ASTROPHYSICAL PARAMETERS OF LS 2883 AND IMPLICATIONS FOR THE PSR B1259–63 GAMMA-RAY BINARY^*

Since model fitting can only give values for T_eff and log g, we need an accurate distance to LS 2883 to derive M_* and L_*. We use interstellar atomic lines in the spectrum of LS 2883 to study the radial velocity distribution of material along this line of sight (ℓ = 3042, b = −10). Figure 2 displays three strong interstellar lines in the spectrum of LS 2883, the two components of the Na i doublet and one of the members of the Ca ii doublet. All three lines (and other interstellar lines, like CN 3875 Å) show the same morphology, with two clearly separated components. The first component, with low positive velocity, is likely due to nearby clouds associated with the Southern Coalsack, which shows local standard of rest (LSR) velocities in the range −10 to +8 km s⁻¹ in CO maps (Nyman et al. 1989). The second feature is a combination of several weaker components with negative velocities (between −14 km s⁻¹ and −36 km s⁻¹), values produced by clouds in the Sagittarius Arm. Very similar components are observed in the interstellar lines of HD 112272 (ℓ = 3035, b = −15), a B0.5 Ia supergiant believed to be a member of Cen OB1 (Hunter et al. 2006).

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In this direction, the H i shell GSH 305+01–24, with dynamical d = 2.2 ± 0.6 kpc, has an average velocity −24 km s⁻¹ and is believed to be associated to Cen OB1 (McClure-Griffiths et al. 2002). LS 2883 shows interstellar components more negative than this value, suggesting that it is beyond this shell. In fact, the Galactic rotation curve would place LS 2883 at ≳2.5 kpc (see the inset of Figure 2). More distant stars along this sight line show narrow components at ≈−50 km s⁻¹, believed to arise from clouds in the Norma–Centaurus Arm, at d ≳ 4 kpc (Kaper et al. 2006, and references therein). The lack of this component in LS 2883 sets an upper limit to its distance and firmly places it near Cen OB1.

Photometric measurements of LS 2883 in the literature (Klare & Neckel 1977; Schild et al. 1983; Westerlund & Garnier 1989; Drilling 1991) suggest some variability, at the level of a few hundredths of a magnitude, typical of Be stars. Taking (B − V) = 0.73 as representative, the intrinsic color corresponding to the model fit (see below), (B − V)₀ = −0.28, implies E(B − V) = 1.01. Not all this reddening is interstellar, as the disks of Be stars give rise to circumstellar reddening due to stronger emission at longer wavelengths (e.g., Dachs et al. 1988). The correlation between EW(Hα) and E^cs(B − V) from Dachs et al. (1988), valid solely for isolated Be stars, predicts E^cs(B − V) = 0.11, higher than for most Be stars. Higher values are observed in Be/X-ray binaries, but values ≳0.3 mag are generally associated with transient events (e.g., Reig et al. 2007). Therefore, it seems sensible to assume LS 2883 to have interstellar E(B − V) = 0.8–0.9 mag.

We have also estimated the color excess using four interstellar diffuse bands (DIBs) with EW >100 mÅ in the spectrum of LS 2883: λ5780, λ5797 (Herbig 1993), λ6202, and λ6614 (Rawlings et al. 2003). λ4430 is difficult to measure. Though there is some dispersion, all support E(B − V) between 0.8– 0.9 mag. We shall thus assume E(B − V) = 0.85. Members of Cen OB1 near LS 2883 have E(B − V) between 0.7 and 1.1 (Humphreys 1978).

The extinction law in this direction does not differ significantly from the average R = 3.1 law (Winkler 1997). We observed two luminous stars close to LS 2883 from SAAO. For LS 2888 (7' away), we derive a spectral type B0.2 III. Using photometry from the literature (Klare & Neckel 1977; Schild et al. 1983) and standard calibrations for intrinsic colors (Fitzgerald 1970) and magnitudes (Turner 1980), we estimate E(B − V) = 0.83 and d = 2.9 ± 0.5 kpc. For LS 2882, only 30'' away from LS 2883, we derive a spectral type B1 IV. Unfortunately, there is no accurate photometry published for this star. Its 2MASS (J − K_S) color, however, indicates that it is reddened by an amount very similar to LS 2888. The spectral types and magnitudes are fully compatible with the three stars being at similar distances.

Therefore, direct measurements and indirect evidence are consistent with the idea that LS 2883 has interstellar E(B − V) = 0.85 ± 0.05 and is a member of Cen OB1. The distance to this association has been studied by different authors, with most recent values converging toward d = 2.3 kpc, though values up to d = 2.5 kpc are reported (Kaltcheva & Georgiev 1994; Humphreys 1978, and references therein). We will assume that LS 2883 is located at the distance to the association, even though values as high as 2.8 kpc seem compatible with the data available. Values lower than 2.0 kpc seem to be excluded by the kinematic data contained in the interstellar lines to LS 2883.

Stellar parameters have been calculated using Fastwind (Puls et al. 2005), a spherical non-LTE model atmosphere code with mass loss, developed to model detailed spectral line profiles of hot and luminous stars. The best-fit model is shown in Figure 3.

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We determined the stellar rotational velocity using the Fourier transform method. We first degraded the spectrum to R= 10,000 for a better signal-to-noise ratio. Because of the large broadening, many lines are blended. We took unblended line wings and mirrored them (thus producing a symmetric line) before calculating the Fourier transform. This procedure gives results consistent with measurements for the blended lines. Our values, which rest on the metallic lines O ii 4254 Å and C ii 4267 Å, are v_rotsin i = 235 ± 15 km s⁻¹ (projected rotational velocity; to be refined further below) and ζ = 115 ± 50 km s⁻¹ (so-called macroturbulence). Errors simply represent the dispersion of individual values.

Stellar parameters were obtained by visual fitting to the Balmer, He i/He ii and Si iii/Si iv lines (see, e.g., Repolust et al. 2004; Simón-Díaz 2010). The fit is not as accurate as in these works, since the heavy veiling by emission lines makes the continuum definition a difficult task and some diagnostic lines either have emission components (such as He i 4471 Å) or are affected by nearby emission lines (as, for example, Si iii 4552 Å). The best fit is obtained for T_eff = 32, 000⁺²⁰⁰⁰₋₁₀₀₀ K and log g = 3.8^+0.3_−0.2, where the uncertainties have been obtained following the procedures discussed in Section 6 of Repolust et al. (2004). A normal He abundance (N(He)/(N(H) +N(He)) = 0.09) is consistent with the observed spectrum, although a slightly increased He abundance is possible. The lines typically used to estimate the mass-loss rate are strongly contaminated by emission components, preventing us from obtaining an accurate value. We have adopted the mass-loss rate expected for a spherical star of the luminosity derived below according to the recipes of Vink et al. (2000), resulting in a thin wind with no effect on the emergent profiles.

Using d = 2.3 ± 0.4 kpc, E(B − V) = 0.85 ± 0.05, and R = 3.1 ± 0.1, we derive M_V = −4.4 ± 0.4. From the model-fit spectrum and the absolute magnitude, we derive the values for R_*, L_*, and M_* listed in Table 1. The fitted parameters correspond to an O9.5 V star according to the observational scale of Martins et al. (2005), in good agreement with the morphological spectral classification that we derive from our spectra.

However, for fast rotators, there are strong differences in effective gravity between the polar and equatorial regions, resulting in important temperature gradients and oblateness (Townsend et al. 2004, and therein). The binary mass function f(M_NS) = 1.53 M_☉ (Johnston et al. 1994) implies an orbital inclination angle of i_orb = 247^+5.9_−5.4 for a standard neutron star mass of 1.4 M_☉. Melatos et al. (1995) find a tilt of 10° between the orbital plane and circumstellar disk, expected to lie on the stellar equatorial plane. Therefore, we are seeing LS 2883 under a low (∼35°) inclination and the parameters obtained must mainly reflect the characteristics of the hotter polar region.

For a centrally condensed star, the critical rotational angular velocity (gravity and centrifugal forces are equal at the equator) is given by

$$\begin{equation} \Omega _{\rm crit}= \sqrt{\frac{8GM_{*}}{27 R^3_{\rm pole}}}\,. \end{equation} \tag{ 1 }$$

A star rotating at Ω_crit will have R_eq = 1.5R_pole (Cranmer & Owocki 1995). In the case of LS 2883, with a deprojected v_rot = 410 km s⁻¹, a rough estimation suggests that R_eq > 1.1R_pole and ω ≡ Ω_*/Ω_crit ≳ 0.85, meaning that two-dimensional effects will be important.

For a start, in fast rotators, both the Full Width at Half Maximum (FWHM) of lines and the Fourier method underestimate v_rotsin i (Townsend et al. 2004; Fremat et al. 2005). We therefore correct v_rotsin i using Figure 8 of Fremat et al. (2005), finding v'_rotsin i = 260 ± 15 km s⁻¹. The deprojected velocity is then v'_rot ≈ 450 km s⁻¹, even closer to the critical value.

Though a complete two-dimensional treatment of the stellar surface is beyond our scope, we can perform a quick evaluation of the effects of fast rotation. From the T_eff and log g derived from our analysis (apparent values), we estimate the T_eff, log g, and M⁰_V of a non-rotating star that would give the same apparent parameters when rotating at the same v_rot as LS 2883. For this, we use an iterative method based on the calculations of Fremat et al. (2005) and the tables of Collins et al. (1991). With these new values, we calculate other stellar parameters and iterate again to take into account the change in the inclination due to the change in M_*. The results of this procedure are the stellar parameters that LS 2883 would have if it did not rotate (Table 2, left panel) and its most likely actual parameters, taking into account fast rotation (Table 2, right panel).

LS 2883 presents important differences in T_eff and log g between the polar and equatorial regions, rendering the apparent parameters little more than an approximate guess. The hypothetical non-rotating LS 2883 would have parameters roughly corresponding to an O8 V star. Its observed spectrum is a consequence of fast rotation. The mass derived, 31 M_☉, is somewhat high for these parameters, but is subject to large uncertainties, as it depends strongly on the corrections for fast rotation and the distance assumed.