- Email: [email protected]
Stark broadening of spectral lines in chemically peculiar stars: Te I lines and recent calculations for trace elements
New Astronomy Reviews 53 (2009) 246–251
Contents lists available at ScienceDirect
New Astronomy Reviews journal homepage: www.elsevier.com/locate/newastrev
Stark broadening of spectral lines in chemically peculiar stars: Te I lines and recent calculations for trace elements Zoran Simic´ a,*, Milan S. Dimitrijevic´ a, Andjelka Kovacˇevic´ b a b
Astronomical Observatory, Volgina 7, 11060 Belgrade, Serbia Department for Astronomy, Faculty for Mathematics, Studentski Trg 16, 11000 Belgrade, Serbia
a r t i c l e
i n f o
Article history: Available online 2 September 2009 PACS: 32.70.Jz 95.30.Ky 97.10.Ex
a b s t r a c t With the development of astronomical observations from space, spectral lines of trace elements can now be observed in stellar spectra with good resolution, and atomic data for such atoms and ions have an increasing significance. We review here work in Belgrade on the influence of Stark broadening of trace elements on stellar spectra and present new determinations of Stark broadening parameters of neutral tellurium. Also the corresponding Stark and Doppler widths are compared in atmospheres of A type stars. Ó 2009 Elsevier B.V. All rights reserved.
Keywords: Stark broadening Line profiles Atomic data Stellar atmospheres Te I Cr II
1. Introduction Stark broadening of neutral atom and ion lines is of interest not only for laboratory, laser produced, fusion or technological plasma investigation but also for astrophysical plasma, particularly for synthesis and analysis of high-resolution spectra obtained from space born instruments. With the development of new space techniques, importance of data on trace element spectra increases. The spectral lines of tellurium, one of the least abundant elements in the Earth’s lithosphere, but with cosmic abundance larger than for any element with atomic number greater than 40 (Cohen, 1984), are observed in stellar spectra. For example, Yuschenko and Gopka (1996), identified one line of tellurium in the Procyon photosphere spectrum, and determined the abundance of this element as log NðTeÞ ¼ 3:04 (in the scale log NðHÞ ¼ 12:00). de Lester (1994) notes that the three s-only isotopes of tellurium Te-122, 123 and 124 provide a unique opportunity to investigate s-process systematics, and for the estimation of the temperature and neutron density during helium burning in red giant stars. Chayer et al. (2005) observed tellurium spectral lines in ultraviolet spectra of the cool DO white dwarf * Corresponding author. E-mail addresses: [email protected] (Z. Simic´), [email protected] (M.S. Dimitrijevic´), [email protected] (A. Kovacˇevic´). 1387-6473/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.newar.2009.08.005
HD199499, obtained with the Far Ultraviolet Spectroscopy Explorer (FUSE), the Goddard High Resolution Spectrograph (GHRS – on the Hubble Space Telescope) and the International Ultraviolet Explorer. They report as well presence of tellurium lines in FUSE and GHRS spectra of the cool DO dwarf HZ21. Since the DO white dwarfs represent the non-DA white dwarf cooling sequence with effective temperatures from approximately 45,000 K up to around 120,000 K (Dreizler and Werner, 1996), Stark broadening is very important for analysis of their spectra. Consequently, the corresponding line broadening parameters for Te I at the low temperature limit (45,000–50,000 K) and tellurium in various ionization stages for the whole temperature range of interest for DO white dwarf atmospheres are needed. Atomic data for other trace elements are also important. For example, chromium is one of the most peculiar elements in the atmospheres of magnetic chemically peculiar stars. Cr II lines were found for example in Alpha UMi (Polaris) and HR 7308 by Andrievsky et al. (1994). Spectral lines of Cu III are of particular interest for the diagnostics and modelling of plasma created in electromagnetic macro particle accelerators (see Rasheig and Marshall, 1978). Moreover, analysis of 11 spectra of HgMn stars (Jacobs and Dworetsky, 1981), where Stark broadening is the main pressure broadening mechanism, showed the clear presence of copper and even its overabundance in 10 of 11 investigated stars. Recently for example, copper abundances in a large sample of metal-poor
Z. Simic´ et al. / New Astronomy Reviews 53 (2009) 246–251
stars have been investigated (Primas and Sobeck, 2008), and zinc spectral lines are also identified in stellar spectra (Adelman, 1994). Selenium, a trace element without previous astrophysical significance, is now detected in the atmospheres of cool DO white dwarfs (Chayer et al., 2005). Many examples show presence in hot stellar atmospheres of ionized manganese, gold, indium, tin, ruthenium, rare earths and other trace elements which before the epoch of space born stellar spectroscopy were astrophysically insignificant, but now the need for their atomic data is increasing. High-resolution spectra allow us to study different broadening effects using well-resolved line profiles. Stark broadening is the most important pressure broadening mechanism for A type stars and especially for white dwarfs. Neglecting this mechanism may therefore introduce significant errors into abundance determinations and spectra modellisation. Here we use the semiclassical perturbation method (Sahal-Bréchot, 1969a,b) to calculate the Stark broadening parameters for 4 Te I multiplets within the ultraviolet, visible and infrared wavelength range, for temperatures between 2500 K and 50,000 K. Within this range are temperatures of interest for A and B type stars and DA, DB and cool DO white dwarfs where Stark broadening is of interest. Such temperatures may be of interest also for the modelling of subphotospheric layers even in cooler stars. Results obtained will be used for analyzing the influence of Stark broadening in A type stellar atmospheres. Also a review of work performed in Belgrade on the investigations of Stark broadening influence in stellar spectra is given.
The theoretical and computational differences between calculations performed by our group using the theory of Sahal-Bréchot (1969a,b) and semi-classical Stark broadening results given in Griem (1974) are explained in detail in Dimitrijevic´ and Sahal-Bréchot (1996). The formulae for the ion-impact broadening parameters are analogous to the formulae for electron-impact broadening. We note that the fact that the colliding ions could be treated using impact approximation in the far wings should be checked, even for stellar atmosphere densities. It is possible also to perform calculations ab initio, using atomic energy levels and oscillator strengths calculated together with the Stark broadening parameters (Ben Nessib et al., 2004; Ben Nessib, 2009). When the semiclassical perturbation formalism can not be applied in an adequate way, due to the lack of reliable atomic data, a modified semiempirical formalism has been used. According to the modified semiempirical (MSE) approach (Dimitrijevic´ and Konjevic´, 1980; Dimitrijevic´ and Kršljanin, 1986, for review see Dimitrijevic´ and Popovic´, 2001) the electron impact full width at half maximum (FHWM) of an isolated ion line is given by
1=2 2 2 4p h 2m k pffiffiffi W ¼N 3c m2 pkT 3 8
þ
2. Theory
f
i i
X
! R2ii0
i0
Calculations have been performed within the semiclassical perturbation formalism, developed and discussed in detail by SahalBréchot (1969a,b). This formalism, as well as the corresponding computer code, has been optimized and updated several times (see e.g. Sahal-Bréchot, 1974; Dimitrijevic´ and Sahal-Bréchot, 1984; Dimitrijevic´ et al., 1991; see also review Dimitrijevic´, 1996). Within this formalism, the full width of an isolated spectral line of a neutral emitter broadened by electron impact ðWÞ can be expressed in terms of cross sections for elastic and inelastic processes as
W¼
k2 N pc
Z
vf ðvÞdv
X i0 –i
rii0 ðvÞ þ
X
!
rff 0 ðvÞ þ rel þ W R ;
d¼
k2 N 2p c
vf ðvÞdv
Z
RD
f 0 –f
2pqdq sin 2/p s:
gðxni ;ni þ1 Þ þ Dn–0
f
X f0
f
! R2ff 0 Dn–0
9 = gðxnf ;nf þ1 Þ ; ;
ð3Þ
where n and ‘ are principal and angular momentum quantum numbers, and R2‘k ;‘k0 ; k ¼ i; f is given by
X k0
!
R2kk0
¼ Dn–0
2 3nk 1 2 n þ 3‘2k þ 3‘k þ 11 ; 9 k 2Z
ð4Þ
in the Coulomb approximation. In Eq. (3)
x‘k ;‘k0 ¼ E=DE‘k ;‘k0 ;
ð5Þ
k = i, f where E ¼ 32 kT is the electron kinetic energy and
ð1Þ
DE‘k ;‘k0 ¼ E‘k E‘k0 ;
ð6Þ
is the energy difference between levels ‘k and ‘k 1ðk ¼ i; f Þ. Also
and the corresponding line shift d as
Z
247
ð2Þ
R3
Here, k is the wavelength of the line originating from the transition with initial atomic energy level i and final level f ; c is the velocity of light, N is the electron density, f ðvÞ is the Maxwellian velocity distribution function for electrons, q denotes the impact parameter of the incoming electron, and /p is the phase shift due to the polarization potential. The inelastic cross sections rjj0 ðvÞ (where j ¼ i or f) and elastic cross section rel are determined according to Chapter 3 in Sahal-Bréchot (1969b). The cut-offs (needed for the calculation of inelastic and elastic cross sections and the shift), included in order to maintain for the unitarity of the S-matrix, and to take into account Debye screening are described in Section 1 of Chapter 3 in Sahal-Bréchot (1969b). W R gives the contribution of the Feshbach resonances (Fleurier et al., 1977) and this term is zero if the emitters are neutral atoms. Other differences between neutral and ionized emitters is that for calculations of the cross sections rectilinear perturber paths are taken for neutral ones and hyperbolic paths for ionized species.
xnk ;nk þ1 E=DEnk ;nk þ1 ;
ð7Þ
where for Dn – 0 the energy difference between energy levels with nk and nk þ 1; DEnk ;nk þ1 , is estimated as
DEnk ;nk þ1 2Z 2 EH =n3 k :
ð8Þ
In Eq. (4) the effective principal quantum number is defined by
nk ¼ ½EH Z 2 =ðEion Ek Þ1=2 ;
ð9Þ
Z is the residual ionic charge i.e. the charge of the rest of atom as ‘‘seen” by optical electron (for example Z ¼ 1 for neutral atoms, 2 for singly charged ions, etc.), and Eion is the appropriate spectral series limit. In Eq. (3) T is the electron temperature, while gðxÞ (Griem, 1968) and g~ðxÞ (Dimitrijevic´ and Konjevic´, 1980) denote the corresponding effective Gaunt factors. In comparison with the semiclassical perturbation approach (Sahal-Bréchot, 1969a,b), the modified semiempirical approach requires much less atomic input data. In fact, if there are not perturbing levels strongly violating the assumed approximation, we only
Z. Simic´ et al. / New Astronomy Reviews 53 (2009) 246–251
248
need the energy levels with Dn ¼ 0 and ‘if ¼ ‘if 1, since all perturbing levels with Dn – 0, needed for a full semiclassical calculation are lumped together and estimated approximately. If for the nearest perturbing levels the condition E=DE 6 2 is satisfied the simplified version of the Eq. (3) (Dimitrijevic´ and Konjevic´, 1986) can be used. 3. Results and discussions Using the semiclassical perturbation method we obtained Stark widths and shifts of four Te I multiplets for a perturber density of 1016 cm3 and temperatures from 2500 up to 50,000 K. Calculations were performed using the atomic energy levels given by Moore (1971). The oscillator strengths required were calculated using the Coulomb approximation method described by Bates and Damgaard (1949) and the tables of Oertel and Shomo (1968). For higher levels, the method described by van Regemorter et al. (1979) was applied. Results obtained for electron-, proton-, and helium ion-impact broadening parameters are shown in Table 1. The quantity C (given in Å cm3), when divided by the corresponding full width at half maximum, gives an estimate for the maximum perturber density for which the line may be treated as isolated and the tabulated data may be used. WIDTH (Å) denotes the full line width at half maximum in Å, while SHIFT (Å) denotes line shift in Å. We note that, in the wings, the impact approximation for ions should be checked and that ions will be quasi-static in the far wings. For perturber densities lower than those tabulated here, Stark broadening parameters vary linearly with perturber density. The nonlinear behaviour of Stark broadening parameters at higher densities is the consequence of the influence of Debye shielding and was analyzed in detail in Dimitrijevic´ and Sahal-Bréchot (1984). As an example of the influence of Stark broadening in atmospheres of hot stars we present in Figs. 1 and 2 Stark widths of the 6s 5 So —7p 5 P (5125.2 Å) multiplet, and the Te I 6s 5 So —6p 5 P
(9903.9 Å) multiplet compared with Doppler widths for a model ðT eff ¼ 10; 000 K; log g ¼ 4:5Þ of A type star atmosphere (Kurucz, 1979). Doppler broadening in hot atmospheres is an important broadening mechanism and by comparison of Stark and Doppler widths one can judge its importance. Even if Doppler broadening dominates the line centre, Stark broadening may influence line wings. Our results are presented in Fig. 1 as a function of Rosseland optical depth s. It is interesting that the Stark broadening mechanism is absolutely dominant in comparison with the thermal Doppler mechanism in deeper layers of the stellar atmosphere (log s > 0:8) for the 5125.2 Å multiplet. There is no experimental or other theoretical data for the comparison with the calculated Stark broadening parameters of Te I spectral lines. The present demonstration in Figs. 1 and 2 that Stark broadening of Te I lines is important in deeper layers in A type star atmospheres for modelling and analyzing of neutral tellurium spectra, confirms previous findings for a number of trace elements. The investigations of the influence of Stark broadening in stellar spectra started in Belgrade in 1988, when the influence of this broadening mechanism was analyzed for a typical late B type stellar atmosphere with T eff ¼ 13; 000 K and log g ¼ 4:2 (Lanz et al., 1988). Attention was drawn to the errors introduced by the practice of taking 10 times the classical value of the natural width when the Stark width of a spectral line is unknown, and demonstrated the significance of taking into account this broadening mechanism. Stark broadening of rare earth ions (La II, La III, Eu II and Eu III) was considered in chemically peculiar Ap stars by Popovic´ et al. (1999a) and found that its neglect introduces errors in equivalent width synthesis and corresponding abundance determination. Also, the influence of Stark broadening on the so called ‘‘zirconium conflict”, namely the difference in abundances obtained from weak Zr II optical lines and strong Zr III lines (detected in UV) in the spectrum of HgMn star v Lupi, was considered (Popovic´ et al., 2001a).
Table 1 This table shows electron-, proton- and He II- impact broadening parameters for Te I for perturber density of 1016 cm3 and temperatures from 2500 up to 50,000 K. Transitions and wavelengths (Å) are also given in the table. By dividing C by the corresponding full width at half maximum (Dimitrijevic´ et al., 1991), we obtain an estimate for the maximum perturber density for which the line may be treated as isolated and tabulated data may be used. The validity of the impact approximation has been estimated for data shown in this table, by checking if the collision volume (V) multiplied by the perturber density (N) is much less than one (Sahal-Bréchot, 1969a,b). An asterisk denotes values where 0:1 < NV 6 0:5. Values with NV > 0:5 are deleted from the table. Perturbers
Electrons
Transition
Protons
Helium ions
T (K)
WIDTH (Å)
SHIFT (Å)
WIDTH (Å)
SHIFT (Å)
WIDTH (Å)
SHIFT (Å)
TeI 5p P—6s S (2244.9 Å) C = 0.46E+19
2500 5000 10,000 20,000 30,000 50,000
0.413E02 0.492E02 0.586E02 0.662E02 0.690E02 0.721E02
0.360E02 0.419E02 0.492E02 0.556E02 0.571E02 0.552E02
0.111E02 0.124E02 0.139E02 0.156E02 0.167E02 0.182E02
0.965E03 0.112E02 0.128E02 0.145E02 0.156E02 0.171E02
0.884E03 0.992E03 0.111E02 0.125E02 0.134E02 0.145E02
0.754E03 0.879E03 0.101E02 0.115E02 0.124E02 0.136E02
TeI 5p4 3 P—6s5 So (2372.7 Å) C = 0.57E+19
2500 5000 10,000 20,000 30,000 50,000
0.387E02 0.457E02 0.548E02 0.625E02 0.656E02 0.687E02
0.343E02 0.399E02 0.467E02 0.531E02 0.547E02 0.533E02
0.106E02 0.118E02 0.133E02 0.149E02 0.159E02 0.173E02
0.925E03 0.107E02 0.122E02 0.138E02 0.149E02 0.162E02
0.844E03 0.946E03 0.106E02 0.119E02 0.127E02 0.138E02
0.724E03 0.841E03 0.965E03 0.110E02 0.118E02 0.129E02
TeI 6s5 So —7p5 P (5125.2 Å) C = 0.57E+19
2500 5000 10,000 20,000 30,000 50,000
0.125 0.146 0.170 0.196 0.212 0.230
0.758E01 0.912E01 0.944E01 0.894E01 0.770E01 0.638E01
*
0.818E01 0.842E01 0.855E01 0.865E01 0.871E01 0.880E01
*
*
*
*
0.825E01 0.842E01 * 0.851E01 * 0.855E01 0.861E01
*
*
*
2500 5000 10,000 20,000 30,000 50,000
0.143 0.151 0.170 0.194 0.209 0.226
0.698E01 0.808E01 0.948E01 0.109 0.113 0.112
0.680E01 0.688E01 0.697E01 0.707E01 0.714E01 0.724E01
0.188E01 0.217E01 0.248E01 0.282E01 0.303E01 0.331E01
0.668E01 0.677E01 0.684E01 0.690E01 0.694E01 0.700E01
0.146E01 0.171E01 0.196E01 0.224E01 0.241E01 0.264E01
43
3 o
TeI 6s5 So —6p5 P (9903.9 Å) C = 0.99E+20
0.180E01 0.215E01 0.251E01 0.288E01 0.311E01 0.341E01
0.167E01 0.197E01 * 0.227E01 * 0.246E01 0.271E01
Z. Simic´ et al. / New Astronomy Reviews 53 (2009) 246–251
249
10
1
Stark Doppler 1
0.01
0.1
W[Å]
W[Å]
0.1
0.001
0.01
0.0001
0.001
1e−005 −5
0.0001
−4
−3
−2
−1
0
1
2
3
Stark Cu III Stark Zn III Stark Se III Doppler Cu III Doppler Zn III Doppler Se III 0
2
log τ
4
6
8
10
Optical depth
Fig. 1. Thermal Doppler and Stark widths for TeI 6s5 So —7p5 P (5125.2 Å) multiplet as functions of optical depth for an A type star ðT eff ¼ 10; 000 K; log g ¼ 4:5Þ.
1
Fig. 3. Thermal Doppler and Stark widths for Cu III 4s 2 F—4p2 Go (k = 1774.4 Å), Zn III 4s 3 D—4p 3 Po (k = 1667.9 Å) and Se III4p5s 3 Po —5p3 D (k = 3815.5 Å) spectral lines for a DB white dwarf atmosphere model with T eff ¼ 15; 000 K and log g ¼ 7, as a function of optical depth s5150 .
Stark Doppler
10
0.1 1
W[Å]
W[Å]
0.01
0.001
Stark log g=7 Stark log g=8 Stark log g=9 Doppler log g=7 Doppler log g=8 Doppler log g=9
0.01
0.0001
1e−005 −5
0.1
−4
−3
−2
−1
0
1
2
3
log τ Fig. 2. Thermal Doppler and Stark widths for Te I 6s5 So —6p5 P (9903.9 Å) multiplet as functions of optical depth for an A type star ðT eff ¼ 10; 000 m; log g ¼ 4:5Þ.
In a number of papers, the influence of Stark broadening on Au II (Popovic´ et al., 1999b), Co III (Tankosic´ et al., 2003), Ge I (Dimitrijevic´ et al., 2003a), Ga I (Dimitrijevic´ et al., 2004) and Cd I (Simic´ et al., 2005) on spectral lines in chemically peculiar A type stellar atmospheres was investigated and for each spectrum investigated atmospheric layers are found where the contribution of this broadening mechanism is dominant or could not be neglected. As a model for the atmosphere of an A type chemically peculiar star, a model with stellar parameters close to those of v Lupi HgMn star of Ap type was used. Such investigations were also performed for DA and DB white dwarf atmospheres (Popovic´ et al., 1999b; Tankosic´ et al., 2003) and it was found that for such stars Stark broadening is dominant in practically all relevant atmospheric layers. For example, the influence of Stark broadening on Cu III, Zn III and Se III spectral lines in DB white dwarf atmospheres was also investigated by Simic´ et al. (2006) for 4s 2 F—4p 2 Go (k = 1774.4 Å), 4s 3 D—4p 3 Po (k = 1667.9 Å) and 4p5s 3 Po —5p 3 D (k = 3815.5 Å) by using the corresponding model with T eff ¼ 15; 000 K and log g ¼ 7 (Wickramasinghe, 1972). For the model atmosphere of the DB white dwarfs the prechosen optical depth points at the standard wavelength ks = 5150 Å (s5150) are used in Wickramasinghe
0.001 0
2
4
6
8
10
Optical depth Fig. 4. Thermal Doppler and Stark widths for Se III spectral line 5s 3 Po —5p 3 D (k = 3815.5 Å) for a DB white dwarf atmosphere model with T eff ¼ 150; 00 K and 7 6 log g 6 9, as a function of optical depth s5150 .
(1972) and in Simic´ et al. (2006). As one can see in Figs. 3 and 4, for the plasma conditions in the DB white dwarf atmospheres, thermal Doppler broadening is much less important compared to Stark broadening. For example the Stark width of the Se III 3815.5 Å line is larger than the Doppler one by up to two orders of magnitude within the range of optical depths considered. Much larger Stark widths in DB white dwarf atmospheres in comparison with A type stars are the consequence of larger electron densities due to much larger log g and larger T eff , so that electron-impact (Stark) broadening is more effective. Hamdi et al. (2008) investigated the influence of Stark broadening on Si VI lines in DO white dwarf spectra for 50; 000 K 6 T eff 6 100; 000 K and 6 6 log g 6 9. It was found that the influence increases with log g and is dominant in broad regions of the atmospheres considered. In Popovic´ et al. (2001b), Stark broadening of 38 Nd II lines was analyzed in spectra of B, A, F and G type stellar atmospheres. It was found that the maximum influence of Stark broadening of Nd II lines is for A type stars. For G and F type stars the influence of Stark broadening decreases due to the decrease of effective electron
1
Residual intensity
Residual intensity
1 0.8 0.6
0.8 0.6
0.4
0.4
0.2
0.2
0 3401.5
Cr II 3422.73
1.2
Cr II 3421.60
Cr II 3403.25 Cr II 3403.31
Cr II 3402.40
Cr II 3402.26
1.2
Cr II 3421.20
Z. Simic´ et al. / New Astronomy Reviews 53 (2009) 246–251
250
3402
3402.5
3403
3403.5
3404
3404.5
0 3420
3420.5
3421
Wavelength, [Å] Fig. 5. Comparison between the observed Cr II 3403.30 line profile (dots) and synthetic calculations with the Stark parameters from paper by Dimitrijevic´ et al. (2007) (full line) and those from Kurucz (1993) (dashed line).
temperature and degree of ionization. Namely at T around 10,000 K, which is typical for A type stars, hydrogen becomes mainly ionized and the role of Stark broadening increases. For B type stars this influence decreases due to decrease of the surface gravity and related electron density. Also with the increase of temperature the number of Nd II ions decrease, and that of Nd III increases so that Nd II emission is weaker. It was demonstrated also that the neglecting of Stark broadening mechanism introduces for the Nd II lines in A type stars an error of between 10% and 45% in the equivalent widths and corresponding errors in the abundances. A detailed investigation of Stark broadening of Cd III lines in F0–B0 type stars and DA and DB white dwarfs was performed by Milovanovic´ et al. (2004) with similar conclusions. Dimitrijevic´ et al. (2003b) investigated the influence of Stark broadening on neutral silicon lines in spectra of normal late type A star HD 32115 and Ap stars HD 122970 and 10 Aql. They found that the synthetic profile of the k 6155.13 Å Si I line fits much better with the observed one when it was calculated using the Stark width and shift. Also authors reproduced the asymmetric and shifted profile of this line in HD 122970 reasonably well using the uniform distribution of neutral silicon and their results for Stark broadening parameters. Authors stressed that with their theoretical Stark broadening parameters the sensitivity of Si I k 6155.13 Å asymmetry to Si abundance changes in the 10 Aql atmosphere, can be successfully used in empirical studies of abundance stratification. They found also that for the Si I lines considered the contribution of electron impact is dominant, but impact with protons and He II ions should be taken into account as well. Similar results were found by Dimitrijevic´ et al. (2005) for neutral chromium lines in the spectrum of magnetic Ap star b Cr B where, depending on the electron temperature the contribution of proton-impact broadening may be even larger than the electron-impact contribution. Cr II lines in the spectrum of the Ap star HD 133792, for which careful abundance and stratification analysis has recently been performed by Kochukhov et al. (2006) were analyzed by Dimitrijevic´ et al. (2007). HD 133792 has an effective temperature of T eff ¼ 9400 K; log g ¼ 3:7, and a mean Cr overabundance +2.6 dex relative to the solar Cr abundance (Kochukhov et al., 2006). All calculations were carried out with the improved version SYNTH3 of the code SYNTH for synthetic spectrum calculations. Stark damping parameters were introduced in the spectrum synthesis code. The stratified Cr distribution in the atmosphere of HD 133972 derived by Kochukhov et al. (2006) was used. Fig. 5 shows a comparison between the observed line profiles of Cr II lines 3403.30 Å and
3421.5
3422
3422.5
3423
3423.5
3424
Wavelength, [Å] Fig. 6. The same as in Fig. 5 but for the Cr II 3421.20, 3422.73 lines.
synthetic calculations with the Stark damping constants from Kurucz (1993) line lists and with the data of Dimitrijevic´ et al. (2007). Good agreement between observations and calculations for a set of weak Cr II lines proves the use of the stratified Cr distribution, while all four strong Cr II lines demonstrate a good accuracy for the theoretical Stark broadening parameters obtained (Dimitrijevic´ et al., 2007) (Fig. 6). This opens up a new possibility of checking the theoretical and experimental Stark broadening results with the help of stellar spectra, which will be particularly interesting with the development of space born spectroscopy, building of giant telescopes of the new generation and increase of accuracy of computer codes for modellisation of stellar atmospheres. The Cr II lines analyzed in Dimitrijevic´ et al. (2007) are particularly suitable for such purpose since they have good clean wings where the influence of Stark broadening is the most important. Acknowledgements This work is a part of the Project 146 001 ‘‘Influence of collisional processes on astrophysical plasma lineshapes”, supported by the Ministry of Science and Technological Development of Serbia. References Adelman, S.J., 1994. MNRAS 271, 355. Andrievsky, S.M., Kovtyukh, V.V., Usenko, A., 1994. A&A 281, 465. Bates, D.R., Damgaard, A., 1949. Trans. Roy. Soc. Lond., Ser. A 242, 101. Ben Nessib, N., 2009. New Astron. Rev. 53, 255. Ben Nessib, N., Dimitrijevic´, M.S., Sahal-Bréchot, S., 2004. A&A 423, 397. Chayer, P., Vennes, S., Dupuis, J., Kruk, J.W., 2005. ApJ 630, L169. Cohen, B.L., 1984. Geochim. Cosmochim. Acta 48, 203. de Lester, J.R., 1994. ApJ 434, 695. Dimitrijevic´, M.S., 1996. Zh. Priklad. Spektrosk. 63, 810. Dimitrijevic´, M.S., Konjevic´, N., 1980. JQSRT 24, 451. Dimitrijevic´, M.S., Konjevic´, N., 1986. A&A 172, 345. Dimitrijevic´, M.S., Kršljanin, V., 1986. A&A 165, 269. ˇ ., 2001. J. Appl. Spectrosc. 68, 893. Dimitrijevic´, M.S., Popovic´, L.C Dimitrijevic´, M.S., Sahal-Bréchot, S., 1984. A&A 136, 289. Dimitrijevic´, M.S., Sahal-Bréchot, S., 1996. Phys. Scripta 54, 50. Dimitrijevic´, M.S., Jovanovic´, P., Simic´, Z., 2003a. A&A 410, 735. Dimitrijevic´, M.S., Sahal-Bréchot, S., Bommier, V., 1991. A&AS 89, 581. Dimitrijevic´, M.S., Dacˇic´, M., Cvetkovic´, Z., Simic´, Z., 2004. A&A 425, 1147. Dimitrijevic´, M.S., Ryabchikova, T., Popovic´, L.Cˇ., Shylyak, D., Khan, S., 2005. A&A 435, 1191. Dimitrijevic´, M.S., Ryabchikova, T., Popovic´, L.Cˇ., Shylyak, D., Tsymbal, V., 2003b. A&A 404, 1099. ˇ ., Dacˇic´, M., 2007. A&A 469, Dimitrijevic´, M.S., Ryabchikova, T., Simic´, Z., Popovic´, L.C 681. Dreizler, S., Werner, K., 1996. A&A 314, 217. Fleurier, C., Sahal-Bréchot, S., Chapelle, J., 1977. JQSRT 17, 595.
Z. Simic´ et al. / New Astronomy Reviews 53 (2009) 246–251 Griem, H.R., 1968. Phys. Rev. 165, 258. Griem, H.R., 1974. Spectral Line Broadening by Plasmas. Academic Press, New York. Hamdi, R., Ben Nessib, N., Milovanovic´, N., Popovic´, L.Cˇ., Dimitrijevic´, M.S., SahalBréchot, S., 2008. MNRAS 387, 871. Jacobs, J.M., Dworetsky, M.M., 1981. In chemically peculiar stars of the upper main sequence. In: 23rd Int. Coll. Astrophys., Liege, Reports, Univ. Liege, p. 153. Kochukhov, O., Tsymbal, V., Ryabchikova, T., Makaganyk, V., Bagnulo, S., 2006. A&A 460, 831. Kurucz, R.L., 1979. Astrophys. J. Suppl. Ser. 40, 1. Kurucz, R.L., 1993, CDROMs 13, 22, 23, SAO, Cambridge. Lanz, T., Dimitrijevic´, M.S., Artru, M.C., 1988. A&A 192, 249. Milovanovic´, N., Dimitrijevic´, M.S., Popovic´, L.Cˇ., Simic´, Z., 2004. A&A 417, 375. Moore, C.E., 1971. Atomic energy levels. US Department of Commerce, vol. II. NBS, Government Printing Office, Washington, DC. Oertel, G.K., Shomo, L.P., 1968. ApJS 16, 175.
251
ˇ ., Dimitrijevic´, M.S., Ryabchikova, T., 1999a. A&A 350, 719. Popovic´, L.C ˇ ., Dimitrijevic´, M.S., Tankosic´, D., 1999b. A&AS 139, 617. Popovic´, L.C ˇ ., Milovanovic´, N., Dimitrijevic´, M.S., 2001a. A&A 365, 656. Popovic´, L.C ˇ ., Simic´, S., Milovanovic´, N., Dimitrijevic´, M.S., 2001b. ApJS 135, 109. Popovic´, L.C Primas, F., Sobeck, J., 2008. AIP, Conf. Proc. 1001, 230. Rasheig, S.C., Marshall, R.H.J., 1978. J. Appl. Phys. 49, 2540. Sahal-Bréchot, S., 1969a. A&A 1, 91. Sahal-Bréchot, S., 1969b. A&A 2, 322. Sahal-Bréchot, S., 1974. A&A 35, 321. Simic´, Z., Dimitrijevic´, M.S., Milovanovic´, N., Sahal-Bréchot, S., 2005. A&A 441, 391. Simic´, Z., Dimitrijevic´, M.S., Popovic´, L.Cˇ., Dacˇic´, M., 2006. New Astron. 12, 187. ˇ ., Dimitrijevic´, M.S., 2003. A&A 399, 795. Tankosic´, D., Popovic´, L.C van Regemorter, H., Hoang Binh, Dy., Prud’homme, M., 1979. J. Phys. B 12, 1073. Wickramasinghe, D.T., 1972. Mem. R. Astron. Soc. 76, 129. Yuschenko, A.V., Gopka, V.F., 1996. Astron. Astrophys. Trans. 10, 307.
Contents lists available at ScienceDirect
New Astronomy Reviews journal homepage: www.elsevier.com/locate/newastrev
Stark broadening of spectral lines in chemically peculiar stars: Te I lines and recent calculations for trace elements Zoran Simic´ a,*, Milan S. Dimitrijevic´ a, Andjelka Kovacˇevic´ b a b
Astronomical Observatory, Volgina 7, 11060 Belgrade, Serbia Department for Astronomy, Faculty for Mathematics, Studentski Trg 16, 11000 Belgrade, Serbia
a r t i c l e
i n f o
Article history: Available online 2 September 2009 PACS: 32.70.Jz 95.30.Ky 97.10.Ex
a b s t r a c t With the development of astronomical observations from space, spectral lines of trace elements can now be observed in stellar spectra with good resolution, and atomic data for such atoms and ions have an increasing significance. We review here work in Belgrade on the influence of Stark broadening of trace elements on stellar spectra and present new determinations of Stark broadening parameters of neutral tellurium. Also the corresponding Stark and Doppler widths are compared in atmospheres of A type stars. Ó 2009 Elsevier B.V. All rights reserved.
Keywords: Stark broadening Line profiles Atomic data Stellar atmospheres Te I Cr II
1. Introduction Stark broadening of neutral atom and ion lines is of interest not only for laboratory, laser produced, fusion or technological plasma investigation but also for astrophysical plasma, particularly for synthesis and analysis of high-resolution spectra obtained from space born instruments. With the development of new space techniques, importance of data on trace element spectra increases. The spectral lines of tellurium, one of the least abundant elements in the Earth’s lithosphere, but with cosmic abundance larger than for any element with atomic number greater than 40 (Cohen, 1984), are observed in stellar spectra. For example, Yuschenko and Gopka (1996), identified one line of tellurium in the Procyon photosphere spectrum, and determined the abundance of this element as log NðTeÞ ¼ 3:04 (in the scale log NðHÞ ¼ 12:00). de Lester (1994) notes that the three s-only isotopes of tellurium Te-122, 123 and 124 provide a unique opportunity to investigate s-process systematics, and for the estimation of the temperature and neutron density during helium burning in red giant stars. Chayer et al. (2005) observed tellurium spectral lines in ultraviolet spectra of the cool DO white dwarf * Corresponding author. E-mail addresses: [email protected] (Z. Simic´), [email protected] (M.S. Dimitrijevic´), [email protected] (A. Kovacˇevic´). 1387-6473/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.newar.2009.08.005
HD199499, obtained with the Far Ultraviolet Spectroscopy Explorer (FUSE), the Goddard High Resolution Spectrograph (GHRS – on the Hubble Space Telescope) and the International Ultraviolet Explorer. They report as well presence of tellurium lines in FUSE and GHRS spectra of the cool DO dwarf HZ21. Since the DO white dwarfs represent the non-DA white dwarf cooling sequence with effective temperatures from approximately 45,000 K up to around 120,000 K (Dreizler and Werner, 1996), Stark broadening is very important for analysis of their spectra. Consequently, the corresponding line broadening parameters for Te I at the low temperature limit (45,000–50,000 K) and tellurium in various ionization stages for the whole temperature range of interest for DO white dwarf atmospheres are needed. Atomic data for other trace elements are also important. For example, chromium is one of the most peculiar elements in the atmospheres of magnetic chemically peculiar stars. Cr II lines were found for example in Alpha UMi (Polaris) and HR 7308 by Andrievsky et al. (1994). Spectral lines of Cu III are of particular interest for the diagnostics and modelling of plasma created in electromagnetic macro particle accelerators (see Rasheig and Marshall, 1978). Moreover, analysis of 11 spectra of HgMn stars (Jacobs and Dworetsky, 1981), where Stark broadening is the main pressure broadening mechanism, showed the clear presence of copper and even its overabundance in 10 of 11 investigated stars. Recently for example, copper abundances in a large sample of metal-poor
Z. Simic´ et al. / New Astronomy Reviews 53 (2009) 246–251
stars have been investigated (Primas and Sobeck, 2008), and zinc spectral lines are also identified in stellar spectra (Adelman, 1994). Selenium, a trace element without previous astrophysical significance, is now detected in the atmospheres of cool DO white dwarfs (Chayer et al., 2005). Many examples show presence in hot stellar atmospheres of ionized manganese, gold, indium, tin, ruthenium, rare earths and other trace elements which before the epoch of space born stellar spectroscopy were astrophysically insignificant, but now the need for their atomic data is increasing. High-resolution spectra allow us to study different broadening effects using well-resolved line profiles. Stark broadening is the most important pressure broadening mechanism for A type stars and especially for white dwarfs. Neglecting this mechanism may therefore introduce significant errors into abundance determinations and spectra modellisation. Here we use the semiclassical perturbation method (Sahal-Bréchot, 1969a,b) to calculate the Stark broadening parameters for 4 Te I multiplets within the ultraviolet, visible and infrared wavelength range, for temperatures between 2500 K and 50,000 K. Within this range are temperatures of interest for A and B type stars and DA, DB and cool DO white dwarfs where Stark broadening is of interest. Such temperatures may be of interest also for the modelling of subphotospheric layers even in cooler stars. Results obtained will be used for analyzing the influence of Stark broadening in A type stellar atmospheres. Also a review of work performed in Belgrade on the investigations of Stark broadening influence in stellar spectra is given.
The theoretical and computational differences between calculations performed by our group using the theory of Sahal-Bréchot (1969a,b) and semi-classical Stark broadening results given in Griem (1974) are explained in detail in Dimitrijevic´ and Sahal-Bréchot (1996). The formulae for the ion-impact broadening parameters are analogous to the formulae for electron-impact broadening. We note that the fact that the colliding ions could be treated using impact approximation in the far wings should be checked, even for stellar atmosphere densities. It is possible also to perform calculations ab initio, using atomic energy levels and oscillator strengths calculated together with the Stark broadening parameters (Ben Nessib et al., 2004; Ben Nessib, 2009). When the semiclassical perturbation formalism can not be applied in an adequate way, due to the lack of reliable atomic data, a modified semiempirical formalism has been used. According to the modified semiempirical (MSE) approach (Dimitrijevic´ and Konjevic´, 1980; Dimitrijevic´ and Kršljanin, 1986, for review see Dimitrijevic´ and Popovic´, 2001) the electron impact full width at half maximum (FHWM) of an isolated ion line is given by
1=2 2 2 4p h 2m k pffiffiffi W ¼N 3c m2 pkT 3 8
þ
2. Theory
f
i i
X
! R2ii0
i0
Calculations have been performed within the semiclassical perturbation formalism, developed and discussed in detail by SahalBréchot (1969a,b). This formalism, as well as the corresponding computer code, has been optimized and updated several times (see e.g. Sahal-Bréchot, 1974; Dimitrijevic´ and Sahal-Bréchot, 1984; Dimitrijevic´ et al., 1991; see also review Dimitrijevic´, 1996). Within this formalism, the full width of an isolated spectral line of a neutral emitter broadened by electron impact ðWÞ can be expressed in terms of cross sections for elastic and inelastic processes as
W¼
k2 N pc
Z
vf ðvÞdv
X i0 –i
rii0 ðvÞ þ
X
!
rff 0 ðvÞ þ rel þ W R ;
d¼
k2 N 2p c
vf ðvÞdv
Z
RD
f 0 –f
2pqdq sin 2/p s:
gðxni ;ni þ1 Þ þ Dn–0
f
X f0
f
! R2ff 0 Dn–0
9 = gðxnf ;nf þ1 Þ ; ;
ð3Þ
where n and ‘ are principal and angular momentum quantum numbers, and R2‘k ;‘k0 ; k ¼ i; f is given by
X k0
!
R2kk0
¼ Dn–0
2 3nk 1 2 n þ 3‘2k þ 3‘k þ 11 ; 9 k 2Z
ð4Þ
in the Coulomb approximation. In Eq. (3)
x‘k ;‘k0 ¼ E=DE‘k ;‘k0 ;
ð5Þ
k = i, f where E ¼ 32 kT is the electron kinetic energy and
ð1Þ
DE‘k ;‘k0 ¼ E‘k E‘k0 ;
ð6Þ
is the energy difference between levels ‘k and ‘k 1ðk ¼ i; f Þ. Also
and the corresponding line shift d as
Z
247
ð2Þ
R3
Here, k is the wavelength of the line originating from the transition with initial atomic energy level i and final level f ; c is the velocity of light, N is the electron density, f ðvÞ is the Maxwellian velocity distribution function for electrons, q denotes the impact parameter of the incoming electron, and /p is the phase shift due to the polarization potential. The inelastic cross sections rjj0 ðvÞ (where j ¼ i or f) and elastic cross section rel are determined according to Chapter 3 in Sahal-Bréchot (1969b). The cut-offs (needed for the calculation of inelastic and elastic cross sections and the shift), included in order to maintain for the unitarity of the S-matrix, and to take into account Debye screening are described in Section 1 of Chapter 3 in Sahal-Bréchot (1969b). W R gives the contribution of the Feshbach resonances (Fleurier et al., 1977) and this term is zero if the emitters are neutral atoms. Other differences between neutral and ionized emitters is that for calculations of the cross sections rectilinear perturber paths are taken for neutral ones and hyperbolic paths for ionized species.
xnk ;nk þ1 E=DEnk ;nk þ1 ;
ð7Þ
where for Dn – 0 the energy difference between energy levels with nk and nk þ 1; DEnk ;nk þ1 , is estimated as
DEnk ;nk þ1 2Z 2 EH =n3 k :
ð8Þ
In Eq. (4) the effective principal quantum number is defined by
nk ¼ ½EH Z 2 =ðEion Ek Þ1=2 ;
ð9Þ
Z is the residual ionic charge i.e. the charge of the rest of atom as ‘‘seen” by optical electron (for example Z ¼ 1 for neutral atoms, 2 for singly charged ions, etc.), and Eion is the appropriate spectral series limit. In Eq. (3) T is the electron temperature, while gðxÞ (Griem, 1968) and g~ðxÞ (Dimitrijevic´ and Konjevic´, 1980) denote the corresponding effective Gaunt factors. In comparison with the semiclassical perturbation approach (Sahal-Bréchot, 1969a,b), the modified semiempirical approach requires much less atomic input data. In fact, if there are not perturbing levels strongly violating the assumed approximation, we only
Z. Simic´ et al. / New Astronomy Reviews 53 (2009) 246–251
248
need the energy levels with Dn ¼ 0 and ‘if ¼ ‘if 1, since all perturbing levels with Dn – 0, needed for a full semiclassical calculation are lumped together and estimated approximately. If for the nearest perturbing levels the condition E=DE 6 2 is satisfied the simplified version of the Eq. (3) (Dimitrijevic´ and Konjevic´, 1986) can be used. 3. Results and discussions Using the semiclassical perturbation method we obtained Stark widths and shifts of four Te I multiplets for a perturber density of 1016 cm3 and temperatures from 2500 up to 50,000 K. Calculations were performed using the atomic energy levels given by Moore (1971). The oscillator strengths required were calculated using the Coulomb approximation method described by Bates and Damgaard (1949) and the tables of Oertel and Shomo (1968). For higher levels, the method described by van Regemorter et al. (1979) was applied. Results obtained for electron-, proton-, and helium ion-impact broadening parameters are shown in Table 1. The quantity C (given in Å cm3), when divided by the corresponding full width at half maximum, gives an estimate for the maximum perturber density for which the line may be treated as isolated and the tabulated data may be used. WIDTH (Å) denotes the full line width at half maximum in Å, while SHIFT (Å) denotes line shift in Å. We note that, in the wings, the impact approximation for ions should be checked and that ions will be quasi-static in the far wings. For perturber densities lower than those tabulated here, Stark broadening parameters vary linearly with perturber density. The nonlinear behaviour of Stark broadening parameters at higher densities is the consequence of the influence of Debye shielding and was analyzed in detail in Dimitrijevic´ and Sahal-Bréchot (1984). As an example of the influence of Stark broadening in atmospheres of hot stars we present in Figs. 1 and 2 Stark widths of the 6s 5 So —7p 5 P (5125.2 Å) multiplet, and the Te I 6s 5 So —6p 5 P
(9903.9 Å) multiplet compared with Doppler widths for a model ðT eff ¼ 10; 000 K; log g ¼ 4:5Þ of A type star atmosphere (Kurucz, 1979). Doppler broadening in hot atmospheres is an important broadening mechanism and by comparison of Stark and Doppler widths one can judge its importance. Even if Doppler broadening dominates the line centre, Stark broadening may influence line wings. Our results are presented in Fig. 1 as a function of Rosseland optical depth s. It is interesting that the Stark broadening mechanism is absolutely dominant in comparison with the thermal Doppler mechanism in deeper layers of the stellar atmosphere (log s > 0:8) for the 5125.2 Å multiplet. There is no experimental or other theoretical data for the comparison with the calculated Stark broadening parameters of Te I spectral lines. The present demonstration in Figs. 1 and 2 that Stark broadening of Te I lines is important in deeper layers in A type star atmospheres for modelling and analyzing of neutral tellurium spectra, confirms previous findings for a number of trace elements. The investigations of the influence of Stark broadening in stellar spectra started in Belgrade in 1988, when the influence of this broadening mechanism was analyzed for a typical late B type stellar atmosphere with T eff ¼ 13; 000 K and log g ¼ 4:2 (Lanz et al., 1988). Attention was drawn to the errors introduced by the practice of taking 10 times the classical value of the natural width when the Stark width of a spectral line is unknown, and demonstrated the significance of taking into account this broadening mechanism. Stark broadening of rare earth ions (La II, La III, Eu II and Eu III) was considered in chemically peculiar Ap stars by Popovic´ et al. (1999a) and found that its neglect introduces errors in equivalent width synthesis and corresponding abundance determination. Also, the influence of Stark broadening on the so called ‘‘zirconium conflict”, namely the difference in abundances obtained from weak Zr II optical lines and strong Zr III lines (detected in UV) in the spectrum of HgMn star v Lupi, was considered (Popovic´ et al., 2001a).
Table 1 This table shows electron-, proton- and He II- impact broadening parameters for Te I for perturber density of 1016 cm3 and temperatures from 2500 up to 50,000 K. Transitions and wavelengths (Å) are also given in the table. By dividing C by the corresponding full width at half maximum (Dimitrijevic´ et al., 1991), we obtain an estimate for the maximum perturber density for which the line may be treated as isolated and tabulated data may be used. The validity of the impact approximation has been estimated for data shown in this table, by checking if the collision volume (V) multiplied by the perturber density (N) is much less than one (Sahal-Bréchot, 1969a,b). An asterisk denotes values where 0:1 < NV 6 0:5. Values with NV > 0:5 are deleted from the table. Perturbers
Electrons
Transition
Protons
Helium ions
T (K)
WIDTH (Å)
SHIFT (Å)
WIDTH (Å)
SHIFT (Å)
WIDTH (Å)
SHIFT (Å)
TeI 5p P—6s S (2244.9 Å) C = 0.46E+19
2500 5000 10,000 20,000 30,000 50,000
0.413E02 0.492E02 0.586E02 0.662E02 0.690E02 0.721E02
0.360E02 0.419E02 0.492E02 0.556E02 0.571E02 0.552E02
0.111E02 0.124E02 0.139E02 0.156E02 0.167E02 0.182E02
0.965E03 0.112E02 0.128E02 0.145E02 0.156E02 0.171E02
0.884E03 0.992E03 0.111E02 0.125E02 0.134E02 0.145E02
0.754E03 0.879E03 0.101E02 0.115E02 0.124E02 0.136E02
TeI 5p4 3 P—6s5 So (2372.7 Å) C = 0.57E+19
2500 5000 10,000 20,000 30,000 50,000
0.387E02 0.457E02 0.548E02 0.625E02 0.656E02 0.687E02
0.343E02 0.399E02 0.467E02 0.531E02 0.547E02 0.533E02
0.106E02 0.118E02 0.133E02 0.149E02 0.159E02 0.173E02
0.925E03 0.107E02 0.122E02 0.138E02 0.149E02 0.162E02
0.844E03 0.946E03 0.106E02 0.119E02 0.127E02 0.138E02
0.724E03 0.841E03 0.965E03 0.110E02 0.118E02 0.129E02
TeI 6s5 So —7p5 P (5125.2 Å) C = 0.57E+19
2500 5000 10,000 20,000 30,000 50,000
0.125 0.146 0.170 0.196 0.212 0.230
0.758E01 0.912E01 0.944E01 0.894E01 0.770E01 0.638E01
*
0.818E01 0.842E01 0.855E01 0.865E01 0.871E01 0.880E01
*
*
*
*
0.825E01 0.842E01 * 0.851E01 * 0.855E01 0.861E01
*
*
*
2500 5000 10,000 20,000 30,000 50,000
0.143 0.151 0.170 0.194 0.209 0.226
0.698E01 0.808E01 0.948E01 0.109 0.113 0.112
0.680E01 0.688E01 0.697E01 0.707E01 0.714E01 0.724E01
0.188E01 0.217E01 0.248E01 0.282E01 0.303E01 0.331E01
0.668E01 0.677E01 0.684E01 0.690E01 0.694E01 0.700E01
0.146E01 0.171E01 0.196E01 0.224E01 0.241E01 0.264E01
43
3 o
TeI 6s5 So —6p5 P (9903.9 Å) C = 0.99E+20
0.180E01 0.215E01 0.251E01 0.288E01 0.311E01 0.341E01
0.167E01 0.197E01 * 0.227E01 * 0.246E01 0.271E01
Z. Simic´ et al. / New Astronomy Reviews 53 (2009) 246–251
249
10
1
Stark Doppler 1
0.01
0.1
W[Å]
W[Å]
0.1
0.001
0.01
0.0001
0.001
1e−005 −5
0.0001
−4
−3
−2
−1
0
1
2
3
Stark Cu III Stark Zn III Stark Se III Doppler Cu III Doppler Zn III Doppler Se III 0
2
log τ
4
6
8
10
Optical depth
Fig. 1. Thermal Doppler and Stark widths for TeI 6s5 So —7p5 P (5125.2 Å) multiplet as functions of optical depth for an A type star ðT eff ¼ 10; 000 K; log g ¼ 4:5Þ.
1
Fig. 3. Thermal Doppler and Stark widths for Cu III 4s 2 F—4p2 Go (k = 1774.4 Å), Zn III 4s 3 D—4p 3 Po (k = 1667.9 Å) and Se III4p5s 3 Po —5p3 D (k = 3815.5 Å) spectral lines for a DB white dwarf atmosphere model with T eff ¼ 15; 000 K and log g ¼ 7, as a function of optical depth s5150 .
Stark Doppler
10
0.1 1
W[Å]
W[Å]
0.01
0.001
Stark log g=7 Stark log g=8 Stark log g=9 Doppler log g=7 Doppler log g=8 Doppler log g=9
0.01
0.0001
1e−005 −5
0.1
−4
−3
−2
−1
0
1
2
3
log τ Fig. 2. Thermal Doppler and Stark widths for Te I 6s5 So —6p5 P (9903.9 Å) multiplet as functions of optical depth for an A type star ðT eff ¼ 10; 000 m; log g ¼ 4:5Þ.
In a number of papers, the influence of Stark broadening on Au II (Popovic´ et al., 1999b), Co III (Tankosic´ et al., 2003), Ge I (Dimitrijevic´ et al., 2003a), Ga I (Dimitrijevic´ et al., 2004) and Cd I (Simic´ et al., 2005) on spectral lines in chemically peculiar A type stellar atmospheres was investigated and for each spectrum investigated atmospheric layers are found where the contribution of this broadening mechanism is dominant or could not be neglected. As a model for the atmosphere of an A type chemically peculiar star, a model with stellar parameters close to those of v Lupi HgMn star of Ap type was used. Such investigations were also performed for DA and DB white dwarf atmospheres (Popovic´ et al., 1999b; Tankosic´ et al., 2003) and it was found that for such stars Stark broadening is dominant in practically all relevant atmospheric layers. For example, the influence of Stark broadening on Cu III, Zn III and Se III spectral lines in DB white dwarf atmospheres was also investigated by Simic´ et al. (2006) for 4s 2 F—4p 2 Go (k = 1774.4 Å), 4s 3 D—4p 3 Po (k = 1667.9 Å) and 4p5s 3 Po —5p 3 D (k = 3815.5 Å) by using the corresponding model with T eff ¼ 15; 000 K and log g ¼ 7 (Wickramasinghe, 1972). For the model atmosphere of the DB white dwarfs the prechosen optical depth points at the standard wavelength ks = 5150 Å (s5150) are used in Wickramasinghe
0.001 0
2
4
6
8
10
Optical depth Fig. 4. Thermal Doppler and Stark widths for Se III spectral line 5s 3 Po —5p 3 D (k = 3815.5 Å) for a DB white dwarf atmosphere model with T eff ¼ 150; 00 K and 7 6 log g 6 9, as a function of optical depth s5150 .
(1972) and in Simic´ et al. (2006). As one can see in Figs. 3 and 4, for the plasma conditions in the DB white dwarf atmospheres, thermal Doppler broadening is much less important compared to Stark broadening. For example the Stark width of the Se III 3815.5 Å line is larger than the Doppler one by up to two orders of magnitude within the range of optical depths considered. Much larger Stark widths in DB white dwarf atmospheres in comparison with A type stars are the consequence of larger electron densities due to much larger log g and larger T eff , so that electron-impact (Stark) broadening is more effective. Hamdi et al. (2008) investigated the influence of Stark broadening on Si VI lines in DO white dwarf spectra for 50; 000 K 6 T eff 6 100; 000 K and 6 6 log g 6 9. It was found that the influence increases with log g and is dominant in broad regions of the atmospheres considered. In Popovic´ et al. (2001b), Stark broadening of 38 Nd II lines was analyzed in spectra of B, A, F and G type stellar atmospheres. It was found that the maximum influence of Stark broadening of Nd II lines is for A type stars. For G and F type stars the influence of Stark broadening decreases due to the decrease of effective electron
1
Residual intensity
Residual intensity
1 0.8 0.6
0.8 0.6
0.4
0.4
0.2
0.2
0 3401.5
Cr II 3422.73
1.2
Cr II 3421.60
Cr II 3403.25 Cr II 3403.31
Cr II 3402.40
Cr II 3402.26
1.2
Cr II 3421.20
Z. Simic´ et al. / New Astronomy Reviews 53 (2009) 246–251
250
3402
3402.5
3403
3403.5
3404
3404.5
0 3420
3420.5
3421
Wavelength, [Å] Fig. 5. Comparison between the observed Cr II 3403.30 line profile (dots) and synthetic calculations with the Stark parameters from paper by Dimitrijevic´ et al. (2007) (full line) and those from Kurucz (1993) (dashed line).
temperature and degree of ionization. Namely at T around 10,000 K, which is typical for A type stars, hydrogen becomes mainly ionized and the role of Stark broadening increases. For B type stars this influence decreases due to decrease of the surface gravity and related electron density. Also with the increase of temperature the number of Nd II ions decrease, and that of Nd III increases so that Nd II emission is weaker. It was demonstrated also that the neglecting of Stark broadening mechanism introduces for the Nd II lines in A type stars an error of between 10% and 45% in the equivalent widths and corresponding errors in the abundances. A detailed investigation of Stark broadening of Cd III lines in F0–B0 type stars and DA and DB white dwarfs was performed by Milovanovic´ et al. (2004) with similar conclusions. Dimitrijevic´ et al. (2003b) investigated the influence of Stark broadening on neutral silicon lines in spectra of normal late type A star HD 32115 and Ap stars HD 122970 and 10 Aql. They found that the synthetic profile of the k 6155.13 Å Si I line fits much better with the observed one when it was calculated using the Stark width and shift. Also authors reproduced the asymmetric and shifted profile of this line in HD 122970 reasonably well using the uniform distribution of neutral silicon and their results for Stark broadening parameters. Authors stressed that with their theoretical Stark broadening parameters the sensitivity of Si I k 6155.13 Å asymmetry to Si abundance changes in the 10 Aql atmosphere, can be successfully used in empirical studies of abundance stratification. They found also that for the Si I lines considered the contribution of electron impact is dominant, but impact with protons and He II ions should be taken into account as well. Similar results were found by Dimitrijevic´ et al. (2005) for neutral chromium lines in the spectrum of magnetic Ap star b Cr B where, depending on the electron temperature the contribution of proton-impact broadening may be even larger than the electron-impact contribution. Cr II lines in the spectrum of the Ap star HD 133792, for which careful abundance and stratification analysis has recently been performed by Kochukhov et al. (2006) were analyzed by Dimitrijevic´ et al. (2007). HD 133792 has an effective temperature of T eff ¼ 9400 K; log g ¼ 3:7, and a mean Cr overabundance +2.6 dex relative to the solar Cr abundance (Kochukhov et al., 2006). All calculations were carried out with the improved version SYNTH3 of the code SYNTH for synthetic spectrum calculations. Stark damping parameters were introduced in the spectrum synthesis code. The stratified Cr distribution in the atmosphere of HD 133972 derived by Kochukhov et al. (2006) was used. Fig. 5 shows a comparison between the observed line profiles of Cr II lines 3403.30 Å and
3421.5
3422
3422.5
3423
3423.5
3424
Wavelength, [Å] Fig. 6. The same as in Fig. 5 but for the Cr II 3421.20, 3422.73 lines.
synthetic calculations with the Stark damping constants from Kurucz (1993) line lists and with the data of Dimitrijevic´ et al. (2007). Good agreement between observations and calculations for a set of weak Cr II lines proves the use of the stratified Cr distribution, while all four strong Cr II lines demonstrate a good accuracy for the theoretical Stark broadening parameters obtained (Dimitrijevic´ et al., 2007) (Fig. 6). This opens up a new possibility of checking the theoretical and experimental Stark broadening results with the help of stellar spectra, which will be particularly interesting with the development of space born spectroscopy, building of giant telescopes of the new generation and increase of accuracy of computer codes for modellisation of stellar atmospheres. The Cr II lines analyzed in Dimitrijevic´ et al. (2007) are particularly suitable for such purpose since they have good clean wings where the influence of Stark broadening is the most important. Acknowledgements This work is a part of the Project 146 001 ‘‘Influence of collisional processes on astrophysical plasma lineshapes”, supported by the Ministry of Science and Technological Development of Serbia. References Adelman, S.J., 1994. MNRAS 271, 355. Andrievsky, S.M., Kovtyukh, V.V., Usenko, A., 1994. A&A 281, 465. Bates, D.R., Damgaard, A., 1949. Trans. Roy. Soc. Lond., Ser. A 242, 101. Ben Nessib, N., 2009. New Astron. Rev. 53, 255. Ben Nessib, N., Dimitrijevic´, M.S., Sahal-Bréchot, S., 2004. A&A 423, 397. Chayer, P., Vennes, S., Dupuis, J., Kruk, J.W., 2005. ApJ 630, L169. Cohen, B.L., 1984. Geochim. Cosmochim. Acta 48, 203. de Lester, J.R., 1994. ApJ 434, 695. Dimitrijevic´, M.S., 1996. Zh. Priklad. Spektrosk. 63, 810. Dimitrijevic´, M.S., Konjevic´, N., 1980. JQSRT 24, 451. Dimitrijevic´, M.S., Konjevic´, N., 1986. A&A 172, 345. Dimitrijevic´, M.S., Kršljanin, V., 1986. A&A 165, 269. ˇ ., 2001. J. Appl. Spectrosc. 68, 893. Dimitrijevic´, M.S., Popovic´, L.C Dimitrijevic´, M.S., Sahal-Bréchot, S., 1984. A&A 136, 289. Dimitrijevic´, M.S., Sahal-Bréchot, S., 1996. Phys. Scripta 54, 50. Dimitrijevic´, M.S., Jovanovic´, P., Simic´, Z., 2003a. A&A 410, 735. Dimitrijevic´, M.S., Sahal-Bréchot, S., Bommier, V., 1991. A&AS 89, 581. Dimitrijevic´, M.S., Dacˇic´, M., Cvetkovic´, Z., Simic´, Z., 2004. A&A 425, 1147. Dimitrijevic´, M.S., Ryabchikova, T., Popovic´, L.Cˇ., Shylyak, D., Khan, S., 2005. A&A 435, 1191. Dimitrijevic´, M.S., Ryabchikova, T., Popovic´, L.Cˇ., Shylyak, D., Tsymbal, V., 2003b. A&A 404, 1099. ˇ ., Dacˇic´, M., 2007. A&A 469, Dimitrijevic´, M.S., Ryabchikova, T., Simic´, Z., Popovic´, L.C 681. Dreizler, S., Werner, K., 1996. A&A 314, 217. Fleurier, C., Sahal-Bréchot, S., Chapelle, J., 1977. JQSRT 17, 595.
Z. Simic´ et al. / New Astronomy Reviews 53 (2009) 246–251 Griem, H.R., 1968. Phys. Rev. 165, 258. Griem, H.R., 1974. Spectral Line Broadening by Plasmas. Academic Press, New York. Hamdi, R., Ben Nessib, N., Milovanovic´, N., Popovic´, L.Cˇ., Dimitrijevic´, M.S., SahalBréchot, S., 2008. MNRAS 387, 871. Jacobs, J.M., Dworetsky, M.M., 1981. In chemically peculiar stars of the upper main sequence. In: 23rd Int. Coll. Astrophys., Liege, Reports, Univ. Liege, p. 153. Kochukhov, O., Tsymbal, V., Ryabchikova, T., Makaganyk, V., Bagnulo, S., 2006. A&A 460, 831. Kurucz, R.L., 1979. Astrophys. J. Suppl. Ser. 40, 1. Kurucz, R.L., 1993, CDROMs 13, 22, 23, SAO, Cambridge. Lanz, T., Dimitrijevic´, M.S., Artru, M.C., 1988. A&A 192, 249. Milovanovic´, N., Dimitrijevic´, M.S., Popovic´, L.Cˇ., Simic´, Z., 2004. A&A 417, 375. Moore, C.E., 1971. Atomic energy levels. US Department of Commerce, vol. II. NBS, Government Printing Office, Washington, DC. Oertel, G.K., Shomo, L.P., 1968. ApJS 16, 175.
251
ˇ ., Dimitrijevic´, M.S., Ryabchikova, T., 1999a. A&A 350, 719. Popovic´, L.C ˇ ., Dimitrijevic´, M.S., Tankosic´, D., 1999b. A&AS 139, 617. Popovic´, L.C ˇ ., Milovanovic´, N., Dimitrijevic´, M.S., 2001a. A&A 365, 656. Popovic´, L.C ˇ ., Simic´, S., Milovanovic´, N., Dimitrijevic´, M.S., 2001b. ApJS 135, 109. Popovic´, L.C Primas, F., Sobeck, J., 2008. AIP, Conf. Proc. 1001, 230. Rasheig, S.C., Marshall, R.H.J., 1978. J. Appl. Phys. 49, 2540. Sahal-Bréchot, S., 1969a. A&A 1, 91. Sahal-Bréchot, S., 1969b. A&A 2, 322. Sahal-Bréchot, S., 1974. A&A 35, 321. Simic´, Z., Dimitrijevic´, M.S., Milovanovic´, N., Sahal-Bréchot, S., 2005. A&A 441, 391. Simic´, Z., Dimitrijevic´, M.S., Popovic´, L.Cˇ., Dacˇic´, M., 2006. New Astron. 12, 187. ˇ ., Dimitrijevic´, M.S., 2003. A&A 399, 795. Tankosic´, D., Popovic´, L.C van Regemorter, H., Hoang Binh, Dy., Prud’homme, M., 1979. J. Phys. B 12, 1073. Wickramasinghe, D.T., 1972. Mem. R. Astron. Soc. 76, 129. Yuschenko, A.V., Gopka, V.F., 1996. Astron. Astrophys. Trans. 10, 307.