscopir line. of-sightvelocities. In actual situations, it always exists. Therefore one should lake il into accounl. Asevridenced in Par er I, though the stratification could change the position of the line formatiocore of AIg15172.7 and cause the asymmetry of the line core about the shifted line centerin the model atnosphere of surnspot umbra. it has litle inftence on the core width or theline formation rngion. On the other hand, it does cause changes of the formation regionsof some other wavelength points. For instance. at Aλ = - 150 nLA, the concavity coveringthe temperature minimum between the two major fornation regions in fig.3 (a) of Paper I .disappeared in fi5.4 of the same paper.To investigatc the influence on the distribution patern of formation region of these fourlines. we also set some line of sight velocity (Vo2) stratificatio, li all the cases. thte velocitydistribut ion does not alter cither the width of the line formation core or its formation region.t hough its wavele ngth range is generally shifted with the drift of the line center. The wavelengthcovrage asynmtry of the line formation core about the shifted line center generally occurs.中国煤化工MYHCNMHGioy I'ropertics of Solar Chronospheric Line Formation Processs79Furthernore. the distribution patterIls of the fornntion rogions of all the wavelength pointswithin four lines in the three model atmnospheres are little affected.4 DISCUSSIONWe have explored the distribution or wavelength-dependence of the formuationl regions ofwavelength poirts within the frequently used solar chrunosphteric lincs, Hn, H;, CalH andC'a118542 in the cases of the quiet Sun, faint and bright flares. We find that the tern solarchrornospheric l ne should be carefully treated. For even the line formation core. like H; in thequiet Su, the pholospheric layers contribute no negligible escape pholons. and in the bright.Haring regions it can form in the trarisition region. Though only four lines are studied in thispaper. the situation can be applied to other lines. For exarnuple, the dist ribution of format ionregions of wavelrngth points of CallH is also suitablc for that of CalK line, because they haveclose atomic paranmeters. The distribution of Call 8542 call be applied to that of bor h CaJI 8498and Call 8662 lincs.[t is found that the liue formation core is a useful concept in the investigating of linefornation property. It is an entity to divide the line band when considering the line fornationprocess. Its wavelength width annd formation region are little affected by the stratification ofthe line-of-sight velority. and only when the Ilagneto-induced line spltting occurs at the linecenter does it lcse its presence (ser Paper II). Furthermore. we have reached the point that ifone wants to gr usp the property of line formnation, the four aspects investigated above shouldbe considered.'e have setu that the formation regions of differenl lines respond to the variation in at-mospheric conditions with dilferent sensitivity. First, the broadening or conpressing of the lineformation core e.nd linc formation region display dillerenl sensitivity to the variation when theline format ion rgions consistently tend to be shallower and narrower in flaring processcs. Thedepth coverage of the line formation region is generally Inust sensitive to at mospheric physicalchaunge. But this does not mnean that the formation regions of the other wavclength pointswithin the line d not respond to the variation. Rather! For examplc. the situation has beenlmet that sornc v'avelcngth point forms il the photosphere in the quiet Sun bul its fornlation rgion is located 门n the chrolosphere in the flare case, like |O入| = 660mA of Ha. |Aλ| = 440 ImAof H3. Sorne We velength point forms in both phutosphere and chromosphere in the quiet Sun.like |O入| = 42CmA of Har. but its formation region covers only the chrornospheric layers incase of bright fl ure. Mlore examples can be found, siuch as the variation in fornation region of|AX{ = 280mA of H3 froni the quicet Sun to the faint Aare. Sorme wavelength points forel inthe ternperat urt minimum region in the quiet Sun. bnt its main contribution conmes only fronthe chromosphere in the fAares. like |△λ| = 280mA of CalHI. Furt bermore, cven within onelinc under the sarne atuospheric variat ion, the formation region of one wavelength point Ilay"be extended wt ilc another one may be counpressed. On the whole. though the lernperat lurestratification is not the uriquc ingredient to determine the dlistribution, it is the most inpor-rant factor affec ting tlte linc fornation property. Especially, the temperature miniuurn regionplays a eruciai role in these chromospheric line formation processes. Arcording to whether thetemperature mi nimum contributes siguificauntly to the escape line photons, the dist ributions offormation regions of the wavelength points within the chroniospheric lines can be class ified intorwo kinds. One contains a significant contribution from the temperature Ininimnun region andthe ut her dors 11ot.中国煤化工MYHCNMHG80Z. Q.Qu& 2. X11Frorn the account above. the distributions of the fornation regions of the two hydlrogen linesbeloig to the fir:t kind and those of the two ionized caleium lines to the second one. llowewer.the 'los stratificr tion rmay change one kind to another. as evidenced in .IgI 5172.7 studied inPaper I.Acknowledgerr.ents This paper is sponsored by Ilem 19973016 of National Science Founda-tion of China and National Major Project 973 under the grant G2000078401. The authors ;aregraleful to Dr. MI. D. Ding for his genereous supplying the line pararmeter calculation.ReferencesDing M. D.. Fang C.1989, A&A.225, 20.1.Mlachado M. E, Avrett E. 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