J. Plasma Fusion Res. SERIES, Vol.7 (2006) 161-164

Collisional-Radiative Model for Fe Ionsand X-Ray Spectra from Early-Type Stars
YAMAMOTO Norimasa∗ , KOHMURA Takayoshi1 ,KITAMOTO Shunji, SHIBAZAKI Noriaki and KATO Takako2
Rikkyo University, Tokyo 171-8501, Japan
1 Kogakuin University, Hachioji 192-0015, Japan
2 National Institute for Fusion Science, Toki 509-5292, Japan（Received: 30 October 2004 / Accepted: 30 September 2005）

Abstract
We constructed a collisional-radiative model for L-shell Fe ions and analyzed X-ray spectra from earlytype star (OB stars) observed with Chandra. Our model includes a large number of energy levels from Hlike to Mg-like Fe ions. Assuming quasi-steady states we can also construct the model of non-equilibrium
ionization by solving the rate equations for excited states. Atomic data are calculated mainly by the Hullaccode. Using our model, we analyzed three early type stars observed by Chandra and estimated electron
density and temperature of the X-ray emitting plasma from the intensity ratios of X-ray spectral lines.
Keywords:
early type star, Chandra, X-ray, collisional-radiative model, L-shell Fe ion
1．Introduction
X-rays from early-type massive stars were serendipitously discovered by the Einstein satellite in 1978 [1,2]. Soon after that, two models for their X-ray emission mechanism were proposed. One is coronal model[3] and the other one is stellar wind-shock model [4].
X-ray line profile is expected to be diﬀerent dependingon these models. In case of the corona model, line profiles are expected to be symmetric and sharp. On theother hand, in case of the stellar wind shock model, lineprofiles are expected to be blue-shifted and asymmetric.
Recently, high resolution spectral observation by Chandra makes it possible to study the actual line profileof the early type stars [5, 6]. Analysis of the Chandra
HETG spectrum of ζ Pup using the stellar wind-shockmodel, which considers Doppler shifts and photoelectric absorption, indicates that the most inner radius of
the X-ray emission region, Rin , is roughly 1.3∼1.4 timesof the stellar radius, R∗ , and the optical depth is roughly
4 [6]. However the radius of the X-ray emission region derived from the intensity ratio between the forbidden and the intercombination lines of He-like ions is∼ 4.0R∗ [7].
The observed spectra show not only lines from Hlike and He-like ions, but also those from L-shell Feions. Therefore, we constructed a collisional-radiativemodel for L-shell Fe ions in order to deduce informa-tion, electron density and electron temperature etc., ofthe plasma by analyzing intensity ratios of the measured
spectra of L-shell Fe ions with the similar method.
Compared with other models [8, 9], our model includes high excited states n > 7 in order to calculate thepopulation density in non-ionization equilibrium and tocalculate correct ionization balance. In this paper, weestimated electron density and temperatures using sixlines of Ne-like Fe ions observed in the spectra fromthree early type stars, τ Sco, δ Ori and ζ Pup assuming
optically thin plasma and ionization equilibrium.
2．Observation
The analyzed spectral data are obtained by MEG(medium energy grating) and HEG (high energy grating) of HETG (high energy transmission grating) onboard Chandra. The Data are reduced using tools ofCIAO v3.0 and extracted the dispersed spectral data restricting the area of the CCD image. We created theauxiliary response file using the CIAO tools and used
the response matrix file of the detector supplied by thehard ware team. Our analyzed three stars, τ Sco, δ Ori
and ζ Pup, were observed with the exposure time of72.1 ks, 49.0 ks and 67.6 ks, respectively.
Some selected lines, mainly H-like ions Lyα and Nelike Fe ions lines, of three early type stars are fitted by aC 2006 by The Japan Society of Plasma

Corresponding author’s e-mail: n-yamamoto@esi.nagoya-u.ac.jp∗ Present address: EcoTopia Science Institute, Nagoya University, Nagoya 464-8601 Japan

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Science and Nuclear Fusion ResearchCollisional-Radiative Model for Fe Ions and X-Ray Spectra from Early-Type Stars

Gaussian function and the velocity by the line centroid
shift and HWHM (half width half maximum) velocity
are calculated. For τ Sco, X-ray lines have no centroid
shift and the HWHM velocity of about 200 km s−1 . For
δ Ori, X-ray lines have almost no centroid shift and theHWHM velocity are ranging between 400 km s−1 and
600 km s−1 . Centroid shifted and HWHM velocity forζ Pup are −600 ∼ −800 km s−1 and 600 ∼ 1000 km s−1 ,respectively. Note that the negative centroid shift means
blue shift of line center. Thus we can recognize thatemission lines of the early type stars show variety of
their profiles, suggesting the other unknown parameterin the X-ray emission mechanism.

We constructed rate equations as;
dNi=−
Wi j Ni +W ji N j ,dtjj(1)where Wi j are total transition rates from i to j. Thenwe calculated the population density of excited statesassuming quasi-steady states, where population densities Ni of an excited state i is expanded by population
densities Nk of a ground state k as follows,
Ni = Σk ri (k) Ne Nk ,(2)

where Ne is the electron density and ri(k) is the population density coeﬃcient. From a state k to a state k byassuming quasi-steady state for ground states, eﬀective
excitation, de-excitation, ionization and recombination
rate coeﬃcients S CRkk ,3．Collisional-radiative model for L-shell Feions
We constructed a collisional-radiative model for
L-shell Fe ions. This model includes energy levels of single excited states, nl for H-like, 1snl
for He-like, 1s2 nl for Li-like, 1s2 2snl and 1s2 2pnl
for Be-like, 1s2 2s2 nl, 1s2 2s2pnl and 1s2 2p2 nl forB-like, 1s2 2s2 2pnl, 1s2 2s2p2 nl and 1s2 2p3 nl for Clike, 1s2 2s2 2p2 nl, 1s2 2s2p3 nl and 1s2 2p4 nl for Nlike, 1s2 2s2 2p3 nl, 1s2 2s2p4 nl and 1s2 2p5 nl for Olike, 1s2 2s2 2p4 nl, 1s2 2s2p3 nl and 1s2 2p6 nl for F-like,1s2 2s2 2p5 nl and 1s2 2s2p6 nl for Ne-like, 1s2 2s2 2p6 nl for
Na-like and 1s2 2s2 2p6 3lnl for Mg-like Fe ions. Energy levels of 2 ≤ n ≤ 5 are treated with fine structure, those of 6 ≤ n ≤ 9 are distinguished by theirconfiguration and those of 10 ≤ n are treated with laveraged configuration. Maximum principal and orbital quantum number of our model are nmax = 20 andlmax = 4(l = 0, 1, 2, 3, 4), respectively. Some of these
excited states are in autoionizing states. The contributions of the autoionizing states are included as dielectronic recombination processes. The following atomic
processes are included in our model; excitation / deexcitation by electron impact, ionization / three-bodyrecombination, radative transition, radiatve recombination, autoionization / dielectronic capture and dielectronic recombination. We used atomic data of 2 ≤ n ≤ 5calculated by HULLAC code [10]. Atomic data ofn > 6 were approximated by data of hydrogen-like ions.
Our model includes all atomic processes between
levels of L-shell Fe ions except the dielectronic recombination from the excited states. Dielectronic recombination processes are included for the excited levels for 2 ≤ n ≤ 5. The dielectronic recombination
rate coeﬃcient was calculated by using branching ratio
Aa /( Aa + Ar ). The current calculation of ionization
balance by our model is not enough, because of insuﬃcient inclusion of dielectronic recombination.

(k )
S CR
Wk,Ikk = Σi ri(3)are calculated. By constructing rate equations of theground states using eﬀective transition rate coeﬃcients,ionization balance is calculated without assumption ofcomplete steady state and population densities in nonionization equilibrium are also calculated using eq.(2).
4．Estimation of Te and Ne
Electron density and temperature are estimated fromthe line intensities of L-shell Fe ions, especially of Nelike Fe ions. Electron density is estimated by using intensity ratio of 2s2 2p5 3s(J = 1) to 2s2 2p5 3s(J = 2) [11]where a density eﬀect in population densities between2s2 2p5 3s(J = 1) and 2s2 2p5 3s(J = 2) is used, as shownin Fig.1. Figure 2 shows the intensity ratio as a function of electron density. The intensity ratio has a large
dependence on the electron density between 1012 cm−3
and 1015 cm−3 . On the other hand, the ratio has a small
dependence on the electron temperature. The intensity
ratio of the measured line spectra was determined by Cstatistic fitting used Gaussian function profile. We show
determined 90% confidence regions of the intensity ratios in Fig.2, where centroide shift velocity of two 3slines of δ Ori and ζ Pup were assumed to that of Nelike Fe ions at 16.7800 Å. Electron density by the ratioof τ Sco was determined to be Ne < 5x1012 cm−3 . However that of δ Ori and ζ Pup could not be determinedby large error range, because of broad line shape of Fe
XVII (17.0510 Å) and Fe XVII (17.0960 Å). We haveto note that the intensity ratio is also aﬀected by opticallight, although we neglected it.
Electron temperature is estimated by using an intensity ratio of 2s2 2p5 3d to 2s2 2p5 3s states [12]. The intensities of 3d and 3s lines are obtained from the sum of162

Collisional-Radiative Model for Fe Ions and X-Ray Spectra from Early-Type Stars

Fig. 3 The intensity ratio of 3d to 3s lines as a functionof electron temperature. Boxes in this ﬁgure indicate a parameter error range. The height of box
is range of 90 % conﬁdence level for intensity ratio and the side of box is error range of electrontemperature.
Fig. 1 The measured X-ray spectra of MEG +1/–1 orderof three early type stars with Chandra. Top, middle
and bottom panels are X-ray spectra in range of10∼18 Å of τ Sco, δ Ori and ζ Pup

dence of the ratio for T e . Photoelectric absorption crosssections assumed solar abundance are 3.5x10−22 cm2
and 4.8x10−22 cm2 around 15 Å and 17 Å, respectively.
In case of τ Sco, using NH = 3.16x1020 cm−2 [13], theintensity ratio increases about 5%. Since the calculated
ratio is approximately flat at T e = 100 − 500 eV, insuﬃcient estimation of the ratio may be a fatal. For L-shell
Fe ions, high precious atomic data are also required. Inaddition to that, influence of the contamination of lines
around 15 Å isn’t small in analysis for broad line shapeas δ Ori and ζ Pup. We note that we neglect the resonance scattering eﬀects which strongly aﬀect the resonance transition.
5．Summary
We constructed a collisional-radiative model for Lshell Fe ions in optical thin plasma. Our model isgeneralized model to assume quasi-steady state for
non-ionization equilibrium. In this paper, we analyzed the measured intensity ratios of three early typestars with Chandra. Electron density and temperature by assuming optical thin plasma are estimated.
In order to estimate electron densities and temperatures more accurately, the absorption in optical around5500 ∼ 6500 Å(∼ 2 eV) and the resonance scattering
are required to be taken into account. We will develop our calculation of ionization balance on fine structure including all dielectronic recombination and photoionization. We will improve our calculation of line profiles by considering the radiative transfer.

Fig. 2 The intensity ratio of 3s (J = 1) to 3s (J = 2) as afunction of electron density. Solid, dashed anddot-dashed lines are at Te = 300 eV, 500 eV and
700 eV, respectively. A dotted straight line is lower
limit of 90 % conﬁdence level on the intensity ratio of τ Sco. For ζ Pup and δ Ori, ranges of 90 %conﬁdence level on the intensity ratio exceed theintensity range of this ﬁgure.

three transitions among levels of fine structure levels.
The intensity ratio as a function of electron temperature
is shown in Fig.3. Electron temperatures of τ Sco andδ Ori were determined to be 60 − 180 eV and < 120 eV,respectively. The temperature is very low comparing
to T m = 432 eV of Ne-like Fe ions, T m is temperature
at maximum emissivity. For underestimation of T e , weconsidered two problems, an eﬀect of N H , where NH iscolumn density for stellar absorption, and weak depen-Acknowledgements
N. Y., T. K., S. K. and N. S. are partially supported by163

Collisional-Radiative Model for Fe Ions and X-Ray Spectra from Early-Type Stars

Grant-in-Aid for Scientific Research (C) of Japan Society for the Promotion of Science, 16540221, 2004.

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