theoretical effect of various broadening abstract · the line-opacity profile is lorentzian, with a...

377

THEORETICAL EFFECT OF VARIOUS BROADENING

PARAMETERS ON ULTRAVIOLET LINE PROFILES

Eric PeytremannSmithsonian Astrophysical ObservatoryCambridge, Massachusetts

ABSTRACT

We study the relative importance of variousdamping parameters in ultraviolet lines under con-ditions of normal stellar atmospheres(10,000°K <_ T ff <. 30,000°K, log g = 4) . It is

found that the damping by electron collisions isalways much smaller than either the radiative orthe classical damping, except for lines that arisefrom high-excitation levels and do not thereforedevelop strong damping wings. A damping constantequal to 10 times the classical value is alwaysmuch too large when compared to the more realistic(electron + radiative) damping.

I. INTRODUCTION

The spectra of 0 and B stars show a large number of metal-lic lines in the ultraviolet region of the spectrum — thatis, between the Lyman limit and approximately 2000 A. Werefer the reader to the results presented at the IAU Symposium36 (Houziaux and Butler, 1970). Some of these lines are sostrong that they can be observed with a resolution as low as10 A (Code and Bless, 1970) . These strong lines can be heavi-ly saturated and hence develop important damping wings. Soone must pay some attention to the damping parameters thatone is going to use in line-profile calculations. In additionto the ordinary spectral analysis of each individual line,calculation of the wings of these strong lines must be carriedout carefully because (a) they may account for a nonnegligiblefraction of the total blanketing effect, and (b) they mayblock out a substantial amount of energy from the spectral

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378 SCIENTIFIC RESULTS OF OAO-2

ranges (narrow or broad) to which they belong. Point (a) con-cerns the structure of atmospheric models, and (b) relates tothe effects of these lines on such observable quantities aslow-resolution spectroscopy, or narrow-to-broad-band photome-try. Earlier attempts to calculate blanketed models withultraviolet lines have included a damping constant equal to10 times its classical value (see Adams and Morton, 1968;Hickok and Morton, 1968; Bradley and Morton, 1969; Wayne vanCitters and Morton, 1970). The reason is perhaps that theirvalue represents empirically rather well the damping in solar-type atmospheres. But under solar conditions, the broadeningby collisions with neutral particles is a predominant dampingmechanism, whereas in the hotter atmospheres studied here, itis not. In this paper, we compare various damping parametersand from them calculate a number of line profiles. The rangeof temperatures considered is such that damping by collisionswith neutral hydrogen can be neglected — that is, the temper-atures are representative of model atmospheres with effectivetemperature Teff larger than 10,000°K. The upper limit of thetemperature range has been taken equal to Teff = 30,000°Kbecause in hotter atmospheres, the effects of non-LTE are ex-pected to be very large (Mihalas and Auer, 1970) .

II. DAMPING PARAMETERS

For metallic lines, which are the only ones considered inthis study, we shall consider two damping mechanisms:

1. Natural, or radiative, damping YR/ which, for a linewith upper level u and lower level &, is given by

YR = Z AAi + Z AUJ . (1)E.i<E£ Ej<Eu

Here, the A£J_ ' s are the transition probabilities from level £to level i, and Auj, from level u to level j, measured insec"1 . The summations are carried over all levels i lowerthan level £, and all levels j lower than u. The line-opacityprofile is Lorentzian, with damping constant YR-

2. Broadening by electron collisions. According to Sahal-Bre"chot (1969a,b) and to Chapelle and Sahal-Brechot (1970),the impact approximation is valid for electron collisionsunder the conditions of normal stellar atmospheres. Hence,the line-opacity profile is Lorentzian, with a damping parame-ter Ye (sec'

1), where Ye i-s proportional to the number densityof the perturbers, that is to the electron density Ne (cm-3).

BROADENING PARAMETERS FOR ULTRAVIOLET LINE PROFILES 379

Because both these broadening mechanisms give rise to Lo-rentzian profiles, the resulting profile is Lorentzian, withdamping y equal to

Y = YR + Ye (sec-1) . (2)

The damping due to collisions with protons or He+ ions ismuch less than the electron damping (Sahal-Brechot and Segre,1970) . As we shall see, the electron damping itself plays aminor role in all cases where damping wings are strong.Hence, we neglect the damping due to collisions with H+ andHe+ ions. We shall also compare the radiative and electrondamping to the classical damping yc,

yc = 0.221 x 1016/A2 (sec-1) , (3)

where X is the wavelength of the line in angstroms. A numberof model atmospheres with ultraviolet line blanketing havebeen computed with 10 times yc, the value of Morton and hiscoworkers cited earlier. Because the classical value fordamping is easy to compute, it would be useful to derive anempirical value of the damping constant as a multiple of yc,for the following reasons. First, the computation of line-blanketing effects involves lengthy calculations (hundreds orthousands of lines); it is desirable to keep the number withinreasonable limits. Second, for many of these lines, the datafor YR and ye are simply unavailable. If, however, the radi-ative damping YR and the electron damping ye are available forthe very strong lines, we can make the following predictions.If YR is predominant, the damping mechanism does not give anyinformation on the properties of the atmosphere, because YRis essentially an intrinsic atomic parameter. On the otherhand, if ye is predominant, the damping part of the line pro-files would give us information on the state of the gas,mainly the electron density and only slightly, the temperature.This information would then play the role of a gravityindicator.

To carry out these various comparisons, we selected thosemultiplets for which the necessary data were available. Thesedata, together with some other basic line data, are displayedin Table 1. For each multiplet, we indicate the name of theion in the first column, followed by the abundance by numberlog e (with log e(H) = 12), the ionization potential X(in ev),the wavelengths A(A), and the oscillator strengths log gf ofeach multiplet's lines. Next, we give the excitation poten-tials (in ev) of the lower (Xj ) and upper (Xu) levels. Final-ly, the last three columns contain the electron dampingCe = 10

6 Ye/Ne at T = 20,000°K, the radiative damping YR/


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the classical damping Yc. The two latter are in units10~8 sec"1, and Yc nas been calculated according to equation(3) .

The values of the electron damping have been taken fromSahal-Br£chot and Segre (1970) . It should be noted that thetemperature dependence of Ye is weak. In most cases of inter-est, Ye varies like i--

0*25. Also, the damping Ye is the samefor all lines of a given multiplet (Chapelle and Sahal-Brechot, 1970) .

The radiative damping YR has been calculated according toequation (1) by searching through the tables of atomic-transi-tion probabilities by Wiese, Smith and Miles (1969) and byWiese, Smith and Glennon (1966). The log gf values have alsobeen taken from these tables. No critical discussion of thecontents of these tables has been attempted. It could bethat lifetimes of some levels are missing, which would leadto radiative-damping constants that are too small. (This maybe the case of multiplet Si II at A = 1808 A.) We give onlyone value of YR for each multiplet because the variations ofYR within a given multiplet are at most ±0.1 x 108 (sec"1).

Before we discuss these various damping parameters, wedescribe Figure 1. It shows the damping log Ye and log YR foreach multiplet of Table 1 (in units sec"1). The open circlesindicate the electron damping, and the crosses the radiativedamping. Each multiplet is labeled by its wavelength. TheYe is for an electron density Ne = 10

1!*(cm~3) and a tempera-ture T = 20,000°K. This density corresponds to rather highvalues of the optical depth (T5QOO ~ 1) n atmospheres witha gravity log g = 4 and Teff > 10,000°K. In shallower layers,where the lines are more likely to be formed, the electrondamping would be lower. And in atmospheres with lower gravi-ties, it would be still lower. Thus, the values of Ye in Fig-ure 1 must be considered as upper limits in most cases ofastrophysical interest. Also shown in Figure 1 is the classi-cal damping Yc/ together with 10 times Yc, as a function ofwavelength.

From Table 1 and Figure 1, we can easily draw the follow-ing conclusions:

1. The electron damping is nearly always lower than theradiative damping, even with the rather high value ofNe = 10

1'*(cm~3) . The only lines for which the electron dampingis important are those arising between very highly excitedlevels. Hence, these lines are not strong, and damping doesnot play an important role.

2. For most lines whose lower level is not too highly ex-cited (and which may therefore be very strong), the radiativedamping is between 1/3 and 3 times the classical damping. Oneexception is the already mentioned multiplet of Si II at


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A = 1808 A.3. For all lines that qualify to develop strong damping

wings, the value Y = 10 Yc is much too large, by a factor 3 atleast, with respect to either YR or Y = R + Ye-

4. The radiative damping being predominant, we do not ex-pect any gravity effect on the line profiles via the dampingmechanism. This answers the question that we raised previous-ly-

III. ULTRAVIOLET LINE PROFILES AND EQUIVALENT WIDTHS

In this section, we consider how our various damping para-meters influence the profiles and equivalent widths of stronglines. These lines are supposed to be formed in stellar


atmospheres with effective temperatures Teff ranging from10,000 to 30,000°K and with a surface gravity log g = 4. How-ever, because we want to study the relative effects of thedamping parameters with respect to each other, we do not worrytoo much about the degree of realism of our computations (i.e.,abundances, microturbulence, etc.). So we simply indicate howthe calculations have been performed, without any criticaldiscussion of matters not directly related to the dampingproblem.

To calculate our line profiles, we used the program ATLAS(Kurucz, 1969), modified to calculate metallic-line profilesand equivalent widths (Peytremann, 1970). The basic assump-tions are those of classical model atmospheres: plane-parallel and in hydrostatic and radiative equilibrium. Occu-pation numbers are given by the Saha-Boltzmann relations.The source function is calculated according to the Milne-Eddington relation, with scattering by free electrons. (Ray-leigh scattering is negligible at these high temperatures.)The line opacities are treated in pure absorption. With theseassumptions, it is clear that the line cores are incorrect,but they are rather narrow as compared to the strong dampingwings. As stated previously, we are currently interested inthese damping wings, and it is precisely these that contributemostly to the equivalent widths of strong lines, as we shallsee later.

The line-opacity profiles are given by Voigt functions cal-culated according to Baschek, Holweger, and Traving (1966).At each frequency, we sum up the continuous opacities and theopacities of all the relevant lines (blends). In our case,we take into account all lines of a given multiplet. Also,for clarity, we do not include the opacities of nearby hydro-gen lines. The equivalent widths have been computed accord-ing to Baschek et al. (1966) with the following exception.Most of the lines studied here are so broad that the residualfluxes

rx = F(A)/FC(A) (4)

are calculated with respect to the continuum FC(A) and not, asusual, to the continuum at the line-center wavelength (F(x) isthe flux in the line, and Fc(x) is the continuum flux). How-ever, since the computation of the flux at each frequencypoint is time consuming, we calculate only three continuumpoints for each multiplet and obtain the FC(A) values by para-bolic interpolation. This completes our description of thecomputational method.

The actual data entering the computations are (a) the modelatmospheres and (b) the line data. (a) The models are hydro-gen line-blanketed models calculated with the unmodified pro-


gram ATLAS (Kurucz, 1969). The ratio of helium to hydrogenby number is equal to 1/9. At our temperature(10,000 >_ Teff - 30,000°K), metals are unimportant as electrondonors. The gravity has been taken as log g = 4. As we shallsee, the effect of the electron density (and hence of thegravity) is so weak that no attempt has been made to calculateline profiles at lower gravities, where the contribution ofthe electron broadening would be still weaker. Finally, thead hoc microturbulence parameter that enters the Voigt func-tion has been set equal to 5 km sec"1. The strong linesstudied here depend very little on the microturbulence veloci-ty, because their damping wings are far broader than theDoppler core, and some calculations with velocities equal to0 and 10 km sec"1 have indeed confirmed this. (b) The linedata are contained in Table 1. The actual values of the abun-dances and of the partition functions are those contained inour version of the program ATLAS (Peytremann, 1970).

IV. RESULTS AND DISCUSSION

We did not calculate the profiles of all the lines listedin Table 1, at each temperature. In Figures 2 to 9, we dis-play typical results. At the present time, we cannot compareour results to observations, because, for one reason, theinstrumental profiles must be known in order to fold them in-to the theoretical profiles. Moreover, the definition of ob-served residual fluxes or equivalent widths depends on anaccurate definition of the continuum. This is difficult, andperhaps impossible, if the observed spectral feature isblended with a large number of adjacent lines; this indeed iswhat is observed on ultraviolet spectral scans (Houziaux andButler, 1970).

Figures 2 and 3 show the profiles of the multipletsA1083 (N II), and A1206.51 (Si ±11). The ordinates are theresidual fluxes r^ defined by (4), and the abscissas give thewavelength in angstroms. The profiles shown here are formodels with Teff = 20,000°K. The various profiles are labeledwith Ye f°r electron damping, YR + Ye for electron plus radia-tive damping, and YC for classical damping (Figure 3 only).Also shown are the profiles with 10 times the classical damp-ing. Figure 3 also shows the pure Doppler profile (Y = 0).It is seen that 10 YC gives lines much too broad, as comparedto the more realistic Y = YR + Ye case; Ye alone gives tooweak profiles, but its effect is important if we compare it tothe zero-damping case (Y = 0, Figure 3). Figure 2, which dis-plays a six-component multiplet, shows a striking differencebetween the cases Ye and ^Ye + YR) and the case 10 YC- Where-as the former profiles are resolved into four components, the


01095

figure. 1.—?fio kite.* o£ the. multiple.t o& N II at X - 1 0 B 5 A,f jo t a mode.1 with T £ / / = 2 0 , 0 0 0 ° K . ye, YR + Ye, and 10 yc

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latter does not show any significant resolution of the multi-plet's components. To check this, one would need instrumentalresolutions on the order of 0.5 A at X - 1100 A, provided thatthe multiplet is not blended with other lines.

Figures 4 to 9 show the equivalent widths log W as a func-tion of the effective temperature log Teff of the models. Theequivalent widths are in angstroms and are defined as usual by

00

W = / (1 - rx)dX , (5)o

where r^ has been defined by (4). The various curves arelabeled with the same damping parameters given in Figures 2and 3 and defined in Section 2. Each figure shows the resultsfor a multiplet defined by its wavelength. Also shown are theion and the number of components of each multiplet (fordetails, see Table 1). The multiplets of our sample all de-velop strong damping wings (compare with the pure Dopplercase, T = 0). Some of them (X1083, Figure 4; X1108, Figure 5;X1206, Figure 6; X1334, Figure 8) show these strong dampingwings over larcre effective temperature ranges. We reach thesame conclusions as in §11 and from the analysis of Figures 2and 3. We note that although the electron damping has littleeffect, its relative contribution to the total damping YR + Yeis larger at Teff = 10,000°K than at higher temperatures (see,for example, Figures 5 and 6) because in the layers at whichthe wings of these lines are formed, the electron densitiesare higher at Teff = 10,000°K, than at higher temperatures.An indirect consequence is that if any non-LTE effects existin these regions of line-wing formation, they would be en-hanced at higher temperatures.

We now summarize. As stated before, the conditions consid-ered here are those that prevail in atmospheres hotter than,say, 10,000°K, that is, where collision broadening by neutralparticles is negligible.

First a damping constant of 10 times the classical value ismuch too large, by comparison with the more realistic case ofelectron-plus-radiative damping. This is not necessarily truefor lines whose lower level is highly excited, but these linesare not expected to form strong damping wings anyway.

Second, for the strong lines we are dealing with, the ef-fect of electron damping is generally much smaller than thatof radiative damping. So we do not expect observable gravityeffects due to the broadening mechanisms.

Third, in most cases studied here, the electron-plus-radia-tive damping gives more or less the same results as the clas-sical damping. Compared to many other sources of errors,these differences are not dramatic. For calculations that


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involve hundreds or thousands of lines (blanketed model atmos-pheres) or that concern lines with unavailable damping data,we would therefore suggest, as a rule of thumb, to use theclassical damping constant rather than that 10 times greater.

This work has been done while the author held an ESRO-NASAInternational Fellowship. The research was supported in partby contract NAS 5-1535 from the National Aeronautics andSpace Administration.

REFERENCES

Adam-6, T. F. and Mo it on, V. C. 1968, Ap. J. 752. 795.BcL6c.fce.fe, B., ttolu)e.ge.i, H. and Jiavlng, G. 1966, kbhandl. Hamb.

Ste.inu). Mill, no. 1.Biadle.y, P. T. and Moiton, V. C. 7 9 6 9 , Ap. J. 7 5 6 . 687 .Code., A. V. and Ble.&4, R. C. 7 9 7 0 , In (MLttiavlolut

Spe.ctia and Re.late.d G/ioand-BaAe.d Obt>e.ivatlont>V. Re.lde.1 Pabl. C o . ) p. 7 7 3 .

Chape.lle., J. and Sahal-Biichot, S. 1970 , Attfi. and Ap. 6_, 4 7 5 .Hlckok, f . R. and Motton, V. C. 1968, Ap. J . 7 5 2 . 2 0 3 .Houz-taux, L. and Batle.fi, H. E., e.dA. 7 9 7 0 , Jin Ultn.avlole.t

Bte.i.lan. Spe.c.tfta and Re,late.d G/Loand-Ba*e.d Qbt>e.>ivat<ioni>(Votidmht: V. Re.<ide.l Pabl. C o . ) .

Katiucz, R. L. 1969 , -in The.on.y and Obt>e.>ivat<ion ojj Notimal Ste.1-mo&phe.tie.&, e.d. 0. Glnge.fu.c.k lCamb/u.dge.: M. 1. T., p. 375.

, V . and Aue>t, L . H . 7 9 7 0 , Ap . J . 7 6 0 . 7 7 6 7 .Pe.ytie.mann, E. 7 9 7 0 , The.AlA, Un<ive.K><ite. de. Ge.n~e.ve..Sanal-Bi£c.hot, S. 1969a , k&tl. and Ap. ]_, 91.

7 9 6 9 6 , ki>ti. and Ap. 2_, 3 2 2 .Sakal-Biickot, S. and Se.gi£, E. 7 9 7 0 , to be. pablli>he.d In

Wayne.' van Cltte.u, G. and Moiton, V. C. 1 9 7 0 , Ap. J . 7 6 7 . 695 .. , W. L., Smith, M. ft/ , and Gle.nnon, 8. M. 7 9 6 6 , A/SRPS-

W8S, £.. , W. L. , Smith, M. W. and MHz*, B. M. 7 9 6 9 , WSRPS-WBS, 2_2.

theoretical effect of various broadening abstract · the line-opacity profile is lorentzian, with a...

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