A&A 460, 751-758 (2006)
DOI: 10.1051/0004-6361:20065242
K. G. Strassmeier1 - J. B. Rice2
1 - Astrophysical Institute Potsdam, An der Sternwarte 16,
14482 Potsdam, Germany
2 -
Department of Physics, Brandon University, Brandon, Manitoba R7A
6A9, Canada
Received 21 March 2006 / Accepted 13 June 2006
Abstract
Aims. We present the first Doppler images of the single pre-main-sequence star PW And. Its position in the HR-diagram suggests it to be in the rapid-braking phase just prior to arrival on the ZAMS.
Methods. Images are obtained from seven individual spectral lines as well as from 5-nm wide chunks of spectrum that invert a total of 58 line profiles simultaneously.
Results. Cool spots with temperature differences with respect to the stellar photosphere of up to 1200 K are detected. Spot occurrence is mostly within an equatorial band up to 40
of the stellar equator and thus contradicts magnetic-flux tube emergence models based on young K-star properties that predict an emerging latitude in two distinct bands of +45-55
.
This confirms previous suggestions that current magnetic-flux tube models predict emergence latitudes too low for G-dwarfs and too high for K-dwarfs, which may be caused by the fact that the G-dwarf models heavily rely on comparisons with the Sun. We also redetermine the absolute parameters of PW And in the light of a missing Hipparcos parallax and revise its age to be more near 20 Myr, in agreement with its logarithmic lithium abundance of
.
A precise rotational period of 1
was found from our photometric data in 2004.
Key words: stars: activity - stars: starspots - stars: imaging - stars: individual: PW Andromedae - stars: pre-main sequence - stars: fundamental parameters
PW And is a rapidly-rotating single K2 dwarf within the Local
Association moving group (Ambruster et al. 1994; Montes et al. 2003). Isochrone fitting of its position in the
color-magnitude diagram suggests an age of just 30-80 Myr
(López-Santiago et al. 2003) in agreement with its
lithium abundance of nearly primordial value (3.0-3.4 on the
scale; Ambruster et al. 1994; Wichmann et al.
2003; López-Santiago et al. 2003). This suggests
that PW And is likely still a pre-main-sequence star that had not
had time enough to mix and burn its lithium, rather than being just
a very young main-sequence star. Unfortunately, PW And lacks a Hipparcos parallax and is therefore difficult to place in the H-R
diagram. Ambruster et al. (2003) made an attempt to compute
absolute radii from the Barnes-Evans relation and the
Stefan-Boltzmann law but obtained radii significantly smaller than
the indirectly measured
(from
and the rotation
period), which is clearly not physical and also suggestive of a
pre-main-sequence nature.
The star is photospherically and chromospherically very active and
already appeared in Bidelman's (1985) list of stars with
Ca II H&K and H
emission. Hooten & Hall
(1990) had determined a photometric rotation period of
1.745 days. Rotational line broadening was measured by several
groups to be 21-23 km s-1 with various techniques. Just recently,
a redetermination of absolute stellar parameters as well as
extensive spectroscopic observations of activity indicators were
presented by López-Santiago et al. (2003), and we
refer the reader to this paper for further references. No direct
detections of its surface magnetic field exist to date.
In this paper, we present the first Doppler image of PW And. Doppler imaging is a technique to reconstruct the surface temperature distribution from periodic variations of a star's spectral line profiles (e.g. Rice 2002). Over the one and a half decades since Doppler imaging of cool stars began, approximately 70 active cool stars have had one or more images of their surfaces (a recent listing is given by Strassmeier 2002). These stars include T Tauri, FK Comae, RS CVn-type stars as well as rapidly-rotating main-sequence stars. There are now comparisons that can be made among all the images of these stars, and in some cases there is even time tracking of images that allow us to see the time development of the active regions and in particular to note contrasts in behavior with the Sun.
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Figure 1: New high-precision photometry of PW And in 2004. a) Periodogram from the combined V and y data. The x-axis is in units of cycles per day. b) V (pluses) and y (dots) photometry. The x-axis is in fractional days from JD 2 453 000. c) Phased light and color curves with the ephemeris in Eq. (1). Note that the b-y curve is differential with respect to HD 1440. The spectroscopic observations were obtained during the interval 2 453 243-50. |
High-resolution spectroscopic observations were obtained with the
f/8 Gecko spectrograph at the 3.6-m Canada-France-Hawaii
(CFH) telescope on Mauna Kea, Hawaii. Data were obtained over four
nights (Aug. 26-27, 30-31), a gap of two nights was necessary to
obtain optimum phase coverage. Now equipped with the CAFE fiber
feed module (Baudrand & Vitry 2000) Gecko provides
a spectral resolution of 120 000 in 8th order at 643 nm with a 5%
better throughput in the red than with the mirror train. The
spectrograph is not cross dispersed but, in combination with the
13.5
m-pixel EEV1 CCD, gives a 10 nm
wavelength range. CAFE feeds light through a 27 m-long 100
m
Ceram-Optec fiber to a four-slice Bowen-Walraven image slicer
before it enters the collimator. A single lithium spectrum was
obtained with an order-sorting filter in the 9th order.
Seeing at CFHT was always between an astounding 0.30
to
0.8
and all integrations on PW And were set to an exposure
time of
s. This allowed for a total of 27 spectra
centered at 643.0 nm and one spectrum centered at 671.0 nm with an
average signal-to-noise (S/N) ratio of around 170:1 per single
exposure per pixel. The time series also included five flat-field
exposures per every target integration, totalling to up to 30-40
fairly evenly distributed flats per night. Twenty bias readouts at
the beginning and at the end of each night and up to five
integrations of a Th-Ar comparison-lamp spectrum throughout the
night ensured a proper calibration of our spectra.
Stellar comparison targets were also observed with the same
set-up, among them the bright and relatively inactive stars
AX Mic = HD202560 (M0V), Eri (K2V) and HD 166620 (K2V) as
well as the radial-velocity standard stars
Ser (F6V;
+6.58 km s-1) and
Ari (K2III; -14.51 km s-1) (Scarfe et al.
1990).
All spectra were reduced and extracted using the Interactive Reduction and Analysis Facility (IRAF) provided by NOAO. More details of the standard reduction procedure were given in previous papers (e.g. Strassmeier & Rice 2003).
High-precision photometry of PW And was obtained with the University
of Vienna 0.75 m twin automatic photoelectric telescopes (APTs) at
Fairborn Observatory in southern Arizona (Strassmeier et al.
1997). The T7-APT observed from JD 2 452 187 through 2 453 310
an achieved an external precision of 3.2 mmag, the T6-APT during the
period 2 453 259-286 achieved an external precision of 1.7 mmag.
This included a dedicated one-month run shortly after the CFHT
observations with both telescopes (from 2 453 259-286). The T7-APT
used Johnson
filters, the T6-APT used Strömgren byfilters. A total of 649 V, 455 I, 726 b, and 736 y data
points were obtained. The duty cycle for one group execution was 7.8 min and 9.8 min for T7 and T6, respectively. Integration time was 25 s in VI and 30 s in by. All the measurements were done
differentially with respect to HD 1440 (B-V=1.06; Hog et al.
2000). Check star was HD 1281 (K5). Johnson data are
transformed to absolute values with the continuous observations of
up 60 nightly standards. Strömgren data are just differentially.
For further details on the observing procedure and the data
reduction we refer to Granzer et al. (2001).
The only time-series photometry in the literature is that of
Hooten & Hall (1990) from photometric data taken
during three observing seasons in 1985-88. Periods of
,
,
and
days were obtained
for the three observing seasons, respectively. The authors
recommended the 1.745-day period to be their most reliable since
it had the least scatter. This period was adopted by
López-Santiago et al. (2003) for their bisector
analysis. Abbott et al. (1995) had obtained Four-College
APT data in fall 1994 and quoted a photometric period of 1.75 days. However, from their abstract it is not clear whether this
period was determined in that paper or just quoted.
Figure 1a shows the result from our Fourier analysis. The light
curve is nearly sinusoidal and a FFT analysis seems appropriate. We
applied the program package MUFRAN (Kolláth 1990), which is
a collection of methods for analyzing multi periodic and unevenly
sampled data. Standard discrete Fourier transforms of the
light-curves were calculated, followed by a non-linear least-square
fit of the frequencies found. The combined V and y data were
used and a period of
days resulted in the lowest
residuals. This period differs by just 0.9% from the Hooten & Hall
period but is almost a factor 100 more precise and thus supersedes
this and all other previous values.
We phase all data in this paper according to the following
ephemeris
The rotational velocity
of PW And was measured by
several authors using differing techniques. Fekel (1997)
obtained
km s-1 from broadening measurements of a
number of unblended lines and an assumption of an appropriate
radial-tangential macroturbulence. Griffin (1992) listed
(rms) km s-1 from Coravel traces. López-Santiago et al. (2003) determined
km s-1 from the width
of the cross-correlation function of lines in an echelle spectrum
versus an inactive reference star.
We have redetermined
implicitly during the
Doppler-imaging procedure. This takes into account the
line-profile deformations due to spots, incorporates all lines in
our spectra, and fits all rotational phases simultaneously, not
just a single spectrum. Compared to other determinations this
should, in principle, give the most accurate value. Our best value
is
km s-1, where the error has been estimated from
trial inversions and represents the sum of errors from, e.g.
different abundances, continuum misplacement, imperfect wavelength
and flat-field calibration, stray light in the spectrograph etc.
Together with the photometric period the minimum radius becomes
.
Adopting our most-likely
inclination of
from the Doppler-imaging
procedure (Sect. 4.2), the radius of PW And is
1.16
+0.15-0.11
.
Note that inclinations between
40
and 52
are equally likely though. For comparison, a
normal K0-K2 main sequence star is expected to have
0.81-0.75
(e.g. Gray 1992); the ZAMS radii
would be even slightly smaller. PW And is thus not a main-sequence
star but rather a pre-main-sequence object, as suggested by
López-Santiago et al. (2003). Using both the
Stefan-Boltzmann law and the Barnes-Evans relation, Ambruster et al. (2003) had obtained radii smaller than the observed
which, of course, as they mentioned themselves, is
unphysical. In the light of our more precise values, the problem
must lie with the assumption of the unspotted brightness and color
that must be adopted for the two methods.
The brightness-averaged surface temperature from our maps in
Sect. 4.2 is 4800 K. Due to the lack of a Hipparcos
parallax, we must use this temperature and above absolute radius
to obtain the luminosity of 0.640 .
This is likely a
lower value because it is based on the brightness-averaged
temperature of our single Doppler image in 2004.7. If the star
were seen without its spots its effective temperature may be
5000 K, and its luminosity correspondingly
0.753
.
The difference suggests a missing energy of
erg s-1, which would make the star 8% more
massive than quoted below. A comparison with the evolutionary
tracks and isochrones from Baraffe et al. (1998)
suggests a mass of 1.07
and an age of
20 Myr.
As a comparison, the D'Antona & Mazzitelli (1997)
tracks favor more a mass of 1.10
.
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Figure 2:
A lithium spectrum of PW And at R=120 000 ( top). The
Li I 670.8 nm line is the strong line in the center. Its
equivalent width is 278 mÅ corrected for the contribution from an
inactive star ![]() ![]() |
We have also measured the Li I 670.8-nm feature in a single
R=120 000,
spectrum (Fig. 2) and obtained
an equivalent width of
mÅ after subtracting a spectrum
of the K2-dwarf
Eri. The latter contributes 22 mÅ over
the total width of the lithium line in PW And, as does a similar
spectrum of the K0-dwarf 70 OphA. The non-LTE curves ofgrowth of
Pavlenko & Magazzú (1996) for a 5000 K/
model convert this equivalent width into a logarithmic Li abundance
of
(on the
scale). In case we use a
4750 K/
model, which is more like the
brightness-averaged surface temperature of PW And, the conversion
gives 2.60 dex. These abundances are significantly smaller than the
previous determination of 3.4 dex by López-Santiago et al.
(2003) based on
K, but likely still in
agreement with the 3.0 dex given by Ambruster et al. (1994).
Our corrected equivalent width is also in very good agreement with
the value of 273 mÅ listed by Wichmann et al. (2003) and
267 mÅ listed by López-Santiago et al. (2003). The
discrepancy thus likely comes from the curve-of-growth calibration
adopted by López-Santiago et al. and the inherent uncertainties of
the Pavlenko & Magazzú (1996) NLTE calibration.
TempMap computes an error function that represents the degree to which the predicted spectrum from a current trial image of a star (starting with a blank surface) differs from the observed spectrum and then altering the parameters of the image to iteratively reduce the error function to a minimum consistent with the error of the observations. The squared difference between the forward calculation and the observation is summed over all wavelengths and a full set of observations spaced in time through the full cycle of phases of the star's rotation. A regularizing functional of the minimization process - maximum entropy in our case - is used so that the line profiles calculated from the image produced do not overfit the observed spectra. For a full discussion of Doppler Imaging and the process of regularization see Rice (2002) and Piskunov & Rice (1993) and for TempMap tests see Rice & Strassmeier (2000).
In the current application, the local line profiles were
calculated from ten Kurucz (1993) model atmospheres covering
3500 K to 5500 K of fixed
of 4.5 for the purpose of
recovering the local effective temperatures. Photometry was not
included in the inversions because our APT data were not strictly
simultaneous with the spectroscopy. A more detailed account of the
numerical procedure and a recent application to a cool
pre-main-sequence star can be found in Strassmeier et al.
(2005).
Microturbulence was determined from Blackwell-diagrams as prescribed
by Gray (2000). The equivalent widths of ten iron lines were
measured and converted to an iron abundance as a function of
microturbulence with a curve-of-growth analysis. These abundances
show that all lines seem to converge at a microturbulence of 2 km s-1 and an optimal value for the abundance of iron of 7.5 (on the usual
(H) = 12.00 scale). We note that this is in discordance with
the metallicity of -0.78 dex listed in the Geneva-Copenhagen
catalog (Nordström et al. 2004).
Table 1 again summarizes the relevant astrophysical data of PW And.
Parameter | PW And | Reference |
Spectral type | K2V | López-Santiago et al. |
age | 30-80 Myr | López-Santiago et al. |
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this paper | |
b-y | 0
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Nordström et al. (2004) |
(V-I)C | 1
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this paper |
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4.5 | (adopted) |
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5000 K | this paper |
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4800 ![]() |
this paper |
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23.9 ![]() |
this paper |
Rotation period | 1
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this paper |
Inclination | 46![]() ![]() ![]() |
this paper |
Radius | 1.16
+0.15-0.11 ![]() |
this paper |
Luminosity | 0.64 ![]() |
this paper |
Mass | 1.07 ![]() |
this paper |
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this paper |
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this paper |
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this paper |
1 Brightness-averaged temperature from the Doppler images.
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Figure 4: Doppler image of PW And from the full-spectrum approach. Otherwise as in Fig. 3. |
We first proceeded with a line-by-line inversion and its parameter
optimization. Our major lines were Ca I 643.9 (363),
Fe I 643.0 (244), Fe I 642.1 (228), Fe I 641.9 (166), Fe I 641.1 (267), Fe I 640.8 (218),
Fe I+Fe I 640.0 (417), and Fe I 639.3 (250),
where the number in parenthesis is the average equivalent width in mÅ, errors are usually 3-4 mÅ. Plots of the full
wavelength range of similar stars were shown in previous papers,
e.g. in Strassmeier & Rice (2003). We abandoned the
close iron blend at 640.0 nm from our input because of resulting
uncertainties of its central wavelength and relative line strength
due to the likely contamination from a weak CN line. Note that the
other two close iron lines at 641.94 nm (excitation potential of
4.7 eV) and 642.13 nm (excitation potential of 2.2 eV) are solved
for simultaneously from the beginning and show consistent results.
The fitting errors that we achieve for the individual lines and line
pairs are comparable, e.g.
for the Fe I 641.9 + 642.1 pair corresponding to a S/N ratio of 122:1. The ideal
fit would be achieved for S/N ratio that matches the observed one,
i.e. on average 170:1. Error is defined here as
,
where n is the number of spectrum
points in all of the observations, i.e. the number of pixels per
phase times the number of phases. This number of data points is such
that the problem is essentially over-determined and the
least-squares fit predominates. We have two to three times as many
profile points per star in total as we have pixels (2592) visible on
the surface of each star. Although the strong Ca I 643.9 line
could be fitted to the same level, its surface map remained markedly
different: besides the correct recovery of the main features seen in
the other lines, a circumpolar ring warmer by
400 K than
and a tiny, 10-degree diameter, cool polar spot
remained in the Ca image. We are confident that these are partially
imaging artifacts coming from, i) the high sensitivity of the
local-line strength of Ca I 643.9 at the temperature of PW
And; ii) the small rotational broadening compared to the large
intrinsic width of the line and; iii) is caused by a chromospheric
contribution to the line profile. The latter makes also Fe I 643.0 an error-prone line, although its recovery is not as
strikingly different than from Ca. The Ca I 643.9-nm local
line width is 40% higher (FWHM 0.145 Å) than for the other
Fe I lines, except Fe I 643.0, which is 20% wider.
Therefore, we assigned half weight for both lines for the average
map and for the full-spectrum inversion.
We run a grid of solutions for each line for
and
inclination i with fixed microturbulence, abundances, and
transition probabilities. Overall best fits were achieved with
of
km s-1 and i=46.0
6.5
.
Errors are rms values from the different lines and line pairs and
just suggest the ranges within the true value must lie.
Our final averaged image is shown in Fig. 3. It is a
brightness averaged temperature map from Ca I 643.9 (half
weight), Fe I 643.0 (half weight), Fe I 642.1,
Fe I 641.9, Fe I 641.1, Fe I 640.8, and
Fe I 639.3. Representative data and the fits for one line
pair - Fe I 642.1 nm and Fe I 641.9 nm - are shown in
Fig. 5. It appears there are unknown weak lines causing a
depression between these two iron lines with respect to the fit
shown. We could not identify these blending lines assuming solar
abundances. Therefore, this region was given zero weight during the
inversion. Respective fits for all wavelength regions are given in
the electronic appendix (Figs. A.1-A.5). The brightness-averaged surface
temperature from all spectral lines is K (rms) with a
range of surface temperatures between 3780 K and 5200 K. The
photospheric temperature is of course higher than the
brightness-averaged value and we estimate it more like 5000 K. Only
few surface pixels were recovered with 5200 K, and we discharge
them as artificial.
We then proceed with the inversion of the entire wavelength range of
our spectra (639.2-644.0 nm). Each rotational phase then consists of
a data vector of length 3060 wavelength points or 5.5 nm. It
contains the major imaging lines listed above plus a total of 51 blends. A weight list is added to T EMPM AP in which each
wavelength pixel is assigned a weight. Per default the file consists
of 3060 unit weights, but the regions outside of (2
+ 0.1 nm) of a line center, i.e. all mostly continuum, were given
zero weight. The Ca I 643.9-nm and the
Fe I 643.0-nm
lines were given half weight again, see above. The rest remained at
unity. Our final image with the full-spectrum synthesis approach is
shown in Fig. 4. Because the fits for a particular line are
not easily distinguishable by eye from the single-line fits, we do
not give a separate figure.
PW And does not show a cool polar spot nor any distinctive
high-latitude spots. The maps are dominated by several low-latitude
spots between latitudes of +40
and -20
(the latter
close to the limit of visibility at -44
)
and temperatures of
1200 K below the photospheric value. The locations of these
spots are consistently recovered in all single-line inversions as
well as in the full-spectrum inversion. We are therefore quite
confident about their reality. Its recovered contrasts vary by
approximately
100 K from line to line but agree to within
20 K in the average map and the full-spectrum map.
The visible polar region shows two unusual warm features with
average relative temperatures of up to 200 K above the photospheric
temperature (at longitudes of roughly 20
and 150
and a
latitude of +60
;
see Figs. 3 and 4). These
regions appear to be significant because they show up to some extent
in the recovery from all lines. The high contrast in the average and
the full-spectrum map is mostly due to the inclusion of the Ca
I 643.9-nm line though and, although to a lesser extent, also the
Fe I 643.0-nm line, despite that we gave them only half
weight. A recovery with zero weight and full weight did not change
the resulting contrast significantly. The other lines recover these
features with a temperature difference of no more than 150-200 K
above the photospheric temperature and, usually, would not be
considered significant.
Figure 6 compares latitudinally averaged temperatures from the
single-line maps. It demonstrates that the main spot activity on
PW And takes place below latitudes of +40.
There is some
evidence of spot activity below the equator but the Doppler-imaging
technique is not capable of recovering accurate latitudes close to
the visibility limit. Therefore, we can not conclude that there
exists indeed a symmetric spot-activity belt as on the Sun.
The overall spot morphology of PW And resembles that of today's Sun.
Activity seems to be concentrated below +40
latitude and
consists of at least six individual cool spots. Spot sizes are
10-100 times larger than solar spot groups, despite a solar-like
radius of 1.16
.
Two regions
200-K warmer than the
photosphere at latitudes of approximately +60
could be
interpreted as high-latitude chromospheric plages that are still
seen in the stronger photospheric lines. Although PW And is a very
young, likely pre-main-sequence star (
20 Myr), we see no
evidence of mass accretion in its optical spectrum. The alternative
interpretation of warm spots due to accretion impacts from a
circum-stellar disc onto the stellar surface seems therefore not
appropriate (but see Strassmeier et al. 2005 for a classical
T Tauri star).
One of the theoretically interesting comparisons we can make is to
see if the model predictions for the latitudinal location of the
active regions (Schüssler et al. 1996) fit well with
observations. Generally, the work of Schüssler et al. and others
involves calculating the trajectory of the magnetic flux tubes
throughout the convective envelope from their source within the
overshoot layer between the radiative core and the envelope up to
the surface where they become visible. Granzer et al.
(2000) expanded this work to pre-main-sequence stars of
masses between 0.4 to 2.4 .
For stars of comparable
rotation rate, the stars with deeper convection envelopes should
have their surface spot activity predominantly at higher latitudes.
Figure 7 shows the calculation results for a model based on the
PW And parameters in Table 1. Its convection zone reaches 60% of the stellar radius and is assumed to behave as a rigid
rotator. The initial field strength at the bottom of the convection
zone is chosen so that the magnetic flux reaches values typical for
large solar active regions (1014 Wb). For more details we refer
to Granzer et al. (2000). The model predicts the majority
of the magnetic flux to surface at a latitude of ,
in
obvious disagreement with the Doppler observations that show most
spots spread between 0-40
with a tendency towards +30
.
Most convincingly, the model does not predict any flux below
a latitude of
30-35
,
in disagreement with our
observation. Some flux tubes are predicted to emerge even at
latitudes as high as +70
.
The question whether it is the
"warm'' features, i.e. the ones near a latitude of +60
in our
image, that are to be compared to the flux-tube models rather than
the cool spots remains to be determined. After all, solar analogy
may not apply and the warmer plage-like features could carry most of
the magnetic flux.
In several of our earlier papers (e.g. Rice & Strassmeier 1998 and Kövári et al. 2004), we showed that the activity on two young main-sequence stars, LQ Hya (K2V) and EK Dra (G1.5V), seemed to run counter to this expectation. This was confirmed for the very young G0-star HD171488 (Strassmeier et al. 2003) along with a number of other G-dwarfs from the literature (see Table 4 in above paper). For a star as cool as LQ Hya (K2), one would have expected the deeper convection envelope and thus higher-latitude spot activity, yet the activity seemed more concentrated to the equator than for the early G dwarfs EK Dra and HD171488, where the activity was more in the form of a polar cap. On the contrary, the images in Donati et al. (2003) for 1998-2001 did show a small polar spot simultaneous with low latitude spots. PW And (K2) is a bit younger and more massive but otherwise comparable to LQ Hya, and shows predominantly equatorial active regions counter to the expectations from models.
Are PW And and LQ Hya directly comparable? PW And is more massive
than LQ Hya, 1.07
versus 0.8
,
it is possibly
also younger,
20-30 Myr compared to
100 Myr of LQ Hya, and marginally cooler,
of 5000 K compared to
5070 K of LQ Hya (each
50-100 K though). Its lithium
abundances are also very similar (
2.8-2.9 dex) and the
rotation periods are even within a few percent. We could therefore
assume similar interior structure and predict the same preferential
flux-tube surfacing latitudes than for LQ Hya (shown in Fig. 8 in
Kovári et al. 2004). These simulations predict a
most probable surfacing latitude of 40
,
with a total range of
possible emergence latitudes of between 30
and 70
.
This
is only in agreement with the observation that neither PW And nor
LQ Hya shows a cool polar spot. The model still fails to predict
truly equatorial spots though, as we mostly see on PW And and on
LQ Hya. However, this may be a meaningless inconsistency because of
the difficulty for the recovery to achieve very accurate latitudes,
i.e. better than one resolution element on the stellar surface.
Also, because the flux tube simulations start in the super-adiabatic
layer beneath the convection zone, the surfacing latitudes could be
questioned because of the questionable applicability of a pure
interface-layer dynamo to very active late-type stars (see, e.g.,
Saar 1998). On the low-mass end of the ZAMS, Mullan &
MacDonald (2001) suggested that even a M6 star should still
have a radiative core and therefore an interface-dynamo component.
At the spectral type of K2 and the mass of 1.07
of PW And,
we would expect the interface component to dominate. Furthermore, as
suggested by Mackay et al. (2004), the values for surface
meridional flow must be increased by around a factor of 10 (
100 m s-1) in order to produce magnetic flux at high
latitudes, which then would make truly equatorial spots even less
likely.
Once stellar models incorporate magneto-convection, stellar
evolutionary tracks may become distinctively different. Mullan &
MacDonald (2001) found that for two stars with the same mass
(valid for masses up to 0.6 ), the magnetic star has a
larger radius and a smaller effective temperature than the
non-magnetic star. So far, we can not quantify this for very young
stars with masses above 0.6
.
However, Ambruster et al.
(2003) speculate that the active, Pleiades-age K dwarfs are
actually more massive than their spectral class indicate. If so, our
interior models used to host the flux tube emergence (cf. Granzer
et al. 2000) may be inappropriate as well and, more
importantly, the flux tube's starting points in the super-adiabatic
layer would be wrong in the first place. We speculate that this
could have a dramatic impact for the predicted surface latitudes of
flux-tube emergence.
Acknowledgements
J.B.R. acknowledges support from the Natural Science and Engineering Research Council of Canada (NSERC). K.G.S. is grateful to the German Science Foundation (DFG) for support under grant STR645/1-1. We both thank Nadine Manset and the other CFHT staff for their continuous support. Thanks also to Dr. Thomas Granzer for computing the flux-tube models for us.
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Figure A.1:
Fe I 639.3-nm line profile data and fits for all
27 phases. Phase is indicated in degrees (0-360![]() |
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Figure A.2:
Fe I 640.8-nm line profile data and fits for all
27 phases. Phase is indicated in degrees (0-360![]() |
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Figure A.3:
Fe I 641.1-nm line profile data and fits for all
27 phases. Phase is indicated in degrees (0-360![]() |
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Figure A.4:
Fe I 643.0-nm line profile data and fits for all
27 phases. Phase is indicated in degrees (0-360![]() |
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Figure A.5:
Ca I 643.9-nm line profile data and fits for all
27 phases. Phase is indicated in degrees (0-360![]() |