ABSTRACT

PROPOSED PROGRAM

HR 1217 is an Ap SrCrEu star with V=6.001. At RA (2000) = 03 55 16, Dec (2000) = -12 05 54, it is observable from both hemispheres with transit at local midnight in late November.

From Broad Band Linear Polarization (BBLP) Studies (Leroy et al. 1996) it is known that the rotational inclination is i = 140 deg and the magnetic obliquity is beta = 147 deg. Thus, the magnetic and pulsation poles at magnetic (pulsation) maximum are seen at i + beta = 73 deg, and, at magnetic (pulsation) minimum, at i - beta = 7 deg. The rotation period is 12.4610 d (Mathys & Hubrig 1997). To resolve the rotational sidelobes fully, a three-week run is needed.

HR 1217 is the roAp star which most closely resembles the sun in the character of its amplitude spectrum. Kurtz et al. (1989) observed HR 1217 for 365 hr at eight observatories over a time-span of three months in 1986. From an amplitude spectrum of a 37% duty-cycle subset of their data it is easy to see the characteristic alternating spacing of 33.5 microHz, 34.5 microHz, 33.5 microHz, 34.4 microHz expected for alternating even and odd l-modes, as well as the rotational side-lobes generated by the oblique pulsation.

From standard A star models Shibahashi & Saio (1985) calculated that:

INSERT FORMULAE HERE

$\left({\nu }_{n,1}-{\nu }_{n-1,2}\right)-\left({\nu }_{n-1,2}-{\nu }_{n-1,1}\right)\approx 6\mu \text{Hz}\&neq;\left({\nu }_4-{\nu }_3\right)-\left({\nu }_3-{\nu }_2\right)=-1.41\mu \text{Hz}$

$\left({\nu }_{n,0}-{\nu }_{n-1,1}\right)-\left({\nu }_{n-1,1}-{\nu }_{n-1,0}\right)\approx 2\mu \text{Hz}=\left({\nu }_5-{\nu }_4\right)-\left({\nu }_4-{\nu }_3\right)=1.59\mu \text{Hz}$

The approximate equality in the second equation above argues that the even l-modes are l = 0 radial modes, rather than quadrupole modes which give the wrong spacing in the first equation. However, there are theoretical doubts about the l = 0 interpretation based on arguments about the magnitude of the magnetic perturbations to the eigenmode frequencies (Cunha 1999), and on possible effects of the surface inhomogeneities (Balmforth et al 2000). In particular, the latter authors calculate that the perturbation to the frequencies are of the order of 3 microHz - similar to the small spacings - so that no mode identifications based on the spacings are possible.

Higher s/n observations by WET over the entire rotation cycle will determine the amplitudes and phases of the rotational sidelobes to high precision. This was not possible in the previous campaign of Kurtz et al. (1989). These rotational sidelobes describe the ``shape'' of the pulsation mode - i.e. they describe how the amplitudes and phases vary as the mode is viewed from different aspect as the star rotates. This is not possible in any other type of star, and there is no other roAp star which presents the opportunity to do this for both even and odd modes. This campaign will provide a currently-unique first opportunity to determine how the modes - both even and odd - are distorted by the magnetic field from normal modes. That, in turn, should allow us to determine whether the even modes are distorted radial or quadrupole modes. (This is a method of mode-typing only possible in roAp stars.) We can then begin to develop the theory of how the magnetic field interacts with, and controls the distortion of the modes. The only other data set which constrains this problem is that of HR 3831, but in that case there is only a single distorted dipole mode. HR 1217 is vastly richer in information with many modes and both odd and even modes. Once the modes degrees are determined we can then reverse the problems of Cunha (1999) and Balmforth et al. (2000): We will know the mode types, hence can use the spacings to constrain the theoretical models for the magnetic perturbations and surface inhomogeneity perturbations to the pulsation frequencies. This is a first opportunity to do this. The theory of the interaction of magnetic fields with stellar pulsation is primitive. This is both because it is a tremendously difficult problem, and because the data to constrain models are nearly non-existent. This campaign will rectify that.

All of the observed modes of HR 1217 are amplitude modulated with the rotation period -- indicating that the l = 0 modes are distorted, probably by the magnetic field. This effect is also seen in the roAp star HR 3831. The l = 1 modes are amplitude modulated as expected for the i and beta given by the BBLP.

The sixth frequency is separated by an inexplicable 50 microHz which is 3/4(delta nu_0), i.e. 3/4 of the large spacing. Models indicate that the pulsation frequencies are near to, or exceed the critical frequency, so nu_6 may be determined by this, or non-adiabatic effects. This is not known. In addition, in the previous study nu_6 appeared as a rotationally split doublet. This is also not expected or explained, but may be an artefact of low s/n. With the higher precision WET data set we will try to detect the ``missing mode'' between nu_5 and nu_6 -- i.e. the mode that is expected at 1/2(delta nu _0).

``Secondary'' frequencies were found by Kurtz et al. (1989). Those are probably caused by frequency variability, but this is also not known or studied. Frequency variability is common in Delta Sct stars, RR Lyrae stars, pulsating white dwarfs, and roAp stars, amongst others. The physics of such variability is not understood. In most cases it can be demonstrated not to be evolutionary. The previous study of HR 1217 indicated that frequency variability may be present in as short a time as three weeks. With the duty cycle of the WET, the project proposed here will be able to examine this for several different pulsation modes. Whether the frequency changes for these modes are identical or different will place a strong constraint on the mechanism.

HR 1217 was observed spectroscopically in a multi-site campaign of the STACC network in 1998. Those data are still under analysis, but preliminary results indicate that the amplitudes of the pulsation modes are not the same in network in 1998. Those data are still under analysis, but preliminary results indicate that the amplitudes of the pulsation modes are not the same in equivalent width, as in the photometric data. The results of that campaign will be known to WET, and the combined data will give unprecedented constraints for mode identification.

Immediate objectives for the WET

1. redetermine the frequency spectrum to higher precision. The frequencies are separated by ~3 d^-1 giving mediocre results even from the previous study with its 29% duty cycle; WET is needed. All frequencies are at, or above, the calculated critical frequency; models are poor and probably inadequate; next to nothing is known about the precise frequency spacing expected, so precision determination is a first step. We will have a theoretically unsolved problem to work on.
2. determine the amplitudes and phases of the rotational sidelobes to measure the distortion of the modes from pure spherical harmonics. This is particularly interesting for the modes thought to be l = 0. The problem of how magnetic fields interact and modify pulsation modes in the atmospheres of stars is essentially unstudied. The only other star for which there are data is HR 3831, and it has a single distorted dipole mode. The presence of both distorted dipole modes and radial modes should constrain the interaction more than has been previously possible. Little has been done previously.
3. remeasure the separation of nu_6 to see if it really is 50 microHz = 3/4(delta nu_0). If it is, an explanation is needed.
4. find out if nu_6 is a rotational doublet; if it is, an explanation is needed.
5. try to detect the ``missing mode'' between nu_5 and nu_6 -- i.e. the mode that is expected at 1/2(delta nu_0).
6. study possible frequency variability on a time-scale as short as the WET run.
7. use the frequencies to model the star using the best Ap models available. The atmospheres of Ap stars are abnormal. HR 1217 has been studied spectroscopically for abundances, magnetic field and abundance patches; frequency fitting asteroseismically may give better knowledge of the atmospheric structure which would then feed back to better understanding of the abundances. Ryabchikova et al. (1997) found (in their abundance analysis of HR 1217) ``a systematic difference between surface gravities obtained from spectroscopy and from both asteroseismology and evolutionary tracks is found for the roAp stars [HR 1217], Alpha Cir, and Gamma Equ''.
8. search for additional frequencies from a better amplitude spectrum, with lower noise levels, than in the previous study.

Telescope Justification

The aperture is not needed to collect more photons for the bright star HR 1217. It is needed to reduce scintillation noise.

NB: Larger aperture reduces scintillation noise.

Number of nights needed

Justification of requested time and lunar phase

Thus the three-week request avoids the full moon because of the proximity of the full moon (transiting near midnight) to HR 1217. Because of the need for a duty cycle as near to 100% as possible, this problem cannot be solved by scheduling the observations for another month when the star does not transit at midnight, since that would cut short the lengths of the individual observatory's runs. This is especially true for northern observatories, given the -12 deg declination of the star.

Furthermore, the rotational ephemeris predicts pulsation and magnetic maxima for the nights of 18 November and 1 December. These are very well-placed in the three week period requested. It is important to have good coverage of two pulsation maxima during the 1.7 rotation periods observed. More astrophysical information can be extracted from the maxima than the minima, although obser vations of the latter are mandatory to extract the rotational sidelobes which describe the form of the amplitude modulation with rotation.

In summary for this section: the three weeks requested are not flexible, except to be moved by a few days later. Dates within 14 November -- 9 December are needed, and this span is only slightly longer than the desired three weeks. Full moon must be avoided because of proximity of the target star and the moon at that time, and known problems with internal reflections in many telescopes. There is no alternative which avoids this problem and allows observations to be made through full moon.

References

Cunha, M. S., 1999, Ph. D. Thesis, Cambridge University.

Kurtz, D. W., Matthews, J. M., Martinez, P., Seeman, J., Cropper,
M., Clemens, J. C., Kreidl, T. J., Sterken, C., Schneider, H., Weiss, W.  W.,
Kawaler, S. D., Kepler, S. O., van der Peet, A., Sullivan, D. J., and Wood, H.
J., 1989, MNRAS, 881

Leroy, J.-L., Landolfi, M., Landi Degl'Innocenti, 1996, A&A, 311, 513

Mathys, G., Hubrig, S., 1997, A&AS, 124, 475

Ryabchikova, T. A., Landstreet, J. D., Gelbmann, M. J., Bolgova, G.
T., Tsymbal, V. V., Weiss, W. W. 1997, A&A, 327, 1137

Shibahashi, Saio, H., 1985, PASJ, 37, 245

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