arXiv:0804.2392v1 [astro-ph] 15 Apr 2008 oeetrn h ebrigWl-ae W)sae tthe at 10 stage, least at (WR) lasting be Wolf-Rayet which, phase, of He-burning and (LBV) end O variable the drives blue entering which luminous fore process the key into the B-type being as accepted widely ntecnnclpcueo h vlto fvr asv ( massive very of evolution the of 40 picture canonical the In Introduction 1. in ubrt uha hs fPCgior the Cygni from P of distinct those is as such and outbursts 1994) giant Davidson & (Humphreys LBVs fLV,drn hc h trehbt rgtesvariatio brightness exhibits the which of ph during Doradus S LBVs, the during of loss we mass SNe variable some of of manifestation curves a light radio the quasi-per in the observed LBVs modulations that that proposed suggested they explode; (2006) Vink might themselves & Kotak the Recently as CcSNe. LBVs of to points that a idence as explode to expected is (CcSN). object the core-collapse 2006), Vink & Eldridge h eyedo h B phase. LBV the of during end exploded very star ac- massive the resulted to presumably be single, SN would a the explanation that while simpler cept LBV, A companion. the WR to the attributed from coinci is explosion 2006jc pre-SN system the SN progenitor scenario, alternative with this an In as 2006jc. star SN WR eruption, a for con and LBV-like system LBV binary an massive an of a ing suggest undergo never (2007) have al. to et stars Pastorello explosion observed WR ea an that to been 2007 of Given was previously prior star. al. star et Wolf-Rayet progenitor years Pastorello the (WNE) that 2007; type two argue al. (2007) just et al. Foley et Foley eruption 2006; giant al. et (Nakano a have to VSo h L nporme26D52Aad278.D-0270. and 276.D-5020A programme in VLT the on UVES edo Send ⋆ oebr1,2018 13, November srnm Astrophysics & Astronomy ∼ M flt,teehsbe rwn oyo bevtoa ev- observational of body growing a been has there late, Of neetnl,tepoeio fS 06cwsobserved was 2006jc SN of progenitor the Interestingly, ae nosrain tteErpa otenObservatory Southern European the at observations on Based - antds hsvraiiyi omnlc amongst commonplace is variability This magnitudes. 1-2 ⊙ outflow words. Key consistent periods d and 2 been velocities SN wind only of with previously spectrum along have profiles, the profiles in Such helium history. and evidmass-loss hydrogen convincing of most profiles the of possibly P-Cygni favour present in we evidence Here observational pernovae. mounting been has There 3 2 1 tr eg agre l 94,terl fms osis loss mass of role the 1994), al. et Langer (e.g. stars ) ff rn eussto requests print srpyisgop meilCleeLno,Bakt Lab Blackett London, College Imperial group, Astrophysics rahOsraoy olg il rah T19G Northe 9DG, BT61 Armagh, Hill, College Observatory, Ireland Armagh Northern 1NN, BT7 Belfast, Belfast, srnm eerhCnr,Dprmn fPyis&Astrono & Physics of Department Centre, Research Astronomy N20 j vdnefrLVsproa progenitors? supernovae LBV for Evidence gj: 2005 SN uenve eea uenve niiul(N20g,S 2005gj, (SN individual supernovae: – general supernovae: .rnl,e-mail: C.Trundle, : aucitn.ctrundle08˙1 no. manuscript 5 r Mye adr2003; Maeder & (Meynet yrs direct .Trundle C. [email protected]. rgntr fasubset a of progenitors η Carina. 1 .Kotak R. , ihLVslasu ocnetS 05jt nLVprogenitor. LBV an to 2005gj SN connect to us leads LBV’s with iodic M rat or ABSTRACT dent sist- with ase rly tce nLmnu leVrals hssrkn resembla striking This Variables. Blue Luminous in etected neytfrsc rgntr.W n utpeasrto co absorption multiple find We progenitors. such for yet ence 1 rtr,Pic osr d odn W 2BZ SW7 London, Rd, Consort Prince oratory, ns re & ). uiosBu aibe LV)bigtedrc progenitor direct the being (LBVs) Variables Blue Luminous ..Vink J.S. , - y colo ahmtc hsc,TeQensUniversity Queen’s The Physics, & Mathematics of School my, nIreland rn 0g,wihw nepe sbiga mrn fteprogenit the of imprint an being as interpret we which 005gj, tl eansm yrgnadhlu hl N20j showed before hydrogen 2006jc to SN due while features helium spectral no and hydrogen is outburs some undergone core e retain have that Pastorello still the LBVs occur. known that models, to out core-collapse point current (2007) for in H enough words, core most evolved its other in not reached In indeed, even phase; phase. not has LBV burning star the the after models, soon evolutionary predic or not do during models collapse evolution stellar current that is plode an undergone have also may 2006gy, and SN Finally η 2007a). IIn hin morphologies type interesting (Smith luminous 1987A Other the LBV SN of object. in medium single circumstellar similarities the a the confirmed is be from this to come pre- remains not in it or but source 2005gl, whether luminous SN very of a images detected explosion (2007) al. et Gal-Yam fteotrlyr,and layers, outer removed the outburst of pre-explosion the that inconceivable not .Frbt pcstetre a bevdfr20 ihasli a 8660-10255 with and s 2300 Å for 6705-8520 observed was of target arms the 3760- epochs red both of the For blue Å. in the and spectrograph in 8600 Å, the coverage and 4985 of providing 4370 arms at thus to wavelengths employed, red used central Åwas and was with blue setup #2 the standard Dichroic into The 2006). light o al. the date et (Aldering explosion split an 2005 assuming Sep. respectively, Spectrograph days 22 374 Echelle correspond and epochs Ultra-Violet 86 These Telescope. the to Large Very with the on 2005 2006, Dec. (UVES) 17 Oct. the on 1 obtained were and 2005gj SN of spectra Optical reduction and acquisition Data 2. stars. massive vari- very Dor of S endpoints of the of mass-loss as suggestion them variable betrays the the ables that support (2006) Vink to & evidence Kotak spectroscopic show we lines. strong to rise give necessarily not a-yeeuto ro oepoin(mt ta.2007b). al. et (Smith explosion to prior eruption Car-type oeta rbe ihaseai nwihLV ex- LBVs which in scenario a with problem potential A explode. may LBVs that indications other are There ee epeetteitiun aeo N20g o which for 2005gj SN of case intriguing the present we Here, 02c–cruselrmte tr:eouin winds, evolution, stars: – matter circumstellar 2002ic)– N 2 ...Meikle W.P.S. , / rta eiulaonso rH may He or H of amounts residual that or 3 ∼ 5d oee,i is it However, d. 65 c fthe of nce

c mponent fsu- of s ⋆ S 2018 ESO ors of core- t most al. t e- ts ts f t , . 2 C.Trundle: SN 2005gj: Evidence for LBV supernovae progenitors?

Fig.1. Left: Optical spectra of SN 2005gj at 86 and 374 days after explosion, after correction for the of the host . Right: Multiple component Gaussian profile fits to the Hα profile for both epochs; day 86 in top panel and day 374 in bottom panel (Table 1). Units of the axes are the same as the left panel. width of 1′′. 6 and a seeing of ∼ 1′′. 05 providing resolutions of ∼6 Table 1. Parameters of the gaussian fits to the narrow compo- −1 and 4.5 km s in the blue and red arms, respectively. nents of Hγ,α & He i 7065 Å lines of SN 2005gj at 86 and 374 The data were reduced with the UVES pipeline implemented days after explosion. ‘Narrow E’ - the narrow emission compo- in the ESO-MIDAS software. Wavelength calibration was car- nent, ‘NAC (a)’ and ‘NAC (b)’ - the blue and red absorption ried out using Th-Ar arcs taken on the same night as the components respectively. Each profile has been fit by multiple SN 2005gj exposures, while flux calibration and telluric subtrac- gaussian profiles, representing the broad, intermediate and nar- tion of the data was done with respect to the standard LTT1020. row components of the profile. The flux calibrated spectra extracted from each chip and cor- rected to the rest frame are presented in Fig. 1. A redshift of ± Fit properties Narrow E NAC (a) NAC (b) 0.0616 0.0002,as found byAldering et al. (2006), was adopted Day 86: H as it was consistent with our data. α ± ± ± 3. Spectral Analysis λ (Å) 6564.29 0.02 6558.35 0.06 6561.25 0.06 FWHM (km s−1) 128 ± 2 70±6 133±21 The optical spectra of SN 2005gj are dominated by Hα in emis- L (1040 ergs s−1) 1.61±0.02 0.14±0.01 0.20 ±0.02 −1 sion. The profile consists of a strong narrow emission compo- vedge (km s ) 295 ± 57 120 ± 75 nent superimposed on broad emission wings (Fig. 1). Such Hα Day 86: Hγ profiles are the hallmarks of SN IIn spectra (‘n’ standing for λ (Å) 4341.39±0.02 4338.01±0.10 4340.04±0.10 ‘narrow’), believed to arise from massive progenitors that have FWHM (km s−1) 97 ± 3 68 ± 5 115 ± 4 undergone substantial mass-loss prior to explosion (Schlegel L (1040 ergs s−1) 0.15±0.04 0.04±0.01 0.12±0.05 −1 1990). The multi-component profiles are characterised by broad vedge (km s ) 286 ± 57 115 ± 64 underlying emission due to SN ejecta, an intermediate emission Day 86: Hei7065 resulting from shocked material at the interaction front between λ (Å) 7066.33±0.03 7062.61±0.09 7063.97±0.10 −1 the ejecta and the CSM, while the narrow component presum- FWHM (km s ) 64 ± 3 22 ±9 62±15 L (1040 ergs s−1) 0.10±0.02 0.006±0.001 0.022±0.004 ably arises from unshocked CSM photoionised by the SN. −1 A striking feature of the P Cygni-like component of the Hα vedge (km s ) 160± 59 95 ± 57 profile at 86d is the presence of two clear absorption troughs Day 374: Hα (Fig. 1). This has previously not been observed in SN spectra. λ (Å) 6562.60±0.04 6559.70 ±0.12 FWHM (km s−1) 88± 10 110 ± 23 That this feature is associated with the SN is clear, given the 40 −1 evolution of the profile between the two epochs. Aldering et al. L (10 ergs s ) 0.18± 0.09 0.028± 0.005 −1 ± (2006) noted that the absorption component in the narrow P- vedge (km s ) 190 64 Cygni profile was asymmetric and extended far out towards the blue edge.Due to the higherresolutionof ourspectra (c.f. resolu- −1 tions of a few hundred km s Aldering et al. 2006; Prieto et al. intensity dropped by 17×10−16 ergs−1 cm−2 s−1, a single ab- 2007), we were able to resolve this narrow component. Careful sorption trough remained, and a broad blue shoulder had de- inspection of the data revealed clear double absorption troughs veloped, probably corresponding to the emergence of [O i]. To in our day 86 spectrum associated with Hγ, He i 7065Å (Fig. 2), obtain quantitative information from these profiles we have de- and also Hδ, and He i 6078Å albeit with poorer signal-to-noise composed them with multiple Gaussian profiles for the individ- ratios. By ∼400d, the Hα profile had changed significantly: the ual emission and absorption peaks. The fits are shown in Figs. 1 C.Trundle: SN 2005gj: Evidence for LBV supernovae progenitors? 3

Fig. 2. Multiple Gaussian profile fits to the 86 d spectrum for Hγ (left), and Hei 7065Å (right).The flux on the y-axes are given in units of 10−16 ergs−1 cm−2 s−1.

Fig. 3. Comparison of the Hα profile of SN 2005gj in velocity & 2 and their physical parameters are summarised in Table 1. space with that of the luminous blue variables, AG Car & HD The Hα emission profiles at both epochs were fit by 3 Gaussians 160529. Data taken from Stahl et al. (2001, 2003). representing the aforementioned broad, intermediate and nar- row emission components, however this intermediate component i was not detected in the Hγ & He 7065 Å profiles. In addition strong resonance lines (vedge). Unfortunately, there are no such to the emission peaks, the Hα profile from day 86 was fit with resonance lines in the optical, and so we will use the Balmer and double absorption components, whilst only a single absorption He i lines to estimate this velocity from their absorption com- trough was required for the day 374 spectra. ponents. As these lines are not saturated, vedge is likely to un- Due to our incomplete wavelength coverage, particularly to derestimate the terminal velocity (Prinja et al. 1990). From the −1 the blue of Hα, the velocities determined from the Gaussian Hα narrow absorption feature, we find a vedge of 295 kms at fits to the broad emission peak are subject to large uncertain- 86d with an additional component at 120 km s−1 whereas the ties. From the Balmer lines we determine an ejecta velocity of −1 −1 component at 374d has an intermediate velocity of 190 km s . 30000 ± 5000 km s at day 86, which is consistent with that The Hγ feature at day 86 gives velocities consistent with those derived by Aldering et al. from their day 11 spectra. At day 374 i − found from Hα, however the bluer component of the He profile the velocity decreased to 15500 ± 5000 km s 1. The intermedi- −1 appears at a lower velocity with a maximum vedge of160km s . ate Hα emission component was fit by a Gaussian with FWHM −1 −1 We can attempt to derive an estimate of the mass-loss rate 2560 ± 30 kms on day 86 and 1680 ± 30 kms on day 374. from the Hα feature. Following Salamanca et al. (1998), LInt = Hα Whilst this measurement is a good indication of the shock veloc- ˙ 3 ǫHα Mvs /4vw where, ǫHα isanefficiency factor that peaks at ∼0.1. ity for the symmetric profile presented at day 86, this is not the Int L is the luminosity of the intermediate component, vw is the case for the asymmetric profile on day 374. In this later spectra Hα wind velocity and vs is the shocked CSM velocity. At day 86, the narrow Hα feature is redshifted with-respect-to the interme- −2 −1 this implies M˙ = 6.4 and 2.6 ×10 M⊙ yr from the high (295 diate component, this has been seen in a number of Type IIn −1 −1 / km s ) andlow (120km s ) velocity components. At day 374, spectra such as SN 1997ab, 1997eg & the hybrid Type Ia IIn −2 −1 −1 the derived M˙ is 1.7×10 M⊙ yr using vw = 190 km s and SN 2002ic (Kotak et al. 2004). This is generally attributed to −1 self-absorption in the intermediate component which preferen- vs = 2850 km s , one should note that the shock velocity is a tially attenuates the red wing of the profile (Salamanca et al. little less certain in this case (see Sect. 3). These are very large 1998). A better measurement of the shock velocity is therefore mass-loss rates but are typical of those derived from the Hα lu- the velocity of the blue edge of the profile at zero intensity, minosity in supernovae which show strong interaction between which is 2850 ± 200 km s−1. The luminosities inferred from the the ejecta and CSM (e.g. SNe 1997ab, 2002ic Salamanca et al. narrow line intensities at day 86 agree well with those derived 1998; Kotak et al. 2004). However, Kotak et al. found that mass- by Aldering et al., with a significant decline in the luminosi- loss rates derived from dust measurements in the infrared area ties derived from the narrow component from 1.6×1040 ergs−1 magnitude lower. A similar observation can be made by com- to 1.8×1039 ergs−1 by day 374. paring the mass-loss rates of SN 2005gj derived here and that Other, less dramatic features in the spectra comprise a broad of Prieto et al. from x-ray luminosities. Several caveats must be α feature at ∼ 8500 Å, probably a blend of the Ca ii infrared triplet borne in mind when estimating mass loss rates via H profiles. i Two of the most serious shortfalls involve the unknown ioni- with O 8446. There is a weak, broad feature centered on 7300Å sation conditions and uncertainties in ǫ . Realistic constraints which, depending on the SN type, can be identified as either [Ca Hα ii ii can only be derived from detailed modelling which is beyond ] or [Fe ], with the latter being typically present in the late- the scope of this work. time spectra of SNe Ia. The [Ca ii] lines however, are typically observed in the spectra of Type IIn and Ib/c SNe at &100d. 4. SN 2005gj: Properties of the unshocked CSM 5. Discussion These narrow P-Cygni features which are commonly found SN 2005gj has been compared to the prototype for the hybrid amongst Type IIn, are thought to represent the outflow of un- Type Ia/IIn objects, SN 2002ic (Aldering et al. 2006). SN 2002ic shocked CSM surrounding the SN event. As such, it provides was initially classified as a Type Ia, due to the presence of S insight into the environment prior to the SN explosion and on ii lines and a blue shifted absorption feature of Si ii 6335 Å, the wind properties of the SN progenitor itself. Stellar wind ter- but was quickly reclassified as a hybrid Type Ia/IIn due to the minal velocities, v∞, are usually measured from the blue edge of presence of multi-componentBalmer lines signifying interaction 4 C.Trundle: SN 2005gj: Evidence for LBV supernovae progenitors? with the surroundingcircumstellar medium (Hamuy et al. 2003). multiple shells occur in the very early stage of the WR-lifetime This was an exciting discovery as the presence of circumstellar and hence if such a scenario was implied for SN 2005gj, its hydrogenin the spectra of a type Ia supernovae would shed light WR-phase would have been short-lived. on the nature of Type Ia progenitors. One scenario put forward While the morphological resemblance of the line profiles by Hamuy et al. is that the dense CSM could representmass-loss observed in SN 2005gj and in LBVs is impressive enough, from an asymptotic-giant-branch (AGB) star. Unfortunately, the an even more compelling similarity is that of LBV wind ve- true classification and interpretation of SN 2002ic remains un- locities with those derived from the absorption components of der debate. In particular, Benetti et al. (2006) argue that it can SN 2005gj. LBV velocities lie in the ∼50–300km s−1range, in equally well be compared to a core-collapse SN, such as the strikingly good agreement with those derived from SN 2005gj type Ic SN 2004aw. This comparison is most convincing at late (Table 1), which are larger than those observed in AGB winds epochs, in fact the resemblance of SN 2002ic to type IIn SNe (∼10km s−1) and red-supergiant winds and much lower than had been noted earlier (e.g. Hamuy et al. 2003). typical WR-star winds. Typical timescales of S Doradus mass- In spite of the Hα feature indicating CSM interaction, the loss events in LBVs are on the scale of years up to ∼100 early time optical spectra of SN 2002ic were undeniably Ia- yrs (van Genderen 2001). From a simple calculation we can like (see Fig. 3 Hamuyet al. 2003). Alderinget al. (2006) & determine the timescales of the profile variations detected in Prieto et al. (2007) argue that SN 2005gj could be compared to SN 2005gj. Using an intermediate ejecta velocity of 22500 the overluminous Type Ia, SN 1991T ‘diluted’ by the presence km s−1, a time variation of 288 days and an edge velocity of 300 −1 of significant CSM. However, the typical Ia spectral features due km s we get Pw=Rejecta/vedge ∼ 60 yrs. Thus the timescales to S ii and Si ii which formed the crux of the Ia-evidence for associated with mass-loss events in LBV and SN progenitors SN 2002ic, are barely discernible in the spectra of SN 2005gj. are consistent. Note the 60 yr timescale is only an upper limit They attribute this to stronger interaction of the SN 2005gj with as we have not obtained a well-sampled temporal dataset of the CSM than for SN 2002ic, arguingthat this claim is supported high-resolution spectra. Hence the variations are likely to be by its broader light curve and higher Hα luminosities. on shorter timescales still consistent with S Doradus variations. On the basis of the data presented here, we cannot verify Even the change into a single absorption component (374d) or exclude the type Ia identification of SN 2005gj. However, mimics the behaviourof LBVs such as AG Car which show sim- we present an alternative scenario that is consistent with the ilar variations on timescales of years (Fig. 3). observations. We focus our attention on the double absorption For SN 2005gj the line profiles, wind velocities and wind pe- troughs seen in the day 86 spectrum. Only in one other SN spec- riodicity are remarkably reminiscent of LBVs and provide sig- tra, SN 1998S, have double absorption troughs been dectected nificant support for a direct link between supernovae and lumi- (Bowen et al. 2000; Fassia et al. 2001). However the shape of nous blue variables. This may have a huge impact on our under- the lines differ significantly. In SN 1998S a narrow P-Cygni pro- standing of massive star evolution since current theory predicts file of ∼50 kms−1is superimposed on a broad, shallow absorp- that LBVs, which are in a short-term, intermediary phase of evo- tion profile (Bowen et al. 2000, see Fig. 8). Additionally, this lution, should not undergo core-collapse. absorption decreases in relative intensity from lower to higher Balmer lines, suggestive of an optical depth dependence that is 6. Acknowledgements inconsistent with the SN 2005gj spectra. Chugai et al. (2002) in- The authors acknowledge fruitful discussions with L. Dessart & voke several mechanisms that could accelerate the circumstellar N. Langer. gas aroundSN 1998S. These models have been tailored to match the early-time spectra of SN 1998S and it is difficult to see how References these might be tailored to the significantly later epochs of our Aldering, G., Antilogus, P., Bailey, S., & et al., 2006, ApJ, 650, 510 data. This type of test may provide some insight but is beyond Benetti, S., Cappellaro, E., Turatto, M., & et al., 2006, ApJL, 2, 129 the scope of this letter. Bowen, D. V., Roth, K. C., Meyer, D. M. & Blades, J. C. 2000, ApJL, 536, 225 Here we would like to stress the likeness of the profiles in Chugai, N. N., Blinnikov, S. I., Fassia, A., & et al., 2002, MNRAS, 330, 473 SN 2005gj with another stellar object: Luminous Blue Variables. Eldridge, J.J., Vink, J.S., 2006, A&A, 452, 295 Fassia, A., Meikle, W. P. S., Chugai, N. N., & et al., 2001, MNRAS, 325, 907 Multiple-absorption component Hα profiles have been detected Foley, R.J., Smith, N., Ganeshalingam, M., & et al., 2007, ApJ, 657, L105 in many LBVs, viz AG Carinae, R127, R81, HD160529, R66, Gal-Yam, A., & et al., 2007, ApJ, 656, 372 & P-Cygni (Wolf et al. 1981; Stahl et al. 1983,a, 2001, 2003; Hamuy, M., Phillips, M. M., Suntzeff, N. B., & et al., 2003, Nature, 424, 651 Leitherer et al. 1994). Fig. 3 shows several examples of the Hα Humphreys, R.M., & Davidson, K., 1994, PASP, 106, 1025 Kotak, R., Meikle, W. P. S., Adamson, A., & Leggett, S. K., 2004, MNRAS, 354, profiles of LBVs gleaned from the literature. In LBVs these L13 multiple-absorption component profiles signify their history of Kotak, R. & Vink, J.S., 2006, A&A, 460, L5 episodic mass-loss events. Vink & de Koter (2002) interpreted Langer, N., Hamann, W-R., Lennon, M., & et al., 1994, A&A, 290, 819 the variable mass-loss and wind velocity behaviour of LBVs as Leitherer, C., & et al., 1994, ApJL, 428, 292 being due to a change in the ionization of the dominant wind Meynet, G., Maeder, A., 2003, A&A, 404, 975 Nakano, S., Itagaki, K., Puckett, T., & Gorelli, R., 2006, Cent. Bur. Electron. driving ion Fe (wind bistability). This mechanism was also in- Tel., 666, 1 voked to explain the variations in the radio lightcurves of tran- Pastorello, A., Smartt, S. J., Mattila, S., & et al., 2007, Nature, 447, 829 sitional SNe (Kotak & Vink 2006). However, regardless of the Prieto, J. L., Garnavich, P. M., Phillips, M. M., & et al., 2007, AJ, submitted mechanism the resemblance of the double-troughed LBV Hα Prinja, R. K., Barlow, M. J., & Howarth, O. D., 1990, ApJ, 361, 607 Salamanca, I., Cid-Fernandes, R., Tenorio-Tagle, G., & et al., 1998, MNRAS, profiles to that of SN 2005gj remains. 300, L17 An interesting hydrodynamical simulation by Schlegel, E.M., 1990, MNRAS, 244, 269 van Marle et al. (2007) shows the evolution of CSM around a Smith, N., 2007a, AJ, 133, 1034 Smith, N., Li, W., Foley, R.J, & et al., 2007b, ApJ, 666, 1116 60M⊙ star as it evolves from main-sequence to core-collapse via Stahl, O., Wolf, B., Klare, G., & et al., 1983, A&A, 127, 49 an LBV and WR phase. This simulation shows the formation Stahl, O., Wolf, B., Zickgraf, F.-J, & et al., A&A, 120, 287 of multiple absorption components from CSM shells formed Stahl, O., Jankovics, I., Kov´acs, J., & et al., 2001, A&A, 375, 54 by a fast WR wind running into an LBV shell. However these Stahl, O., G¨ang, T., Sterken, C. & et al., B, 2003, A&A, 400, 279 C.Trundle: SN 2005gj: Evidence for LBV supernovae progenitors? 5

Wolf, B., Stahl, O., de Groot, M.J.H & Sterken, C., 1981, A&A, 99, 351 van Genderen, A.M., 2001, A&A, 366, 508 van Marle, A. J., Langer, N., & Garc´ıa-Segura, G., 2007, A&A, 469, 948 Vink, J.S. & de Koter, J.S., 2002, A&A, 393, 543