Astronomy&Astrophysicsmanuscriptno.aa26489 (cid:13)cESO2016 Thursday14thJanuary,2016 H-alpha features with hot onsets. I. Ellerman bombs R.J.Rutten 1 LingezichtAstrophysics,’tOosteneind9,4158CADeil,TheNetherlands 2 InstituteofTheoreticalAstrophysics,UniversityofOslo,P.O.Box1029,Blindern,N-0315Oslo,Norway ReceivedMay7,2015/AcceptedJanuary13,2016 ABSTRACT EllermanbombsaretransientbrighteningsofthewingsoftheBalmerlinesthatuniquelymarkreconnectioninthesolarphotosphere. 6 TheyarealsobrightinstrongCaiiandultravioletlinesandinultravioletcontinua,buttheyarenotvisibleintheopticalcontinuumand 1 theNaiDandMgiblines.ThesediscordantvisibilitiesinvalidateallpublishedEllermanbombmodeling.Iarguethattheassumption 0 ofSaha-Boltzmannlower-levelpopulationsisinformativetoestimatebomb-onsetopacitiesforthesediversediagnostics,evenand 2 especiallyforHα,andemploysuchestimatestogaugethevisibilitiesofEllermanbombonsetsinallofthem.TheyconstrainEllerman bombformationtotemperatures10000–20000Kandhydrogendensitiesaround1015 cm−3.SimilarargumentslikelyholdforHα n visibilityinothertransientphenomenawithhotanddenseonsets. a J Keywords. Sun:activity–Sun:atmosphere–Sun:magneticfields 3 1 1. Introduction These diverse EB visibilities and non-visibilities invalidate ] R the EB modeling published so far. Kitai (1983), Berlicki et al. SEllerman (1917) discovered intense short-lived brightenings of (2010), Bello González et al. (2013) and Berlicki & Heinzel .the extended wings of the Balmer Hα line at 6563Å which (2014) performed Hα synthesis from best-fit ad-hoc perturba- h are called “Ellerman bombs” (henceforth EB) since McMath tionsofastatic1Dstandardmodelofthesolaratmospheretore- petal.(1960)or“moustaches”aftertheirrediscoverybySeverny produceobservedHαwingbrightenings.Thesemodelingefforts - o(1956).TheextensiveEBliteraturewasreviewedbyRuttenetal. weresummarizedinPaperIVtogetherwiththeirfailures:non- r(2013).RecentstudiesarediscussedinVissersetal.(2015).This reproductionoftheobservedphotosphericanchoringofEBsin t spapertreatsEBvisibilities. internetwork lanes (Paper I), non-reproduction of EB brighten- a inginIRISSiivandCiilines(PaperIII),andnon-reproduction [ BelowIreferfrequentlytoaseriesofobservationalEBstud- ofEBnon-visibilityintheNai DandMgiblines(PaperIV). ies using high-quality imaging spectroscopy and polarimetry 1 Inadditiontothesead-hocHα-synthesisattemptstherehave with the CRisp Imaging SpectroPolarimeter (CRISP, Scharmer v been numerical MHD simulations of EB reconnection by Ar- etal.2008)attheSwedish1-mSolarTelescope(SST,Scharmer 0 chontis & Hood (2009), but without any spectral synthesis or 8etal.2003).PaperI(Watanabeetal.2011)establishedthatEBs verification, and by Nelson et al. (2013) who probably did not 2are a purely photospheric phenomenon. Paper II (Vissers et al. emulateanEBnorobservedone(PaperIII). 32013) added evidence that EBs mark magnetic reconnection of In the present paper I discuss EB visibilities assuming lo- 0strongopposite-polarityfieldconcentrationsandtreatedtheirap- cal thermodynamic equilibrium (LTE) for line extinctions, i.e., .pearanceinultravioletcontinuumimagesfromtheAtmospheric 1 Saha-Boltzmann lower level populations. This assumption may 0Imaging Assembly (AIA, Lemen et al. 2012) onboard the So- seem surprising for such utterly non-equilibrium fast-changing 6larDynamicsObservatory(SDO,Pesnelletal.2012).PaperIII dynamicphenomena,sinceEBsmarkmagneticreconnectionat 1(Vissers et al. 2015) presented the marked appearance of EBs :inultravioletSiiv,CiiandMgiilinesinspectratakenwiththe smallspatialandshorttemporalscales(PaperI,PaperII),includ- v ingnear-instantaneousheating,bi-modaljetformation(PaperI, InterfaceRegionImagingSpectrograph(IRIS,DePontieuetal. i PaperIII),hot-cloudexpansion(PaperIII),andpossiblycooling X2014).PaperIV(Ruttenetal.2015)confirmedEllerman’sstate- cloudsintheiraftermath(PaperIII,PaperIV). rment that EBs are not obvious in the optical continuum nor in atheNai DandMgiblines. Assuming LTE (i.e., validity of Boltzmann and Saha parti- tioning over atomic levels and ionization stages) seems totally In summary, the visibilities of EBs are now well docu- out of the question for EBs. Even the assumption of statistical mented. They present a rich set of constraints with large and equilibrium(SE,time-independentlevelandstagepopulations) puzzlingvariety.EBsappearverybrightandwithextraordinary seemshighlyquestionable.Thisassumptionisthebasisforboth spectral extent in Balmer-line wings, also bright but less ex- non-LTE modeling (NLTE, meaning SE including all pertinent tendedinthewingsofCaiiH&KandCaii8542Å,verybright bound-boundandbound-freepopulationprocesses)andcoronal- in the IRIS Cii 1334 & 1335Å and Siiv 1394 & 1403Å dou- equilibriummodeling(CE,admittingonlycollisionalexcitation blets,andbrightandverybrightinAIA’s1700and1600Åchan- andionizationandonlyradiativedeexcitationandrecombination nels, respectively. However, they are transparent in the optical includingdielectronic),butSEisunlikelytoholdinEBs.These continuum and also absent or nearly absent in optical neutral- then require non-equilibrium modeling (non-E, i.e., solving all atomlines(Fei,Nai,Mgi). pertinentpopulationandradiationequationstime-dependently). Articlenumber,page1of13 A&Aproofs:manuscriptno.aa26489 MyLTEapproachbelow(Sect.3)mayseemevenmoresur- by the Saha and Boltzmann laws as fraction of the total ele- prisinginviewofmybackground(e.g.,Rutten2003,henceforth mentdensityN ,N thetotalhydrogendensity,A theelemen- E H E RTSA). LetmeemphasizeattheoutsetthatrealisticEBmod- talabundance,N /N , f thelower-to-upperoscillatorstrength, E H lu eling does require 3D time-dependent non-E MHD simulation ϕ the area-normalized extinction profile in wavelength, χ the includingnon-E3Dspectralsynthesis.TheactualNLTEdepar- induced-emissionprofile,hthePlanckconstant,ktheBoltzmann turesmayreach1010 (10dex)ormore,farbeyondthe0.01–0.1 constant,andT thetemperature.Theprofilesϕandχdifferinthe dexdeparturesdiscussedinabundanceanalyses.However,such case of partial frequency redistribution (PRD) but are equal for computationshavebeenaccomplishedinfullonlyfor1Dcases, completeredistribution(CRD). in 2D only with questionable shortcut recipes. The 3D case re- Thelinesourcefunctionisgivenby: mainsprohibitive(Carlsson&Leenaarts2012).Leenaartsetal. (2012,2015)thereforerestrictedtheirnumerical3DHαforma- Sl =(1−ε−η)J+εB+ηSD, (2) tionstudiestoasinglesimulationsnapshot. where ε is the photon destruction probability (the fraction of In this paper I first argue on the basis of published model- photoexcitations followed by direct collisional upper-to-lower ingthattheLTEsimplificationcanservetogaugepotentialEB deexcitation), η the photon conversion probability (the fraction visibilities.ThecruxistoassumeLTEnotallthetimebutonly ofphotoexcitationsfollowedbydetourupper-to-lowerpaths), J during hot and dense EB onsets and only for line extinctions, the angle-averaged intensity (profile-averaged J for CRD or a notforlinesourcefunctions.Ithencombinethisonsetassump- wavelength-dependentmixofthemonochromatic J forPRD), tionwiththeobservedEBvisibilitiestodefinetheprobableEB λ B the Planck function for the local temperature, and SD a for- parameterdomain. malsourcefunctionwhichcollectivelydescribesallmulti-level The organization of the paper is as follows. The next sec- upper-to-lowerdetourchains(sometimeswrittenas B(TD)with tion gives background. It starts with basic equations and their TD a formal detour temperature as in Eqs. 8.5–8.82 of Jefferies implementation. It then treats three published solar-atmosphere 1968). Eq. 2 is the multi-level extension of the two-level ver- models:the1DSEstaticmodelofAvrett&Loeser(2008),the sion including scattering (Eq. 10 of Hummer & Rybicki 1967, 2D time-dependent non-E MHD simulation of Leenaarts et al. Eq. 1.95 of Rybicki & Lightman 1979, Eqs. 3.94 and 3.105 of (2007), and the 1D SE static model of Fontenla et al. (2009). RTSA,Eq.14.34ofHubený&Mihalas2014)andfollowsfrom All three were intended to mimic the solar atmosphere, but I thatfollowingSect.8.1ofJefferies(1968). treatthemasfictitiousstellaratmospheresnamedALC7,HION FortheWienapproximationwithhc/λkT>1thesimpleex- and FCHHT-B. The HION atmosphere inspired this study. The pressionshold: ALC7andFCHHT-Bchromospheressupplyinstructivelinefor- mationdemonstrationseventhoughtheyarepoorrenderingsof αl ≈ b αLTE, (3) the actual solar chromosphere. From these examples I distill l Sl ≈ (b /b) B. (4) recipes for estimating line extinction (Sect. 2.5). Sect. 2.6 con- u l cludes the background part by defining observational terms to This is the case for all diagnostics treated here (Caii8542Å avoidconfusions. reaches λkT = hc at 16800K, Hα at 21900K). These equa- The analysis (Sect. 3) boils down to plotting and interpret- tions illustrate that extinction NLTE (b (cid:44) 1) and source func- ingclassicaldiagrams.Figure4comparesLTEtoCEionization tionNLTE(b /b (cid:44)1)aredifferententitiles,asareextinctionand equilibria,thelatterfollowingJordan(1969),becausewithinthe u l sourcefunctionthemselves. SE assumption these represent extremes. Figure 5 emulates the The emergent intensity which conveys our telescopic diag- famousdiagram1inFig.8ofPayne(1925)(firstprintedinFig.1 nostics is usually well approximated by the Eddington-Barbier ofPayne1924andredrawninFig.5-6ofNovotny1973). estimate I ≈ S(τ=1) for optically thick formation with τ the Sects.4and5addabriefdiscussionandconclusions. opticaldepthalongthelineofsight.Fornon-irradiatedoptically thin slabs it is I ≈ jD = τS, with emissivity j = αS per cm, geometricalthicknessD,andopticalthicknessτ. 2. Background InthethickcaseextinctionNLTEaffectsonlytherepresenta- 2.1. Equationsandimplementation tiveτ=1samplingdepth(Eq.3),whereassourcefunctionNLTE affectstheintensitydirectly.Inthethincasebothextinctionand Thissectionspecifiesthebasiclineformationequationsusedto source function NLTE affect the intensity directly by together computeandinterpretFigs. 1and3–5below. settingtheemissivity. Thelineextinctionpercmpathlengthisgivenby(RTSAEq. NLTE SE spectrum synthesis codes, such as the workhorse 9.6): RHcodeofUitenbroek(2001),solvethecoupledpopulationand radiation equations for all transitions and locations pertinent to πe2 λ2 nLTE (cid:34) b χ (cid:35) selectedlines,oreventhewholespectrum.IuseRHinthelatter αl = b l N A f ϕ 1− u e−hc/λkT , (1) m c c l N H E lu b ϕ modeinSect.2.2below. e E l For the simpler LTE extinction evaluations I updated IDL where e is the electron charge, m the electron mass, c the ve- codes to compute ionization and molecule mixes and partial e locity of light, λ the line wavelength, b the lower-level and b pressures for given elemental composition that were developed l u theupper-levelNLTEpopulationdeparturecoefficientdefinedas by J. Sánchez Almeida (1992, 1997) and are partly based on b ≡ n/nLTE, nLTE/N the lower-level population density given Wittmann(1974)followingMihalas(1967).Ifoundtheminthe l E githubLTErepositoryofA.AsensioRamosandextendedthem 1 ItaughtmakingSaha-Boltzmanngraphstohundredsofstudentsat withdataandroutinesintheSolarSoftCHIANTIpackage(e.g., Utrechtandelsewherewithalabexercise“CeciliaPayne”(availableon Dereetal.1997,Landietal.2013).Mycodesareavailableunder mywebsite).Itusesafictitiousandunpronounceabledidacticelement IDLonmywebsite. called“Schadeenium”afterUtrechtastrophysicistAertSchadee(1936– 1999),whoinventeditforteachinginthe1970s. 2 Correction:deletetheminusinthesecondversionofEq.8.8. Articlenumber,page2of13 R.J.Rutten:H-alphafeatureswithhotonsets.I.Ellermanbombs 2 ALC7 −7 ALC7 H α 8000 H α 1 on) K] log b 0 lower −8og (fracti B, S, J [ 6000 −9l 4000 −1 2 ALC7 ALC7 Ca II 8542 Å −1 8000 Ca II 8542 Å 1 lower on) K] log b 0 upper −2log (fracti B, S, J [ 6000 Fig.1. SEformationofEBdiagnosticsinthe −3 4000 ALC7 model atmosphere of Avrett & Loeser −1 (2008) computed with the RH code of Uiten- 2 ALC7 0 ALC7 broek(2001). Ca II K 8000 Ca II K Left, solid: logarithmic NLTE population de- 1 lower on) K] parture coefficients b ≡ n/nLTE as function of log b 0 upper −−21log (fracti B, S, J [ 6000 hbeLaueecifgfth,ohprtd,aatnhrseeehsle.pudep:cptleiovrgelaleyrvitebhllmofiofcrthltohewelielnor-ewleievdreellnetpvifioelepdualniadn- 4000 tions normalized by the total element density −1 (axisscalestotheright). 2 Left, dotted: the same fractional population in ALC7 ALC7 Mg II k 0 8000 Mg II k LTE. 1 on) K] Right:PlanckfunctionBλ(thinsolid,thesame log b 0 lower −1og (fracti B, S, J [ 6000 iq(nduaaasnlhltieptdiae)ns,elilansr)ee,saopnulgorlctete-eadfvuenarcsatgioreendpSrineλstee(snnostaliittdyiv).JeTotheremJseλ- l peratures to avoid the Wien sensitivity of the upper −2 4000 Planckfunctionandsoobtaindirectlycompara- −1 blescales.ForPRDlines(CaiiKandMgiik) 2 S and J are shown for line center and the ALC7 lower ALC7 λ λ Mg I b 8000 Mg I b emergent-profilepeaksanddips.Thethreever- 2 2 log b 01 upper −−54og (fraction) B, S, J [K] 6000 TtdcioechplaeulthmStiτnc<λko=sBnd3ley,sfip1fl,nio0etrs.3thlc,ieonrerehrseepcsieegpcnhotttinesvdrewlotyhone(trithneheettohbtebualll<ecofutpbhrtlvaicdenai)d-l. l vergencesatleft. 4000 Remarkable: at left the very deep dip in the −1 −6 dashed Hα population curve, the relative flat- 2 ALC7 −3 ALC7 nessoftheCaii8542ÅandCaiiKpopulation Na I D 8000 Na I D curves,theutterflatnessoftheMgiikpopula- 1 1 log b 01 upper −4og (fraction) B, S, J [K] 6000 adtpinaoodnpntulNcylauathriivoigeDn,hs1afvnrlaoodlwmuteehpreohlfoleatvSoregnl≈ess.ucJAchtrftiooormrnigoHfhostαprhtthaheceerricoMdsiossgcvitoehbrre2-- −5l temperatureminimumfrombackscatteringand 4000 theoverallsimilarityofthescatteringS≈Jde- −1 clinesofalllines,includingindependentlyscat- 0 500 1000 1500 2000 0 500 1000 1500 2000 teringPRDwings. height [km] height [km] 2.2. ALC7:EBdiagnosticsin1DSEmodeling Figure 1 shows extinction parameters at left, source func- tion parameters at right. They were computed with the 1D RH This section presents and discusses the formation of EB diag- version of Uitenbroek (2001) including NLTE line blanketing nosticsinquiescentconditionsinordertoestablishtheirnormal with the full compilation of Kurucz (2009). PRD was adopted behavior. for Caii K and Mgii k; CRD for the others. The IRIS Cii and Figure 1 presents EB diagnostics assuming SE and Siiv lines were excluded because they form in the ALC7 TR E.H.Avrett’slatestempiricalstatic1Dmodel(Avrett&Loeser andposenumericaldifficulties. 2008).BelowIquestionthevalidityofsuchplane-parallelmod- els,buttheydoremainexemplaryfordemonstratingfullyunder- In the lefthand column the divergences between the dashed standablesolar-likelineformation,inthiscaseinthecomputa- anddottedfractionalpopulationcurvescorrespondtothedepar- tionalatmosphere“ALC7”. ture of logb from zero. All plots show increasing b < b di- l u l Articlenumber,page3of13 A&Aproofs:manuscriptno.aa26489 vergence with height due to photon losses. Equation 4 implies 6 that these divergences translate into equal divergences between A B C S and B, but the equivalent temperature representation used at 4 rightproduceslargerdivergenceatlongerwavelengthforgiven m bu/bl. M Hα (top panels of Fig. 1) has discordant formation across 2 the upper ALC7 photosphere because this is transparent in this high-excitationline(dashedcurveinthefirstpanel).Theradia- 0 tion field there builds up from backscattering from the opaque overlying ALC7 chromosphere (Rutten & Uitenbroek 2012). 0 5 10 15 Mm Thelower-levelpopulation,hencetheHαlineextinction,nearly equalstheSaha-BoltzmannvalueuptotheALC7TRthanksto Fig.2. SchematicEBintheHIONatmosphere.AsketchedEB(white, the huge Lyα opacity producing Sl ≈ J ≈ B in this line, with nearx=5)issuperimposedonthelastpanelofFig.1ofLeenaartsetal. (2007) in which the black–blue–green–orange color coding quantifies smallwigglesfromradiativeLyαsmoothing(Sect.2.4). NLTEoverpopulationoftheHin=2levelrangingfrom1to1014.The TheHαsourcefunction(secondpanel)behaveslikeastan- superimposedpinkarchrepresentsaschematicHαfibril.Slantedlines dard scattering one, i.e., domination of the first two terms in ofsight(µ=0.71)tothetop,middle,andbottomoftheEBaremarked Eq. 2 that together cause a scattering decline in bu/bl. Hα A,B,andC. hasoftenbeencalled“photoelectric”followingThomas(1957), meaning dominance of the third term in Eq. 2 over the second, but across the ALC7 chromosphere it is simply a resonance- tonsoriginatesodeepthatthelinecoreintensitydoesnotsense scattering line with a source function decline like all others in the ALC7 chromosphere. These lines have large extinction in- Fig.1 creaseoverLTEfromminority-stagephotonsuction(Brulsetal. Since the ALC7 chromosphere is near-isothermal there is 1992).Belowthat,Mgishowsasteepdeparture-coefficientde- goodresemblancetotheclassicdemonstrationoftwo-levelscat- cline from overionization by ultraviolet radiation from below teringbyAvrett(1965),exceptthatεisnotconstant. (Rutten&Uitenbroek2012). √ The outward S decline from such scattering (“ ε law”) Insummary,Fig.1showsthatLTEextinctionisareasonable causes a dark line core which is often called “self-absorption” assumptionfortheseEBdiagnosticsthroughouttheALC7chro- inultravioletspectroscopy. mosphere. In particular, it is valid for the Balmer lines and the In the ALC7 atmosphere the Hα core forms halfway the Balmer continuum and for Mgii k, whereas it even represents chromosphere,butmostescapingphotonsactuallyoriginatedin considerableunderestimationfortheCaiilinesandNai D1.Itis thedeepALC7photospherewhereεreachesunity.ForHαthe anoverestimationonlyforMgib2. ALC7 chromosphere is only a scattering re-director. If it were EB-like hot and dense features embedded in such an atmo- absent the emergent Hα profile would remain the same, origi- spherewillhavelargercollisionalcoupling,especiallywhenhy- natinginasimilarscatteringdeclinewithinthephotosphere. drogen ionization boosts the electron density and ε, and be yet In actual solar Hα images such scattering (but 3D) oblit- closertoLTE. erates the granulation imprint although this has larger intrinsic contrastthanchromosphericfinestructure,makingthelattervis- 2.3. HION:HαextinctionboosttopasthotLTE ible.Wherethechromosphericslabhaslargerdensitytheτ=1 locationmovesoutwardalongthescatteringdecline,makingHα ThissectionpresentsthemotivationforassumingLTEextinction core darkness primarily a density diagnostic (Leenaarts et al. inhotonsetsofdynamicalphenomena. 2012). Thisassumptionwasinspiredbythenumericalnon-EMHD Caii8542Å(secondrow)formsataboutthesameheightas simulationofLeenaartsetal.(2007).ItdidnotaddressEBsbuta HαinALC7,buthasabetter-behavedsourcefunctionthatfol- verticalplanecontainingtwoopposite-polaritystrong-fieldcon- lows the temperature until it drops down from scattering. The centrations resembling solar network with less magnetic inter- b curve in the lefthand panel shows substantial increase from network in between. Its theme was non-E modeling by permit- l photon losses in the Caii infrared lines. The initial dip in the tingandevaluatingtime-dependenthydrogenionizationandre- populationcurvefollowsthetemperaturethroughtheBoltzmann combination. By being 2D and MHD it represented a sequel to sensitivity. theseminal1Dnon-EHDsimulationofCarlsson&Stein(2002) Caii K behaves very similar to Caii8542Å, but its core in which the physics of non-E hydrogen population processes forms higher and PRD applies, shown by sampling S and J at wasanalyzedforacousticshocksinthelowersolaratmosphere. the K , K and K wavelengths (cf. Shine et al. 1975). The b BelowIrefersomuchtothissimulationthatItreatitasthe 3 2 1 l curvefirstrisesfromphotonlossesintheCaiiinfraredlinesthat atmosphere of a hypothetical star called “HION” (for Hi ion- are shared through collisional lower-level coupling, then from ization).Itsatmosphereexistsonlycomputationallybutyethas photon losses in H&K. They offset the Caii depletion by ion- solar-likeproperties. izationthatwouldoccurinLTE(dottedcurve). In the HION atmosphere shocks occur copiously as field- Mgii k behaves much as Caii K, but the 18 times larger guided ones producing dynamic fibrils near the magnetic con- Mg abundance makes it form in the ALC7 TR. Its PRD wings centrations and as less field-restricted ones in the quieter inter- formacrosstheALC7chromosphere.Thehigherionizationen- network that resemble the acoustic 1D shocks of Carlsson & ergy (15.0eV instead of 11.9eV) makes Mgii fully dominant Stein(1997). throughout the ALC7 chromosphere (dashed curve in the left- Figure2superimposesasketchofanEBbasedontheSST hand panel), resulting in pure LTE extinction and textbook de- images in Papers I-IV on a snapshot of the HION atmosphere. clineoftheb curve. I use the latter as a scenic illustration of how the actual shock- u Mgib andNai D (lastrows)havetheirτ=1escapelevels riddenlowersolaratmospherearoundanEBmaylooklike.The 2 1 in the onset of the ALC7 chromosphere, but the escaping pho- twoopposite-polarityfieldconcentrationsatx=4andx=12Mm Articlenumber,page4of13 R.J.Rutten:H-alphafeatureswithhotonsets.I.Ellermanbombs 4 FHC IHHT-B 23 -6 8000 FHC IHHT−B Fig. 3. SE formation of Hα, Lyα, and Lyβ 2 log b -02 1 123 --180log (fraction) B, S, J [K] 6000 B SS,, JJ LLyy αβ i(fphn2ryao0ndtm0hero9elRg)sFuehiCnntotHwetlhenHsev&eNTflo-sLUBrTnmitaE=eatntm1dbo,eorf2pos,Fape3rihktg.eu(.Trr21eeh0,eo1cufo2dse)aFi.nffisoThgncehRtideeeHnnalletnasrfdetebhsdtuafonalottlds-r. -12 4000 S, J H α tedNLTEandLTEfractionalpopulationcurves -4 are for n = 2. The righthand panel shows the 0 500 1000 1500 2000 0 500 1000 1500 2000 correspondinglinesourcefunctions. height [km] height [km] closely resemble the actual kilogauss magnetic concentrations Hαextinctionsmoothingtonearbyhotinstances.Thisisdueto thatconstitutesolarnetwork.Besidesthemandelsewherefinely- Lyαresonantscattering.IillustrateitinFig.3usingtheFCHHT- structured thin shocks (black to dark blue) run up and push BatmosphereofFontenlaetal.(2009). the transition region (TR, onset of the light-blue area) to large The FCHHT-B atmosphere is similar in construction and heights, of order 3 Mm. Large cool clouds appear behind the propertiestotheALC7atmosphere.Themaindifferenceisthat shocks(greentoorange).Thissceneisverydynamic:theHION ALC7obtainschromosphericextentfromaddingturbulentpres- TRinHIONdancesupanddownover2–4 Mmheightininter- sure constrained by observed non-thermal line widths while network and over 1.5–2.5 Mm in and near the field concentra- FCHHT-Bobtainsextentfrombest-fitmanipulationofthelocal tions. gravity.TheFCHHT-Batmospherehasalowhigh-lyingtemper- WhatdoesthisHIONscenehavetodowithassumingLTE? ature minimum adjacent to an abrupt rise to a near-isothermal (It actually depicts Hα NLTE b departures of twelve orders of chromosphere(BcurveinFig.3)intendedtoreproducedarkin- l magnitudeintheorangeclouds!)Theessentialnon-Ehydrogen- fraredCO-linecores. ionizationphysicsisthatcollisionaltransitionsbetweenHin=1 Iusethissuddenriseasemulatingahotfeatureembeddedin andn=2aresoscarceincoolpost-shockgasthattherehydrogen a cool atmosphere. The downward radiation from this hot edge ionization/recombinationbalancingisslow(Kneer1980;Carls- maybeseenasrepresentinghowacylindricalhotEBirradiates son & Stein 2002), leaving the ion state and with it the top of cool gas around it. The large b and b peaks in Fig. 3 arise 2 3 the hydrogen atom highly overpopulated with respect to Saha- fromdownwardLyman-linescatteringfromtheoverlyingchro- Boltzmann partitioning during the 3–5 minute cool intermezzo mosphere.EvenattheverylargeopticaldepthswhichtheLyman untilthenextshockpasses. linesreachthere,theirlocalscatteringdiffusessomeoftheirin- The shocked HION atmosphere is sampled in Fig. 2 of tense chromospheric J ≈ B radiation into the cool underlying Leenaarts et al. (2007) with the bottom panels showing the Hi FCHHT-B layers. The Lyα irradiation boosts the n = 2 popu- n=2populationgoverningtheextinctionofHα(Eq.1).Thefirst lation and with it the Hα extinction by a factor 400 at 100 km keypointisthatitreachesthemomentaryLTEvalueinshocks. belowtheedge. This results from high temperature (about 7000K) and large Lyβ has a similar off-edge S ≈ J scattering halo as Lyα. electrondensityincreasefromhydrogenionization(above1per- Overh=1000−1500kmtheLyαradiationconfinementcauses cent), to values 1010 −1011cm−3, together boosting ε for Lyα b ≈b ≈1, so there Lyβ has the same degree of source func- 2 1 sufficientlytocouplen=2tothegroundstatewithintheshocks. tion NLTE as Hα since they share n = 3 as their upper level The second key point is that in between successive shocks the (Eq. 4) and its depopulation by Hα photon losses. Their S di- n=2 population remains at or near this high level, even while vergence from B at right differs through the representation as the temperature drops thousands of degrees, because the top of formaltemperatures(whichremovesPlanckfunctionsensitivity thehydrogenatomisdecoupledfromthegroundstateduringthe towavelength). retardedrecombination. Thus,boththeHαandBalmer-continuumopacitiesarenear- 2.5. RecipesforHαextinctioninEBonsets LTEintheshocksandremainatthesehighvaluesbetweenthem. The gigantic overpopulations indicated by the orange clouds in InowapplytheabovetoEBonsets.TheupshotfromSects.2.3 Fig.2andthecorrespondinglargeseparationsbetweenthethick and2.4isthatforhotdenseinstancesinthelowsolaratmosphere andthincurvesinthebottompanelsofFig.2ofLeenaartsetal. onemay:(1)assumeSaha-Boltzmannlower-levelpopulationfor (2007)simplymeanthattheactualn=2populationdoesn’ttrack theextinctioncoefficientofHα,(2)applysuchboostingalsoas thecoolintermezzi. an opacity halo to cooler surrounding gas, and (3) maintain it duringcoolersubsequentepisodes.Thesearetherecipesapplied inthispaper. 2.4. FCHHT-B:HαextinctionboosttonearbyhotLTE Similar to the shocks pervading the HION atmosphere for ThissectionaddressestheeffectofLyαscatteringnearhotfea- whichtheserecipeshold,EBsaremomentaryheatingeventsin tures. thelowatmospherebutyetdeeper,hotteranddenser.Itherefore Inter-shocktemporalconstancyofthen = 2populationalso suggest that the LTE recipes also apply to the hydrogen n=2 impliesconstancyoftheLyαsourcefunctionwhichhasS≈J≈ population in EBs. They then hold for both Hα extinction and b B(T) where hydrogen is predominantly neutral (Eqs. 2 and Balmer-continuumextinction. 2 4) which it remains even in the HION shocks. Leenaarts et al. Do the recipes apply also to other EB diagnostics? This (2007) did not admit Lyα or other Lyman radiation in HION, questionistwofold:isSaha-Boltzmannpopulationpartitioninga but it is interesting to note that, in addition to the temporal Hα goodapproximationfortheirextinctionathotmomentsathigh extinction smoothing to the hottest preceding instances in the density, and do they possess a memory for such momentarily nearpastduetoslowrecombinationsettling,thereisalsospatial highextinctionastheBalmerlinesandcontinuumhave? Articlenumber,page5of13 A&Aproofs:manuscriptno.aa26489 In contrast to Hα, most other EB diagnostics are ground- bler structures making up “arch filament systems” in emerging state resonance lines and have extinction near or at the LTE activeregions. value if the pertinent ionization stage is the dominant one. For IRIS bombs (IB) are short-lived small-scale active-region them,inparticularSiiv,thequestioniswhetherSahaappliesin brighteningsthatshowverybrightIRISCiiandSiivlineswith photospheric-densitygasheatedtohightemperature. verybroaddoublypeakedprofilesandsuperimposedabsorption The second recipe issue is the presence of a memory for blends indicating cool overlying gas. In their discovery paper previous hot-feature extinction due to retarded recombination. Peteretal.(2014)suggestedthatthesearepocketsofhotgasin This cannot be illustrated with static modeling. However, the theupperphotosphereandmaycorrespondtoEBsinHα.InPa- Hi example shows that it occurs when there is a large initial perIIIwefoundthattheyaremorelikelyFAFswhileEBsmay jumpinthetermstructureofthelowerstage(Carlsson&Stein alsoshowIBsignaturesintheiraftermaths. 2002). Hei is an obvious candidate (Golding et al. 2014), but unfortunatelytherearenoreportsofEBvisibilityinHei D or 10830Å.TheNai D,Mgib,CaiiandMgiilineswillbem3uch Photosphere, chromosphere, clapotisphere. Paper I con- cluded that EBs are a photospheric phenomenon, but also that lessretarded(cf.Wedemeyer-Böhm&Carlsson2011;Leenaarts they reach up to one Mm or more. A one-Mm tall feature etal.2013).However,retardedrecombinationmaywellapplyto embedded in the ALC7 atmosphere would have its top in the Cii1334&1335ÅandSiiv1394&1403Åbecausetheirpre- ALC7 chromosphere; that part would then be called chromo- cedingionshavelargeinitialjumps:Cihasa13eVgapbetween spheric. However, we designated EBs instead as fully non- low and high levels, the Siiii resonance lines are like Lyα near chromospheric, hence implicitly photospheric, because even 1200Å.Theselargestepsslowdownrecombinationtothelower theirtopsalwaysremainshieldedbythefibrilcanopyobserved stagewhenthatbecomesdominantincoolgas,justasforHiin inHαlinecenterinactiveregions.WhatwemeantisthatEBs HIONpost-shockgas. areembeddedincoolgaswithupper-photospheretemperatures, aspresentbetweenshocksintheinternetworkareasoftheHION atmosphereinFig.2whereitreaches3Mmheight,higherthan 2.6. Terminology EBs. Thissectiondefinesobservationalnomenclatureusedintheanal- However, recently Ph. Judge (private communication) in- ysisinSect.3. sistedthatoneshouldrestrict“photosphere”toitsoriginalmean- ing: the domain where the bulk of the solar radiation flux es- capes. I follow his admonishment here and restrict “photo- EB,MC,FAF,IB. ForclarityIlistanddefinevariousEB-related sphere” to this thin shell which reaches no higher than about observedphenomenahere. 400kmaboveτ =1.ItsupperlayersaresimilarintheALC7, 5000 Ellerman bombs (EB) adhere to the definition by Ellerman HION and FCHHT-B atmospheres, with a temperature decline (1917): sudden intense brightenings of the extended Hα wings thatisalsocloselythesameinLTEradiative-equilibriummod- (“moustaches”)thatoccurexclusivelyincomplexbipolaractive els.Thereasonisthatthisisthemosthomogeneouspartofthe regionsandhavethediversevisibilitiesdescribedinSect.1. solarinternetworkatmosphere,abovethegranulationandbelow Magneticconcentrations(MC)denotethekilogaussstrong- shock formation and not too magnetized; linear undulations of fieldelementsthatmakeupsolarnetwork.Theyarebestknown the acoustic p-mode pattern and internal gravity waves repre- as faculae or G-band bright points, but also appear as bright sentitsmajorperturbations.Thevisiblecontinuumescapeisde- pointsinthe1700Åcontinuumandespeciallyinthebluewing scribedfairlywellbyLTEasasmallleakfromalargethermal ofHα(Leenaartsetal.2006).Thelatterpropertyhascausedfre- pool. Theoretical radiative-equilibrium modeling and empirical quent confusion with EBs (Rutten et al. 2013). Paper I showed 1Dstaticmodelingapplybesttotheupperphotosphere. that at high resolution upright flame morphology in limbward The name “chromosphere” was given by Lockyer (1868) viewingisadistinctiveEBcharacteristic.ItwasusedinPaperII to the pink shell he saw spectroscopically (literally) around to establish EB brightness criteria, but these may fail close to the sun, with the beautiful color due to emission in Hα, Hβ, disk center (Paper III) where differentiation with the MCs that and Hei D . It then became the name of what causes the flash 3 produce EBs (as in the serpentine U-loop pull-up scenario of spectrum (Athay & Thomas 1961), but in the past decades it EBformationofe.g.,Bernasconietal.2002,Pariatetal.2004, became synonymous with the raised temperature plateau over Isobeetal.2007,Archontis&Hood2009,Pariatetal.2009)is h≈500−2000kminAvrett-stylestandardmodelsasALC7. lesseasy,asalreadypointedoutbyEllerman(1917)andlaterby I prefer to return to Lockyer’s naming and therefore define Bruzek&Durrant(1977). ason-diskchromospherewhatoneobservesinHα.Inactivere- With “FAF” I denote small sudden brightenings in AIA gionsthisisadensecanopyoflongopaquefibrils.Isketchedone 1600Å images with filamentary morphology. Similarly to EBs asexampleinFig.2becauseHIONdoesnotcontainsuchfibrils they appear as sudden brightenings in complex active regions, (an issue addressed in the next paper in this series). Note that but they are elongated, change faster, and show rapid appar- the green arches in Fig. 2, which resulted from photon suction ent motion. They seem to start as EB-like reconnection events byHαwherehydrogenionizes,areartifactsbecausetheHION butthenbreakthroughthechromosphericcanopyandaffectthe computation did not include photon losses in the Lyman lines. higheratmosphere(PaperIII).Pariatetal.(2009)notedthemin InHIONtheHin=2levelthereforeactedeffectivelyasground 1600ÅimagesfromTRACE,calledthem“transientloops”,and statefortheHiatomtop. reported them as a new phenomenon – but probably Hα-core With these definitions a third name is needed for shocked “microflares” (e.g., Shimizu et al. 2002) describe similar out- coolgasinhigh-reachingsub-canopydomainsinsolarinternet- bursts. In Rutten et al. (2013) we noted them as “small flaring work areas and also present in HION internetwork (Fig. 2). I arch filaments and microflares” and abbreviated this to FAF = onceagainuse“clapotisphere”(Rutten1995). “flaringarchfilament”inPaperIII,butabetternameis“flaring Thus,amajordifferencebetweentheALC7andHIONatmo- active-region fibril” to avoid confusion with the larger and sta- spheres is that ALC7 possesses a static 1D isothermal chromo- Articlenumber,page6of13 R.J.Rutten:H-alphafeatureswithhotonsets.I.Ellermanbombs H I II CE In my opinion HION comes much closer to the actual Sun 100 even while it is only 2D and has no internetwork-covering Hα n o 10-2 fibrils.IregardthetemperaturestratificationofALC7-like“stan- acti dard”chromospheres,foralltheirphenomenaldidacticvalue,as fr 10-4 artifacts from unrealistic static modeling. They do not describe 10-6 a mean over actual temperature fluctuations because their con- 100 H II LTE struction through ultraviolet spectrum fitting suffers from non- on 10-2 linear Wien temperature sensitivity and therefore favors shocks cti (Fig. 4 of Carlsson & Stein 1994.) Indeed, the ALC7 chromo- a fr 10-4 sphere has similar temperature, ionization and electron density 10-6 astheHIONshocks. Worse, while every solar-atmosphere column must have a Mg III CE minimumtemperatureandasteeprisetothecoronasomewhere, 1.0 II n IV the HION atmosphere suggests that their heights fluctuate so fractio 0.5 I wimiludmly”tahnadtt“htehesttartainc-smitioodnerlienggionno”tiaornesuosfel“etshse.temperaturemin- 0.0 MgII III IV V LTE 1.0 VI VIIVIIIIX 3. Analysis n o acti 0.5 3.1. LTE–CEcomparisons fr Figure4comparesthefractionalpopulationsofionizationstages 0.0 ofH,Mg,CandSibetweenCE(upperpanelsperpair)andLTE (lowerpanels). C I II CE 1.0 III The upper panels are from CHIANTI and represent “Car- on oleJordan”diagramsfollowingJordan(1969)whoselandmark fracti 0.5 IV Fphigo.to3srpehperreesepnotpsutlhaetisoonladri-sctorirbountaiocnosu.nterparttoPayne’sstellar- 0.0 The lower panels of Fig. 4 are not strictly “Cecilia Payne” 1.0 C II III IV V LTE diagramsbecausetheydonotincludeBoltzmannexcitationfor n particular lines but show only the distribution over successive o acti 0.5 ionization stages defined by the Saha equation. They are also fr basedonCHIANTIdata(ionizationenergiesandtermstructures 0.0 defining partition functions). The large electron density corre- spondstofullhydrogenionizationofALC7gasath=850km. 1.0 Si II III V CE These extreme assumptions bracket the temperature regime in which the EB diagnostics form. Of course neither is likely n actio 0.5 I vIRalIiSd,libnuets,hbeerehaIvseumggoersetatshathteElBowoenrseLtTvEispibainleitlietsh,anevtehneiunpptheer fr IV CEpanelperpair. 0.0 The peak widths are defined by the ionization energies and 1.0 Si II III IV V VI VIIVIIIIXLTE areexceptionallylargefortheclosed-shellionsMgiii,Cv,and on Siv, and of course for Hii which suffers no competition from acti 0.5 higherstages. fr Thehydrogencurves(firstpairofpanels)areplottedonlog- 0.0 arithmic scales in view of the enormous hydrogen abundance: 4.0 log (tem4p.5erature) [K] 5.0 even at only NHi/Ntotal =10−5 neutral hydrogen still competes with the dominant stages of the most abundant metals. For CE Fig. 4. CE/LTE ionization-stage population comparisons for H, Mg, suchpresenceextendsashighas100000K.ForLTEthebreak- C, and Si. Upper panel of each pair: CE distribution with temper- evenionizationpointshiftsbelow10000K. ature (CHIANTI gives no values below 10000K). Lower panel of The next pair (Mg) shows that due to the similarity of the eachpair:LTEdistributionwithtemperatureforfixedelectrondensity MgiiandHiionizationenergies(15.0and13.6eV,respectively) Ne=1014 cm−3.For10timeslowerNe theLTEcurvepatternsremain theMgiitoMgiiitransitionoccursverysimilartoHitoHiiion- similarbutthepeaksshiftleftwardoverabout−0.05inlog(T)andbe- ization. Hence, the resonance Mgii h&k and Hi Lyman lines comenarrower.Thefirstpairforhydrogenhaslogarithmicy-axes;the will have similar presence apart from the 2.5104 extinction ra- dashedcurvesareonthelinearscalesoftheotherpanels.Remarkable: tiopergivenfeature(abundanceratio),unlesstheyalsodifferin the substantial leftward CE to LTE shifts and the wide presences of Mgiii,Cv,andSiv. being closer to the LTE limit or to the CE limit or in departure fromSE. ThethirdandfourthpairsareforCandSi.Theyshowsimilar patterns, with wide peaks for the first and especially the fourth sphere,HIONahighlydynamiclow-lying2Dnetworkchromo- ions. In CE the Siiv presence peaks with relatively low ampli- sphere made up of dynamic fibrils and a highly dynamic high- tude at log(T) ≈ 4.9 (T ≈ 80000 K) as quoted by Peter et al. reaching2Dinternetworkclapotisphere.Thisdifferenceisenor- (2014),butinLTEitpeaksalreadyatT≈25000Kandalsowith mous. muchlargeramplitude.SincetheSiivlinesintheEBspectraof Articlenumber,page7of13 A&Aproofs:manuscriptno.aa26489 N = 1016 N = 1016 25 0 H Hα center 0 H C II Si IV −1m] Hα −5 Å −3] nction) [c −5 H− bf + ff −5 MCNaag IIII Db821542 Å MCag IIII Kk 20nsity) [cm xti Thomson de g (e NHI Ne 15og ( lo −10 −10 l Rayleigh 10 0 N = 1015 0 N = 1015 25 H H C II Hα center Si IV −1m] −3] on) [c −5 Hα −5 Å −5 Ca II 8542 Å Mg II k 20y) [cm g (extincti −10 THh− obmf +so fnf −10 N MNag II Db21 CNa II K 15og (densit Fig.5. Payne-styleextinctioncomparisonsfor o HI e l l solargasassumingLTE. Top to bottom: total hydrogen density N = Rayleigh 1016,1015,1014,1013 cm−3, correspondingH to heights 350, 615, 850 and 1150km in ALC7 −15 −15 10 0 0 (Fig.1).Thelogarithmicextinctionscalesalong N = 1014 N = 1014 25 they-axesshiftupwardbetweenpanelstocom- H H C II pensateforthedensitydecrease.Thehorizontal lineaty=−7marksopticalthicknessunityfor Hα center Si IV aslabof100kmgeometricalthickness. −1m] −5 −5 −3] Left: the upper two solid curves show Hα ex- nction) [c Hα −5 Å Ca II 8542 Å Mg II k 20nsity) [cm −wttrini5hbceuÅtnitoi.ounTnsiahnfteoglrtiahnliieVnrdoeciaesgrnottSleiintrdasartckenuadrbdvrieonoafitdshaeefnHoiwronlig∆tn.sλgmT=ahatrek−∆l5odλwiÅs=-- xti −10 Thomson −10 Na I D Ca II K de est solid curve results when Stark broadening g (e 1 15og ( isneglected.Thedashedcurveisthetotalcon- o l tinuousextinctionattheHαwavelength,made l H− bf + ff NHI Mg I b2 Ne upbyH−andHibound-freeandfree-freetran- sitions and by Thomson and Rayleigh scatter- −15 −15 ing. The dotted curves show the separate con- 10 tinuumcontributions(thetoptwoforHibound- freeandfree-freeextinctionarenotlabeled). N = 1013 N = 1013 25 Right: the Hα line-center extinction is shown H H again (uppermost solid curve) but over a dou- C II bled temperature range. It is compared with −1on) [cm] −5 Hα center −5 Si IV 20−3y) [cm] tCaChnaeidiiili1KnN3e3a-a5cine.D7dn11tCeÅra(edii(xod8ttoi5tnet4tcd2et)di,Åo)na(andondofdtM-dtShagiesiihviekIdR1)(3I,dS9aM3s.hgl7ie5nidbeÅ)s2, g (extincti −10 ThoHmαs o−n5 Å −10 CNaa III D81542 Å MCag IIII Kk 15og (densit (caudonnanddstehcirnoenudneo)tai.utnhsTuoeshhxueotsiwsnsecccattohitotneendrciaonstmgo1.lpi7Tde0ht0icenuÅgtrwvndoeeuuseiotsrtlaoitdlhHhecyu−t,drovrHteoas-li o l l gen density NHi and free electron density Ne N N onacomparable(butnon-shifting)logarithmic −15 H− bf + ff −15 HI Mg I b2 e scalespecifiedalongthey-axesatright. Remarkable: at left the large effect of Stark 10 broadening.AtrightthelargeHαextinctionat 5000 10000 15000 20000 10000 20000 30000 40000 hightemperature. temperature [K] temperature [K] Articlenumber,page8of13 R.J.Rutten:H-alphafeatureswithhotonsets.I.Ellermanbombs PaperIIIreachonlyEBthicknessτ≈1theymaybeformedon scattering would cause moustaches, making the suggestion of therisingbranchandrepresentonlyT≈15000−20000K. Engvold & Maltby (1968) incompatible with the observed EB transparencyinthecontinuum. In addition, other lines such as Caii H and Caii8542Å do 3.2. HαextinctioninLTE show EB moustaches but less wide than Hα (Hashimoto et al. Figure 5 shows extinction-versus-temperature diagrams that I 2010;privatecommunicationfromR.Rezaei).ForThomsonre- wish to call “Cecilia Payne diagrams” although they are some- distributiontheyshouldhavesimilarextentsinceitactsthesame what more elaborate than Payne’s curves. First, they show the foranylinewithsimilarcorebrighteningbelowthefibrilcanopy. LTElineextinctioncoefficientratherthanthelower-levelSaha- Fortunately, the first column of Fig. 5 also suggests a more Boltzmannpopulationbymultiplyingwiththetransitionproba- viable EB moustache mechanism: linear Stark broadening by bility,thelineprofile,andthecorrectionforstimulatedemission electrons. In the second panel a 100-km slab is optically thick (withbl=bu=1inEq.1).Second,theydonotshowcurvesfor (extinctionabove10−7cm−1)intheHαwingat∆λ=−5Åfrom fixed electron pressure but for fixed total hydrogen density NH line center at all temperatures above 8000K, while it becomes (a parcel of solar gas in which the electron density varies with onlybarelyopaqueinthecontinuumatT =11000−15000K. temperatureaccordingtothedegreeofionization,especiallyof This parameter domain may therefore explain EB visibility in hydrogen). theHαwingtogetherwithtransparencyinthecontinuum.How- NH diminishes in ten-fold steps from top to bottom. In the ever,itisessentialthatlinearStarkbroadening,aspecificagent ALC7atmospherethesevaluescorrespondtoheights350,615, for Balmer lines, is included in the line formation computation 850,and1150km,respectively,samplingitsupperphotosphere since without it the Hα wing has less extinction than the con- andlowerchromosphere(Fig.1).Theextinctionscalesalongthe tinuum. This is demonstrated by the lowest solid curve, which lefthandy-axesshiftaccordingly. resultsfromonlyaccountingforradiationdampingandVander The horizontal line at y = −7 corresponds to optical thick- WaalsbroadeningasdonebyBelloGonzálezetal.(2013). ness unity along 100 km path length and schematically repre- Thethirdsolidcurvefromthetopineachlefthandpanelre- sentsanEBinsidewaysviewing.Abovethislinea100kmslab sults when a Voigt function is used for the linear Stark broad- appearsopticallythick,belowitopticallythin. ening (as is done in the RH code) instead of the Holtsmark Thissectiondiscussesthefirstcolumn.Itshowscomparisons distribution. It lies slightly lower due to the slower Lorentzian betweenHαandthecontinuum.Thevariouscurveswerecom- ∼ (∆λ)−2 wing decay then Holtsmark ∼ (∆λ)−5/2 decay, which putedusingtheformulaeandtablesinGray(2005)fortheele- through area normalization produces profile cross-overs in the ment mix of Asplund et al. (2009). For Hα linear Stark broad- wingsfurtheroutthan∆λ=−5Å. eningwasincludedusingGray’sequation(11.49)withthefirst The sampling wavelength ∆λ=−5 Å of these comparisons approximation of Sutton (1978) for the Holtsmark distribution. wasselectedbecausetheobservedEBexcessspectruminFig.2 TheSahaequationwasiteratedforhydrogen,heliumandthefirst of Kitai (1983) suggests the start of optical thinness at about two ionization stages of the abundant metals in order to obtain this wavelength for slab-like profile formation. In this EB the thefree-electrondensity(shownatright). moustacheextentwasover10Åoneachsideoflinecenter.Note ThecomparisonsinthefirstcolumnofFig.5wereprompted thatEllerman(1917)specifiedbombextentsupto∆λ=15Å;so by the suggestion of Engvold & Maltby (1968) that the fre- didSeverny(1956)formoustaches. quency redistribution which occurs in thermal electron scatter- Thus,linearStarkbroadeningseemsaviablemechanismto ingmaycausetheextraordinaryEBmoustachesbyshiftingHα transfer Hα photons from the locally bright but obscured line line-core photons over large electron Dopplershift into the far core to escape in the outer wings and pass through overlying Hα wings. They stipulated that for this mechanism EBs must contain sufficient free electrons to offset the very small Thom- fibrils.SimilarlytoThomsonredistribution,itrequiressufficient soncross-sectionσ =6.6510−25cm2,quantifyingthatelectron hydrogenionizationbutithasmuchlargercross-section.Iiden- densityN =1016cmT−3wouldbeneededalonga1000-kmlineof tify it therefore as a key agent producing bright extended Hα e moustaches and making the Balmer lines display the EB phe- sightthroughanEBtogainopticalthicknessoforderunity.They nomenonsospectacularly. suggestedthatthismaybereachedthroughhydrogenionization inphotosphericgas. Myinitialenthusiasmforthismechanism(Sect.6ofRutten 3.3. LTEextinctionofEBdiagnostics etal.2013)wasundonebythetestsshownhere,basedonsim- ilar tests by J. Leenaarts (private communication). Neutral hy- InowturntothesecondcolumnofFig.5.ItcomparestheLTE drogenextinctioninthePaschencontinuumtakesoverfromH− extinctionofHαwiththatofotherEBdiagnostics,againasfunc- extinctionalreadybelowT=10000K,whereasThomsonscat- tionoftemperaturebutoveralargertemperaturerange.Thedif- tering becomes the dominant continuum agent above 10000K ferent curves show LTE line-center extinction for the specified only below hydrogen density N ≈ 1013cm−3 (bottom panel) lines and the Balmer continuum extinction at 1700Å, defined H withextinctionbelow10−10cm−1 sothatonlyoneperthousand by their Boltzmann and Saha sensitivities to temperature and Hα photons would be Thomson-scattered and Doppler-shifted electrondensity.Theelectronandneutralhydrogendensitiesare in a 100-km EB slab. For more scattering the density must be overplottedinthebottompartofeachpanel,withaxisscalesat higher,butthensuchaslabbecomesopaqueinthePaschencon- right. tinuum. ThelittleplateauatthestartoftheNecurveinthetoppanel, IntheALC7chromospherethePaschenextinctiondropssig- also evident in the 1700Å curve, illustrates that ionization of nificantlybelowtheLTEvalue(dashedcurveinthefirstpanelof abundant metal atoms provides the electrons for H− extinction Fig. 1) due to photon losses in Hα, but in HION this happens in the low-temperature photosphere. At higher temperature the onlyinthegreenarchesinFig.2,notintheshocksorthepost- electronscomemostlyfromhydrogen.Thecross-overpointwith shock cool clouds. Therefore, the graphs in Fig. 5 suggest that 50%hydrogenionizationandNHi≈Ne shiftsfromT≈12000K EBswouldbeobservedinthecontinuumwellbeforeThomson to T ≈8000K from top to bottom. The curves and their cross- Articlenumber,page9of13 A&Aproofs:manuscriptno.aa26489 over temperature values change correspondingly between pan- Rayleigh)scatteringat1700Å.InthetoppanelsofFig.5these els,butnotdrastically. curves mimic the Hα curve because both are set by the hydro- Inthelefthandcolumnthesecondpanelsuggestedlog(N )≈ gen n=2 population. In the lower panels Thomson extinction H 15 and T >∼10000K as viable target parameters to obtain Hα flattens the 1700Å curves, similarly to the dashed 6563Å con- wing visibility combined with continuum transparency for the tinuumcurves(withPascheninsteadofBalmerextinction)inthe 100-kmslab.TherighthandcolumnpermitssuchLTEvisibility lefthand column. The 1700Å curve peaks just below the τ=1 estimationalsofortheotherEBdiagnostics.Idiscussthemone lineforthe100-kmslabinthesecondpanel;thicknessrequires byone. awiderslaborlargerdensity. Below 10000K the 1700Å extinction is dominated by Hα. The uppermost solid curve in each panel is again the Hα bound-free Sii and Fei edges, but at higher temperature the line-center extinction, identical to the corresponding curves at main agent is the Balmer continuum. This is already evident left. The most striking feature in these graphs is the discordant in the classic LTE continuum extinction diagrams (in German) behavior of Hα due to its combination of exceedingly large el- in Figs. I–XV of Vitense (1951), the third landmark thesis by emental abundance and exceedingly large excitation energy. In a heroine of astrophysics emulated here. They have been re- eachgraphtheHαline-centerextinctionshowsasteeprisewith drawn(inEnglishandwithbettergraphics)inFigs.3-12A–Oof temperature due to its Boltzmann population factor, followed Novotny(1973).Idonotincludethecool-gasSiiandFeicon- by a decline due to hydrogen ionization which is considerably tributions here because LTE would give severe overestimation temperedbytheever-increasingrelativeexcitation.Atlowtem- alsoforsurroundinggas.Theyarediminishedthroughphotoion- peratureHαhasnosignificantextinctionwhatsoever,butabove ization already in the upper photosphere of 1D standard mod- T≈8000KHαbecomesmuchstrongerthanCaii K,thereverse els(Vernazzaetal.1981)andarefurtherdepletednearhotEBs of their photospheric ratio, and Hα even beats Mgii k signif- throughirradiationbythese. icantly above T = 12000 K. This extraordinary strength may Theultravioletcontinuaareallstronglyresonant-scattering, actuallyyetincreasethroughthemuchslowerdecayforCEion- as evident from the superb formation diagrams in Fig. 36 of ization(Fig.4)combinedwithBoltzmannexcitationforcingby Vernazza et al. (1981). In their VALIIIC model the Eddington- Lyα. Barbierτ=1heightsaround1700Årangeover300–500km,but AnumericalfitofthelocationsofthepeaksoftheHαextinc- mostphotonsarethermallycreatedinthedeepphotosphereand tion curves, which are defined by the sensitivities of the Boltz- thenscatteroutwithaS ≈J declinewhich,oppositetotheline mann,Saha,profileshapeandinducedemissiontermsinEq.1, scatteringinFig.1,has J > Bfromthecombinationoftemper- showsthattheseobey: ature gradient setting by optical photon losses, deep formation, large Wien temperature sensitivity, and the gradient sensitivity log(n /N )=0.683 log(N )−14.8, (5) 2 H H of the Lambda operator (Chapt. 4 of RTSA). A deeply located whichprovidesaquickestimateofthemaximumextinctionthat temperature increase boosts J and the emergent continuum in- HαcanreachindynamicalsituationswithonsetLTEvalidity. tensity across the ultraviolet while an increase near τ=1 does TheHαandCaii8542ÅcurvescrossatT≈7000−8000K. not.EvenalonglineofsightCinFig.2thebrightfootofanEB The100-kmslabisopticallythickatthiscurvecross-overinall sohasultravioletvisibility,beitdiffusefromsurroundscattering panels, conform the invisibility of EBs at the centers of these bytheremainingSiandFeatomsandintheBalmercontinuum linesfromobscurationbythefibrilarcanopy(PaperI). boostedbyLyαirradiation. Hα’s special combination of very large high-temperature Large depth provides the density needed for noticeable extinction with very small low-temperature extinction also im- Balmer-continuum brightening (Fig. 5). In addition, since EBs pliesthatahigh-temperatureslabembeddedincoolgascandis- are bi-modal jets, compression at the lower shock likely en- playlargeHαwingemissivitywithinatransparentenvironment, hancesthelocalBalmer-continuumproduction. withoutshieldingalonglinesofsightasCandBinFig.2.Fig.5 The 1700Å–Hα-wing comparisons in Fig. 6 of Paper II, suggests that cool surrounding gas will not have any Hα opac- Fig. 4 of Rutten et al. (2013), and Figs. 2, 6, 9 of Paper III in- ity. The fractional population curve (dashed) in the first panel deed suggest, even at the low AIA resolution, that EBs appear ofFig.1showsthatintheALC7atmospheretheHαopacityis more extended in the 1700Å images than in the Hα-wing im- indeed negligible between the deep photosphere and the chro- ages,thatthe1700ÅimagesfavorEBfeet,andthattheseshow mosphericplateau. the largest blurring. The IRIS spectra in Paper IV indeed show Close to an EB absorption of Lyα photons from the EB it- EBbrighteninginthe1400Åcontinuum. self boosts the surrounding n = 2 population as demonstrated in Sect. 2.4, but the extent of such halos is small and they oc- cur only in the Hα core in which the halo is invisible anyhow Caiilines. Caii KandCaii8542ÅhavesimilarcurvesinFig.5 fromobscurationbyoverlyingfibrils.IntheouterHαwingssur- except for the Boltzmann sensitivity of the latter. In both lines roundingcoolgaslacksmoustacheopacityfromshortageoffree the slab is thick for the target parameters, but overlying cooler electrons for Stark broadening. The therefore unmolested Hα- fibrils are yet thicker so that only wing brightenings result, at moustache sharpness permits, at sufficiently high angular reso- smallermoustacheextentthenforHαsincetheselinessufferno lution,toresolveveryfinesubstructurewithinEBs,asobserved Starkbroadening.Thisisalsoconformobservations(PaperIIfor inHashimotoetal.(2010)andPaperI. Caii8542Å,Hashimotoetal.2010forCaii H). Also, the hotter EB top observed along line of sight A re- At temperatures above their cross-overs in Fig. 5 Hα and tains large Hα emissivity thanks to the slow extinction decline Caii8542Åhaveoppositetemperaturesensitivity,implyingthat forincreasingtemperature. theCaii8542ÅwingsfavorcoolerEBfeet,theHαwingshot- ter EB tops. This is seen in Fig. 3 of Paper II. In addition, the Balmer continuum. The second solid curve is the continu- downward-directed part of a bi-modal EB jet favors blue-wing ous extinction due to hydrogen and continuous (Thomson and emission, also evident in that figure. Furthermore, the larger Articlenumber,page10of13