Mon. Not. R. Astron. Soc. 372, 286–292 (2006) doi:10.1111/j.1365-2966.2006.10857.x
The discovery of 8.0-min radial velocity variations in the strongly ⋆ magnetic cool Ap star HD 154708, a new roAp star
D. W. Kurtz,1† V. G. Elkin,1 M. S. Cunha,2 G. Mathys,3 S. Hubrig,3 B. Wolff4 and I. Savanov5 1Centre for Astrophysics, University of Central Lancashire, Preston PR1 2HE 2Centro de Astrofisica da Universidade do Porto, Rua das Estrelas, 4150 Porto, Portugal 3European Southern Observatory, Casilla 19001, Santiago 19, Chile 4European Southern Observatory, Karl-Schwarzschild-Str. 2, 85748 Garching, Germany 5Astrophysical Institute Potsdam, an der Sternwarte 16, 14482 Potsdam, Germany
Accepted 2006 July 24. Received 2006 July 23; in original form 2006 May 9
ABSTRACT HD 154708 has an extraordinarily strong magnetic field of 24.5 kG. Using 2.5 h of high time resolution Ultraviolet and Visual Echelle Spectrograph (UVES) spectra we have discovered this star to be an roAp star with a pulsation period of 8 min. The radial velocity amplitudes in the rare earth element lines of Nd II,NdIII and Pr III are unusually low – ∼60 m s−1 – for an roAp star. Some evidence suggests that roAp stars with stronger magnetic fields have lower pulsation amplitudes. Given the central role that the magnetic field plays in the oblique pulsator model of the roAp stars, an extensive study of the relation of magnetic field strength to pulsation amplitude is desirable. Key words: stars: individual: HD 154708 – stars: magnetic fields – stars: oscillations – stars: variables: other.
those of the roAp stars; in particular, it shows enhanced lines of Pr 1 INTRODUCTION and Nd and apparent abundance differences between Pr II and Pr III The magnetic A stars are important for the study of the interaction of and between Nd II and Nd III. This is a typical signature of the roAp stellar magnetic fields with rotation, pulsation and atomic diffusion, stars (Ryabchikova et al. 2004), although it does not occur for the all of which have implications for many fields of stellar astrophysics. recently discovered, longer period (P = 21 min), more luminous As with many physical systems, extreme cases may provide tests of roAp star HD 116114 (Elkin et al. 2005a). HD 154708, therefore, our understanding of these systems. Recently Hubrig et al. (2005) appears to be a good candidate to be an roAp star, and a most discovered one of the strongest magnetic fields known for an upper interesting one at that, given its strong magnetic field. main sequence chemically peculiar star, Hs=24.5 ± 1.0 kG, in It is clear that there is a close relationship between the mag- the cool Ap star HD 154708 (Teff ≈ 6800 K). The only star known at netic field and pulsation in roAp stars. The oblique pulsator model that time to have a stronger field than this is the much hotter (Teff ≈ (Kurtz 1982) assumed that the pulsation axis is aligned with the mag- 14 500 K; Leckrone 1974) Bp Si star HD 215441 (Babcock’s star) netic axis and was able to explain most pulsation properties of roAp with a mean field modulus of B=34 kG (Babcock 1960). Since stars. Three important consequences result from the direct effect of then Kochukhov (2006a) discovered a strongly non-dipolar field in the magnetic field on pulsations in roAp stars (see e.g. Bigot & the late Bp star HD 137509, from which he inferred a mean surface Dziembowski 2002; Saio & Gautschy 2004; Saio 2005; Cunha field of Hs=29 kG. Another very strong field has been also found 2006). First, the eigenfrequencies are shifted away from their non- in the cool Ap star HD 178898 by Elkin, Kudryavtsev & Romanyuk magnetic values. Secondly, the eigenfunctions near the surface are (2002) for which Ryabchikova et al. (2006) determined a mean modified in such a way that they no longer can be described well surface field of Hs=17.5 kG. by a single spherical harmonic of a given degree, l. Thirdly, slow Hubrig et al. (2005) found that HD 154708 has a luminosity and Alfven´ waves are constantly generated, and later dissipated, taking temperature that place it at the cool end of the range of known roAp away part of the pulsation energy. Some of these features depend stars. They also found that its elemental abundances are similar to mostly on the magnetic field configuration and on the degree of the modes, while others depend essentially on the magnetic field magnitude and on the structure of the surface layers of the star. The ⋆Based on observations collected at the European Southern Observatory, magnetic field is also expected to have important indirect effects on Paranal, Chile, as part of programme 075.D-0145. pulsations, through the influence it has on convection. In fact, the †E-mail: [email protected] magnetic suppression of convection in the outer layers of roAp stars
C 2006 The Authors. Journal compilation C 2006 RAS The discovery of 8.0-min variations in HD 154708 287 seems to be necessary in order to account for the excitation of the version of table 2 in Kurtz & Martinez (2000), lists them with some high overtone pulsations observed (Balmforth et al. 2001; Cunha useful data, and with references to a recent photometric study and 2002; Saio 2005). Thus, the intensity and configuration of the mag- a recent spectroscopic study, as well as a discovery paper, or early netic field are likely to be determinant also for the excitation of the study. oscillations. Cunha & Gough (2000) (see also Cunha 2001; Saio & Gautschy 2004) showed that the dissipation of pulsation energy through slow 2 OBSERVATIONS AND DATA REDUCTION Alfven´ waves is maximal for particular combinations of pulsation Our spectroscopic observations were obtained at the Very Large frequency and magnetic field intensity, and suggested that such dissi- Telescope (VLT) using the Ultraviolet and Visual Echelle Spectro- pation could be important for mode selection in roAp stars. Recently, graph (UVES). We observed HD 154708 for 2.5 h on 2005 May Saio (2005) performed non-adiabatic calculations taking into ac- 19–20 (JD 245 3510) using 40-s exposures with 25-s readout and count the direct effect of the magnetic field on pulsations and found overhead times, giving a time resolution of 65 s and a total number that for some magnetic field intensities the energy losses through of spectra of 140. The CCD images were independently processed the dissipation of slow Alfen´ waves are indeed sufficient to stabilize by VGE and BW using UVES pipeline recipes and the ESO MIDAS high overtone p modes, even when convection in the outer layers package to extract one-dimensional (1D) spectra. Both reductions of roAp stars is assumed to be suppressed by the magnetic field. gave similar results. The extracted spectra were normalized to the Additionally, he found that the dissipation through Alfven´ waves continuum and each spectrum was corrected in velocity to the Solar leads to the stabilization of the low overtone p modes. Along with System Barycentre. The spectra range from 4970 to 7010 Å with a the helium settling due to diffusion in the absence of convection small gap about 60 Å wide near 6000 Å. The signal-to-noise ratio in (Theado,´ Vauclair & Cunha 2005), this stabilizing effect gives a the individual spectra ranges from 35 to 180, where we define that good explanation of why δ Scuti pulsations have not been found in signal-to-noise ratio as the ratio of the measured noise level in a (rel- these stars. Finally, Saio found excitation of dipole and quadrupole atively) line-free section of continuum compared to the continuum (ℓ = 1, 2) modes primarily for higher overtones, in good agreement level. This value varies across the orders of the spectrum. with observations of roAp stars (see e.g. Kurtz & Martinez 2000). Precise radial velocities were measured for a number of spectral All these results suggest that magnetic field strength and configu- lines by the centre-of-gravity method and by fitting Gaussians, sep- ration are important in both mode selection and excitation in roAp arately for each line, and for each of the Zeeman components for stars. Whether the magnetic field also influences the amplitude of lines for which this is possible. Generally, the central π components the oscillations and how such influence may depend on the mag- are sharper than the σ components and give more precise radial ve- netic field properties, is an issue that still needs to be looked at locity measurements than the whole line. Gaussian fitting was only closely. used for unblended lines which are well approximated with Gaus- There is no known correlation between magnetic field strength for sians, and it gives similar results to the centre-of-gravity method. For roAp stars and observed pulsation frequencies (from which mode spectral line identification we used several data bases and other pub- overtone may be estimated with an appropriate model), or with lished sources: the Vienna Atomic Line Data Base (VALD)1 (Kupka pulsation amplitude. Testing for such correlations is not yet easy. et al. 1999), the Atomic Spectra Data Base NIST,2 the Data Base Amplitudes in roAp stars are strongly a function of atmospheric on Rare Earths At Mons University (DREAM)3 (Biemont,´ Palmeri height; in the case of HD 99563, for example, the radial velocity & Quinet 1999; Quinet & Biemont´ 2004), the line lists for roAp amplitude increases from about zero to nearly 5 km s−1 within the stars from the Vienna Asteroseismology along the Main Sequence core of the Hα line alone (Elkin, Kurtz & Mathys 2005b). There (AMS) group site.4 For a small number of lines we used some other is no guarantee that photometric amplitudes sample the same depth published sources. Frequency analyses were performed using both in each star, either, so it is a challenge to select a parameter that the MIDAS TSA package and a discrete Fourier transform programme characterizes the observed amplitude. (Kurtz 1985). Similarly, but not quite so extremely, a uniform measure of mag- netic field for all stars is not easy to make. For stars that have Zeeman-split components, the surface field can be measured. That 3 DATA ANALYSIS AND RESULTS is somewhat variable over the rotation period of the star, and many The radial velocity pulsational amplitudes in the roAp stars depend stars have unknown rotation periods. For many other roAp stars on the spectral lines analysed. This is understood to be the result of only the effective magnetic field strength can be measured from po- short radial wavelengths of the pulsations modes, the vertical strat- larization studies, and then a solution to the magnetic geometry is ification of some elements, such as the rare earths Nd and Pr, and needed to give a measure of the polar field strength. For strong tests the increasing pulsation amplitude with height in the atmosphere. of theoretical studies of roAp stars uniform and complete studies In some cases radial nodes are also visible in the observable at- of the magnetic fields over full rotational periods are needed, and mosphere. See e.g. fig. 3 of Saio & Gautschy (2004), or fig. 8 of a complete spectroscopic survey of all the roAp stars for radial ve- Saio (2005) where nodes above τ 5000 = 1 can be seen in theoreti- locity studies is needed to characterize the frequencies (overtones) cal models. Observationally, examples of nodes have been seen in and amplitudes. For the latter, model atmospheres of these most HD 137949 (Mkrtichian, Hatzes & Kanaan 2003; Kurtz, Elkin & peculiar objects are also needed. Clearly, there are great challenges Mathys 2005a) and in HD 99563 (Elkin et al. 2005b), among other here. roAp stars. We therefore tested HD 154708 for pulsation in radial velocity and have discovered the presence of a single frequency of ν = −1 2.088 mHz (P = 8.0 min) with amplitudes in the range 30–60 m s , 1 http://www.astro.uu.se/∼vald/ depending on which spectral lines are studied. Therefore, this mag- 2 http://physics.nist.gov netically most extreme cool Ap star is a new roAp star, of which 3 http://w3.umh.ac.be/∼astro/dream.shtml there are now 35 known. Table 1, which is an expanded and updated 4 http://ams.astro.univie.ac.at
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Table 1. The rapidly oscillating Ap stars.
2 1/2 HD HR/name V Spectral Period Bmax A(Hα) HsHeff Ref. type (min) (mmag) (m s−1) (kG) (kG)
6532 8.45 Ap SrCrEu 7.1 5 0.22(1) 1 9289 9.38 Ap SrEu 10.5 3.5 483 ± 26 0.54(2) 2, 3 12098 8.07 F0 (HD) 7.61 3 1.46(14) 4 12932 10.25 Ap SrEuCr 11.6 4 770 ± 47 0.53(2) 5 19918 9.34 Ap SrEuCr 14.5 2 827 ± 97 0.80(1) 3 24712 1217 6.00 Ap SrEu(Cr) 6.2 10 0.40(7) 6, 7, 8 42659 6.77 Ap SrCrEu 9.7 0.8 148 ± 9 0.39(1) 3 60435 8.89 Ap Sr(Eu) 11.4–23.5 16 495 ± 25 0.30(1) 9, 10 80316 7.78 Ap Sr(Eu) 7.4 2 277 ± 26 0.18(1) 11 83368 3831 6.17 Ap SrEuCr 11.6 10 0.50(14) 6, 12, 13 84041 9.33 Ap SrEuCr 15.0 6 202 ± 33 0.48(1) 3 86181 9.32 Ap Sr 6.2 4.6 0.40(1) 14 99563 8.16 F0(HD) 10.7 10 2528 ± 23 0.57(3) 15, 16, 17 101065 Przbylski’s 7.99 Controversial 12.1 13 336 ± 11 (2.3) 1.22(2) 6, 18, 19 star 116114 7.02 Ap 21.3 – 29 ± 7 5.96 1.92(1) 20 119027 10.02 Ap SrEu(Cr) 8.7 2 (3.16) 0.50(1) 3 122970 8.31 – 11.1 2 152 ± 26 0.29(2) 21 128898 α Cir 3.20 Ap SrEu(Cr) 6.8 5 254 ± 4 0.20(10) 6, 22, 23 134214 7.46 Ap SrEu(Cr) 5.6 7 180 ± 12 (3.09) 0.40(8) 24 137909 β CrB 3.68 F0p 16.2 – 5.46 0.67(513) 25 137949 33 Lib 6.67 Ap SrEuCr 8.3 3 328 ± 5 (4.67) 1.60(9) 26, 27, 28 150562 9.82 A/F(p Eu) 10.8 0.8 (4.84) 1.20(1) 3 154708 8.76 Ap 8.0 – 9 ± 25 (24.50) 6.43(3) 29 161459 10.33 Ap EuSrCr 12.0 1.3 1.76(1) 30 166473 7.92 Ap SrEuCr 8.8 2 65 ± 9 (7.19) 1.60(10) 31, 32 176232 10 Aql 5.89 F0p SrEu 11.6 0.6 0.31(6) 33, 34 185256 9.94 Ap Sr(EuCr) 10.2 3 0.71(1) 35 190290 9.91 Ap EuSr 7.3 2 3.23(2) 30 193756 9.20 Ap SrCrEu 13.0 0.9 0.19(1) 30 196470 9.72 Ap SrEu(Cr) 10.8 0.7 1.48(1) 30 201601 γ Equ 4.68 F0p 12.4 3 (3.89) 1.00(18) 36, 37 203932 8.82 Ap SrEu 5.9 2 0.22(5) 38 213637 9.61 A(p EuSrCr) 11.5 1.5 (5.24) 0.54(2) 39 217522 7.53 Ap (Si)Cr 13.9 4 0.61(4) 40 218495 9.36 Ap EuSr 7.4 1 0.91(1) 30 Note. Column 3: the V magnitudes are taken from the Cape Survey (Martinez 1993), from table 1 of Kurtz (1990), or from SIMBAD, in that order of preference. Column 4: the spectral types listed are primarily from the Michigan Spectral Catalogue (Houk & Cowley 1975; Houk 1978, 1982; Houk & Smith-Moore 1988). Column 5: for multiperiodic stars the period of the mode with the highest amplitude is listed. Column 6: this is the typical peak-to-peak variation for a night when the star is ‘up’ in amplitude. Column 7: the radial velocity amplitude given is the semi-amplitude for the whole of the narrow Hα core using VLT UVES data from our survey of roAp stars (see Kurtz et al. 2005b). Column 8: the mean magnetic field given is the average over the whole rotation cycle when this has been well observed. For other stars where the entire rotation cycle has not yet been observed, or the rotation period is unknown, the value given in parentheses is the average of the available measurements. 2 1/2 Column 9: the rms longitudinal field Heff was computed from measurements published by Bychkov et al. (2003), Mathys (2003), Hubrig et al. (2004a,b, 2006) and Ryabchikova et al. (2005). The number of available measurements is given in parentheses. Column 10: references given in the last column are to the discovery paper, and/or to a more recent paper that studies and discusses the pulsation of the star photometrically or spectroscopically: 1 – Kurtz et al. (1996); 2 – Kurtz, Martinez & Tripe (1994b); 3 – Martinez & Kurtz (1994); 4 – Girish et al. (2001); 5 – Schneider, Kreidl & Weiss (1992); 6 – Kurtz (1982); 7 – Kurtz et al. (2005c); 8 – Mkrtichian & Hatzes (2005a); 9 – Matthews, Wehlau & Kurtz (1987); 10 – Elkin et al. (2005b); 11 – Kurtz et al. (1997b); 12 – Kochukhov (2006b); 13 – Kurtz et al. (1997a); 14 – Kurtz & Martinez (1994); 15 – Dorokhova & Dorokhov (1998); 16 – Handler et al. (2006); 17 – Elkin et al. (2005b); 18 – Mkrtichian & Hatzes (2005b); 19 – Martinez & Kurtz (1990); 20 – Elkin et al. (2005b); 21 – Handler et al. (2002); 22 – Balona & Laney (2003); 23 – Kurtz et al. (1994a); 24 – Kreidl & Kurtz (1986); 25 – Hatzes & Mkrtichian (2004); 26 – Kurtz et al. (2005a); 27 – Mkrtichian et al. (2003); 28 – Kurtz (1991); 29 – this paper; 30 – Martinez, Kurtz & Kauffmann (1991); 31 – Kurtz et al. (2003); 32 – Kurtz & Martinez (1987); 33 – Hatzes & Mkrtichian (2005); 34 – Heller & Kramer (1990); 35 – Kurtz & Martinez (1995); 36 – Kochukhov & Ryabchikova (2001); 37 – Martinez et al. (1996); 38 – Martinez, Kurtz & Heller (1990); 39 – Martinez et al. (1998); 40 – Kreidl et al. (1991).
In general, Fe-peak elements arise in a line-forming layer around Thus the range of radial velocity pulsation amplitudes in known log τ 5000 ∼−0.5 where the pulsation amplitude is small, or zero roAp stars is large. For β CrB, Hatzes & Mkrtichian (2004) found if close to a node; the narrow core of the Hα line arises between for a large section of spectrum a radial velocity amplitude of only −1 −5 τ 5000 −2 and the rare earth elements Nd, Pr and others form 3.5ms . For HD 166473, Mathys, Kurtz & Elkin (2006) have mostly higher than the Hα core at log τ 5000 −4. shown that there is no variation in 61 Fe lines at a precision of
C 2006 The Authors. Journal compilation C 2006 RAS, MNRAS 372, 286–292 The discovery of 8.0-min variations in HD 154708 289
Figure 1. Amplitude spectra for various lines in HD 154708. The top row, left- and right-hand panel, and the second row left-hand panel show, respectively, the amplitude spectra for 16 Nd II lines, seven Nd III lines and six Pr III lines. Each set of lines shows the same pulsation frequency independently. The second row right-hand panel shows the amplitude spectrum for 154 lines of a variety of ions to reduce the noise; the signal is unequivocal. In the left-hand panel of the third row we show the amplitude spectrum for the narrow, interstellar line of Na I where no signal is present and the highest noise peaks in the frequency range of interest are below 10 m s−1 for this single line. The low frequency peak is caused by a slow drift in the wavelength scale over the 2.5 h of observations, during which no comparison spectrum was observed. This demonstrates the level of radial velocity stability of UVES over this time-span. Finally, the right-hand panel of the third row shows the amplitude spectrum for Hα which shows no signal, although a signal at the level of the upper panels might be lost in the noise in this case.
1.3ms−1, whereas rare earth element lines in that star have ampli- (see fig. 3 of Hubrig et al. 2005), we measured the radial velocities tudes up to 100 m s−1. At the other end of the scale the core of the in each Zeeman component separately. No obvious, clear signal of Hα line in HD 99563 shows amplitudes ranging from zero to nearly pulsational variability can be seen above the noise for any individual 5kms−1 from the top to the bottom of the core of the line. See Kurtz, line, or component of a line. Elkin & Mathys (2005b) for a discussion of some of the systematics We therefore analysed a small set of the lowest noise Nd II,NdIII of the observed radial velocity pulsation behaviour of 10 roAp stars and Pr III lines as ensembles. Fig. 1 shows the amplitude spectra observed with VLT UVES. for these three ions separately, and for an ensemble of 154 lines of Elkin et al. (2005a) discovered longer period (21-min) pulsation various elements, where an unambiguous pulsational signal can be in HD 116114, which is more luminous than other roAp stars and seen. Fig. 1 also shows the amplitude spectrum for the Na I inter- does not show the Nd and Pr ionization disequilibrium that is typical stellar line at 5890 Å where there is no signal. The fact that we see of the roAp stars (Ryabchikova et al. 2004). One of the strongest the signal independently for different sets of lines and there is no signals in that star was found for La II. signal in the interstellar Na I line is proof that HD 154708 is an roAp We thus began our search for pulsational variability in HD 154708 star. with a line-by-line study of the radial velocity variations, concen- Fig. 1 also shows the amplitude spectrum for the core of the Hα trating on the rare earth element lines of Nd II,NdIII and Pr III, and line where there is no signal detected. However, the noise level is on the core of the Hα line. Because of the large Zeeman splitting such that a signal of a similar amplitude to that seen for the rare earth
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Table 2. Least-squares fit of ν = 2.088 mHz to the radial velocity variations tains the oscillations. For a given eigenmode, in the deeper layers the spectral lines of various sets of ions. The phases are with respect to we find essentially an acoustic wave. The depth dependence of the t0 = MJD 245 3510.0. The final column is the standard deviation of one amplitude of this wave is well known from non-magnetic studies. observation (from one spectrum out of the 140) to the fit. Higher up, there is a region where the oscillation has a magneto- acoustic nature and, higher still, a region where it becomes essen- Ion Number ν A φσ tially magnetic, with a displacement perpendicular to the magnetic of lines (mHz) (m s−1) (radians) (m s−1) field direction (if the frequency is sufficiently high, an acoustic run- All 154 2.088 35 ± 3 −1.59 ± 0.10 360 ning wave will also be found in the outermost layers, with displace- Nd II 16 2.088 58 ± 13 −1.37 ± 0.22 418 ment parallel to the magnetic field direction). The depth dependence Nd III 7 2.088 61 ± 13 −1.48 ± 0.21 282 of the wave amplitude is expected to be different for each of these Pr III 6 2.088 94 ± 18 −1.65 ± 0.20 378 regions. Moreover, the position of these regions in relation to the Nd II + Nd III + Pr III 29 2.088 65 ± 8 −1.48 ± 0.13 381 photosphere depends on the ratio between the magnetic and gas Hα 1 2.088 9 ± 25 2.87 ± 2.93 210 pressures, which in turn, depends on the intensity of the magnetic La II 14 2.088 23 ± 10 −0.73 ± 0.41 296 field. If we naively assume that the oscillations in similar stars, but Ce II 6 2.088 29 ± 24 −2.76 ± 0.83 494 Ba II 2 2.088 33 ± 17 1.42 ± 0.51 201 with different magnetic field intensities, have the same amplitude Cr II 3 2.088 27 ± 14 −2.82 ± 0.52 205 below the magnetic boundary layer, we should expect to find differ- Na I (interstellar) 2 2.088 10 ± 4 −1.62 ± 0.42 50 ent amplitudes at the photosphere, and a correlation between latter and the magnetic field intensity. In the column 8 of Table 1 we list the surface magnetic field modulus for those roAp stars for which it is known (Cowley et al. element lines could be lost in the noise. It is typical of other roAp 2000 for HD 101065; Mathys 2003, and unpublished data). All of stars to have Hα amplitudes less than that for Nd and Pr with the these stars show resolved Zeeman multiplets. Other roAp stars do exception of HD 137949, for which Hα has the highest amplitude not; this may be because of rotationally broadened lines masking the (Kurtz et al. 2005b). magnetic splitting in more rapid rotators, or it could be because of The peak in the amplitude spectrum of the 154 lines shown in weaker field strengths. In some extreme cases, such as HD 101065, it Fig.1isatν = 2.088 mHz (P = 8.0 min). We have fitted this fre- may even be the case that the extreme line blanketing can also mask quency to the data sets shown in Fig. 1, plus some lines of other ions Zeeman splitting (or nearly so; see Cowley et al. 2000). It can be seen which do not show any significant peaks in their amplitude spectra in Table 1 that the lowest radial velocity amplitude stars we named with the results given in Table 2. The apparently higher amplitude above, viz. HD 116114, HD 137909, HD 166473 and HD 154708 of the Pr III lines compared to the Nd II and Nd III lines seen in Fig. 1 all are in the Hs list and have strong fields. On the other hand, some is not statistically significant. Lines of other ions shown have no of the highest photometric amplitude stars, HD 60435, HD 99563 significant signal. and HD 101065 are not in the Hs list. Of course, for example, in the case of HD 154708 we do not know the rotational aspect at the time the magnetic and pulsation measurements were made, and in the case of HD 99563 the rotational broadening could mask the 4 DISCUSSION Zeeman splitting. Thus no conclusion can yet be drawn from the We have shown that HD 154708 is a low-amplitude roAp star with noted tendency. radial velocity amplitudes for the rare earth ions Nd II,NdIII and To understand better the role the magnetic field strength plays Pr III of the order of 60 m s−1. This is unusually low for an roAp star. for the pulsation amplitudes, we decided to examine the correlation Kurtz et al. (2005b) examined the pulsation amplitudes for one line between the rms longitudinal fields and the measured amplitudes. of each of these three ions for 10 roAp stars; all except HD 137949 The mean longitudinal magnetic field is the average over the stellar had substantially higher amplitudes – many 100s to 1000s of m s−1 hemisphere visible at the time of observation of the component of – than HD 154708. A few other roAp stars that have low rare earth the field parallel to the line of sight, weighted by the local emergent element radial velocity amplitudes are HD 166473 (Kurtz, Elkin spectral line intensity. The rms longitudinal field presented in col- & Mathys 2003), HD 116114 (Elkin et al. 2005b) and HD 137909 umn 9 of Table 1 is computed from all n measurements according (β CrB; Hatzes & Mkrtichian 2004). to HD 154708 is an exceptional star, being one of the coolest, and n 1/2 having by far the strongest magnetic field strength, of any roAp 1/2 1 H 2 = H 2 . (1) star. This raises the question of whether the strong magnetic field eff n eff i i=1 may result in low pulsation amplitude. The process that limits the amplitude of pulsations in roAp stars is not well studied or well Fig. 2 shows the radial velocity amplitude given in Table 1 for the understood (Dziembowski 1988). Thus, it is not possible at present whole of the narrow Hα core versus the rms longitudinal magnetic to establish whether the magnetic field plays an important role, or fields. Although no clear correlation is evident, this figure gives influences at all, the absolute amplitude of the oscillations. However, some hint that higher amplitudes tend to be found in roAp stars assuming that the amplitude of the oscillations is limited by some with weaker magnetic fields. However, we should keep in mind that unknown physical process that is common to all roAp stars, we can the mean longitudinal magnetic field is aspect dependent, and for a still ask whether the magnetic field intensity and configuration in substantial part of roAp stars only single measurements have been each star will influence the amplitudes that are actually observed at carried out so far. the surface. Given the central role the magnetic field plays in the oblique pul- The dynamics in the outer layers of a roAp stars are best charac- sator model of the pulsations of roAp stars, any possible correlation terized by considering three different regions, distinguished by the between magnetic field strength and pulsation amplitude is impor- role that the magnetic field plays in the restoring force that main- tant and needs to be explored more deeply. That is not a simple
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