a r X i v :a s t r o -p h /0604283v 1 12 A p r 2006
Mon.Not.R.Astron.Soc.000,1–6(2006)Printed 5February 2008
(MN L A T E X style ?le v2.2)
Discovery of magnetic ?elds in the βCephei star ξ1CMa
and in several Slowly Pulsating B stars ?
S.Hubrig 1?,M.Briquet 2?,M.Sch¨o ller 1,P.De Cat 3,G.Mathys 1,and C.Aerts 2
1European
Southern Observatory,Casilla 19001,Santiago,Chile
2Instituut
voor Sterrenkunde,Katholieke Universiteit Leuven,Celestijnenlaan 200B,B-3001Leuven,Belgium
3Koninklijke Sterrenwacht van Belgi¨e ,Ringlaan 3,B-1180Brussel,Belgium
Accepted 2006Enero 99.Received 2006Enero 98
ABSTRACT
We present the results of a magnetic survey of a sample of eight βCephei stars and 26
Slowly Pulsating B stars with FORS 1at the VLT.A weak mean longitudinal magnetic ?eld of the order of a few hundred Gauss is detected in the βCephei star ξ1CMa and in 13SPB stars.The star ξ1CMa becomes the third magnetic star among the βCephei stars.Before our study,the star ζCas was the only known magnetic SPB star.All magnetic SPB stars for which we gathered several magnetic ?eld measurements show a ?eld that varies in time.We do not ?nd a relation between the evolution of the magnetic ?eld with stellar age in our small sample.Our observations imply that βCephei stars and SPBs can no longer be considered as classes of non-magnetic pulsators,but the e?ect of the ?elds on the oscillation properties remains to be studied.Key words:Hertzsprung-Russell (HR)diagram -stars:magnetic ?elds -stars:os-cillations -stars:fundamental parameters -stars:individual:ξ1CMa
1INTRODUCTION
A long-term monitoring project aimed at asteroseismology of a large sample of slowly pulsating
B (SPB)stars and βCephei stars was started by researchers of the Institute of Astronomy of the University of Leuven several years ago.This initiative started after a number of new pulsating B stars had been discovered from the Hipparcos mission (e.g.,De Cat &Aerts 2002;Briquet et al.2003).βCephei stars are short period (3–8h)pulsating variables of spectral type O9to B3(8–20M ⊙)along the main sequence with low-order pressure (p)and/or gravity (g)modes.SPB stars are situ-ated in the H-R diagram just below the βCephei stars.They are less massive (3–9M ⊙)B-type stars which show variabil-ity with periods of the order of one day due to multiperiodic high-order low-degree g mode oscillations.Thanks to the Hipparcos mission the number of SPB stars increased from 12to more than 80(Waelkens et al.1998).
The study of the pulsation properties of SPB and βCephei stars requires observations with a long time-base.Indeed,modes with closely spaced periods occur.As was
?
Based on observations obtained at the European Southern Observatory,Paranal,Chile (ESO programmes 072.D-0377(A),073.D-0464(A),073.D-0466(A),and 075.D-0295(A)).?E-mail:shubrig@https://www.doczj.com/doc/3a8240674.html,
?Postdoctoral Fellow of the Fund for Scienti?c Research of Flan-ders (FWO)
pointed out by De Cat &Aerts (2002),it is di?cult to in-terpret and explore these multiplets in view of the unknown internal rotation law ?(r )and given the dense theoreti-cally predicted frequency spectra (e.g.,Aerts et al.2006).Recently,Hasan et al.(2005)suggested that high-order g modes are a probe of the internal magnetic ?eld.Their calcu-lations show that frequency splittings of the order of 1%may be due to a poloidal ?eld with a strength of order 100kG,buried in the deep interior of the star.
Neiner et al.(2003a)made the ?rst discovery of a mag-netic ?eld in an SPB star.It concerned ζCas whose domi-nant pulsation mode has a period P=1.56d.The two other detections of a magnetic ?eld in pulsating B stars have been done for βCephei stars:βCep (Henrichs et al.2000)and V2052Oph (Neiner et al.2003b).The measured mean lon-gitudinal magnetic ?elds in all three stars are weak,less than 100G.These discoveries motivated us to perform a system-atic search for magnetic ?elds in SPB and βCephei stars,which started in 2003with FORS 1at the VLT.Our recent measurements in the hydrogen lines of various types of stars of intermediate mass demonstrated that magnetic ?elds can be measured with an error bar as small as 20G (Hubrig et al.2006a,b),enabling us to diagnose even very weak mean lon-gitudinal ?elds.While the last spectropolarimetric data for our program have been released and reduced only in the last months,preliminary results of the survey were already presented in Hubrig et al.(2005,2006b).In this paper we
2S.Hubrig et al.
Table 1.Fundamental parameters for the objects in our sample.In the ?rst two columns we give the HD number and another identi?er.In the following six columns we list spectral type,e?ective temperature,surface gravity,mass,radius,and luminosity.The ?nal two columns give the fraction of the main sequence lifetime and v sin i .Uncertain parameter values are given in italics .
βCephei stars
Slowly Pulsating B stars
4000
420044004600
4800
Wavelength [A]
0.5
0.60.70.80.91.0
N o r m a l i z e d F l u x
?4840
4850
48604870
4880
Wavelength [A]
-0.002
-0.0010.0000.0010.0020.003
0.004
S t o k e s V /I
?
-4.67 10-13 λ2 (1/I ) (d I /d λ) [10-6]
V /I [%]
Figure 1.Stokes I spectrum (left),Stokes V spectrum (centre)and regression detection (right)for ξ1CMa.The thickness of the plotted line in the Stokes V spectrum corresponds to the uncertainty of the measurement of polarization determined from photon noise.
Discovery of magnetic?elds in SPBs3
Table2.The mean longitudinal?eld measurements for our sample ofβCephei and SPB stars observed with FORS1(ESO service programs072.D-0377,073.D-0464,073.D-0466,and075.D-0295).The?rst two columns list the HD number and the modi?ed Julian date of mid-exposure.The measured mean longitudinal magnetic?eld B l is presented in column3.If there are several measurements for a single star,we give the rms longitudinal magnetic?eld and the reducedχ2for all measurements in columns4and5.
HD MJD B l B l χ2/n
[G][G][G][G]
337953244.402272±5718213.512992953454.199-52±3867 3.5
53245.214231±4753572.053-80±35
53629.3055±2213105853454.220-106±46
53630.195-67±2513876452904.016146±57
2458752971.071-120±6872 1.514087353151.192286±6023113.4
53574.415-16±3653454.247-158±78
53630.250-32±2914330953151.192-196±90113 1.7 2632652909.389-119±8072 1.353225.05685±95
53218.357-24±9953234.019-75±73
53630.370-27±2253454.280-8±35
2811453638.390-58±2115705653532.324-39±21
2924853629.322-41±2833 1.616012453151.259456±6023215.5
53630.347-22±2153520.230-77±45
3479852999.05556±82125 3.653600.10919±36
53218.406-205±9853604.108-25±24
53638.366-41±1716057853532.342-45±4173 3.3 4474353475.02924±7035 1.253604.12793±40
53629.343-44±2916178353151.281376±6321014.6 4528453252.365245±6353487.333-88±31
4600553259.3992±7953520.308-113±32
4632853475.046280±4430647.153598.108-122±78
53506.971330±4516347253151.298121±54
5392152999.137-294±6318525.316982053151.312239±70147 5.3
53475.100-71±8753520.333-86±45
53630.401151±2953597.112-26±34
53631.408151±2117786353193.211-21±5444 2.7 7419553002.127-277±108200 5.053597.128-59±26
53138.972-310±9818155853193.251-114±502018.4
53143.972-145±7053227.184236±75
53454.107-65±3953274.144-247±98
53455.080-44±3753275.143-336±63
7456053002.141-199±61146 5.653519.3760±34
53143.986-53±6653520.397-26±31
8595353002.152-131±42103 6.118225553193.234-13±57
53152.970-151±4920654053514.416-51±31
53454.137-52±2320805753192.307104±6613313.9
53455.10910±2153597.166-156±31
9228753008.352-10±5737 2.821557352900.080165±53174 6.9
53454.152-52±2253191.222180±54
11112353455.155-14±38180.253192.290123±66
53475.15422±5153193.321-320±90
12351552824.093-59±50430.953506.41460±45
53454.17917±2753522.420-36±21
present the whole sample and discuss the results of more than80magnetic?eld measurements.
2THE SAMPLE OF PULSATING STARS AND OBSER V ATIONS
Our sample includes eightβCephei stars and26SPB stars selected from De Cat(2002)such as to?t the observational window and having V 8.Their fundamental parameters are listed in Table1.Observations in the geneva photomet-ric system are available for all targets.The mean geneva magnitudes were used to obtain the e?ective temperature log(T e?)and the surface gravity log(g)with the method de-scribed in De Cat(2002)(Columns4and5in Table1). The log(T e?)and log(g)values of HD44743,HD46005,and HD46328are inaccurate because an extrapolation outside the calibration grid was needed.Other stellar parameters were derived from a grid of main-sequence models calcu-lated with the Code Li′e geois d’′Evolution Stellaire(ver-sion18.2,written by R.Scu?aire)described as“grid2”in De Cat et al.(2006).The mass M,the radius R,the lumi-nosity log(L/L⊙),and the age of the star expressed as a fraction of its total main-sequence life f are presented in Columns6to9in Table1.For the most massive stars of our sample,HD44743,HD46328,and HD111123,the up-
4S.Hubrig et al.
per value of15M⊙of the grid models is insu?cient to fully cover the observed errorbox in log(T e?)and log(g).The stars HD45284and HD46005fall outside the main sequence.The uncertain parameters are given in italics in Table1.In addi-tion,we point out that the physical parameters of multiple systems(indicated as SB1and SB2in Column3in Table1), also have to be treated with caution.
For most targets numerous high-resolution spec-troscopic time series were obtained in previous years (Aerts&De Cat2003;De Cat&Aerts2002;Aerts et al. 2004a,b).To estimate the projected rotational velocity v sin i (Column10in Table1),an average of all spectra has been used.For slowly rotatingβCephei and SPB stars,we selected several unblended absorption lines:theλ4560?A Si III-triplet and/or theλ4130?A Si II-doublet.For rapidly rotating stars,only theλ4481?A Mg I-line has been used.We applied the method of least squares?tting with rotationally broadened synthetic pro?les using a Gaussian intrinsic width but without taking into account pulsational broadening.
The spectropolarimetric observations were carried out from2003to2005at the European Southern Observatory with FORS1(FOcal Reducer low dispersion Spectrograph) mounted on the8-m Melipal telescope of the VLT.This multi-mode instrument is equipped with polarization an-alyzing optics comprising super-achromatic half-wave and quarter-wave phase retarder plates,and a Wollaston prism with a beam divergence of22′′in standard resolution mode. In2003and2004,we used the GRISM600B in the wave-length range3480–5890?A to cover all hydrogen Balmer lines from Hβto the Balmer jump.The highest spectral reso-lution of the FORS1spectra achieved with this setting is R～2000.As of April2005,we used the GRISM1200g to cover the H Balmer lines from Hβto H8,and the narrow-est available slit width of0.′′4to obtain a spectral resolving power of R～https://www.doczj.com/doc/3a8240674.html,ually,we took four to eight continu-ous series of two exposures for each sample star using a stan-dard readout mode with high gain(A,1×1,high)and with the retarder waveplate oriented at two di?erent angles,+45?and?45?.For the observations carried out in2005,we used a non-standard readout mode with low gain(A,1×1,low), which provided a broader dynamic range and increased the signal-to-noise(S/N)ratio of individual spectra by a factor of≈2.All sample stars are bright and,since the errors of the measurements of the polarization with FORS1are de-termined by photon counting statistics,a S/N ratio of a few thousand was reached within～30min.More details on the observing technique with FORS1can be found elsewhere (e.g.,Bagnulo et al.2002;Hubrig et al.2004).Determina-tion of the longitudinal magnetic?eld using the FORS1 spectra is achieved by measuring the circular polarization of opposite sign induced in the wings of hydrogen Balmer lines by the Zeeman e?ect.The mean longitudinal magnetic?eld is the average over the stellar hemisphere visible at the time of observation of the component of the?eld parallel to the line of sight,weighted by the local emergent spectral line in-tensity.It is diagnosed from the slope of a linear regression of V/I versus the quantity?g e??λzλ21
dλ
B l +V0/I0,where V is the Stokes parameter which measures the circular polar-ization,I is the intensity observed in unpolarized light,g e?is the e?ective Land′e factor,λis the wavelength,d I/dλis the derivative of Stokes I,and B l is the mean longitudinal ?eld.Our experience from a study of a large sample of mag-netic and non-magnetic Ap and Bp stars revealed that this regression technique is very robust and that detections with B l>3σresult only for stars possessing magnetic?elds.
3ANALYSIS AND RESULTS
The mean longitudinal magnetic?eld B l of the targets is listed in Table2.The rms longitudinal?eld is computed from all n measurements according to:
n
n
i=1 B l 2i 1/2.(1)
Further we give the reducedχ2for these measurements in Column5,which is a statistical discriminant useful to as-sess the presence of a magnetic?eld(Bohlender et al.1993), de?ned as:
χ2/n=
1
σi 2.(2) A longitudinal magnetic?eld at a level larger than3σhas been diagnosed for13SPB stars:HD3379,HD45284, HD53921,HD74195,HD74560,HD85953,HD140873, HD160124,HD161783,HD169820,HD181558,HD208057, and HD215573.The star HD208057has a rather high v sin i value and was classi?ed as a Be star by Merrill&Burwell (1943)due to the detection of double emission in Hα.Al-though the emissison was not con?rmed in later observa-tions,it cannot be ruled out that this star is a Be star. Given the still uncertain status of the magnetic?eld discov-ered by Neiner et al.(2003c)inωOri,HD208057is possibly the?rst Be star with a magnetic?eld detected at3σlevel.
Most stars with multiple measurements haveχ2/n 5.0.The individual measurements show the variability of their magnetic?eld.The time scales of these variations are uncertain due to too few measurements being obtained for each star.Unfortunately,also the rotational variability of the magnetic?eld cannot be proven as the rotational peri-ods are not known for any of these targets.For the SPB star HD181558with the largest number of magnetic?eld mea-surements(six in all)we searched for a correlation between the changes of the magnetic?eld with the pulsation period, but no clear correlation could be detected.
The magnetic?eld ofξ1CMa is detected at more than 6σlevel.Both measurements carried out on two nights sepa-rated by about one month are of the order of300G.In Fig.1 we present Stokes I and V spectra and the regression detec-tion.Spectroscopic and photometric observations revealed thatξ1CMa pulsates monoperiodically and non-linearly in a radial mode with a period of0.209574days,with a veloc-ity amplitude of33km s?1(Saesen et al.2006).Morel et al. (2006)performed an abundance analysis of nine selected βCephei stars and discoveredξ1CMa to be nitrogen en-riched,as well as the threeβCephei starsδCet,V2052Oph, andβCep.It is remarkable that two of them,V2052Oph andβCep,also have a detected longitudinal magnetic?eld of the order of～100G(Neiner et al.2003b;Henrichs et al. 2000).ξ1CMa shows the largest mean longitudinal?eld by a factor of three among these threeβCephei stars.Unfor-tunately,no search for a magnetic?eld has been attempted
Discovery of magnetic ?elds in SPBs
5
Figure 2.The position of the targets in the H-R diagram.The full lines represent boundaries of theoretical instability strips for modes with frequency between 0.2and 30d ?1and ? 3,com-puted for main sequence models with 2M ⊙ M 15M ⊙of “grid 2”in De Cat et al.(2006).The lower and upper dotted lines show the ZAMS and TAMS,respectively.The dashed lines denote evolution tracks for stars with M =15,12,9,6,and 3M ⊙.Filled circles correspond to the stars with detected magnetic ?elds.
yet for δCet.These four stars have another common prop-erty:they are either radial pulsators (ξ1CMa)or their mul-tiperiodic pulsations are dominated by a radial mode (δCet,βCep,and V2052Oph).The presence of a magnetic ?eld in these stars might play an important role to explain these physical characteristics.
The position of the studied SPB and βCephei stars in the H-R diagram is shown in Fig.2.No clear picture emerges concerning the evolutionary stage of stars with de-tected magnetic ?elds.We have to note,however,that the uncertainties of the age of hot stars (Table 1,Column 9)are very large.Furthermore,the whole sample under study con-tains only 14stars with detected magnetic ?elds,so there is a need for more magnetic ?eld measurements to have a good statistics.No hints of relations between the magnetic ?eld strength and other stellar parameters were found.Despite our discovery,the knowledge of the magnetic ?elds in pul-sating B stars remains very incomplete.Magnetic ?elds are known to play an important role in the theoretical interpre-tation of the pulsations in cool rapidly oscillating Ap stars.It is di?cult to explain why non-pulsating chemically pecu-liar hot Bp stars and pulsating stars co-exist in the SPB and βCephei instability strips.It is especially intriguing that the magnetic ?elds of hot Bp stars either do not show any de-tectable variations or vary with periods close to one day,which is of the order of the pulsation period range of SPB stars (Bohlender et al.1987;Matthews &Bohlender 1991).The presented magnetic ?eld measurements in 13SPB stars and in the βCephei star ξ1CMa demonstrate that longitu-dinal magnetic ?elds in these stars are rather weak in com-parison to the kG ?elds detected in magnetic Bp stars.
Although the magnetic ?eld determination method based on circular polarized FORS 1spectra of hydrogen Balmer lines shows the excellent potential of FORS 1for the detection of weak ?elds,it would be particularly impor-tant to measure the ?elds with higher resolution spectropo-larimeters,not only using hydrogen lines but also lines of other chemical elements to be able to study the ?eld con?g-uration at high con?dence level.
The role of the detected magnetic ?elds in the mod-elling of the oscillations of B-type stars remains to be stud-ied.The magneto-acoustic coupling in pulsating B stars will
be far less important than for the roAp stars.The e?ect on the p modes of the βCephei stars is expected to be small (Hasan &Christensen–Dalsgaard 1992)but the g modes of the SPB stars may be slightly a?ected,provided that the in-ternal ?eld strength is a factor 1000larger than the detected value (Hasan et al.2005).In any case,magnetic breaking and angular momentum transport along the ?eld lines now o?er a natural explanation of the slow rotation of our target stars.
REFERENCES
Aerts,C.,De Cat,P.,2003,SSRv,105,453
Aerts,C.,De Cat,P.,Handler,G.,et al.,2004a,MNRAS,347,463
Aerts,C.,De Cat,P.,Kuschnig,R.,et al.,2006,ApJL,in press
Aerts,C.,Waelkens,C.,Daszy′n ska-Daszkiewicz,J.,et al.,2004b,A&A,415,241
Bagnulo,S.,Szeifert,T.,Wade,G.A.,et al.,2002,A&A,389,191
Bohlender,D.A.,Landstreet,J.D.,Brown,D.N.,Thomp-son,I.B.,1987,ApJ,323,325
Bohlender, D.A.,Landstreet,J.D.,&Thompson,I.B.,1993,A&A,269,355
Briquet,M.,Aerts,C.,Mathias,P.,et al.,2003,A&A,401,281
De Cat,P.,2002in ASP Conf.Ser.Vol.259,Radial and Nonradial Pulsations as Probes of Stellar Physics,eds.C.Aerts,T.R.Bedding &J.Christensen-Dalsgaard,196De Cat,P.,Aerts,C.,2002,A&A,393,965
De Cat,P.,Briquet,M.,Aerts,C.,et al.,2006,CoAst,147,48
Hasan,S.S.,&Christensen-Dalsgaard,J.,1992,ApJ,396,311
Hasan,S.S.,Zahn,J.-P.,Christensen-Dalsgaard,J.,2005,A&A,444,L29
Henrichs,H.F.,de Jong,J.A.,Donati,J.-F.,et al.,2000,in ASP Conf.Ser.Vol.214,The Be Phenomenon in Early-Type Stars,eds.M.A.Smith &H.F.Henrichs,324Hubrig,S.,North,P.,Sch¨o ller,M.,Mathys,G.,2006a,AN,327,289
Hubrig,S.,Szeifert,T.,North,P.,et al.,2005,in ASP Conf.Ser.Vol.337,The Nature and Evolution of Disks Around Hot Stars,eds.R.Ignace &K.G.Gayley,236Hubrig,S.,Szeifert,T.,Sch¨o ller,M.,et al.,2004,A&A,415,661
Hubrig,S.,Yudin,R.V.,Sch¨o ller,M.,Pogodin,M.A.,2006b,A&A,446,1089
Matthews,J.M.,Bohlender,D.A.,1991,A&A,243,148Merrill,P.W.,Burwell,C.G.,1943,ApJ,98,153
Morel,T.,Butler,K.,Aerts,C.,et al.,2006,A&A,sub-mitted
Neiner,C.,Geers,V.C.,Henrichs,H.F.,et al.,2003a,A&A,406,1019
Neiner,C.,Henrichs,H.F.,Floquet,M.,et al.,2003b,A&A,411,565
Neiner,C.,Hubert,A.-M.,Fr′e mat,Y.,et al.,2003c,A&A,409,275
Saesen,S.,Briquet,M.,Aerts,C.,2006,CoAst,147,109
6S.Hubrig et al.
Waelkens,C.,Aerts,C.,Kestens,E.,et al.,1998,A&A, 330,215