The Rotation Rates of Massive Stars: How Slow Are the Slow Ones?

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arXiv:1310.4729v1 [astro-ph.SR] 17 Oct 2013 oainrt;ised n yial nesthe infers typically rotation, one lar instead, rate; rotation gamma-rays of bursts 2006). as energetic al. som very et death Yoon in produce (e.g., violent that (e.g., even demises its may hypernova, cloud to cases or 2000), supernova molecular core-collapse Meynet & rotating a from Maeder evolv and the (e.g., life, main-sequence star’s stages star’s of the massive over 1995), collapse a Bodenheimer of initial phases the all influences Rotation Introduction 1. iua,i swl nw htteocrec flreso- large of ac occurrence deriving the complicates par- that seriously In known other curate macroturbulence atmosphere. well from the broadening is called in line it becomes present rotational ticular, then components this issue separate broadening key to A how line-spectrum. broadened served n o ail Cni&Ebt 97 oat ta.1997; al. al et et 2011). Howarth Lefever al. et 2007; Markova 1977; 2010; Simón-D´ıaz Simón-D´ıaz Herrero al. Ebbets 2007; & 2002; et & (Conti al. et rapidly Ryans too ing om(T ehdue h rtzr nteFuirpower Fourier the in zero 2002; first stars the al. et uses Ryans massive tran method (e.g., Fourier (FT) in the applied form example, and For broadening 2007). developed Simón-D´ıaz Herrero rotational & been have and “turbulent” etme 0 2018 20, September srnm Astrophysics & Astronomy o otsasi sntpsil odrcl esr the measure directly to possible not is it stars most For eea ehiusfrsprtn h e the separating for techniques Several ramn ftecmeigbodnn ehnssreferred mechanisms broadening competing the of treatment v intrsi h htshrcsetao asv tr,fo stars, massive of spectra photospheric the in signatures eevd21-92;acpe 2013-10-14 accepted 2013-09-27; Received 4 e words. Key way. under 3 1 2 inr ttsadsi-onhsoiso oainlybra inferred rotationally spectroscopically of dist histories spin-down statistical and the status determining tionary i) for crucial be example, peso asv tr ntepeec fsgicn additi significant of presence the in stars massive of speeds Conclusions. proje infer to Results. used typically methods (GOF) goodness-of-fit Methods. Aims. Context. ae fsc asv tr sciia o nesadn th understanding for critical is stars massive such of rates sin nttt fAtooywt A,BS ..Bx16 70Smol 4700 136, Box P.O. BAS, NAO, with Astronomy of Institute eatmnod srfiia nvria eL aua E-38 Laguna, La de Universidad Astrofisica, de Departamento e-mail: 81679 Universitätssternwarte 1, München, Scheinerstr. nttt eAtosc eCnra,E320L aua Ten Laguna, La E-38200 Canarias, de Astrofisica de Instituto v sin i ≈ hspprivsiae h eiblt fcretmethods current of reliability the investigates paper This i v 40 o u w antcts tr ihmaue oainperio rotation measured with stars test magnetic two our For oainpasakyrl ntelf ylso tr ihmass with stars of cycles life the in role key a plays Rotation [email protected] euesol oaigmgei -tr ihwell-determin with O-stars magnetic rotating slowly use We sin ae o asv tr htaentrotat- not are that stars massive for rates − tr:erytp tr:rtto tr:mgei fields magnetic Stars: – rotation Stars: – early-type Stars: hs nig anu o orl nrtclyo eut fro results on uncritically rely to not us warn findings These i 0k s km 50 wt nlnto angle inclination (with − 1 rmbt h TadGFmtos hs eeeoverestimates severe These methods. GOF and FT the both from aucitn.sundqvist˙rot no. manuscript v sin h oainrtso asv stars massive of rates rotation The ..Sundqvist J.O. i ≈ ms km 0 o lwaeteso ones? slow the are slow How − 1 ute netgtoso oeta hrcmnso h a the of shortcomings potential of investigations Further . i ,fo h ob- the from ), 1 ff .Simón-D´ıaz S. , projected cso such of ects iuino bevdrtto ae fmsiesas i in ii) stars, massive of rates rotation observed of ribution e -uegat,adii xliigtedfiinyo obs of deficiency the explaining iii) and B-supergiants, ked i rprisadfrcntann oeso hi evoluti their of models constraining for and properties eir uigo tr htaentrpdyrotating. rapidly not are that stars on cusing München, Germany tdrtto ae fmsiestars. massive of rates rotation cted ABSTRACT stel- oa irtruec n macroturbulence. and microturbulence as to nlln raeig tlatwhen least at broadening, line onal ed s- e rf,Spain erife, - . sdt eiepoetdrtto speeds rotation projected derive to used 0 aLgn,Tnrf,Spain Tenerife, Laguna, La 205 2 culyioaeterttoa opnn,ads eue to used be can so methods and used of component, values commonly accurate rotational quantitatively pres these derive at the degree is isolate it what Simón-D´ıaz 2013), actually to et al. 2009; et clear Sundqvist al. (b et not 2013; unknown Cantiello al. et largely 2009; Shiode still 2010; al. is et Aerts stars massive see in l spectral broadening addit the of line of physics fit underlying the best because a primarily di However, obtain to the broadening turbulent uses and simply method (GOF) pcrmt ietyextract directly to spectrum rmteosre aito ftelniuia ed(e.g., photomet- or field 2005) longitudinal al. the et obtained Bychkov pe- readily of ric 1980; be rotation variation Landstreet can & The observed Borra stars 2012). massive the magnetic al. from et these Wade of (MiMeS, riod la project detected Mas in with Magnetism Stars the O-stars within collected rotating fields, magnetic slowly scale of spectra quality atclr efcshr ntomgei -tr ihperio with with i.e., O-stars year, magnetic one two than on longer 2007) here al. et focus Howarth we 1978; particular, Borra & Landstreet (e.g., spheres d,adciial vlaeterlaiiyo ohtechni stars. both massive of of regime reliability slow-rotation the the meth evaluate GOF critically and FT and the ods, using speeds rotation projected derive we a,Bulgaria yan, , 3 slne hnoeya,ie,with i.e., year, one than longer ds .Puls J. , ehius spectroscopic Techniques: – / sabove es pcrlvrain asdb hi icmtla magneto circumstellar their by caused variations spectral hsLte et h TadGFmtosb sn high- using by methods GOF and FT the tests Letter This drtto eid ots h ore rnfr F)and (FT) transform Fourier the test to periods rotation ed urn tnadtcnqe odrv rjce rotation projected derive to techniques standard current m 1 ∼ n .Markova N. and , 8 M ⊙ ec,acrt nweg fterotation the of knowledge accurate Hence, . r otlkl asdb ninsu an by caused likely most are v sin 4 v oetcnqe r presently are techniques bove v i sin v sin ∼ < v sin sin ff 0k s km 50 i i n h goodness-of-fit the and , i rn hpso rotational of shapes erent ∼ < i ∼ < rmline-broadening from v ms km 1 epeigteevolu- the terpreting ms km 1 sin on. re -tr with O-stars erved − 1 hsmy for may, This . i . − − 1 1 o hs stars these For . ederive we ,

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2. Observations and method Fig. 2, right panel). The model assumes that large-scale motions occur only radially and/or tangentially to the stellar surface (here As our test objects, we use the Of?p-stars (Walborn 1972) we assume equal contributions in both directions), resultingin a HD191612 and HD108, the two known magnetic O-type stars more triangular-shaped profile (see Gray 2005) as compared to −1 with v sin i ∼< 1kms and macroturbulent velocities in excess isotropic macroturbulence. Testing has shown that, for the same −1 of 50kms (Martins et al. 2012; Sundqvist et al. 2013; Simón- observed line profile, the different shapes of the RT and isotropic D´ıaz & Herrero 2013). Of these two stars, HD191612 has the models result in characteristic macroturbulent velocities that dif- shorter rotation period, P = 538 days, which along with its es- ∼ −1 ◦ fer on average by 20kms (with the RT model yielding sys- timated stellar radius 14.5R⊙ and inclination angle i ≈ 35 − 50 tematically higher values, Markova et al. 2013b), and that the yields v sin i < 1 km/s (Howarth et al. 2007; Sundqvist et al. choice of macroturbulence also affects the derivation of v sin i 2012). For the even longer period of HD108, v sin i < 1 km/s in- (see Figs. 2 and 4, and discussion in Sect. 4). dependent of i (see, e.g., Petit et al. 2013). Although a few more magnetic O-stars with well constrained rotation periods also are known (see compilation by Petit et al. 2013), they all have either 3. Results shorter periods or weaker macroturbulence. Shorter periods im- ply a non-zero and uncertain true projected rotation speed (due Figs. 1 and 2 illustrate the derivation of the projected rotation to uncertain stellar radii and even more so to an often poorly con- speeds for HD191612 and HD108 using the FT and GOF techniques, respectively. The figures reveal how both methods yield strained inclination angle), and lower macroturbulence means a −1 weaker influence of the primary competing broadening mecha- v sin i ≈ 40 − 50kms , a severe overestimation compared to the v sin i ∼< 1kms−1 inferred from the variations of the longitudinal nism that complicates the derivation of accurate v sin i values. 1 Since the aim of this paper is to test current methods using stars magnetic field (see Sects. 1 and 2) . with known (and very slow) rotation rates, we restrict the anal- The GOF contour-maps in Fig. 2 actually display quite wide ysis here to HD191612 and HD108, deferring to a future paper ranges of allowed values for v sin i and macroturbulent velocities, where we note in particular that for HD191612 v sin i ≈ a complete study of all OB-stars with detected surface magnetic −1 fields (see also discussion in Sect. 4). 0 kms cannot be ruled out with a 2σ confidence, even though the best fit indicates a much higher value. However,from the first High-quality spectra are retrieved from the extensive MiMeS minima in the Fourier transforms displayed in Fig. 1 we clearly database, and were obtained using the high-resolution (R ∼ measure projected rotation speeds that deviate significantly from 65000) spectropolarimeter ESPaDOnS at the Canada-France zero. Hawaii Telescope (HD191612) and its twin instrument Narval The line profiles displayed in Fig. 2 are asymmetric, which at the Télescope Bernard-Lyot (HD108). As in Sundqvist et al. can influence the reliability of v sin i values, particularly when (2013), we focus on analyzing the stars’ low states, defined ac- inferred from the FT method (e.g., Aerts et al. 2009). To test cording to when the cyclic Hα emission originating from their whether this asymmetry might be responsible for the overesti- “dynamical magnetospheres” (Sundqvist et al. 2012) is at min- mated projected rotation speeds, we artificially symmetrized the imum. This should minimize any contamination of the photo- blue wings of the OIII lines about their line-centers, and then spheric lines by magnetospheric emission. However, for com- re-analyzed the resulting symmetric profiles. However as illus- parison, in Sect. 3 we also comment briefly on differences be- trated for HD191612 by Fig. 3, these symmetric profiles also tween this low state and the correspondinghigh state, definedby give a clear high-velocity minimum in the Fourier power spec- maximum Hα emission. −1 tra, as well as a GOF contour-mapsimilar to the one displayed in Since Zeeman splitting only contributes ∼ 1-2kms per Fig. 2, resulting again in a best estimate v sin i ≈ 40 − 50kms−1. kG in the optical, and the measured dipolar field strengths of An equivalent analysis of HD108, which is not shown in the HD191612 and HD108 are 2.5kG and ∼ 0.5kG (Wade et al. figure, gives similar results, and symmetrizing the red wings of 2011; Martins et al. 2010), magnetic broadening is negligible the profiles also yields highly overestimated projected rotation for both stars (Sundqvist et al. 2013). This allows us to derive speeds, now on the order of v sin i ≈ 30 − 40 km/s (due to the projected rotational velocities by means of the same techniques somewhat narrower redward wings in the original asymmetric as for non-magnetic stars. For this objective, we use the pho- profiles). To further test the possible impact of such line-profile iacob broad tospheric OIII λ5591line and apply the - tools de- asymmetry and variability, we also analyzed the OIII line dur- veloped by Simón-D´ıaz & Herrero (2013). In summary, the ing HD 191612’s high state (see Sect. 2), but that fitting yielded FT method directly estimates v sin i from the position of the projected rotation speeds on the order of 40 kms−1 as well. first zero in Fourier space, whereas the GOF method convolves synthetic line profiles for a range of projected rotational and macroturbulent velocities, creating a standard χ2-landscape from 4. Discussion and conclusions which a best combination of the two parameters is determined. −1 For simplicity, in this Letter we focus exclusively on the above The central result of this paper is the v sin i ≈ 40 − 50kms mentioned OIII line (as in Markova et al. 2013 and Simón-D´ıaz spectroscopically derived for two (magnetic) O-stars with mea- < −1 & Herrero 2013), but we have verified that a correspondinganal- sured rotation periods implying v sin i ∼ 1kms . Provided ysis of the CIV λ5801 line gives very similar v sin i results (see these results can be extrapolated to O-stars in general (i.e., that also Howarth et al. 2007). there is no additional process that seriously contaminates the analysis here of the magnetic stars’ photospheric line profiles), To be consistent with most recent studies of non-magnetic the largely overestimated v sin i values suggest that, in the pres- massive stars (e.g., Simón-D´ıaz et al. 2010; Najarro et al. 2011; ence of strong line broadening in addition to rotation, neither the Markova et al. 2013a), we adopt the “radial-tangential” (RT) for- mulation of Gaussian macroturbulence (rather than the isotropic 1 We note that while the analysis in this paper is based solely on model used by Sundqvist et al. 2013). This RT model has been spectra collected by the MiMeS collaboration, analysis of complemen- the primary choice in such previous work mainly because the tary iacob spectra for HD 191612 and HD 108 (Simón-D´ıaz & Herrero FT and GOF methods then give consistent v sin i results (see 2013) gives the same overestimated v sin i results as found here. J.O. Sundqvist et al.: The rotation rates of massive stars 3

Fig. 1. Fourier power spectra of the OIII λ5591 line in HD191612 and HD108. In standard analysis, the position of the ﬁrst minimum is used to infer the projected rotation speed of the star.

Fig. 3. The same as Figs. 1 and 2, but now with the observed OIII line artiﬁcially symmetrized about line-center. We note the overlap of the blue and red squares in the middle panel, indicat- ing prefect agreement between v sin i derived from the FT and GOF methods.

Fig.2. Left: Best fits of GOF analysis, with derived projected rotation speeds and characteristic macroturbulent velocities θRT as indicated in the figure. Right: Corresponding contour maps, with 1σ, 2σ, and 3σ confidence intervals indicated. The red squares indicate the best GOF and the blue squares the v sin i derived from the Fourier analysis in Fig. 1 .

FT nor the present implementation of the GOF method is able to derive reliable projected rotation speeds when v sin i ∼< 50 km s−1. Ongoing (e.g., Simón-D´ıaz & Herrero 2013) and future Fig. 4. As Fig. 2, but now assuming isotropic macroturbulence, studies on larger samples will tell whether the stars examined with characteristic velocity θG, instead of radial-tangential (see here indeed are the forerunners of a more general problem. Sect. 2). While a “best fit” is provided in the left panel, the solutions are in principle degenerate in the range v sin i ≈ 0 − 60 Such general shortcomings of the present-day techniques km s−1, as illustrated by the contour maps in the right panel. for inferring low projected rotation speeds may then have 4 J.O. Sundqvist et al.: The rotation rates of massive stars consequences for determining the statistical distribution of accurate v sin i rates in that parameter range (like continuum nor- observed rotation rates of massive-star populations in the malization of shallow lines; see Simón-D´ıaz & Herrero 2013). Galaxy and beyond (e.g., Hunter et al. 2008; Dufton et al. 2013; We thus plan to expand the study here to test the FT and GOF Ram´ırez-Agudelo et al. 2013; Simón-D´ıaz & Herrero 2013). It methods also for such faster rotators, using the significant num- may also help explain the apparentdeficiency of observedO- and ber of relatively fast rotating magnetic B-stars with measured early B-stars with spectroscopically inferred v sin i ≈ 0kms−1,a rotation periods (see Petit et al. 2013) present in the MiMeS long-standing problem (e.g., Penny 1996; Howarth et al. 1997) database. which only for the cases of late O- and B-dwarfs seems to have been alleviated by the consideration of additional broadening Acknowledgements. JOS gratefully acknowledges support from DFG grant Pu117/8-1. The MiMeS project is thanked for providing the observed spec- due to macroturbulence (Simón-D´ıaz & Herrero 2007; Markova tra of HD 108 and HD 191612. SS-D acknowledges financial support from et al. 2013a,b; Simón-D´ıaz & Herrero 2013). Furthermore, the the Spanish Ministry of Economy and Competitiveness (MINECO) under results here may be important for interpreting the evolutionary the grants AYA2010-21697-C05-04, Consolider-Ingenio 2010 CSD2006-00070, status of massive B-supergiants, which are slow rotators, but and Severo Ochoa SEV-2011-0187, and by the Canary Islands Government un- which always seem to display rotation rates a bit higher than der grant PID2010119. zero, on the order of v sin i ≈ 30 − 40kms−1 (Howarth et al. 1997; Markova et al. 2013a,b).If the rates of these B-supergiants References have also been overestimated, it would (at least for masses M ∼> 35M⊙, Markova et al. 2013a,b) bring observations in quantita- Aerts, C., Puls, J., Godart, M., & Dupret, M.-A. 2009, A&A, 508, 409 tive better agreement with current (single star) evolution mod- Bodenheimer, P. 1995, ARA&A, 33, 199 Borra, E. F. & Landstreet, J. D. 1980, ApJS, 42, 421 els that predict these objects at essentially zero rotation speeds Brott, I., de Mink, S. E., Cantiello, M., et al. 2011, A&A, 530, A115 (Brott et al. 2011)2. Bychkov, V. D., Bychkova, L. V., & Madej, J. 2005, A&A, 430, 1143 The overestimations of projected rotation speeds found for Cantiello, M., Langer, N., Brott, I., et al. 2009, A&A, 499, 279 Conti, P. S. & Ebbets, D. 1977, ApJ, 213, 438 the magnetic stars here are most likely a result of insufficient Dufton, P. L., Langer, N., Dunstall, P. R., et al. 2013, A&A, 550, A109 treatments and physics-knowledge of the competing broaden- Gray, D. F. 1973, ApJ, 184, 461 ing mechanisms microturbulence and macroturbulence. For ex- Gray, D. F. 2005, The Observation and Analysis of Stellar Photospheres ample, already Gray (1973) pointed out that classical atmo- (Cambridge University Press, 3rd ed.) spheric microturbulence can give Fourier-space minima in ad- Howarth, I. D., Siebert, K. W., Hussain, G. A. J., & Prinja, R. K. 1997, MNRAS, 284, 265 dition to those resulting from rotation; indeed, for relatively Howarth, I. D., Walborn, N. R., Lennon, D. J., et al. 2007, MNRAS, 381, 433 strong lines like those examined in this paper, tests using syn- Hunter, I., Lennon, D. J., Dufton, P. L., et al. 2008, A&A, 479, 541 thetic profiles show that microturbulent velocities of ∼ 20kms−1 Landstreet, J. D. & Borra, E. F. 1978, ApJ, 224, L5 produce Fourier-space minima at frequencies corresponding to Lefever, K., Puls, J., & Aerts, C. 2007, A&A, 463, 1093 ∼ −1 3 Maeder, A. & Meynet, G. 2000, ARA&A, 38, 143 30-40kms (Simón-D´ıaz & Herrero 2013) . Moreover, since Markova, N., Markov, H., Puls, J., Simón-D´ıaz, S., & Herrero, A. 2011, (at least for lines with saturated cores) the effect of large mi- Bulgarian Astronomical Journal, 17, 54 croturbulence on the line shape can be mimicked by a suit- Markova, N. & Puls, J. 2008, A&A, 478, 823 able combination of rotation and macroturbulence (Simón-D´ıaz Markova, N., Puls, J., Simon Diaz, S., Herrero, A., & Markov, H. 2013a, in & Herrero 2013), in these cases it is difficult to obtain accu- Massive Stars: From alpha to Omega Markova, N., et al. 2013b, Submitted to A&A rate v sin i rates in the slow-rotation regime also when using the Martins, F., Donati, J.-F., Marcolino, W. L. F., et al. 2010, MNRAS, 407, 1423 GOF method. Furthermore, the assumed shape of macroturbu- Martins, F., Escolano, C., Wade, G. A., et al. 2012, A&A, 538, A29 lence also affects the projected rotation speed inferred from a Massey, P., Neugent, K. F., Hillier, D. J., & Puls, J. 2013, ApJ, 768, 6 GOF solution (Simón-D´ıaz & Herrero 2013). Indeed, repeat- Najarro, F., Hanson, M. M., & Puls, J. 2011, A&A, 535, A32 Penny, L. R. 1996, ApJ, 463, 737 ing the GOF analysis in Sect. 3 but now assuming isotropic, Petit, V., Owocki, S. P., Wade, G. A., et al. 2013, MNRAS, 429, 398 instead of RT, macroturbulence results in degenerate solutions Ram´ırez-Agudelo, O. H., Simón-D´ıaz, S., Sana, H., et al. 2013, ArXiv e-prints in the range v sin i ≈ 0 − 60kms−1, as illustrated by the contour Ryans, R. S. I., Dufton, P. L., Rolleston, W. R. J., et al. 2002, MNRAS, 336, 577 maps in Fig. 4. This is consistent with Martins et al. (2012) and Shiode, J. H., Quataert, E., Cantiello, M., & Bildsten, L. 2013, MNRAS, 430, Sundqvist et al. (2013), who obtained reasonable line profile fits 1736 Simón-D´ıaz, S. & Herrero, A. 2007, A&A, 468, 1063 for HD191612 and HD108 when assuming zero projected rota- Simón-D´ıaz, S., Herrero, A., Uytterhoeven, K., et al. 2010, ApJ, 720, L174 tion speeds and this type of isotropic macroturbulence. In sum- Simón-D´ıaz, S. & Herrero, subm. to A&A mary,to make furtherprogressit seems clear that a more realistic Sundqvist, J. O., Petit, V., Owocki, S. P., et al. 2013, MNRAS treatment of photospheric microturbulence and macroturbulence Sundqvist, J. O., ud-Doula, A., Owocki, S. P., et al. 2012, MNRAS, L433 Vink, J. S., Brott, I., Gräfener, G., et al. 2010, A&A, 512, L7 in massive stars is urgently needed. Wade, G. A., Grunhut, J. H., & MiMeS Collaboration. 2012, in Astronomical Finally, this paper has focused on the extent to which reli- Society of the Pacific Conference Series, Vol. 464, Circumstellar Dynamics able v sin i values of slowly rotating massive stars can be derived at High Resolution, ed. A. C. Carciofi & T. Rivinius, 405 by current spectroscopic standard techniques, in the presence Wade, G. A., Howarth, I. D., Townsend, R. H. D., et al. 2011, MNRAS, 416, 3160 of a significant additional line-broadening component. However, Walborn, N. R. 1972, AJ, 77, 312 while for fast rotators the importance of such additional broad- Yoon, S., Langer, N., & Norman, C. 2006, A&A, 460, 199 ening decreases, there are other issues related to the derivation of

2 Resulting from strong wind-induced rotational braking when cross- ing to the cool side of the theoretical “bi-stability jump” of increased mass loss (Vink et al. 2010). 3 Microturbulent velocities of ∼ 20 km s−1 cannot be ruled out for O- type stars, particularly not for O-supergiants (e.g., Massey et al. 2013), but seem a bit high for the case of B-supergiants (e.g., Markova & Puls 2008).