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Physics of Magnetic Stars, 2007, pp. 89­97

Properties of a volume-limited sample of magnetic Ap/Bp stars
J. Power
1 2 3

1,2

, G. A. Wade1 , D. A. Hanes2 , M. Auriere3 , J. Silvester

1,2

Royal Military Collage of Canada Queen's University Observatoire Midi-Pyrenees

Abstract. This pap er describ es a study to deduce fundamental parameters and magnetic field characteristics for all magnetic Ap/Bp stars within a 100 parsec helio centric radius volume. This study has allowed for the first time the determination of an effectively unbiased magnetic field distribution of a sample of intermediate mass stars. From published catalogues and other literature sources, we have identified 57 bona fide magnetic A and B stars in the volume, corresp onding to 1.7% of all intermediate mass stars within 100 parsec of the Sun. The masses of Ap stars range from 1.5 to 6 M , with the p eak of the mass incidence distribution b etween 3.3 and 3.6 M . Observations of 30 of the Ap/Bp stars were obtained using the MuSiCoS sp ectrop olarimeter at the Telescop e Bernard Lyot at Pic du Midi Observatory. These observations will b e used to refine p erio ds, and determine magnetic field strength and geometry.

1

Intro duction

Ap/Bp stars are a class of intermediate mass stars which display magnetic fields and characteristic chemical p eculiarities. These stars show overabundances typically of iron p eak elements, rare earths, and silicon, ranging up to 2 dex ab ove solar. These magnetic chemically p eculiar stars make up a few p ercent of the main-sequence A and B stars. Ap/Bp have globally ordered, predominantly dip olar magnetic fields, with strengths of the order of one kilogauss. The presence of strong, ordered magnetic fields in some main-sequence A and B stars has b een known for nearly one-half of a century (Bab co ck 1947). However the cause of this magnetic field still remains a mystery. Intermediate mass stars are not exp ected to display magnetic fields, as they lack the deep convective envelop es which drive the dynamo effect resp onsible for magnetic fields seen in lower mass stars like the sun. There are two comp eting theories for the generation of the globally ordered magnetic field seen in Ap/Bp stars: the contemp oraneous dynamo effect, and the fossil field field theory. Contemp oraneous dynamo effect theorizes that there is a dynamo effect currently working in the (convective) core of the star. The fossil field theory hyp othesizes that the magnetic field is a remnant, pro duced by a dynamo effect op erating at an earlier evolutionary phase, or swept up from the interstellar medium during star formation. The aim of this study to provide an essentially unbiased assay of the prop erties of magnetic A and B stars in the solar neighb ourho o d. By deducing fundamental parameters and magnetic field characteristics for all magnetic intermediate mass stars within 100 p c helio centric radius volume, this study will allow for the first time the determination of effectively unbiased statistical study of 89


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a sample of Ap/Bp stars.

2
2.1

Sample stars and prop erties
Magnetic A and B Stars Selection

With the availability of accurate parallaxes for nearby stars through the Hipparcos catalogue (ESA 1997), a distance limited sample was determined. A catalogue of all stars within 100 parsecs of the sun was compiled from the Hipparcos database. This list was then filtered for stars with B-V colour index b etween 1.0 and -0.4, which corresp onds to main sequence stars ranging from approximately O to K sp ectral typ es (Gray 2005). The broad range in colour index was chosen to ensure that all intermediate mass stars in the volume were included, while limiting the size of the database which we are required to analyse. From this distance limited sample, Ap/Bp stars were selected through comparison with Renson's General Catalogue of of Ap and Am stars (Renson et al. 1991). Only magnetic chemically p eculiar stars were considered for this study, corresp onding to Renson p eculiarity typ es SrCrEu, Si, He weak Si, SrTi, and He strong (the typ es of chemically p eculiar stars known to display magnetic fields). This requires some care, as the p eculiarity typ e of some stars is incorrectly indicated (e.g. HD 117025 is quite clearly an Ap star, but app ears as Am in Renson's list). Using Renson's catalogue, crossreferencing with the distance limited sample, and verifying the Ap/Bp nature of each candidate in the literature, 52 bona fide Ap/Bp stars were found to b e within 100 p c of the Sun. Essentially all of these stars are bright and well-studied. To ensure that no magnetic A and B stars were overlo oked, a cross-check with the Bright Star Catalogue (Hoffleit et al. 1991) was p erformed. All A, B, and late F stars in the Bright Star Catalogue with a p eculiarity note were examined in the literature for photometric variability and/or magnetic field detection. Five stars not listed as Ap/Bp stars in Renson's catalogue were added to the sample. The final sample of magnetic Ap/Bp stars within 100 p c helio centric radius volume was found to consist of 57 stars. This sample is summarised in Table 1.

2.2

Physical parameters of sample stars

Stromgren and/or Johnson photometry were obtained for each of the magnetic and non-magnetic stars in the complete distance limited sample from the General Catalogue of Photometric Data (Mermillio d 1997). Temp eratures and luminosities were determined for the non-magnetic stars using various photometric calibrations. The Stromgren-based photometric calibration of Balona (1994) for sp ectral typ es O through F was used to determine temp eratures and b olometric corrections when uv by photometry was available. A suitable and reliable Geneva calibration which covered a large temp erature range was never found for the non-magnetic sample. However, the ma jority of stars which had Geneva photometry also had Stromgren photometry, for which Balona's (1994) calibration was used. The Johnson B-V calibration from Gray (2005) was also used for the non-magnetic for those stars of which Stromgren photometry was unavailable. For the Ap/Bp star sample, temp eratures were determined using a variety of techniques. For some stars, observed relative energy distributions (Adelman et al. 1989) were fit using a grid of mo del ATLAS9 flux profiles. For those stars for which observed energy distributions were unavailable, several Stromgren and Geneva photometric calibrations were used and averaged to determine the temp eratures (Balona 1994, Stepien 1994, Hauck and North 1993, Kupka and Bruntt 2001). The average uncertainty was found to b e just under 500 K, consistent with the "realistic" temp erature determination uncertainty for Ap stars suggested by Landstreet (this volume). Luminosites was


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determined using a temp erature-based BC calibration: BC
Ap

( ) = -4.891 + 15.147 - 11.517

2

(1)

where =5040.0/Te (Landstreet 2006). This b olometric correction b est describ es Ap stars b etween 7500K and 18000K. The uncertainty asso ciated with using this calibration is ab out 0.1 mag (Landstreet 2006). Finally, a literature review was conducted to compile a database of other physical parameters of the Ap/Bp sample, such as pro jected rotational velo city (Royer et al. 2002, Abt et al. 2002, Brown and Verschueren 1997, Abt and Morrell 1995, Bohlender et al 1993), magnetic field strength (Bychkov et al. 2005, 2003, Romanyuk 2000, Shorlin et al 2002), and rotational p erio d (Catalano and Renson 1998, Bychkov et al. 2005, ESA 1997).

2.3

HR Diagram

The magnetic and non magnetic star samples were plotted on a Herzsprung-Russell diagram (Figure 1).
HR Diagram
Intermediate mass stars: magnetic and non magnetic 3.5 5.0 M 3
o

Intermediate Mass Sample Ap/Bp sample 4.0 M
o

2.5 LogL/L
o

3.0 M

o

2 2.0 M
o

1.5

1

1.5 M

o

0.5

4.2

4.1

4 LogT/T

3.9
o

3.8

Figure 1: Points with error bars represent the distance limited sample of magnetic A & B stars. The gray points shows the position of the non-magnetic intermediate mass sample, with a lower cut off at 1.5 M . The lower cut off is chosen based on the lowest mass of the Ap/Bp stars in the sample. The solid lines show the theoretical evolutionary tracks and ZAMS (Schal ler et al. 1992) In Figure 1, the star p ositions on the HR diagram, with their uncertainties, are compared with the evolutionary tracks of Schaller et al. (1992) for Z=0.02. Theoretical evolutionary tracks were interp olated b etween those provided by Schaller et al. for completeness. The masses of the magnetic A and B sample were determined by manually comparing their p osition on the HR diagram with that of the tracks, while the masses of the larger sample were computed through an automated pro cess which assumed mean uncertainties for effective temp erature and luminosity. Masses were determined for 54 of the 57 stars in the magnetic A and B sample. HD 12709 and HD 133652 lie b elow the calculated mo dels on the HR diagram, so additional study of these stars


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is required. No available photometry was found for HD 107452, so no temp erature was determined, and hence no mass is available for this star. This star will also b e examined in further detail. The larger sample of non-magnetic stars was filtered to fo cus on the mass range of interest with a lower limit of 1.5 M , chosen based on the lowest-mass stars in the magnetic A & B star sample. We find that there exists a significant numb er of magnetic Ap/Bp stars (2 stars) in the sample in the mass range of 1.5-1.8 M , making 1.5 M in reasonable lower limit for the intermediate mass sample. The final distance limited intermediate-mass sample includes 3297 stars, with masses ranging b etween 1.5 M and 10 M .

3
3.1

Statistics
Perio d Distribution

Perio ds were found in the literature for 49 of the 57 magnetic Ap and Bp stars in the solar neighb ourho o d. The p erio d distribution of the Ap/Bp sample revealed a strong tendency to rotation p erio ds of order 1 day, with few exceptions (Figure 2). The mean p erio d was found to b e 4.5 days, neglecting the 2 stars with significantly longer p erio ds, with a standard deviation of 4.0 days. The distribution displays a clear p eak b etween 3.3 to 5.0 days with steep drop off at shorter p erio ds, and a more gradual drop off at longer p erio ds. Two stars had p erio ds longer than 100 days. The roAp star Equ is a well known extreme slow rotator, with a p erio d of 91.1 years (Bychkov et al. 2006). HD 134214, another well-known roAp stars, has a p erio d of 268 days (Kreidl et al. 1994)

10 9 8 7 6 # 5 4 3 2 1 1 10

Distribution of periods of magnetic A & B stars in the solar neighbourhood

100 Period [days]

1000

10000

Figure 2: The period distribution for the magnetic Ap & Bp stars in the solar neighbourhood. The period is given logarithmical ly across the horizontal axis, and the number in each bin is labeled across the vertical axis.

3.2

Mass Distribution

The mass distribution of Ap/Bp stars in the solar neighb ourho o d (Figure 3) shows a clear maximum b etween 2.1 and 2.4 M . The lower limit of the Ap/Bp distribution is at 1.5 M . The Ap/Bp mass


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distribution is clustered b etween 1.5 and 3.6 M with one exception at 6.0 M . By contrast, the numb er of non-magnetic intermediate mass stars with a particular decreases steeply with increasing mass. The mass incidence distribution of Ap/Bp stars was calculated by dividing the mass distribution of Ap/Bp stars by that of the non-magnetic stars (Figure 4). The mass incidence distribution shows a clear p eak at 3.3 to 3.6 M . Ab ove 3.6 M , the numb er of stars in the sample is sufficiently small that the shap e of the mass incidence distribution is completely uncertain. Of the 3297 stars with masses ab ove the lower limit of 1.5 M within 100 parsecs of the sun, 57 were found to b e Ap/Bp stars. Hence the bulk incidence of of magnetic Ap/Bp stars in the solar neighb ourho o d is 1.7%. This value is substantially smaller than the incidence rep orted by classical studies of magnitude-limited samples (Wolff 1968, Johnson 2004). We are currently attempting to estimate realistic uncertainties asso ciated with this value. If the Ap/Bp sample and non-magnetic stars sample are b oth uncertain by 10%, the uncertainty is 0.4%.

10

Mass Distribution of magnetic Ap/Bp stars in the solar neighbourhood

1000

Mass Distribution of non-magnetic A&B stars the solar neighbourhood

100 1 # # 10 0.1 1 0.01 1 4 5
o

2

3

Mass M

6

7

8

0.1 1

2

3

4

Mass M

5
o

6

7

8

Figure 3: Right: Mass distribution of magnetic A & B stars within 100 pc heliocentric radius. Left: Mass distribution of non-magnetic intermediate mass stars in the solar neighbourhood.

4

Observations and Analysis

Observations of the Ap/Bp sample were obtained using the MuSiCoS sp ectrop olarimeter at the Telescop e Bernard-Lyot at Pic du Midi Observatory. Reduction of the circular p olarization sp ectra was p erformed using the ESPRIT data reduction software package (Donati et al. 1997) Least squares deconvolution (LSD), a multi-line analysis technique, develop ed by Donati et al. (1997), was used to extract the mean Stokes I and Stokes V profiles from each sp ectrum. The mean longitudinal field for each of the observations was determined by taking the first moment of the Zeeman split Stokes V profile (Wade et al. 2000). The longitudinal magnetic field was plotted as a function of phase (Figure 5).

5

Future Work

Using the observations obtained with TBL-MuSiCoS, parameters such as pro jected rotational velo city, p erio d, and magnetic field strength and geometry will b e derived for all 30 observed Ap/Bp stars. Perio ds for each of the observed stars will b e confirmed and refined. The volume radius may b e extended to 200 parsecs to improve the statistics at higher masses. By extending the volume to 200 parsecs the volume sample would include the Sco-Cen asso ciation, and thus would include more higher mass Ap stars.


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Mass Incidence Distribution
Number of magntic A & B stars divided by the number of non- magntic A & B stars

1

0.1

0.01

0.001 1

2

3

4

Mass M

5
o

6

7

8

Figure 4: The mass incidence of Ap/Bp stars, determined from the mass distribution of the Ap/Bp sample and the intermediate mass sample. Above 3.6 M , a sufficiently large sample of stars is not available to provide significant statistics.
HD15144
625 Magnetic Field Strength [Gauss]

HD108662
Period= 2.99787 days
Magnetic Field Strength (Gauss) 600

Period =5.08054 days
Magnetic Field Strength [Gauss]

400

HD148112
Period = 3.02960days

300

600

400

200

575

200

550

100

0

525

0

-200 500 0 0.5 Phase 1 -0.2 0 0.2 0.4 0.6 0.8 1 1.2 -100 -0.2 0 0.2 0.4 0.6 0.8 1 1.2

Phase

Phase

Figure 5: Right: HD15144 is a spectroscopic binary. The period was determined photometrical ly by van Genderen (1971) to be 2.997814 days, which fits wel l with the observed variation of the longitudinal magnetic field determined from observations. Midd le: HD108662 shows strong magnetic variability of the longitudinal magnetic field. The rotational period determined by Rice and Wehlau (1994) fit wel l with a second order sinusoid to the observations. Left: HD148112 star exhibits weak magnetic variability and a nearly constant longitudinal field. The period of 3.04296 days was determined spectroscopical ly by Hatzes (1991)

6

Conclusion

Fundamental parameters have b een determined for a complete sample of intermediate mass stars within 100 parsecs helio centric radius. The Ap/Bp stars have b een carefully identified for this sample and an examination of the statistical prop erties of these stars has b een p erformed. Magnetic intermediate mass stars are found to make up 1.7% of all intermediate mass stars in the solar neighb ourho o d. These stars typically show magnetic and/or photometric variability on the order of several days, but in some cases variability p erio ds are much longer. For this particular sample,


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the masses of the magnetic A & B stars ranged from 1.5 to 6 M , p eaking b etween 3.3 and 3.6 M . New sp ectrop olarimetric observations have b een obtained for essentially all sample AP/Bp stars observable from the northern hemisphere. These data will b e used to refine v sin i estimates, rotational p erio ds, and to determine magnetic fields strengths and geometries. We are planning to extend the sample to 200 parsec helio centric radius in order to refine the statistics at higher masses. Table 1: The distance limited sample of Ap/Bp stars. The spectral types given are those listed by Renson et al. (1991) if available, otherwise they were obtained from the Hipparcos catalogue (ESA 1997). The calculated temperature for each star is given. 1.) calculated from fitting model flux profiles to energy distributions of Adelman et al. 1989. Averaged photometric calibrations were used otherwise: 2.) Kupka & Bruntt (2001), 3.) Hauck & North (1993), 4.) Balona (1994), 5.) Stepien (1993). Derived masses are indicated. Periods, when available, are listed for each of the sample stars. Periods derived from literature: 6.) Bychkov et al. (2005), 7.) Catalano & Renson (1998), 8.) ESA (1997). HD 1185 3980 4778 11503 15089 15144 24712 27309 29305 40312 54118 56022 62140 65339 72968 83368 89822 90763 96616 107452 108662 108945 109026 112185 112413 115735 117025 118022 119213 120198 120709 124224 125248 Sp ectral Typ e A1SI A7 SR EU CR A1 CR SR EU (A1p Si) A4 SR A5 SR CR EU A9 SR EU CR A0 SI Cr A0 SI A0 SI A0 SI A1 SI CR SR A8 SR EU A2p... A2 SR CR A8 SR CR EU A0 HG SI SR A1sp... A3 SR A7 SR A0 SRCR EU A3 SR B5 HE FBL. A1 CR EU MN A0 EU SI CR B9 HE FBL.SI A2m A2 CR EU SR A3 SR CR A0 EU CR B5 HE FBL.P B9 SI A1 EU CR Temp erature (K) 9012 2,3,4 8291 2,3 9217 2,3 9429 3,4,5 8250 1 8372 2,3,4 1.195 7257 2,3,4 12000 1 12052 2,3,4,5 10339 1 10767 2,3,4,5 9819 2,3,4 8100 1 8717 2,3,5 9500 1 7724 2,3 10000 1 9038 2,3,4 9472 2,3,4 10000 1 8875 1 16008 2,4,5 9375 1 11750 1 10474 2,3,4,5 84322,3 9250 1 9000 1 9800 1 16656 2,4,5 12500 1 9542 3,4 log(L/L ) 1.406 1.254 1.414 1.680 1.391 1.93 0.885 1.975 2.303 2.411 1.872 1.525 1.123 1.475 1.498 1.1474 1.954 1.268 1.788 3.772 1.730 1.703 3.295 2.048 2.0233 1.835 1.360 1.474 1.312 1.567 2.668 2.006 1.524 Mass (M ) 2.15 1.95 2.18 2.44 2.07 15.88 6 1.61 3.04 3.47 3.50 2.78 2.34 1.85 2.18 2.28 1.83 2.79 2.04 2.55 2.53 3.42 6.0 2.87 3.05 2.70 2.05 2.23 3.06 2.37 3.17 2.31 Perio d (days) 3.9516 2.5616 1.6093 1.74 7
6 6 6

12.4617 6 1.10496 6 2.9432 7 3.61866 6 3.27533 6 0.92 8 4.28488 6 8.0267 6 4.66548 6 2.851962 6 7.5586 6 3.57 7 2.44 7 5.0805 1.92442 5.0887 5.46939 0.77 7
6 6

6 6

3.722084 6 2.44997 6 1.3879 7 0.520675 9.2954 6
6


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Table 1: (Contd.) HD 128898 130559 133652 134214 137909 137949 140160 140728 148112 148898 151199 152107 170000 170397 176232 201601 202627 203006 206742 220825 221760 223640 Sp ectral Typ e A9 SR EU A1 SR CR EU Ap Si F2 SR EU CR A9 SR EU CR F0 SR EU CR A1 SR CR EU A0 SI Cr A0 CR EU A6 SR CR EU A3 SR A3 SR CR EU A0 SI A0 SI CR EU A6 SR CR EU A9 SR EU A1 SI CR SR A2 CR EU SR A0 SI A1 CR SR EU A2 SR CR EU B9 SI SR CR Temp erature (K) 7822 2,3 9607 2,3,4 12837 2,3,4,5 7335 3,4 7753 1 7545 1 9250 1 10083 3,4,5 96242,3,4 8327 2,3,4 8616 2,3,4 8723 2,3,4 10543 3 9921 2,3,4,5 8000 1 8000 1 8846 2,3,4 10101 2,3,4,5 10214 2,3,4,5 9860 2,3,4 8581 2,3,4 13000 1 log(L/L ) 1.047 1.568 1.797 0.832 1.524 1.125 1.509 1.501 1.868 1.589 1.366 1.469 2.260 1.458 1.270 1.112 2.17 1.599 1.890 1.405 1.882 2.136 Mass (M ) 2.77 2.35 1.58 2.18 1.80 2.26 2.35 2.62 2.27 2.07 2.18 3.27 2.30 1.94 1.83 1.45 2.43 2.73 2.25 2.62 3.42 Perio d (days) 4.4794 6 2.304 6 248 7 18.4868 11.13313 1.59584 1.296 7 3.04296 1.8 7 6.14 7 3.86778 1.71649 2.25454 6.5 7 27027 6 2.122
7

6 6 6

6

6 6 6

1.14077 12.5 7 3.735239

6

6

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