The Atomic Physics Underlying the Spectroscopic Analysis of Massive Stars and Supernovae

0.69 MB·English

by  D. John Hillier

The Atomic Physics Underlying the Spectroscopic
Analysis of Massive Stars and Supernovae
D. John Hillier 1
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Abstract Wehavedevelopedaradiativetransfercode, 1 Introduction

] cmfgen, which allows us to model the spectra of mas-
E sivestarsandsupernovae. Usingcmfgenwecanderive Massive stars are a crucial ingredient of galaxies, and
H fundamentalparameterssuchaseffective temperatures the universe. They enrich the interstellar medium
. andsurfacegravities,deriveabundances,andplacecon- (ISM)withmetals,eitherthrough“quasi-steady”mass
h
p straints on stellar wind properties. The last of these is loss, or when they explode as supernovae (SNe). They
- important since all massive stars are losing mass via a depositmomentumandenergyintotheISM,andionize
o stellar wind that is driven from the star by radiation the surrounding gas, producing colorful nebulae (Hii
r
t pressure, and this mass loss can substantially influence regions). Massive stars also exhibit a wide range of in-
s
a the spectral appearance and evolution of the star. Re- teresting phenomena including radiation driven winds,
[ cently we have extended cmfgen to allow us to un- and colliding winds. Colliding winds, which occur in
1 dertake time-dependent radiative transfer calculations massive star binaries, generate strong shocks that give
v of supernovae. Such calculations will be used to place risetohardX-rayemission(see,e.g.,reviewbyStevens
2 constraints on the supernova progenitor, to place con- 2005). The key tool for understanding massive stars is
7
straints on the supernova explosion and nucleosynthe- spectroscopic analysis.
3
5 sis, and to derive distances using a physical approach Usingspectroscopicanalysiswegenerallywishtoin-
. called the “Expanding Photosphere Method”. We de- fer the fundamental parameters that describe the star
1
0 scribe the assumptions underlying the code and the —itsmass,effectivetemperature,radius,surfacegrav-
1 atomic processes involved. A crucial ingredient in the ity, and surface abundances. From these, and with the
1 codeistheatomicdata. Forthemodelingwerequireac- aid of evolutionary models, we try to infer both the
v: curatetransitionwavelengths,oscillatorstrengths,pho- previous evolutionary history of the star and its future
i toionizationcross-sections,collisionstrengths,autoion- evolution. As we generallycan’t study the evolutionof
X
ization rates, and charge exchange rates for virtually a single star we need to infer/constrain the effects of
r
a all species up to, and including, cobalt. Presently, the complexphysicalprocessesbystudyinggroupsofstars.
availableatomicdatavariessubstantiallyinbothquan- Constraintsprovidedbythese studiescanthenbe used
tity and quality. to improve evolutionary calculations.
There are still significant uncertainties in evolution-
Keywords radiative transfer; atomic data; atomic ary models (e.g., treatment of convection, stellar rota-
processes; stars: winds, outflows, early-type; super- tion, and time-dependent mass loss). Rotation, for ex-
novae: general ample, is now recognized as a crucial factor in massive
star evolution — it affects the evolutionary lifetime of
the star, surface abundances, and the star’s evolution,
D.JohnHillier
and there is a strong interaction between rotation and
DepartmentofPhysicsandAstronomy,
3941OHaraStreet, mass loss (e.g., Meynet and Maeder 2000). Since stars
UniversityofPittsburgh,Pittsburgh,PA,15260 formwith a range of rotationrates,it is no longerpos-
sibletoassignapositionintheHR-diagramtoaunique
mass (e.g., Meynet and Maeder 2000).
There are also uncertainties in spectroscopic analy-
ses. Some of these arise from model assumptions and
2
inadequacies in the atomic data. Others arise from an hot W-R core, together with the dense stellar wind,
incomplete understanding of the stars we are trying to gives rise to an optical spectrum dominated by emis-
model. O stars, for example, show strong evidence for sion lines — the antipathy of normal spectra in which
microturbulentvelocitiesapproachingthesoundspeed, the optical spectral region is dominated by absorption
while Of stars show evidence for macroturbulent ve- lines. Because of the stellar winds, with flow velocities
locities in excess of the sound speed. The origin of oforder1000kms−1,itisconvenienttosolvetheradia-
these velocity fields is unknown. Mass-loss rates are a tive transfer equation in the comoving frame — in this
key ingredient of stellar evolution models, but deriving frame the opacities and emissivities can be assumed to
accurate mass-loss rates is difficult. While wind the- be isotropic.
ory provides a qualitative understanding of mass loss In cmfgen, the primary radiation transport equa-
in O stars, there are fundamental uncertainties since tions to be solved (assuming V ∝ r and spherical ge-
theory predicts, and observations show,that the winds ometry) are
are highly inhomogeneous. As a consequence of the in-
homogeneities,mass-lossratesderivedfromobservation
1 D(r3J ) 1 ∂(r2H ) νV ∂J
depend on the diagnostic used. For more information ν + ν − ν =η −χ J (1)
cr3 Dt r2 ∂r rc ∂ν ν ν ν
on radiation driven winds, mass-loss rates, and prob-
lemsmodelingOstars,thereaderisreferredtoreviews and
by Hillier (2008); Puls, Vink, and Najarro (2008) and
Owocki (2009).
1 D(r3H ) 1 ∂(r2K ) K −J
ν ν ν ν
+ +
cr3 Dt r2 ∂r r
νV ∂H
2 CFMGEN — A Spectroscopic Tool − ν =−χ H . (2)
ν ν
rc ∂ν
Inordertofacilitateanalysisofhotstars(starsinwhich In the above
molecules and energy transport by convection at the
stellar surface can be neglected) we have developed a
non-LTEradiativetransfercode,cmfgen(Hillier1987; [J ,H ,K ]= 1 1[1,µ,µ2]I (t,r,µ)dµ (3)
1990; Hillier & Miller 1998). ν ν ν 2Z−1 ν
The primary purposes of cmfgen are as follows:
are moments of the radiation field, D/Dt is the La-
1. To derive accurate stellar parameters and abun- grangian derivative, I is the specific intensity at time
ν
dancesforcomparisonwith“evolution”calculations. t, location r, frequency ν, and in direction µ, µ=cosθ
2. To provideaccurateEUV(i.e., λ<912˚A) radiation where θ is the angle between the radius vector at r
fields for input to nebular photoionization calcula- and the specific intensity, χ is the (frequency depen-
ν
tions. dent) opacity, and η is the emissivity (e.g., Mihalas
ν
3. To provide fundamental data for the study of star- 1978; Mihalas and Mihalas 1984). When written in
bursts, star formation in galaxies, etc. this form, the equations are deceptively simple — in
4. To provide a better understanding of the hydrody- reality they are very complex. First, these equations
namics of stellar winds. needtobesolvedatalargenumberoffrequencies,typ-
5. To provide distances to Type II SNe using the ex- ically 100,000. Due to the ∂/∂ν term, these equations
panding photosphere method (EPM — e.g., East- are explicitly coupled in frequency. Second, much of
man,Schmidt,andKirshner1996;Baronetal.2004; the physics is hidden in χ and η . In the best case
ν ν
Dessart and Hillier 2006) and its variants. scenariothese aredeterminedby the localtemperature
6. To provide diagnostics of SNe which can place con- and density, but even then the temperature is deter-
straints on the progenitor and the explosion. mined by the radiation transport, and thus there is an
7. To allow the development and testing of approxi- implicit coupling of the opacities and emissivities with
mate methods that can be used in more complex the radiation field.
geometries and in inhomogeneous media. In stellar atmosphere modeling we can neglect the
Lagrangianderivative term, and the equations are eas-
cmfgen has been used to study O Stars; Wolf-Rayet
ily solved (for non-Hubble flows additional terms are
(W-R) Stars;Luminous Blue Variables(LBVs); A & B
introduced). However, for Type II SNe, it has be-
supergiants; and Type I and Type II Supernovae.
come increasingly apparent that to accurately model
cmfgen was originally designed to model spectra
thespectrathe fulltime-dependentradiationtransport
of W-R stars which have a dense stellar wind. The
equations must be solved.
3
3 LTE & non-LTE the 2pelectron. In contrast,LTDR usually refers to
recombinationthroughdoublyexcitedstatesthatlie
Agreatsimplification,applicabletomostmain-sequence closeto,butabovetheionizationlimit(Nussbaumer
spectral types, is the assumption of local thermody- andStorey1983). Asaconsequence,LTDRratesare
namic equilibrium (LTE). With this assumptionweas- sensitive to the atomic structure — a single energy
sumethatthestateofthegasisentirelydeterminedby level close to the ionization edge can dominate the
its temperature and density (and composition). Thus recombination rate at low temperatures
we can use statistical arguments to determine the ion- 3. Bound-bound transitions
izationstateofthegas(Sahaequation)andlevelpopu- 4. Collisionalexcitationandde-excitation. Inhotstars
lations(BoltzmannorSaha-Boltzmannequation). The thisoccursprimarilybyelectrons,butincoolerstars
LTE assumption is valid when collisional processes collisionswithotherspeciesarealsoimportant. For-
(which couple directly with the local gas) dominate tunately, the conditions in stellar atmospheres are
over radiative processes (which couple the gas to gas such that the electrons have a Maxwellian velocity
elsewhere by radiation). distribution, and thus we require collision strengths
In LTE, we require line lists and opacities (due to averagedover a Maxwellian velocity distribution.
bound-free,free-free,andbound-boundprocesses). The 5. Collisional ionization and collisional recombination
opacities,for a givencomposition, aresimply functions (i.e., three-body recombination)
of the density and electron temperature. Deep inside 6. Auger ionization by X-rays (and gamma-rays in
the star radiation diffuses, and the transport of radia- SNe)
tion is dictated by the Rosselandmean opacity defined 7. Charge exchange reactions
by 8. Two-photon emission
9. In SNe, collisional ionization and excitation with
∞ non-thermal (high-energy) electrons that are cre-
1 π 1 dB (T)
ν
= dν . (4) ated via gamma-ray photons and Compton scatter-
χ 3σT3 Z χ dT
R 0 ν ing (see, e.g., Kozma and Fransson 1992).
In the photosphere the situation is very different —
When non-LTE is applicable, there is a tremendous
use of the Rosseland mean opacity is no longer appli-
non-linearcouplingbetween the radiationfieldandthe
cableandwemustsolvetheradiativetransferequation
level populations. The radiation field determines the
at every frequency. To do this we need a detailed de-
electron temperature and level populations which, in
scription of the opacities (Fig. 1). Since the theoreti-
turn, determine the radiation field. As a consequence
cal spectrum is to be compared with observation, it is
iterativetechniquesareusedinordertoobtainfullcon-
important the bound-bound transitions have accurate
sistency between the radiation field and level popula-
wavelengths.
tions (see review by Hubeny 2009).
In O stars, W-R stars and SNe (as well as many
In Type II SNe, even greater complexities are in-
other objects) the assumption of LTE is invalid. In-
troduced. To accurately model Type II SN spectra it
stead we are forced to solve the equations of statistical
is important to include advection terms, which couple
equilibrium — the equations describing how individ-
the populations at one time step to those at an earlier
ual levels in an atom are populated and depopulated.
time step, into the equations of statistical equilibrium.
Because the radiationfield is no longer Planckian(and
Theinclusionofadvectiontermsintotherateequations
describedbythelocalelectrontemperature)theatomic
helps explain the strength of Hα emission in spectra
populations that satisfy these equations will generally
of SN1987A (Utrobin and Chugai 2005; Dessart and
differ from their LTE values. In order to solve for the
Hillier2010)andSN1999em(DessartandHillier2008).
populations many atomic processesneed to be treated.
These include:
1. Photoionization and radiative recombination (i.e., 4 Atomic Details Matter
bound-free processes)
2. Low and high temperature dielectronic recombina- In the construction of model atmospheres the precise
tion (LTDR and HTDR). In high temperature (or details of the atomic opacity are generally unimpor-
classical) dielectronic recombination, recombination tant. However in spectroscopic analyses this is not the
occurs through doubly excited autoionizing states case. In hot stars we often have only a few lines that
with large n (e.g., Burgess 1964). For example, the arise from a given species/ionizationstage. In order to
2pnl states in Ciii that converge on the Civ 2p deduceabundances,itiscrucialthatourmodelfullyde-
state, and which “recombine” through the decay of scribe the formation process of each individual line. In
4
Fig. 1 Illustration of the complex opacity at one location (with T ∼ 40,000K, Ne ∼ 1015cm−3) for a typical model
atmosphere.
LTEthisisrelativelyeasy. Innon-LTEthiscanbevery low-temperature dielectronic recombination. Interest-
difficult,sinceweneedtofullyunderstandtheprocesses inglythe2s3p1Po statepreferentiallydecaysto2p21D
affecting the populations of the levels involved in the ratherthan2s3s1S(Nussbaumer1971;Cardona-Nunez
transition. This means having all the atomic data rel- 1978). Thus λ5696 can be in emission, while λ8500
evant to those levels and, since the population of those (produced by the decay of 2s3p1Po, the lower level of
levels (except in a few special circumstances) depends λ5696) can remain in absorption — a phenomena seen
on the population of other levels in the atom, we re- in Of stars (Ebbets and Wolff 1981).
quire atomic data for the whole atom. Unfortunately Anotherline formationmechanismis continuumflu-
the situationcanbe evenmorecomplexthanthis —in orescence, which is best illustrated by an example. In
some cases line strengths of one species are affected by Civ there is a strong transition at 312˚A which con-
complexinteractionswithanotherspecies. Toillustrate nects the ground state, 2s2S, to the 3p2Po state. As
the complexities, we discuss four examples. wearedealingwitha groundstatetransition,itis usu-
In WC stars, evolved massive stars deficient in H, allyopticallythick,andhencephotonstypicallyscatter
and showing He, C, and O emission lines in their spec- manytimesinthistransitionbeforeescaping,orbefore
tra, Ciii λ5696 is used as one of the key classification being destroyed. Howeverthe 3p2Po level can also de-
diagnostics. In WC4 stars the line is very weak, if not cay via a transition at λλ5801,5812 to the 3s2S state.
absent, while its strength increases (but with scatter) The probability of this occurring is low (∼ 1/170 per
as we move along the spectral sequence from WC4 to scattering) but it does provide a means of converting
WC8 (Torres, Conti, and Massey 1986). Interestingly, farUV photonsinto opticalemission(Hillier 1988). To
other Ciii lines show much less variation in strength get the strength of the observed optical emission cor-
along the spectral sequence (e.g., Conti, Massey, and rect we have to have a good understanding of the Civ
Vreux 1990);thus there is something special about the model atom as well as accurately model the spectral
formation of Ciii λ5696. region around 312˚A — a region which cannot be di-
A simplified Grotrian diagram for the singlet-terms rectly observed in O and W-R stars, and which suffers
of Ciii is shown in Fig. 2. Ciii λ5696 emission is pro- heavy line blanketing by iron group elements. Contin-
ducedbythedecayofthe2s3d1Dstatetothe2s3p1Po uum fluorescence is important in many astrophysical
state (A = 4.3×107s−1). However, photons prefer to objects including W-R stars belonging to the nitrogen
decay from the 2s3d1D to the 2s2p1Po state, with sequence (WN stars), LBVs, and quasars.
A = 6.3 × 109s−1. In early WC stars, most of the Perhapsthe mostfamousexampleofline overlapin-
decaysoccurviathisroute—itisonlywhenthistran- fluencing line strengths is seen in nebula spectra. In
sitionbecomesopticallythick,thatCiiiλ5696isdriven nebula,someOiiilines areseento be unusuallystrong
intoemission(Hillier1989). Tocomplicatemattersfur- — much stronger than would be predicted by recom-
ther, the strength of Ciii λ5696 is also influenced by bination theory. Moreover, line strengths in individ-
5
ual multiplets do not correspond to those observed in 5 Atomic Data Requirements
the laboratory. The explanation lies in the chance
coincidence of an Oiii line (λ303.80) with Heii Lyα Astrophysicists are interested in understanding the
(λ303.78). AstheHeiiLyαtransitionisopticallythick, physical processes and properties of astrophysical ob-
photonsemittedinthetransitionaretrappedandscat- jects (stars, SNe etc). Ideally we would have all the
ter many times. During this scattering process there is required atomic data, and any discrepancies between
achancethatsomeoftheLyαphotonswillbeabsorbed modelsandobservationswouldonlyberelatedtomodel
by Oiii. The upper Oiiilevels haveseveralalternative assumptions and the neglect of crucial physical pro-
decayroutes,someofwhichleadtotheenhancedemis- cesses. Unfortunately this is notthe case — in the real
sion in some lines seen at optical and UV wavelengths. worldonly limited atomic data is available, and it is of
The process is termed Bowen Resonance Fluorescence, mixedquality. While greatstrides havebeen made im-
after its discoverer (Bowen 1934). A more recent and proving the quality and quantity of atomic data (e.g.,
detaileddiscussionofthemechanismisprovidedbyOs- Seaton 1987; Hummer et al. 1993; Kurucz 20091), the
terbrock (1989). availability of atomic data and its quality must always
In O stars a similar overlap occurs. In this case be consideredwhenperformingspectroscopicmodeling
there is a chance overlap of Feiv lines with the Hei to obtain results of astrophysical importance. Given
resonancetransitionat584.33˚A.TheFeivlinesremove limited resources, what are the most crucial data sets
photonsfromthetransition,loweringthepopulationof that are still required?
the1s2p1Po level,whichinturnaffectsthestrengthof Ingeneral,themostimportantelementsforhotstars
Hei singlet levels in the optical spectra (Najarro et al. are H, He, C, N, O (generally referred to as CNO el-
2006). This in turn affects effective temperature deter- ements), and Fe, with Ne, Si, S, and Ar of somewhat
minations, since the ratio of Hei to Heii line strengths lesser importance. In SNe the situation is somewhat
is used as a temperature diagnostic. Prior to the dis- different, with other iron group elements (particularly
coveryofthiseffectitwasknownthattherewereincon- Ni and Co) also being of crucial importance. Even for
sistencies between singlet and triplet Hei lines in some this small subset of species, important atomic data is
Ostars. Theeffectwaserroneouslyascribed(atleastin missing.
thisauthor’sopinion)toaproblemwiththetripletline One of the most important requirements, but per-
strengths. However,in hindsight it is muchmore likely haps the least appreciated, are accurate energy levels
thattheproblemlieswiththe singletlinestrengthsbe- and wavelengths. In general, energy levels and wave-
cause the lower level of most of the optical diagnostic lengths of sufficient accuracy can generally only be ob-
linesiscoupledtothe1s2p1Po statewhosepopulation tainedfromobservation. Asoncenotedtome,gfvalues
isaffectedbyradiation-transfereffectsintheresonance accurateto10%aregreatbutawavelengthaccurateto
transition. 10% is (almost) useless. For CNO elements atomic en-
ergy levels and wavelengths are generally pretty good,
however additional data are still needed. This is espe-
ciallytrueoftheinfraredspectralregion. Additionally,
accurate energy levels are needed for doubly excited
states that lie near, or above, the ionization limit (e.g.
Ciii)sincethe preciselocationofthesestatesisimpor-
tant for determining dielectronic recombination rates,
particularlyatlow temperatures. Measuringthe width
oflinesfromthesestatescanalsogiveanestimateofau-
toionizationprobabilities,providinganimportantcheck
on theoretical calculations.
As regards gf values, there has been a proliferation
of theoretical data which has greatly facilitated the
advances in spectroscopic analyses. In many cases,
the calculations assume LS coupling which is gener-
Fig.2 SimplifiedGrotriandiagram(nottoscale)forCiii. ally adequate for computing mean opacities and model
atmosphere structures, but may not be so useful for
1Atomic data from Robert Kurucz is available at
http://kurucz.harvard.edu/
6
performing non-LTE abundance studies. Theoretical Forotherelementsphotoionizationcross-sectionsare
calculations can often provide reliable gf values, but unavailable. Ofparticularimportanceareelementslike
for some cases the gf values are not sufficiently accu- Co and Ni which have high abundances in SNe. At
rate for analyses. As an example we consider the three presentincmfgen relativelycrudeapproximationsare
mostimportantdecaysfromthe 2p3p3D statein Ciii. used [data for Niii is available — Nahar and Bautista
These are (2001)]. Lines belonging to Scii can also be readily
2s2p3Po -2p3p3D (0.00926,2.7×108s−1, 369.4˚A), identified in Type II SNe spectra, and photoionization
2p3s3Po -2p3p3D (0.166, 1.5×107s−1, 6740.6˚A), data for Sc ions is also unavailable. The case of Sc is
and interesting—Schasrelativelylowabundanceandthus
2s3p3Po -2p3p3D(0.00286,4.6×106s−1,1577.4˚A) it has very little influence on SNe spectra. However it
where the numbers in brackets are the oscillator does produce readily identifiable features, and match-
strength, A value, and wavelength, respectively. Using ing such features does provide a quantitative test of
gf values computed by Nussbaumer and Storey (1984), the spectroscopic model. It also pleases observers (and
Hillier(1987)foundthatthe1577˚AlineintheWCstar sometheorists),whoarequicktopointouttheabsence
HD165763wasmuchstrongerthanwouldbepredicted of Sc features from models.
on the basis of the observed strength of the 6740.6˚A The lack of collisional data is probably the area of
line. Improved calculations by Peter Storey (private most concern. For low lying levels, collisional data is
communication)indeedshowedthatthegfvalueforthe generally available, but for higher levels such data is
1577˚A line was too large, and his revised value (given usually lacking. In such cases approximate formulae,
above) gave much better agreement with observation.
of unknown accuracy, are often used. The formulae
Unfortunately, his calculations also revealed that the
often depend on the gf value of the transition connect-
actual value was quite sensitive to assumptions used in
ing the two levels, but as has been pointed out in the
the calculations.
past (e.g., Mihalas 1978), collisional rates for LS semi-
Another example is the gf values of the Feiv tran-
forbidden or forbidden transitions can be as large as
sitions which overlapthe Hei resonance transition (see
thosefornon-forbiddentransitions. Forthevastmajor-
§4). The two transitions of most interest are
ityofapplicationsweneedcross-sectionsaveragedover
Feiv 3d5 4F – 3d4(3G)4p 2Ho and
9/2 9/2 a Maxwellianvelocity distribution, and it is best tabu-
Feiv 3d5 2D35/2 – 3d4(3G)4p 4Ho7/2. lated as a temperature dependent collisional strength.
Bell and Kurucz (1995) give gf values of 0.00349 and Despite recent improvements (e.g., Przybilla and But-
0.0288for the two transitions,while Beckerand Butler ler2004)therearestilluncertaintieswiththehydrogen
(1995) give 0.00251 and 0.00264. In these cases mea-
collision strengths.
surementsareclearlydesirabletoconstrainthestrength
Charge exchange reactions are of particular impor-
of these lines.
tance in non-LTE modeling. In many cases a charge
Photoionization cross sections are now available for
exchange reaction with H, rather than the recombina-
atoms with even atomic numbers, up to and including
tion rate, determines the ionization balance. An ex-
Fe,primarilythroughthe OPACITYandIronProjects cellent example is O+ + H ⇋ O + H+, which has
(e.g., Seaton 1987; Hummer et al. 1993). These cross- a rate coefficient of order 10−9cm3s−1. Many cross-
sections appear to show reasonableagreementwith ex-
sections for charge reaction rates with H and He have
perimentwhenavailable. Onepossibledeficiencyinthe
beencomputed;aconvenienttabulationisthatofKing-
cross-sections is the location of the resonances, which
don and Ferland (1996). One problem with tabulated
aretheoreticalratherthanexperimental. Erroneouslo-
cross-sections is that the charge exchange channels are
cationscanpotentiallyaffectrecombinationrates(par-
not always provided. Such information is necessary as
ticularly at low temperatures) and there is also the
wegotohighdensity,sincewemustincludethereverse
potential problem of interactions between resonances
reactions in order to recover LTE.
and spectral features. The importance of the latter ef-
Another concern is the paucity of data for charge
fect is unknown. To expedite calculations in cmfgen
exchange reactions with species other than H and He.
we generally smooth the photoionizationcross-sections
This paucity is understandable — H and He have the
(typically with a Gaussian of full-width 3000kms−1).
greatest effect since they are easily the most abun-
Originallythesmoothingwashard-wiredintothecross-
dant elements in most astrophysical contexts. How-
sections, but for most cross-sections the smoothing is
ever, there are objects that are H and/or He deficient.
now a control parameter. This allows us to easily test
In WC stars for example, H is absent, and He, C, and
the influence of the smoothing. As computers become
O have comparable abundances. In SNe a wide range
faster, and especially for 1D models, smoothing is no
of species are present, with C, O, Si, Ne, Fe, Ni, Co
longer a necessity, but rather a computational tool.
7
exhibiting large mass fractions in some regions. De-
spiteadvancesinspectralmodelingofSNe(e.g.,Baron,
Branch,andHauschildt2007;Kasen,Thomas,andNu-
gent2006;KasenandWoosley2009;DessartandHillier
2010), there are still significant uncertainties, and it is
notcurrentlypossibletoidentifyadiscrepancybetween
model and observation that might be due to a charge
exchange reaction.
Acknowledgements I would like to thank the or-
ganizers of the 2010 HEDLA conference for a superb
meeting. Support for program HST-AR-11756.01-A
wasprovidedbyNASAthroughagrantfromtheSpace
Telescope Science Institute, which is operated by the
Association of Universities for Research in Astronomy,
Inc., under NASA contract NAS 5-26555.
8
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