THE VLT-FLAMES TARANTULA SURVEY: THE FASTEST ROTATING O-TYPE STAR AND SHORTEST PERIOD LMC PULSAR—REMNANTS OF A SUPERNOVA DISRUPTED BINARY?

The large rotational broadening of the spectral features makes reliable measurements of the projected rotational velocity, v_eqsin i, difficult. We have used a Fourier transform (FT) approach as discussed by Simón-Díaz & Herrero (2007), supplemented by fitting rotational broadened profiles (PF) to the observed spectral features.

The Balmer lines have significant nebular emission and hence the weaker helium spectra were utilized, as illustrated in Figure 1. The He i line at 4471 Å, although well observed, also showed significant nebular emission and was not analyzed. By contrast the line at 4026 Å showed no evidence of emission and yielded a plausible minimum in the FT for a v_eqsin i of 560 km s⁻¹. The PF methodology leads to a slightly higher estimate (580 km s⁻¹). The He i lines at 4143 and 4387 Å were observed although they are relatively weak. These and the line at 4026 Å were converted into velocity space, merged and analyzed. The two methodologies yielded effectively identical estimates of 640 km s⁻¹; a similar procedure was undertaken for the He ii lines at 4200 and 4541 Å yielding 540 km s⁻¹ (FT) and 510 km s⁻¹ (PF). The He ii line at 4686 Å was found to be sensitive to the normalization with a v_eqsin i of ∼560 km s⁻¹ being estimated.

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The individual results should be treated with caution but overall they imply that this star is rotating near its critical velocity, with the mean value for the FT estimates being 580 km s⁻¹. As discussed by Townsend et al. (2004), projected rotational velocities may be underestimated at these large velocities. For a B0 star rotating at 95% of the critical velocity, this underestimation will be approximately 10%. Hence, our best estimate for the projected rotational velocity is ∼600 km s⁻¹. A lower limit of 500 km s⁻¹ has been adopted, while the upper value will be constrained by the critical velocity of approximately 700 km s⁻¹ from the models of Brott et al. (2011).

This estimate is significantly higher than those (≲370 km s⁻¹) found by Martayan et al. (2006) and Hunter et al. (2009) in their LMC B-type stellar samples. It is also larger than any of the preliminary estimates (≲450 km s⁻¹) for ∼270 B-type stars in the Tarantula survey, although other rapidly rotating O-type stars have been identified. As such it would appear to have the highest projected rotational velocity estimate of any massive star yet analyzed.

Radial velocities were measured by cross-correlating spectral features against a theoretical template spectrum taken from a grid calculated using the code TLUSTY (Hubeny 1988)—see Dufton et al. (2005) for details.

Five spectral regions were considered, viz. Hδ and Hγ (with the cores excluded); He i at 4026 Å; 4630–4700 Å with strong multiplets due to C iii and O ii and an He ii line; and 4000–4500 Å (with nebular emission being excluded). The measurements are in excellent agreement with a mean value of 228 ± 12 km s⁻¹; if the error distribution is normally distributed the uncertainty in this mean value would be 6 km s⁻¹.

From a study of ∼180 presumably single O-type stars in the Tarantula survey, H. Sana et al. (2012, in preparation) find a mean velocity of 271 km s⁻¹ with a standard deviation of 10 km s⁻¹. Preliminary analysis of the B-type stars in the same survey has yielded 270 ± 17 km s⁻¹. VFTS102 lies more than two standard deviations away from these results, implying that it might be a runaway.

While the equatorial regions of VFTS102 will have a lower gravity than the poles (because of centrifugal forces), and hence a lower temperature (because of von Zeipel gravity darkening), we first characterize the spectrum by comparison with those generated with spatially homogeneous models, convolved with a simple rotational-broadening function. We have used both our TLUSTY grid and FASTWIND calculations (Puls et al. 2005), adopting an LMC chemical composition. For the former, the strength of the He ii spectrum implies an effective temperature (T_eff) of ∼32,500–35,000 K, while the wings of the Balmer lines lead to a surface-gravity estimate of ∼3.5 dex (cgs). For the latter after allowing for wind effects, the corresponding parameters are 37,000 K and 3.7 dex. The helium spectra are consistent with a solar abundance but with the observational and theoretical uncertainties we cannot rule out an enhancement.

Given its projected equatorial rotation velocity, VFTS102 is almost certainly viewed at sin i ∼ 1. Hence the relatively cool, low-gravity equatorial regions will contribute significantly to the spectrum. Although their surface flux is lower than for the brighter poles, the analyses discussed above may underestimate the global effective temperature and gravity. However, the rotating-star models discussed below suggest that the effects are not very large. We therefore adopt global estimates for the effective temperature of 36,000 K and 3.6 dex but note that the polar gravity could be as large as 4.0 dex. Varying the global parameters by the error estimates listed in Table 1 leads to significantly poorer matches between observation and the standard models, but, given the caveats discussed above, those errors should still be treated with caution.

For near critical rotational velocities, the stellar mass can be estimated. Howarth & Smith (2001) show that the stellar mass can be written in terms of ω/ω_c,¹⁵ v_eq, and the polar radius. Assuming that sin i ∼ 1 and adopting the critical velocities from our single star models, we can estimate the first two quantities. Additionally for any given value of ω/ω_c, the polar radius can be inferred from the absolute visual magnitude and the unreddened (B−V). The former can be estimated from the luminosity (see Section 3.4) and the latter from our effective temperature estimate and the LMC broadband intensities calculated by Howarth (2011). We find M ≳ 20 M_☉ for v_eq ∼ 600 km s⁻¹ and T_eff ≲ 38,000 K. Only by adopting a smaller value for v_eq can we push the mass limit down, but even with v_eq ∼ 500 km s⁻¹ the mass must exceed ∼17 M_☉.

From extant photometry (see Paper I), the (B−V) color of VFTS102 is 0.35, implying an E(B − V) of 0.6 using colors calculated from our TLUSTY grid. Adopting a standard reddening law leads to a logarithmic luminosity (in solar units) of 5.0 dex, with an E(B − V) error of ±0.1 corresponding to an uncertainty of ±0.1 dex. However, there are other possible sources of error, for example, deviations from a standard reddening law, and hence we have adopted a larger random error estimate of ±0.2 dex.

As VFTS102 is an Oe-type star, its intrinsic colors may be redder than predicted by our TLUSTY grid and indeed an infrared excess is found from published (de-reddened) Two Micron All Sky Survey (2MASS) photometry. Inspection of a K-band VISTA image shows no evidence of contamination by nearby sources. Further evidence for circumstellar material is found in the strong Hα emission, which is double peaked as is the nearby He i line at 6678 Å, which supports our adoption of a sin i ∼ 1. Additionally, there are weak double-peaked Fe ii emission features (e.g., at 4233 Å), consistent with an Oe-type classification. Unfortunately, our photometry and spectroscopy are not contemporaneous but if VFTS102 was in a high state when the optical photometry was taken, we may have overestimated the luminosity of the central star (see de Wit et al. 2006 for color and magnitude variations of Be stars).

Figure 2 illustrates evolutionary tracks for LMC single stars calculated using the methodology of Brott et al. (2011) for an initial equatorial rotational velocity of 600 km s⁻¹, together with that for a more slowly rotating model. The former are evolving chemically homogeneously while the latter follows a "normal" evolutionary path. Ekström et al. (2008) calculated models for a range of metallicities and masses between 3 and 60 M_☉ but found that the stars followed normal evolutionary paths even for near critical rotational velocities.

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The estimated parameters of VFTS102 are consistent with our tracks for initial masses of ∼20–30 M_☉. Our models show a relatively rapid increase in the surface helium abundance due to their homogeneous evolution. For example, the 25 M_☉ model shows an enrichment of a factor of 2 after approximately 4 million years and when the effective temperature has increased to approximately 39,000 K. By contrast the models of Ekström et al. (2008) show no significant helium abundance implying that an accurate helium abundance estimate for VFTS102 would help constrain the physical assumptions.

Below, we first discuss the environment of VFTS102 and then consider a possible evolutionary scenario.

4.2.1. A Pulsar Near VFTS102

VFTS102 lies in a complex environment near the open cluster NGC 2060. In particular it lies close to a young X-ray pulsar PSR J0537-6910 (Marshall et al. 1998) and the Crab-like supernova remnant (SNR) B0538-691 (Micelotta et al. 2009). VFTS102 has an angular separation of approximately 0.8 arcmin from PSR J0537-6910 implying a spatial separation (in the plane of the sky) of approximately 12 pc.

The X-ray emission consists of a pulsed localized component and a more spatially diffuse component, with the latter providing the majority of the energy. The diffuse component was identified in ROSAT and ASCA observations by Wang & Gotthelf (1998a) and interpreted as coming from ram-pressure-confined material with the X-ray pulsar being identified soon afterward by Marshall et al. (1998). Wang & Gotthelf (1998b) analyzed ROSAT HRI observations and suggested that the emission could come from the remnants of a bow shock if the pulsar was moving with a velocity of ∼1000 km s⁻¹. Wang et al. (2001) subsequently analyzed higher spatial resolution Chandra observations, which clearly delineated this emission and implied that the pulsar was moving away from VFTS102. See, however, Chen et al. (2006) for an alternative explanation of the X-ray morphology, which does not imply a high velocity for the pulsar. Figure 3 superimposes these emission contours onto a Hubble Space Telescope (HST) optical image with VFTS102 being near the tail of these contours. As discussed by Wang et al. (2001) the spatial distribution of the diffuse X-ray emission and the SNR optical emission are well correlated. Differences probably arise from a foreground dark cloud and photoionization and mechanical energy input from the nearby open cluster.

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Timing measurements imply that the pulsar has a characteristic age of 5000 years (Marshall et al. 1998), consistent with the age estimate of Wang & Gotthelf (1998b) from analysis of X-ray emission. Spyrou & Stergioulas (2002) discuss the estimation of ages from spin rates and find the results to be sensitive to both the breaking index and the composition of the pulsar core. Indeed, phase-connected braking index measurements for young pulsars (see Zhang et al. 2001 and references therein) yield breaking indices lower than the n = 3 normally adopted with corresponding increases in the characteristic ages. Additionally, Chu et al. (1992) found an age of approximately 24,000 years from the kinematics of the SNR.

Adopting an age of 5000 years would imply that if these objects had been part of a binary system, their relative velocity (v_s) in the plane of the sky would be approximately 2500 km s⁻¹. Increasing this age to 24,000 years would then imply v_s ∼ 500 km s⁻¹. These values, although large, are consistent with a pulsar velocity of 1000 km s⁻¹ in the model of Wang & Gotthelf (1998b) and of ∼600 km s⁻¹ from the separation of the diffuse X-ray and radio emission (Wang et al. 2001). Additionally, Hobbs et al. (2005) found a mean space velocity of approximately 400 km s⁻¹ for a sample of young pulsars with velocities as high as 1600 km s⁻¹. From the theoretical point of view, Stone (1982) found supernova kick velocities normally in excess of 300 km s⁻¹, while more recently Eldridge et al. (2011) estimated kick velocities for a single neutron star of more than 1000 km s⁻¹with a mean value of ∼500 km s⁻¹.

4.2.2. A Binary Evolution Scenario for VFTS102

Irrespective of the origin of VFTS102, it is interesting to consider its likely fate. Stellar evolutionary models of rapidly rotating stars have recently been generated by Woosley & Heger (2006) and Yoon et al. (2006). The latter consider the fate of objects with rotational velocities up to the critical value (v_c). The evolution is shown to depend not only on initial mass and rotational velocity but also on the metallicity. In particular, gamma-ray bursts (GRBs) are predicted to occur only at sub-solar metallicities.

Based on our single star models, VFTS102 has a rotational velocity above ∼0.8v_c and is thus expected to evolve quasi-chemically homogeneously. While Yoon et al. (2006) and Woosley & Heger (2006) estimate the metallicity threshold for GRB formation from chemically homogeneous evolution to be somewhat below the LMC metallicity, the latter note its sensitivity to the mass-loss rate (Vink & de Koter 2005). Indeed, all our most rapidly rotating 20–30 M_☉ models are evolving chemically homogeneously throughout core hydrogen burning (Figure 2), a prerequisite to qualify for a GRB progenitor. In any case, within the context of homogeneous evolution, VFTS102 is expected to form a rapidly rotating black hole and a Type Ic hypernova. This conjecture remains the same within the binary scenario of Cantiello et al. (2007).

Assuming a space velocity of 40 km s⁻¹ for VFTS102 (compatible with its anomalous radial velocity), our evolutionary models imply that VFTS102 will travel ∼300–400 pc before ending its life. This is consistent with the finding of Hammer et al. (2006) that the locations of three nearby GRBs were found several hundred parsecs away from their most likely progenitor birth locations (see, however, Margutti et al. 2007; Wiersema et al. 2007; Han et al. 2010).