Magnetic field moments have been derived as described in the previous
section from 95 observations of 44 stars. These measurements are
presented in Table 3 (click here). The columns give, in order: the star HD (or HDE)
number, the
heliocentric Julian date of mid-observation, the rotation phase (for
stars whose rotation period is reliably known), the longitudinal field
and its estimated uncertainty
, the crossover
and its estimated uncertainty
, the quadratic field
and its estimated uncertainty
, and the number of spectral lines
used for the determination of the field moments. The absence of entries in the
last two columns corresponds to cases when the fit of the measurements
of
by a function of the form given in Eq. (3) yields a negative
value of
. As discussed in Paper V, this may happen when the
square field is small compared to the accuracy which can be achieved in
its diagnosis.
Table 4: Variation of the longitudinal field: least-squares fit parameters
Table 5: Variation of the crossover: least-squares fit parameters
Table 6: Variation of the quadratic field: least-squares fit parameters
For the stars for which observations have been obtained repeatedly
throughout the rotation cycle (including observations already reported in
Papers III to V), the variations of the field moments can be well
represented either by a cosine wave:
or by the superposition of a cosine and of its first harmonic:
In these expressions,
stands for any of the measured quantities
,
, or
.
is the rotation phase, determined using the values of
the period P and of the Julian date HJD0 of the phase origin which
appear in Table 2 (click here). The mean value A0, the amplitude(s) A1 (and
when significant A2), and the phase(s)
(and possibly
) of the variations are derived through a least-squares fit of
the field moment measurements by function (4) or (5). This fit is
weighted according to the uncertainty of the individual measurements.
The results of those fits are presented in Table 4 (click here) (for ; the
amplitudes are denoted Hi,
, and the phases
,
), Table 5 (click here) (for
, amplitudes Xi and phases
), and Table 6 (click here) (for
, amplitudes Qi and phases
). Columns 7 to 9 of these tables give the number
of degrees of freedom about the fit
, the reduced
of the
fit
, and the multiple correlation coefficient R.
Graphical representations of the fits also appear in
several of the phase diagrams plotted below. In those diagrams, the
meaning of the symbols used to represent the data points is as follows.
Filled squares correspond to our measurements of Papers III to V. Our
new data appear either as open squares (for those obtained with the
long camera of CASPEC) or as filled triangles (corresponding to
observations performed with the short camera of CASPEC). When
data of other authors are included in the figures for comparison,
crosses are used to distinguish them. As in the previous papers of
this series, the error bars shown for our measurements correspond to
.
The results obtained will now be discussed star by star.
Only 2 observations of the rapidly oscillating Ap (roAp)
star HD 24712 were discussed in the previous papers of
this series. Five new observations have now been obtained. The resulting
7 measurements of the longitudinal field are plotted together with
Preston's (1972) data in Fig. 1 (click here), against
the phases computed from the value of the rotation period (124572)
favoured by Kurtz & Marang (1987). The phase diagram shown in
Fig. 2 (click here)
rests on the value of the period (124610) proposed in Paper II.
As suspected in that paper, comparison of Figs. 1 (click here) and 2 (click here) strongly
supports the view that the actual value of the rotation period is
(close to) 124610. It has been shown in Paper II that this value is
also consistent with 7 unpublished measurements
Figure 1: Plot of our measurements of the longitudinal field of
HD 24712 and of those of
Preston (1972) against the rotation phase computed
assuming that the rotation period is 124572
(see the text for the meaning of the symbols)
Figure 2: Same as Fig. 1 (click here), but assuming a value of 124610 for the
rotation period
of J.D. Landstreet (private communication). Reasons for the possible inaccuracy of the value derived by Kurtz & Marang (1987) have been discussed in Paper II.
Crossover and quadratic field remain below the detection limit in
HD 24712, not surprisingly given its low and the small
upper limit of its field modulus (Mathys & Lanz 1992).
Figure 3: Phase diagram of our measurements of the mean longitudinal
magnetic field (lower panel), of the crossover (centre),
and of the mean quadratic magnetic field (upper panel) of
HD 83368 (see the text for the meaning of the symbols).
The curves are least-squares fits of the data by sinusoids
HD 83368 is also a roAp star. Its fairly rapid rotation (
)
makes magnetic field diagnosis difficult. This accounts for our present
inability to derive a quadratic field from our only new observation of
this star, and for the rather poor accuracy of the crossover
determination reported here. The latter, however, is not inconsistent
with our
previous data, as can be seen in Fig. 3 (click here). The same figure also shows
that our new
measurement agrees quite well with our
12 earlier determinations. We confirm that, to the achieved
accuracy, the curves of variation of the three field moments discussed
in this paper do not significantly depart from sinusoids. Nevertheless,
the variations of the quadratic field are at the limit of significance,
and their shape cannot be regarded as well established.
Resolved magnetically split lines have been discovered in HD 94660 by
Mathys (1990).
On the basis of photometric observations, Hensberge (1993)
suggested that the rotation period of this star may be close to 2700 d.
This is well supported by the mean magnetic field modulus measurements
of Mathys et al. (1996; hereafter MHLLM). The latter authors also
argued that no longitudinal field variations are detected either in our
own measurements (2 in Paper III and 2 here) or in those of other authors
(Borra & Landstreet 1975;
Bohlender et al. 1993). Given the good accuracy
(of the order of 100 G) of our 4 determinations and their reasonable
distribution in phase (assuming that the rotation period is indeed close
to 2700 d), it appears unlikely that
may vary with a peak-to-peak
amplitude exceeding 300 or 400 G. This is amazing, considering that the
peak-to-peak amplitude of variation of the mean field modulus
of
HD 94660 must be about 300 G or larger, and that large variations of
are seldom observed, even in stars where
is strongly
variable and/or undergoes polarity reversal. In fact, HD 94660
appears as a unique case of a star where one observes
definite variations of
but not of
. This,
consistently with the very anharmonic shape of the field modulus
variations (see Fig. 26 of MHLLM) hints at a rather unusual geometrical
structure of the magnetic field.
We neither detect any significant variation of the quadratic
field. This is not unexpected: the relative amplitude of the latter
should be at most of the same order as the relative amplitude of
variation of the field modulus, that is, about 5%. Such variations are
below the detection limit at the accuracy achieved in the quadratic
field diagnosis. Note also that the ratio between and
is
approximately 1.3.
Finally, crossover can, of course, not be measured in a star rotating so slowly.
Our attention had been called to HD 98457 by its unusually large
photometric variations (Waelkens 1985). Our first two observations of
this star, obtained at phases 0.152 and 0.983, had not allowed us to
detect definitely a magnetic field from the consideration of any of the
three field moments that we are studying (Papers II to V), although
values of the quadratic field were measured at the 2.6 and
levels. We have obtained one new observation, at phase
0.446 (the uncertainty of the relative phasing with respect to our
previous measurements should be less than 0.03). Again, we do not detect
any significant longitudinal field or crossover, while we are unable to
diagnose the quadratic field. Given the improvement of the phase
sampling resulting from this new observation, it seems increasingly
unlikely that HD 98457 may have a very strong magnetic field.
Figure 4: Phase diagram of our measurements of the mean longitudinal
magnetic field (lower panel)
and of the mean quadratic magnetic field (upper panel) of
HD 116458 (see the text for the meaning of the symbols).
The curves are least-squares fits of the data by sinusoids
Like HD 94660, HD 116458 is a star in which magnetically resolved lines have
been discovered by Mathys (1990). The rotation period, ,
has been determined from photometry by Hensberge (1993), who has shown
that it is consistent with our 5 measurements of
presented in Paper II.
These are complemented here by 5 new determinations. All our
longitudinal field measurements are plotted against rotation phase in
Fig. 4 (click here). The variations have a fairly small amplitude but are
undisputable. The reduced
obtained when fitting them by a
cosine curve is somewhat high, but there is no definite indication of
anharmonicity.
HD 116458 rotates too slowly to allow detection of any crossover.
Figure 5: Phase diagram of our measurements of the mean longitudinal
magnetic field (lower panel)
and of the mean quadratic magnetic field (upper panel) of
HD 119419 (see the text for the meaning of the symbols).
The curves are least-squares fits of the data by a cosine wave
(thin curves) and by the superposition of a cosine wave and of its
first harmonic (thick curves)
From the consideration of the upper panel of Fig. 4 (click here), the quadratic
field of HD 116458 shows some hint of variability. However the
amplitude of the corresponding sinusoidal fit is at most marginally
significant (see Table 6 (click here)). As a matter of fact, the field modulus of
this star is not detectably variable (MHLLM), so that we do not expect
to be variable either. Any variation
of
should thus arise
from the contribution of
. It can also be noted that the ratio
between the mean value Q0 of the quadratic field and the mean
magnetic field modulus (see Table 3 (click here) of MHLLM) is 1.33.
Two new observations of HD 119419 have been obtained. When plotted
together with our 20 previous measurements
against the phase computed with the period 26006 (Lanz & Mathys
1991), the two new data show a definite phase shift, indicating that
the period is no longer accurate enough to represent data that span a
timebase of almost 2500 d (compared to less than 750 d for the
measurements reported in the previous papers of this series).
Accordingly, we revised the period determination, deriving an improved
value
from our whole set of longitudinal field measurements. This
value lies within the uncertainty range of the period obtained by Lanz
& Mathys (1991). Note also that our magnetic data are definitely
inconsistent with the value of the period (260562) proposed by
Catalano & Leone (1993) on the basis of photometric data.
The contribution to the curve of variation of of a small but definite
term with twice the rotation frequency of the star is
confirmed (compare the fit of the data by a single sine curve and by
the superposition of a sine and of its first harmonic in the lower
panel of Fig. 5 (click here)). The variations of the quadratic field occur with
an amplitude
too small compared to the accuracy with which
can be
measured to decide definitely whether they show
any departure from harmonicity.
As mentioned in Paper IV, crossover is not clearly detected in HD 119419 (somewhat surprisingly). The upper limit given in Paper IV for this quantity remains unchanged.
In Paper II, we had shown that with the value of 92954 proposed by Babcock (1960) for the rotation period of HD 125248, our 19 longitudinal field measurements could be adequately phased together with those obtained by Babcock (1951) 35 years before or more. By contrast, the use of the revised period value of 929571 suggested by Catalano et al. (1992) introduces a relative phase shift of 0.07 between Babcock's (1951) data and ours, hence quite significantly degrades their agreement. Therefore, we stick to the value of the period proposed by Babcock (1960).
The 2 new measurements of the field moments reported here agree well
with our 19 previous determinations. In particular, ,
, and
all vary nearly sinusoidally (see Fig. 6 (click here)).
A refined value of the rotation period of HD 126515, P=12995, has
recently been derived from the consideration of measurements of its mean
magnetic field modulus spanning 38 years (MHLLM). The same authors also
pointed out the remarkable anharmonicity of the variations of the
longitudinal field, from the simultaneous consideration of measurements
of the latter obtained by Preston (1970) and
van den Heuvel (1971),
and of our data published in Paper III (6 determinations) and reported
here (3 additional points). The anharmonicity is fully confirmed by
unpublished H photopolarimetric determinations of
(kindly
provided by D. Bohlender & G. Hill), which are shown together
with our data in Fig. 7 (click here).
The agreement between the two sets of measurements is
quite good. This is not trivial: significant, as yet not fully
understood differences are observed for some stars between CASPEC
("photographic'') and Balmer-line photopolarimetric
determinations.
Figure 6: Phase diagram of our measurements of the mean longitudinal
magnetic field (lower panel), of the crossover (centre),
and of the mean quadratic magnetic field (upper panel) of
HD 125248 (see the text for the meaning of the symbols).
The curves are least-squares fits of the data by sinusoids
Our measurements alone are not sampling the stellar rotation cycle quite well enough to constrain the shape of the variation curve. Therefore, the fitted amplitude of the first harmonic is hardly significant (see Table 4 (click here)). The contribution of this harmonic is nonetheless quite obvious in the lower panel of Fig. 8 (click here).
Figure 7: Phase diagram of our measurements of the longitudinal field of
HD 126515 and of unpublished determinations of Bohlender & Hill
(see the text for the meaning of the symbols)
Figure 8: Phase diagram of our measurements of the mean longitudinal
magnetic field (lower panel)
and of the mean quadratic magnetic field (upper panel) of
HD 126515 (see the text for the meaning of the symbols).
The curves are least-squares fits of the data by a cosine wave
and its first harmonic (for the longitudinal field) and by a cosine alone
(for the quadratic field)
Similarly, although a simple sinusoid gives an excellent fit to
the variations of , our measurements are somewhat too scarce and not
quite accurate enough to rule out definitely a possible anharmonicity.
The amplitude of the variations of the quadratic field is unusually
large, consistently with the large amplitude of variation of the field
modulus, which has long been known (Preston 1970). However, the ratio
between the maximum and the minimum of
appears smaller than the
ratio between the extrema of
(MHLLM).
Accordingly, the ratio
/
significantly varies along the rotation cycle, ranging approximately
from 1.25 at field modulus maximum to close to 1.50 at field modulus
minimum. This indicates that, at least at some phases, the contribution
of
to the quadratic field must be rather considerable.
Crossover is not detected in HD 126515 as a result of its slow rotation.
After many unsuccessful attempts by various authors, the rotation
period of HD 128898, the brightest of all roAp stars known, has been
determined by Kurtz et al. (1994):
P=44790. Using this value of
the period, our 2 new
observations can be phased together with our 5
older ones within an accuracy of 0.01 cycle. However, when our magnetic
measurements are plotted against phase, no systematic trend is seen for
any of the studied field moments, even though our observations
sample rather well the rotation period.
This is not too surprising, given the low level of
rotational variability shown by the star in photometry or in
spectroscopy. As a consequence, no progress is made in the knowledge of
the magnetic field of HD 128898, with respect to the results already
reported in Papers II to V: and
are below the detection
threshold, while our observations are consistent with a fairly constant
quadratic field of the order of 7.5 kG.
HD 137509 has one of the strongest magnetic fields known in an Ap star
(Paper V). The distribution in phase of our 9 observations of this star
obtained until 1988 was far from ideal (half of the rotation cycle
remained unsampled), so that the variation curves of the various field
moments were poorly constrained. The 5 new observations reported here
improve this situation, and reveal the contribution of a very
significant term with twice the rotation frequency in the variations of
the longitudinal field and of the crossover (see Fig. 9 (click here)). The first
harmonic is
possibly present in the quadratic field curve too, but for this field moment,
our data are not quite conclusive yet. A marked double-wave character
of the variations such as we find in HD 137509 had been observed so
far in the stars HD 37776 (Thompson & Landstreet 1985)
and HD 133880 (Landstreet 1990). This indicates that the magnetic field of
HD 137509 has an unusually important quadrupolar component.
Figure 9: Phase diagram of our measurements of the mean longitudinal
magnetic field (lower panel), of the crossover (centre),
and of the mean quadratic magnetic field (upper panel) of
HD 137509 (see the text for the meaning of the symbols).
The curves are least-squares fits of the data by a cosine wave
(thin curves) and by the superposition of a cosine wave and of its
first harmonic (thick curves)
The 4 new observations of the famous cool Ap star HD 137909 that we
present here fill only partly the gap in phase coverage of our 11 older
data. But, thanks in particular to their better accuracy, they bring a
significant improvement in the definition of the variation curves. For
all three field moments considered here, these curves show no
departure from sinusoids, in contrast with the very anharmonic
behaviour of the field modulus (MHLLM). The quadratic field is
approximately 1.25 times larger than the latter close to maximum, while
the ratio between both goes down to very nearly 1.0 at their minimum.
This remarkably small value of , which had already been
pointed out in Paper V, is unique among the stars that we have
studied. It points to a rather unusual structure of the magnetic
field. In particular, it indicates that at quadratic field minimum, the
magnetic field of HD 137909 must be seen almost purely transversally.
This view is supported by the relative phasing of the curves of
variation of
and of
(which are in quadrature with respect
to each other - see Fig. 10 (click here) and Tables 4 (click here) and 6 (click here)).
But this apparent simplicity is misleading: the
actual geometrical structure of the field of this star appears very
complex and its detailed modelling is quite challenging (Leroy 1995;
Wade 1995).
Figure 10: Phase diagram of our measurements of the mean longitudinal
magnetic field (lower panel), of the crossover (centre),
and of the mean quadratic magnetic field (upper panel) of
HD 137909 (see the text for the meaning of the symbols).
The curves are least-squares fits of the data by sinusoids
Figure 11: Phase diagram of our measurements of the mean longitudinal
magnetic field (lower panel), of the crossover (centre),
and of the mean quadratic magnetic field (upper panel) of
HD 147010 (see the text for the meaning of the symbols).
The curves are least-squares fits of the data by a cosine wave
(thin curves) and by the superposition of a cosine wave and of its
first harmonic (thick curves)
Our 2 new observations of HD 147010 and the derivation of a refined value of its rotation period by Catalano & Leone (1993) do not significantly change the picture of its magnetic field that we had obtained from our previous 17 observations. Accordingly, the reader is referred to the previous papers of this series for a detailed discussion. The updated variation curves are shown in Fig. 11 (click here).
Figure 12: Phase diagram of our measurements of the mean longitudinal
magnetic field (lower panel), of the crossover (centre),
and of the mean quadratic magnetic field (upper panel) of
HD 153882 (see the text for the meaning of the symbols).
The curves are least-squares fits of the data by cosine waves
with the rotation frquency of the star (longitudinal field and crossover)
or with twice that frequeny (quadratic field)
Our 14 observations of HD 153882 published so far were not sampling the rotation period ideally, with a gap in the coverage left between phases 0.1 and 0.5. The 3 new observations reported here all fall in this gap, which allows the variation curves of the magnetic field moments to be better defined. The resulting fits are shown in Fig. 12 (click here). While the longitudinal field and the crossover are adequately represented by a sinusoid with the rotation frequency of the star, we fully confirm the suspicion expressed in Paper V that the best fit to the quadratic field variations is given by a sinusoid with twice the rotation frequency, alone.
Preston (1971) has discovered resolved magnetically split lines in the
spectrum of HD 165474 observed in unpolarized light.
The mean magnetic field modulus of this
star has been studied by MHLLM. According to these authors,
appears to undergo low-amplitude (200 to 300 G peak-to-peak)
variations about a mean value of 6.5 kG, over a (rotation) period
which could not be uniquely
determined, but which may plausibly be quite short (the most probable
value being 254).
Given the fairly large value of the field modulus, it is surprising
that our 3 determinations of the longitudinal field all yield null
values. In particular,
the 2 new measurements reported here are significantly more
accurate than the one published in Paper III and allow us to set a
rather conservative upper limit of the order of
(in absolute
value) for the longitudinal field of HD 165474. However, preliminary
visual examination of an additional CASPEC observation of HD 165474
obtained in July 1996 shows the unmistakable signature of a definite
longitudinal field. Thus our 3 null measurements so far just appear to
be very unfortunately phased.
We have not detected any crossover in HD 165474 (with a quite stringent
upper limit of 1.5
in our last observation). This is
not quite unexpected for a star having resolved magnetically split
lines, but the result is nonetheless non-trivial if the rotation period
is as short as 254 (note that HD 137909, another star with
magnetically resolved
lines with a rotation period of 185, does show significant
crossover).
Our 2 new determinations of the quadratic field yield values of this field moment of the order of 7.0 kG, while a value of 10.1 kG had been obtained in Paper V. However, the uncertainty of the latter was larger, so that there is no major inconsistency between it and the more recent measurements, within the limits of their respective accuracies. Tentatively adopting 7.0 kG as the representative value of the quadratic field, the ratio between this field moment and the mean field modulus (MHLLM) is of the order of 1.08.
Figure 13: Phase diagram of our measurements of the mean longitudinal
magnetic field (lower panel), of the crossover (centre),
and of the mean quadratic magnetic field (upper panel) of
HD 175362 (see the text for the meaning of the symbols).
The curves are least-squares fits of the data by a cosine wave
(thin curves) and by the superposition of a cosine wave and of its
first harmonic (thick curves)
From photometric observations,
Manfroid & Renson (1994) have derived
an unambiguous value of the rotation period of HD 168733
(P=63540), which however seemed inconsistent with the
longitudinal magnetic field measurements of Jones & Wolff (1974).
The 4 observations of this star reported here were obtained as part an
effort to solve this discrepancy. Together with 3 former observations
discussed in Papers II to V, they sample well the rotation cycle.
Still, the standard deviation of the resulting 7 measurements is
only 130 G, that is, quite comparable to the typical uncertainty of the
individual determinations. Thus, we are not detecting any significant
variation. We are led to speculate that, as is known to have
occurred frequently for
diagnosis from photographic plates,
Jones & Wolff (1974) somewhat underestimated the uncertainty of
their measurements (they quote a typical probable error of 150 G), and
that the standard deviation of their data (310 G) only reflects
their random errors. Thus we argue that the longitudinal field of HD 168733
is not detectably variable, and that its mostly constant value is close
to the average of our 7 determinations, -636 G (which is consistent
with the average of all the measurements of Jones & Wolff: -688 G).
The absence of a measurable crossover in HD 168733 is not surprising,
given that fairly sharp spectral lines had been observed at high
dispersion by Mathys &\
Lanz (1992). We had been unable to determine the quadratic field in
Paper V, and we achieve only one marginally significant detection here
(3.7 kG at the level).
Figure 14: Phase diagram of our measurements of the mean longitudinal
magnetic field (lower panel)
and of the mean quadratic magnetic field (upper panel) of
HD 187474 (see the text for the meaning of the symbols).
The curve is a least-squares fit of the longitudinal field
data by a sinusoid
The anharmonicity of the variations of the longitudinal field of HD 175362, first suspected by Borra et al. (1983), has been definitely established in Paper II. A similar anharmonicity was found in Paper IV for the crossover. By contrast, the quadratic field variations could be satisfactorily represented by a sine wave alone (Paper V), although a small contribution of the first harmonic could not be excluded. A relative weakness of the 24 observations of HD 175362 described in Papers II to V is their uneven distribution in phase: 3 groups of points concentrated resp. between phases 0.355 and 0.417, between phases 0.545 and 0.682, and between phases 0.821 and 0.939, plus 3 points between phases 0.087 and 0.132. In other words, less than half of the cycle was sampled densely, and the shape of the variation curves in the remaining large gaps was poorly constrained. The 5 new observations presented here partly fill those gaps and provide some of the missing constraints, but the conclusions about the general shapes of the curves are not altered (see Fig. 13 (click here) and Tables 4 (click here) to 6 (click here)).
Resolved magnetically split lines have been discovered in HD 187474 by
Didelon (1987). Our 4 new observations of this star are rather
unfortunately phased,
since they sample essentially the same half of the 2345 d rotation
period of this star as the 7 observations discussed in Papers II to V.
This is not critical for the longitudinal field, for which excellent
measurements had been secured by Babcock (unpublished, see Paper II)
throughout the whole cycle. But the gap in the quadratic field curve
between phases 0.22 and 0.70 appears particularly regrettable in view
of the quite unusual behaviour of the field modulus in this phase range
- note especially the sharp raise of starting at phase 0.2
(MHLLM). In these conditions, it does not appear suitable to try to find
a mathematical function representing the
data obtained so far.
The fit of a cosine to our
measurements, shown in the lower panel
of Fig. 14 (click here) (coefficients in Table 4 (click here)), must also be regarded as
provisional, although consideration of Babcock's data (see Fig. 33 of
Paper II) suggests that it is probably not too far from reality.
The ratio between the quadratic field and the mean field modulus
between phases 0.8 and 0.2 (where is fairly constant) is
approximately 1.50.
Of course, the very slow rotation of HD 187474 rules out any possibility of detection of crossover.
HD 188041 is another long period (2239, see Hensberge 1993) star with resolved lines (Preston 1971). Our 7 observations (4 of which had already been discussed in the previous papers of this series) are insufficient to characterize the behaviour of its longitudinal field by themselves, but they appear roughly consistent with Babcock's (1954, 1958) data.
No significant crossover nor quadratic field was detected in this star.
The slow drift of the longitudinal field of HD 201601 from 1946 to 1988
has been illustrated in Fig. 37 of Paper II. Leroy et al. (1994) have
presented compelling arguments (based on broad-band linear polarization
measurements) definitely establishing that the observed
variation does result from stellar rotation with an extraordinarily
long period exceeding 70 years. Some ambiguity is left on the exact
value of this period. According to Leroy et al. (1994), its smallest
plausible value appears close to 77 years, but it might possibly be as
long as 110 years. For a period close to the lower limit of this range,
the negative extremum of
was expected in 1994, while longer
periods allow the longitudinal field to keep becoming more negative for
a while still. The 4 new measurements of
reported here show some
hint of a flattening of the variation curve, which may be indicating
that the star is indeed approaching its negative extremum and would
accordingly suggest that the period is close to the low end of the
acceptable range. That the mean field modulus (diagnosed from the
observation of magnetically resolved lines) also seems to be reaching
its maximum (MHLLM) may be another indication of this - but one has to
remember that the
and
extrema do not necessarily coincide
in phase.
Given the long rotation period, one cannot expect to observe crossover in HD 201601.
For the reasons exposed in Sect. 3, quadratic field diagnosis is more
difficult and less accurate here than in Paper V. This explains why,
for HD 201601, quadratic field could be diagnosed only from the spectra
taken with the long camera of CASPEC, and why in spite of the higher
dispersion of the latter, the uncertainty affecting those 2
determinations is larger than that of the measurements of Paper V.
Accordingly, no real progress is achieved here in the knowledge of
this field moment. Based on the (better) data of Paper V alone and on
the only field modulus measurement of MHLLM contemporaneous with them,
the ratio is found to be of the order of 1.85.
MHLLM have derived a refined value of 521 d for the rotation period
of HD 2453, an Ap star with resolved magnetically split lines
(Mathys & Lanz 1992). They have shown that with this value of the
period, the measurement of reported here is consistent with
those of Babcock (1958) and of Wolff (1975). The slow
rotation of the star does not allow crossover to be observed and the
quadratic field cannot be determined.
Our single observation of HD 5737 yields null values of and
, while we could not diagnose the quadratic field. The
longitudinal field had already been studied in detail by Shore et al.
(1990). Their 16 H
photopolarimetric determinations of this field
moment, together with 7 older measurements of Borra et al. (1983),
revealed that it varies mostly sinusoidally between -0.3 and
+0.5 kG over the stellar rotation period. The most accurate value of
the latter, 21652, has been derived by Manfroid & Renson (1994)
from photometric observations in the Strömgren system. Using it, our
observation can be phased with respect to those of Shore et al. (1990)
with an accuracy of 0.03 rotation cycle. Our
value of
G, derived at phase 0.312, is quite consistent
with the value of -314 G predicted for that phase from the best fit cosine
to the data of
Borra et al. (1983) and of Shore et al. (1990).
HD 6532 is a roAp star with a short rotation period: 194 (see Kurtz
et al. 1996 and references therein). As a result of this fast rotation,
its spectral lines show significant Doppler broadening, which
complicates the magnetic field diagnosis. Our observation is, to our
knowledge, the first attempt to detect the magnetic field of this star.
While it yielded null values of the longitudinal field and of the
crossover, a quadratic field of about 22 kG was measured. That
and
, which generally vary in phase quadrature, are both small
at a given phase suggests that the longitudinal field never gets very
large. Although it remains to be confirmed by observations at other
phases, we note that this behaviour is similar to that of the only two
other fast rotating roAp stars whose magnetic field has been studied so
far. Indeed, these stars, HD 83368 and HD 128898, also have
relatively modest longitudinal fields and quite strong quadratic fields
(see Sects. 4.2.2 and 4.2.8).
HD 19918 is another roAp star (Martinez & Kurtz 1994) whose magnetic
field has never been studied. Here we report the detection of a
longitudinal field at the level. Null values are derived
for both the crossover and the quadratic field. But the constraint on
the latter is very weak, with a
upper limit of 21 kG.
A high-resolution (
) observation
in unpolarized light, performed with the ESO Coudé Echelle Spectrograph
(CES) fed by the 3.6 m telescope is significantly more stringent.
Indeed, from this spectrum, the lines of HD 19918 appear quite sharp,
indicating that the field modulus of this star is unlikely to exceed
much 1 kG.
Borra et al. (1983) concluded that HD 22920 almost certainly has a weak
longitudinal field, from the consideration of the average of four
measurements performed by H photopolarimetry, none of which
taken alone yields a firm detection. Our single attempt to determine
is not more successful. But it is noteworthy that it gives a small
positive
value quite consistent with the data of Borra et al.
(1983), thus that it supports these authors' argument about the reality
of the field. We detect no crossover in HD 22920 and we cannot diagnose its
quadratic field.
6 determinations of the longitudinal field of HD 36485 have been
performed through H photopolarimetry by Bohlender et al. (1987),
and these authors have concluded that
in this star is constant,
at a value of -3.4 kG. However, our single
determination yields
a value of -1.9 kG. We cannot decide at present whether the
discrepancy with the conclusion of Bohlender et al. (1987) means that
these authors have misinterpreted their data or
if it results from the use of
different measurement techniques. Indeed, inconsistencies between
longitudinal fields diagnosed with the Zeeman analyzer of CASPEC and
with the H
photopolarimeter have been found for several stars
and are not fully understood (see Paper II; see also Mathys 1989). But
they seldom are so extreme as the difference obtained here for
HD 36485.
No significant crossover is detected in HD 36485, and its quadratic field cannot be diagnosed.
Sargent et al. (1967) performed the first determination of the
longitudinal field of HD 37058 and derived a value of
G. Conti (1970) obtained 5 measurements ranging from
+30 to +1300 G, with uncertainties of 400-600 G. None of Borra
et al.'s (1983) 3 individual values of
(all negative) quite reach
the
level (the
of each of the 3 measurements is just
slightly larger than 300 G), but their average indicates that a field is
detected at the 99.9% confidence level. Therefore Borra et al. (1983)
argue that all observations are consistent with a reversing longitudinal
field varying with a peak-to-peak amplitude of 2 to 3 kG. If this
interpretation is correct, our determination of
, which is much
more accurate than the previous ones, must have been very unfortunately
phased, since it yields a null result too. The value of the rotation
period derived by Pedersen (1979) is regrettably too coarse to test the
relative phasing of our observation with respect to older ones. But the
reality of the field of HD 37058 is supported by our finding of a
fairly significant crossover (at the
level). We also
measure a marginally significant quadratic field, at the
level.
The measurements of the mean magnetic field modulus of HD 50169 by
MHLLM indicate that the period of rotation of this star with
magnetically resolved lines, discovered by Mathys & Lanz (1992), must
be much longer than 4 years. Consistently with this, Babcock (1958)
observed a slow increase of from +670 G in 1953 to +2120 G
three years later. Our own measurement falls between these two values.
Comparison of the value of found here with contemporaneous
data of MHLLM indicate that the ratio between the two quantities is of
the order of 1.7. Of course, no crossover is detected.
HD 55719 is one of the three double-lined spectroscopic binaries
definitely known to contain a magnetic Ap star. The latter has resolved
magnetically split spectral lines (Mathys 1990). Both the
characteristics of the binary system
and the longitudinal field of the Ap component have
been studied in detail by Bonsack (1976). This author's
measurements and his determination of the rotation period have been
rediscussed in detail by MHLLM. Indeed, none of the two values of the
period that he favours is consistent with the field modulus
measurements. MHLLM could not definitely establish the value of the
rotation period, but 847 or 775 days appear as most plausible.
Nevertheless, it seems unavoidable that 2 or 3 of Bonsack's (1976)
measurements are
bound to be inconsistent with the bulk of his data, regardless of what
the rotation period is (they were already discrepant with Bonsack's
preferred period values). Except for these discrepant values, all of
Bonsack's (1976)
data are larger than our 3 measurements. If the
interpretation proposed by MHLLM that the rotation period is longer than
2 years is correct, this hints at the existence of systematic
differences betwen Bonsack's (1976) and our longitudinal field
determinations. This is not unusual but it implies that we need to
accumulate more data before we can hope to use the
measurements
to constrain the rotation period.
The crossover measured in our third observation is too marginal (at the
level) to question the long period hypothesis. The first
two quadratic field determinations (based on spectra recorded with the
long camera of CASPEC) are significantly more accurate than the third
one (for which the short camera was used). Their ratio to the average
field modulus of HD 55719 (MHLLM) is close to 1.3.
The rotation period of HD 70331, one of the hottest Ap stars with magnetically resolved lines, could not be uniquely determined from the consideration of its mean magnetic field modulus, but it must probably be short, two of the most plausible values being 303 and 365 (MHLLM). Longitudinal field measurements may prove very useful to establish the value of the period more reliably. This field moment is determined here for the first time, yielding a large negative value of -2.8 kG. As is often the case for stars with magnetically resolved lines, no significant crossover is detected (although one cannot exclude to observe it at other phases). The large quadratic field is about 1.1 to 1.2 times larger than the field modulus.
Our single determination of the longitudinal field of HD 81009 is fully
consistent with an unpublished variation curve of this moment, obtained
by G. Hill and D. Bohlender (Hill, private communication; see also
MHLLM). Rather remarkably, given the rather long rotation period of
3396 (Waelkens 1985), crossover is detected at a fairly significant
level (). This is fully consistent with the observation of
some Doppler distortion in the split components of the magnetically
resolved lines of this star (resolved magnetically split lines have
first been observed in this star by Preston 1971).
The ratio
at the phase of our observation is approximately 1.75.
HD 93507 is another star with magnetically resolved lines discovered
by MHLLM,
whose longitudinal field has never been measured before. The two
determinations presented here are separated by 0.302 rotation cycle
(the period is 556 d). That they differ by 1 kG suggests that
undergoes quite sizeable variations. The second determination of the
quadratic field, based on a spectrum taken with the long camera, is
considerably more accurate than the first one, for which the short
camera of CASPEC was used. We only compare the former to the field
modulus at the same phase: the ratio between them is 1.07. HD 93507
rotates too slowly to show observable crossover.
The observation of magnetically resolved lines in HD 116114 has
first been reported by Mathys et al. (1993). From the mean field
modulus measurements, it was inferred that the rotation period must be
much longer than 3 years (MHLLM). The first measurement of
which we report here yields a large negative value (-1.9 kG), while
the quadratic field is 1.2 times larger than the field modulus. No
crossover is detected.
The roAp star HD 134214 (Kreidl 1985)
has one of the smallest field moduli measured by MHLLM in any
star with resolved magnetically split lines. These authors were unable
to derive a definite value of the period, but the latter may well be
short. A tentative value of 41456 is suggested by MHLLM. Should this
value prove correct, the two observations reported here would be
separated by only 0.104 rotation cycle. The fact that no significant
measurement of either , or
, or
is obtained from any
of them would then only be a weak constraint.
MHLLM have shown that all previous measurements of
(Babcock 1958; van den Heuvel 1971; Wolff 1975) in the roAp star
HD 137949 (Kurtz 1982), together with our two measurements presented here,
consistently indicate that the star has a very long rotation period
(possibly more than 75 years). The crossover measured from our first
observation is not significant enough (at the
level) to
challenge this conclusion. Our two spectra were taken with the short
camera of CASPEC, and the
determinations have uncertainties
too large to be really meaningful.
We are reporting the first determination of the longitudinal field
of HD 144897, an Ap star with resolved magnetically split lines
(MHLLM). The phase of this observation is about mid-way between the
maximum and the minimum of the field modulus. If the and
extrema roughly coincide in phase (which is not infrequent,
even though some
stars show large departures from this phase relation), we expect
to reach at its maximum a value significantly greater than the already
large +2.0 kG derived here. Not surprisingly, since the rotation period
is fairly long (4843), we observe no crossover. Comparing our good
measurement of
with
at the same phase, the ratio of the two
is found to be 1.13.
Magnetically resolved split lines had been sought (and found - see
MHLLM) in HDE 318107 following North's (1987) report that the rotation
period of this star is 52 d. Somewhat ironically, the field modulus
measurements proved inconsistent with this value of the period. They
were however too noisy to allow MHLLM to establish what the actual
value of the period is. Longitudinal field measurements may prove most
useful to this effect, since the variations of this field moment are
often (relatively) larger than those of . The first determination
of
reported here is promising, since a large positive value
(almost 2.0 kG) is obtained, with a reasonably small uncertainty
(230 G). The achieved determination of the quadratic field is pretty
accurate too. The ratio of
to the average of the
measurements of MHLLM is close to 1.45.
Our interest in HD 166473, originally motivated by the fact that it
is a roAp star (Kurtz & Martinez 1987), grew when resolved
magnetically split
lines were discovered in its spectrum (MHLLM). The mean
magnetic field modulus of this star varies slowly, with a period
still unknown, but definitely
much longer than 3.2 years, and a large relative amplitude. Our
3 measurements of (the first ones ever obtained for this
star) have been performed over 2 months,
close to the maximum of
. Not surprisingly,
shows no
significant variation over that time interval. No crossover is
detected. From the last two, more accurate (long camera) determinations
of the quadratic field, the ratio of the latter to the field modulus
at the time of our observations was 1.30.
The first study of the longitudinal field of HD 176232, a roAp star
(Heller & Kramer 1988), was performed by Babcock (1958). If the
uncertainties he quotes for his 6 determinations of are not
underestimated (as has unfortunately often been the case for
photographic
measurements), these determinations rank among the
most accurate ones ever achieved, and all of them indicate that
HD 176232 has a small (between -315 to +440 G) but definite
longitudinal field. The accuracy of our measurement of
is
significantly worse than the accuracy claimed by Babock (1958), and we
do not detect this field moment, nor crossover or quadratic field.
We neither detect any of the three field moments considered in this study in the roAp star HD 193756 (Martinez & Kurtz 1990). We are not aware of any other attempt to diagnose the magnetic field of this star.
HDE 335238 has long been known to have magnetically resolved spectral
lines, from which a large, variable field modulus is derived (Preston
1971). But probably because of its faintness, it has not been paid much
attention until MHLLM's recent systematic study of the magnetic field
modulus. These authors were unable to derive an unambiguous value of
the rotation period, but they showed that it must without doubt be
between 40 and 50 days. The phase of our observation is accordingly
unknown, and in particular, we cannot relate the quadratic field that
we determine (+10.5 kG) to the field modulus. We also detect a fairly
large negative longitudinal field, and more unexpectedly, a (somewhat
marginal) crossover (at the level).
HD 203932 is another roAp star (Kurtz 1984) whose magnetic field has never been studied before. Our two attempts yield no detection of the longitudinal field or of the crossover, and we were unable to diagnose the quadratic field.
We find no significant variation of nor of
between our 3
observations (spread over slightly less than one year) of HD 216018.
We do not detect any crossover either. All this is consistent with the
very long rotation period (much longer than 3 years) inferred from the
variations of the mean field modulus of this Ap star with magnetically
resolved lines (MHLLM). The ratio of the quadratic field to the field
modulus is of the order of 1.25.
The only hint of a magnetic field that we find in the roAp star
HD 217522 (Kurtz 1983)
is provided by a very marginal ()
quadratic field measurement. Our single observation (which is the
first one aimed at detecting a field in this star) does not show any
significant longitudinal field or crossover.
HD 218495 is another roAp star (Martinez & Kurtz 1990) whose magnetic
field has never been studied. That both the and
determinations yield nonzero values at a low level of significance
(
and
, resp.) may be purely coincidental,
but it may also indicate that the star indeed has measurable longitudinal
field and crossover and that our
single observation was unfortunately phased
approximately mid-way between
the extrema of both those field moments. The quadratic field could not
be diagnosed.