The effect of the surface distribution of elements on measuring the magnetic field of chemically peculiar stars

Abstract

Abstract.A non-homogeneous distribution over the stellar surface of the chemical elements and the presence of a large-scale magnetic field are invoked in order to explain the periodic line strength, photometric and magnetic variability of magnetic chemically peculiar stars. In such a framework, the variability period is identical to the rotational period. In magnetic chemically peculiar stars, the so-called effective magnetic field H eff , the average over the visible stellar disk of the longitudinal field component weighted by the local line strength, is routinely measured from Stokes I and V profiles of selected spectral lines. In spite of evidence that the distribution of the various chemical elements over the stellar surface can be inhomogeneous and different from element to element, H eff values obtained from lines of different elements are often statistically combined to improve the accuracy of effective field measurements. Similarly, mean high S/N profiles are obtained from the profiles of lines of different elements. We have established, by means of R = 115 000 circular spectropolarimetry of the magnetic chemically peculiar star HD 24712 in the 4700−7000 Å range, the dependence of the measurements of H eff on the atomic weight of 24 elements (from carbon to erbium, if possible at different ionisation states). At all 3 rotational phases considered, H eff values derived from different elements can differ by up to 800 G. We find an overall increase in H eff with atomic number and a maximum near Z = 60. The behaviour of sodium is quite singular inasmuch as it always exhibits a negative value of the field, peaking at −0.39 kG when the rare earths give H eff = 1.2 kG. Under the assumption of a dipolar field, we conclude that the elements giving the largest values of H eff are concentrated near the positive polar region and that the other elements are more homogeneously distributed over the stellar surface or concentrated in belts around the magnetic equator. Sodium seems to be localised in the negative magnetic hemisphere only. This picture is corroborated by the equivalent width variability of the lines: up to iron, equivalent widths changes out-of-phase with respect to the H eff variability; elements heavier than iron present equivalent widths that are variable in-phase. We do not find any relation between the respective amplitudes of the equivalent width variations and the atomic numbers of the elements. For iron, the observed equivalent width variability does not seem to be simply related to any non-homogeneous distribution over the stellar surface. We conclude that measurements originating from different elements cannot in general be combined to improve the precision of H eff measurements. Indeed, any modelling attempt based on the periodic variations in H eff is subject to the risk that the sampling of the magnetic field over the stellar surface by the lines of a given chemical element is uneven or incomplete.

Rotational periods of four roAp stars

“…Mathys (1991) proposed a slightly longer period, P rot = 12.4610 d, based solely on magnetic measurements. The latest revision of the rotation period of HD 24712 was performed by Leone & Catanzaro (2004), who derived P rot = 12.4582 ± 0.0006 day based on analysis of equivalent width data available from 1968 to 2002. A small discrepency exists between the period determined by Mathys (based solely on magnetic field data) and the periods determined using equivalent width and photometric data.…”

“…Asterisks -B z data from Mathys (1991) and Mathys & Hubrig (1997) and W λ / W data from Bonsack (1979). Open squares -B z data from Leone & Catanzaro (2004) and W λ / W data from pulsational observations. Pluses (+) represent Preston's (1972) B z measurements from TiCrFe lines.…”

Three-dimensional magnetic and abundance mapping of the cool Ap star HD 24712

“…The variability period found by Preston (1972) was confirmed by photometric observations by Wolff & Morrison (1973). Many studies of the magnetic field of HD 24712 have been carried out (Preston 1972;Brown & Landstreet 1981;Mathys 1991Mathys , 1994Mathys & Hubrig 1997;Ryabchikova et al 1997;Leone et al 2000;Wade et al 2000a;Leone & Catanzaro 2004;Ryabchikova et al 2005Ryabchikova et al , 2007. Below we will use some of these measurements for improving the rotational period of the star.…”

“…For the period search we compiled a list of all published longitudinal magnetic field measurements derived from the spectral lines of Fe-peak elements, which should be among the least variable lines in the spectrum of HD 24712. This list includes the TiCrFe B z data published by Preston (1972), measurements from the Fe i lines by Mathys (1991) and Mathys & Hubrig (1997), longitudinal field derived from the LSD Stokes V profiles of Fe-peak elements by Wade et al (2000a) and Ryabchikova et al (2005), measurements by Leone & Catanzaro (2004) and, finally, measurements from the recent spectroscopic study of pulsations in the atmosphere of HD 24712 performed by Ryabchikova et al (2007). Photopolarimetric longitudinal magnetic field measurements from the Hβ line by Ryabchikova et al (1997) were also included.…”

A Method to Calibrate the High-Resolution Catania Astrophysical Observatory Spectropolarimeter

“…Often a series of four exposures with a sequence a 1 , a 2 , a 2 , a 1 is obtained to measure a Stokes parameter by subtracting any possible derivative in time. A 100 m s −1 radial velocity shift between the ordinary and extraordinary beams could let Stokes V/I be interpreted as a magnetic field of 100 Gauss (Leone & Catanzaro 2004). Unchecked alignements have been wrongly interpreted as the presence of magnetic fields on the central star of Planetary Nebulae (Leone et al 2011).…”