A&A 424, 237-244 (2004)
DOI: 10.1051/0004-6361:20035639
J. B. Rice
1 -
D. E. Holmgren2,
-
D. A. Bohlender3
1 - Department of Physics and Astronomy,
Brandon University,
Brandon, MB, R7A 6A9 Canada
2 -
SMART Technologies Inc., Bay 8, 1460-26th Street NE, Calgary, AB
T2A 7W6, Canada
3 -
Herzberg Institute of Astrophysics,
National Research Council of Canada, 5071 West Saanich Road,
Victoria, BC, V9E 2E7, Canada
Received 6 November 2003 / Accepted 23 May 2004
Abstract
We present a Doppler Image of the oxygen abundance
distribution over the
surface of the star Aur. The symmetry of the oxygen distribution
appears to be consistent with the magnetic field observations such that the
oxygen is highly depleted at the magnetic poles. In contrast to the star
UMa, where the oxygen displayed undepleted solar abundance in a
band around the magnetic equator, for
Aur the instances of more
normal solar levels of abundance occur in bands midway between the magnetic
poles and the magnetic equator. The oxygen abundance at the magnetic equator
is only mildly depleted for
Aur. It is suggested that the oxygen
abundance distribution is consistent with a global field that has a strong
quadrupolar component. A detailed comparison is made
between the oxygen abundance distribution and that of the distribution of
chromium as mapped by Hatzes (1991a). A striking asymmetry is apparent
in the contrasting behaviour of the oxygen and chromium abundance pattern at
the two magnetic poles.
Key words: stars: chemically peculiar
Aur (HD 40312) is a B9p star that was first discussed by
Hiltner & Morgan (1944) as a modestly chemically peculiar
star with variable
spectral line profiles. Two papers, van Rensbergen et al. (1984) and
Adelman et al. (1984), constituted a detailed single
large high resolution
spectroscopic investigation of the star and its variability.
Shortly before the publication of these
papers,
Aur had been included
by Borra & Landstreet (1980) in a catalog of stars for which they had
obtained magnetic field observations with their H
polarimeter. The
effective
field variation was observed to be an almost sinusoidal
waveform with very little scatter in the observations and the
variation ranged
between the extrema of -240G and +360G. Doppler images
of the distribution of iron, chromium and silicon
were reported by Khokhlova et al. (1986)
and by Rice & Wehlau (1990, 1991). A later paper by Hatzes
(1991a) showed that
Aur
exhibited a distribution of chromium over the surface such that there was a
depleted band of the element located at approximately the assumed
location of the magnetic equator.
This distribution of chromium was similar to
that of three stars he had reported on in an earlier
paper,
UMa, 45 Her, and
Her (see Hatzes 1991b).
Table 1:
Observation log for Aur at 7775 Å.
![]() |
Figure 1: The chromium image of theta Aur based on the same dataset as was used for plate 2 of Hatzes (1991a). This was generously provided by Hatzes to allow for more convenient comparison of the chromium and the oxygen image of this paper. The phases have been adjusted so that the images are displayed here on the basis of the ephemeris used in this paper and these images can be compared directly with Fig. 2. Note that the dark areas represent weaker chromium local equivalent width and the light regions represent stronger local line strength. |
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The motivation for this paper on the distribution of oxygen over the surface
of Aur arose from earlier work on the unusual
oxygen distribution on
Ap stars that began with a paper by Gonzales & Artru (1994).
Their observations of the O I triplet at 7775 Å in several Ap stars
showed that these lines exhibit very dramatic line profile variations.
Gonzalez & Artru interpreted the line profile variations for one star,
UMa, in terms
of a belt of very enhanced abundance about the presumed magnetic equator of
the star.
It was clear that with a more complete set of data and detailed Doppler
imaging, a very good map of the oxygen distribution could be obtained to
complement existing iron and chromium abundance maps.
Papers by Rice et al. (1997) and Holmgren & Rice
(2000) revealed sharply defined belts of oxygen and calcium at the
magnetic equator. In particular, for oxygen the abundance pattern consists
of a normal solar abundance in the well-defined equatorial belt, while at
the magnetic poles oxygen is depleted by up to five orders of magnitude
from solar abundances.
In addition, secondary patches
of oxygen are clearly evident that might suggest that the source of the
non-uniform distribution of oxygen could be a multicomponent stellar wind
guided by the global magnetic field where some return fall to the surface
produces the secondary patches.
Given the very interesting oxygen distribution on UMa, its
potential implications for the mechanism responsible for the non-homogeneous
abundance distribution of elements and its capacity to define the axis of
symmetry that presumably is roughly coincident with the axis of magnetic
symmetry, we suspected that a map of the oxygen distribution on another Ap
star such as
Aur would prove to be informative in the sense that it
would support or confuse the apparent symmetry of Ap star oxygen
distribution and the presence of any secondary abundance patches in
comparison with
UMa.
The period of Aur has been fairly well established since Borra &
Landstreet (1980) determined a period of
based on their sequence of magnetic observations. The zero point
for their ephemeris was based on their estimate of
the positive extremum of the magnetic variation.
In a subsequent paper Adelman et al. (1984) adjusted the estimate
of the period to
based on all combined magnetic and spectroscopic
observations.
Hatzes (1991a) further refined the period to
and, based on
his replot of the magnetic observations, adopted a slightly different zero
point for the phases that represented his estimate of the time of positive
magnetic extremum.
The revised estimate of magnetic maximum did not seem significantly
different from the choice of Borra & Landstreet given the magnetic curve
data. It was difficult to be precise about the peak of the curve of
effective magnetic field.
In this paper the zero point of Borra & Landstreet has been
combined with the period of Hatzes. The phases
referred to in this paper are then calculated from:
![]() |
(1) |
To put the observations of the chromium
distribution on Aur from Hatzes' paper (1991a)
into the context of this new ephemeris, we note
that he observes a spot of enhanced chromium abundance at the equator and
that spot extends in latitude to the lower limit of visibility (see Fig. 1
which is from the data of plate 2 in Hatzes 1991a).
The spot is centred near phase 0.88 (roughly 320
)
on Hatzes'original
map and this location would translate to approximately
phase 0.82 (295
)
for our
ephemeris and for the revised phases shown in Fig. 1.
In either event the meridian crossing of this spot
slightly preceeds the estimates of when maximum
positive effective magnetic field occurs based on the observations of
Borra and Landstreet (1980).
Given the uncertainty in identifying the occasion of
the positive extremum in the observations of the effective magnetic field
and given the symmetry evident in the chromium map of Hatzes, it seems that
the spot of strong chromium abundance in his map is probably the
location of the positive magnetic pole on the surface of Aur.
If that is the case, we propose that the phase representing the time of
crossing of the positive magnetic
pole across the stellar meridian is at about phase 0.82 (295
)
using our ephemeris. If it is not the case, the symmetry of the
surface abundance distribution may be displaced from the magnetic orientation.
In a paper based on observations of the V and y light variations of
Aur, Adelman (1997) finds essentially the same period we are using
here but needs an adjustment in the zero point to bring the ephemeris into
phase with the maxima of the light variation. His ephemeris is:
![]() |
(2) |
On the other side of the star from the spot of enhanced chromium that we
take to be the approximate location of the positive magnetic pole is a
region of depleted chromium that Hatzes notes as being at phase
0.50 (about 0.43 = 155 with our ephemeris and as shown in Fig. 1)
and that is centred at
stellar latitude 55
.
This spot would appear to be consistent with the
approximate location of the negative magnetic pole. Between
these two spots there is a belt of depleted chromium that, on one
side of the star, crosses the line of sight at about Hatzes'
phase 0.75 (roughly 240
as shown in Fig. 1).
In the case of the chromium map of
UMa (Hatzes 1991b),
a belt of depleted chromium
abundance clearly outlines the magnetic equator of a simple (probably dipole)
global magnetic field. In the case of the belt of depleted chromium in the
map of
Aur we suspect that, by analogy with
UMa,
the belt traces out the magnetic
equator of a globally symmetric magnetic field. If we concentrate on the
circle of depleted chromium
around the apparent magnetic equator of
Aur instead of the depleted
spot apparently marking the negative magnetic pole, we would identify the
axis of symmetry for the magnetic equator as coming to the meridian of the
stellar disk a little earlier than the central part of the
depleted spot representing the negative
magnetic pole. This axis of symmetry would arrive at
roughly phase 0.40 using Hatzes' ephemeris (or around phase 0.33 = 137
with the ephemeris used here and as the Cr map of Hatzes is shown in Fig. 1).
Based on the chromium maps of Hatzes
(1991a), and continuing with the analogy to
UMa, we
would suspect that a point in the depleted
region at roughly phase 140
and latitude +55
is the approximate location of the axis
of symmetry of the chromium distribution and the
approximate location of the negative magnetic pole. Based on that assumption
and using the ephemeris we have adopted for this paper,
we would expect that we should find the axis of symmetry of
the abundance pattern in the oxygen map (the point that
we propose represents the approximate location of the negative
pole) to be near longitude 135
(phase 0.38) and latitude +55
(i.e.
in the hemisphere of the visible pole). The positive pole should be near longitude
295
and latitude -55
.
The above discussion is important to the interpretation of the oxygen distribution reported below.
![]() |
Figure 2:
Eight phases of the abundance map of the oxygen
distribution over the surface
of ![]() |
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![]() |
Figure 3:
Two Mercator style projections of the oxygen map of ![]() |
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![]() |
Figure 4:
Fit of predicted O I ![]() |
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Sixty-five spectroscopic observations of Aur with a total
exposure time of 40 min each were made over a period of almost
three years from April 2000
to January 2003. The observations were made with the 1.2 m
telescope of the Dominion Astrophysical Observatory using the
9681 camera that gives a dispersion of 5.0 Å mm-1 at a
resolution of about 55 000 at
7775 Å. The detector was a CCD chip of 4k pixels length. To ease removal
of cosmic ray blemishes, each 40 min
exposure is actually a combination of four 10 min observations. The optimal
extraction of each one-dimensional spectrum was performed with MIDAS
and the resultant S/N in the continuum for each of the extracted
spectra was fairly uniformly near 500. Table 1 is a tabulation
of the dates and phases of the observations where the phases are based
on the ephemeris given in the previous section.
A Doppler image of the abundance distribution of oxygen over the surface of
Aur was produced from the spectroscopic observations using the same
code used for the paper on
UMa (Rice et al. 1997).
In choosing the appropriate model atmospheric parameters for use with the
Doppler imaging
code, the comprehensive papers by Adelman et al. (1984)
and by van Rensbergen et al. (1984) were
relied upon. These authors used for the general
properties of the star the values
K and
3.30.
For their atmosphere they used a ten times solar abundance model
and they concluded that the turbulent
velocities for
Aur were very low. The estimate for the radius of
Aur was that it was between
and
.
In the earlier papers on Doppler images of Aur by Rice & Wehlau
(1990, 1991), the values used for
and i were respectively 56.7 km s-1 and 50
.
These maps suggested
that the axis of symmetry that would correspond to the positive magnetic
extremum for the distribution of iron, chromium and silicon was in the
range of 50
to 60
from the visible rotational pole but
different symmetry patterns are hypothesized. Hatzes (1991a)
used
and i of respectively 53
2 km s-1
and 65
for his
Doppler image of the chromium distribution and he
deduced a considerably different
axis of symmetry for the chromium distribution than that of Rice & Wehlau. In
Hatzes work the axis of symmetry for the chromium distribution
that would correspond to the positive magnetic extremum was
at about 130
to the visible rotational pole.
For the Doppler image of this paper the parameters
given in Table 2 were
adopted. The values shown for the atmospheric conditions were chosen to be
consistent with Adelman et al. (1984) and van Rensbergen et al.
(1984) as discussed above. The values adopted
for and i were evaluated independently here by varying
these parameters over a reasonable
range and choosing values that gave a fit to the spectroscopic observations
of
Aur that produced the minimum of error. The
and i of
Table 2 are within the range already established by the previous work.
As has been shown in test papers (Piskunov & Rice 1993; Rice et. al. 1989;
Unruh & Cameron 1995; Rice & Strassmeier 2000), the final
images in Doppler imaging are not very sensitive to variations in i of the order of 10
degrees. The effect of errors in depends on the
of the star
in question but errors of greater than 0.5 to 1.0 km s-1 become significant on the
same dataset. Comparisons between images recovered from different datasets using
different
values depends on the relative values of the resolution and the accuracy of
the allowance for the instrumental profile and also the comparison between the values used for
micro and macroturbulence. As shown in Rice & Strassmeier (2000), even when numerous
of these gross parameters have errors, the image is quite stable and the effect is on gross
properties of the image such as equator to pole abundance or temperature. For a review of
Doppler Imaging and some comparisons of Doppler Imaging by different authors working on the
same star see Rice (2002).
A common strategy for evaluating the effect on the image of more detailed errors within a dataset of line profiles is to produce images from divided datasets. The usual division is to compare an image from the odd spectra observed with the image from the even spectra. The individual images may lose some detail because of the reduced input but a comparison of the variation of the detail in the images caused by stray errors in single spectra can be made. Here we present that comparison in Fig. 3. The two images shown in this figure represent images from two completely different sets of line profiles, the odd spectra from Table 1 and the even spectra. Each set of line profiles is only half as large as the original set.
The map computed for the oxygen distribution of Aur is shown
in spherical projection in Fig. 2
and the Mercator projections of the same map are shown in Fig. 3.
The reason for showing both versions is so that the spherical projection of
Fig. 2 can be directly compared with Fig. 1,
which is a spherical projection of the chromium image of
Aur, while the
Mercator style projections of Fig. 3 allow for easier
identification of specific features by coordinate. To make it more convenient
for the reader to make a comparison between his chromium map and the oxygen
map presented here, Hatzes has generously
provided us with the new Fig. 1 that is based on the
same data as was used for his Plate 2 (Hatzes 1991a).
The fit of the forward calculation of the oxygen line triplet to the observed spectra on a phase-by-phase basis is shown in Fig. 4.
Table 2:
Adopted parameters for Doppler imaging of Aur.
A direct comparison of the oxygen map of Aur in Fig. 2
with that of the oxygen map of
UMa in Fig. 5 shows that
Aur does not have the simple, single belt of normal oxygen abundance
with extreme depletion of oxygen elsewhere that
UMa has.
Only by referring to the discussion about the ephemeris in the second section
of this paper is the more complex pattern for
Aur evident.
There we indicated that
previous work has shown that the negative magnetic pole and the axis of
symmetry of the chromium abundance is near longitude (or phase) 135
and
latitude 55
.
In Fig. 2 we see that there is a double spot of
pronounced depletion of oxygen at this location, and this depleted region is
surrounded by a network of roughly solar oxygen abundance.
Further, at roughly phase
270
to 300
and latitude -30
(near the limit of visibility) we
see another zone of very depleted oxygen abundance where we would expect the
positive magnetic pole. Both of these depletion zones are elongated rather than
circular in shape (in fact, as noted above, the zone at phase 135
is
apparently significantly doubled).
The depleted zone near the positive pole is also apparently surrounded by some
irregular spots of roughly solar abundance but less apparently so than the
depleted double zone at phase 135
.
Generally, the region along the equator
between these two centres of symmetry appears moderately depleted (i.e. at
about abundance [O/H] of less than -3 to as low as -4 when the solar oxygen
abundance is about -3.1).
The stark violation of the symmetry described
here is the large spot of solar to slightly over solar abundance
centred near phase (i.e. longitude) 0
and latitude +30
.
![]() |
Figure 5:
Eight phases of the abundance map of the oxygen
distribution over the surface of ![]() ![]() ![]() |
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Given that Doppler Imaging is, by its nature, less reliable in the regions near the
limit of visiblity in the hemisphere of the invisible pole, the two mercator images
of the oxygen abundance map for Aur shown in Fig. 3 will allow the
reader to judge the reliability of the features we have discussed by directly
comparing the two images formed from separate datasets.
If we calculate the phase of the light curve maximum from the
epoch of Adelman's (1997) ephemeris using our period we get a
phase for maximum light
of 286 as mentioned earlier. It appears that the phase of the maximum
of the light curve is identical with the phase of the passage across
the stellar meridian of the area of depleted oxygen in the lower hemisphere that
we have identified with the positive magnetic pole, as also with the strong
chromium spot in Hatzes' (1991a) map.
Presuming the pattern above represents, in general, two spots of depleted
oxygen near the magnetic poles, with each surrounded by irregular belts of
approximately solar abundance with radii of about 45
to 50
and a
zone around the magnetic equator of slighly below solar abundance, then this
represents a significant deviation from the simple pattern of
UMa.
The pattern for
Aur seems to suggest there is a
significant quadruple component to the
global magnetic field. We ignore the anomalous spot at phase 0
and latitude +30
for now.
Next we compare the oxygen pattern with that of the chromium
abundance distribution
shown in plate 2 of Hatzes (1991a) and Fig. 1 here. Recall that
for UMa the chromium
map of Hatzes (1991b) was an almost perfect negative of the oxygen map we
found in Rice et al. (1997). Where we found normal oxygen in
UMa, Hatzes has a belt of depleted chromium
and at the large regions of
depleted oxygen in the
UMa map, the chromium was of excess abundance
compared with solar.
The comparison of oxygen and chromium for
Aur is almost direct between our Fig. 2
and Hatzes' (1991a) plate 2 (Fig. 1 here which shows
spherical projections with phasing adjusted to approximately
that used in this paper). The depleted, elongated spots of oxygen at the presumed
negative magnetic pole that
we observe here in the oxygen map corresponds to an elongated
region of depleted chromium,
in contrast to the oxygen vs. chromium behaviour observed in
UMa
where depleted regions of oxygen correspond to enhanced
chromium. In the chromium
map the region of depleted abundance at the negative pole is surrounded by a
pattern of enhanced chromium abundance that is quite similar in appearence to
the pattern of solar oxygen abundence seen around the same pole here.
Just to complicate matters, at the presumed location of the positive pole
at longitude 295 and latitude -55
, we
see a feature of strong enhanced chromium abundance matching
the position of an elongated region of depleted of oxygen in
Aur.
This is consistent with the
behaviour in
UMa. Around the presumed
magnetic equator in Hatzes' (1991a)
chromium map we see a belt of much weaker abundance that matches the slightly
below solar abundance belt around the magnetic equator we see here. To
illustrate the resemblence of the belts of lower abundance in the two images,
the reader can compare the images shown at phase 270
in
Hatzes' plate 2 (Fig. 1 here)
which has a remarkable resemblance to the image we show at phase 270
in our
Fig. 2. The only significant contrast between the two images is,
as mentioned above, the large spot of excess
abundance for chromium at the positive
pole in Hatzes' image.
So far we have assumed that the symmetry of the oxygen and chromium maps better defines the locations of the magnetic poles and the phase when the effective magnetic field should be seen at extremum than the estimates of Borra & Landstreet (1980) or Hatzes (1991a) based on the plots of the observations of the effective field. If this assumption is wrong and the aformentioned estimates of the peak in the observations of effective field are fairly accurate, we may have an indication that the field geometry is sufficiently complex that the time of maximum (or minimum) effective field does not coincide with the occasion when the axis of symmetry of the abundance distribution driven by the surface magnetic field is on the central meridian of the stellar disk. The maximum of the light curve does correspond quite closely with the time of passage of the axis of symmetry of the abundance distributions across the central meridian.
Acknowledgements
The authors wish to thank the director of the Dominion Astrophysical Observatory for a generous allocation of observing time. This project was supported by a grant to J. B. Rice through the Natural Sciences and Engineering Research Council of Canada.