Doppler images from dual-site observations of southern rapidly rotating stars – II. Starspot patterns and differential rotation on Speedy Mic

Abstract

We have secured high spatial and temporal resolution spectra of the rapidly rotating K dwarf Speedy Mic (HD 197890) at two sites and a common epoch of observations. The 0.38-d axial rotation period and the V-band magnitude of 9.33 make it a difficult target for Doppler imaging. In order to obtain high signal-to-noise ratio profiles from 300-s exposures, we apply the technique of least-squares deconvolution to the large number of photospheric absorption lines available in each of our spectra. This allows us to derive high-resolution maximum-entropy-regularized Doppler images of the stellar surface. Using these techniques, we also derive radial velocities and accurate projected equatorial rotation velocities which are consistent to within ∼1 km s⁻¹.

Our surface maps reveal one of the most heavily spotted photospheres seen on a rapid rotator, with starspots occurring at all latitudes. At the time of observations, Speedy Mic had no strong polar spot, but it shows spots concentrated in low- and intermediate-latitude bands. We attempt a differential rotation measurement, but lack of sufficient phase coverage allows determination of only a lower limit of 59 d for the time it takes the equatorial regions to lap the polar regions.

We also find variations in the heavily filled-in Hα line which can be attributed to prominences passing in front of the stellar disc. Despite the rapid rotation, the appearance of the same features on consecutive nights of observations shows the clouds to be stable on time-scales of at least a day.

line: profiles, methods: data analysis, techniques: miscellaneous, stars: activity, stars: individual: Speedy Mic (HD 197890), stars: late-type

1 Introduction

Evidence for the young evolutionary status of the late-type star HD 197890 (RA=20^h47^m45.^s02, Dec.=−36.°35′40.″8 J2000.0), or Speedy Mic, is well documented. The ROSAT/WFC all-sky survey detected strong EUV emission from a large flare event in 1990 October (Bromage et al. 1992; Matthews et al. 1994). This was the first detection of magnetic activity on the star. Subsequent measurements by Bromage et al. revealed it to be an ultrafast rotator with a measured projected equatorial rotation velocity, 5 sin i=120 ± 20km s−1. Further determinations have resulted in v sin i estimates of 170±20km s⁻¹ (Anders et al. 1993) and 240±40km s⁻¹ (Matthews et al. 1994). Cutispoto et al. (1997) found a magnitude V_max=9.33 and a B−V colour of 0.93, which is consistent with a K3V spectral classification. It was, however, noted that the corresponding U−B and V−I_c colours were too blue and too red respectively. The differences may be due to HD 197890 being highly active and/or a pre-main-sequence (PMS) object. Favata et al. (1998) find that HD 197890 is in fact very close to the main sequence, indicating a late-PMS or early zero-age-main-sequence status.

Anders et al. (1993) measured the equivalent width (EW) of the Li 6708-Å line, which is blended with the nearby Ca 6717-Å line. They used spectral synthesis to measure an equivalent width of 640±20km s⁻¹ for the blended Li 6708-Å feature. The corresponding range of lithium abundances for a K3V–K5V star is N(Li)=3.75−3.16.

Further studies by Jeffries (1993) revealed the presence of Hα absorption transients similar to those first seen on the K1 dwarf AB Dor by Robinson & Collier Cameron (1986) and Collier Cameron & Robinson (1989a). These transients are thought to be the result of clouds of cool material, analogous to solar prominences, passing at large distances from the rotation axis in front of the stellar disc. The prominences were found to be located at, or above, the corotation radius of the star, and are thought to be trapped in closed magnetic loops.

The short rotation period of 0.380 d (Cutispoto et al. 1997) and the high v sin i combined with close proximity (Hipparcos distance, 44.5±3.2 pc) have elicited much interest. Even as a rapid rotator, Speedy Mic is an extreme example. Despite being well studied, accurate stellar parameters are such as v sin i are still not known with great certainty. Having obtained several sets of time series spectra, we use least-squares deconvolution (Donati et al. 1997) to derive a single high S/N ratio profile from the many photospheric absorption lines available in a single echelle spectrum. Barnes et al. (2000, hereafter Paper I) studied the K0 dwarf PZ Tel in an attempt to measure the differential rotation pattern from sets of maximum-entropy-regularized Doppler images of the stellar surface. Kitchatinov & Rüdiger (1999) have suggested that the rate of absolute differential rotation should be independent of rotation rate and only weakly dependent upon spectral type. If this is the case, and the dynamo process at work on late-type stars drives, or is strongly correlated with, a stellar magnetic cycle (Wilson 1978; Baliunas et al. 1995), we may expect to see a solar-like differential rotation rate on Speedy Mic.

2 Observations

Observations were secured using the Sutherland 1.9-m Telescope at the South African Astronomical Observatory (SAAO), and the GIRAFFE spectrograph on 1998 July 10 and 11. In addition, observations were made on 1998 July 10–14 using UCLES at the Anglo Australian Telescope (AAT). Observations of the target were separated by observations of standard and template stars, and are recorded in Table 1. The 1k×1k tek6 CCD was used at the Sutherland 1.9-m Telescope which, with the grating in the red position, resulted in a central wavelength in the useful extracted data of 6003 Å (range: 5261−7420Å on July 10. On July 11, following a system reboot, the instrumental set-up had to be re-initialized. The resulting configuration was, however, somewhat redward of the July 10 set-up, with the result that five orders in the blue were no longer recorded by the CCD. The shift went unnoticed at the time of observations due to technical/image display reasons. The central wavelength of the useful extracted data was 6167 Å (range: 5261−7420Å). The 2k×4k MITLL CCD chip used in conjunction with UCLES, was windowed to 2088×2496 pixels, and centred on a wavelength of 5307.639 Å (range: 4304−6921 Å).

Table 1.

Observations of Speedy Mic in July.

Weather conditions restricted the number of observations at the end of each night only, at the AAT. We also carried out observations for another programme which required the E79 grating. Hence observations of Speedy Mic on July 11 and 14 used this configuration.

For both data sets, pixel-to-pixel sensitivity variations were removed using flat-field exposures taken with an internal tungsten reference lamp. The worst cosmic ray events were removed at the pre-extraction stage using the figaro routine bclean. The spectra were extracted using echomop, the echelle reduction package developed by Mills (1994). The thorium-argon arc-frames used for wavelength calibration were extracted in conjunction with a target spectrum, and calibrated using this package. The orders were extracted using echomop‘s implementation of the optimal extraction algorithm developed by Horne (1986). echomop propagates error information based on photon statistics and readout noise throughout the extraction process.

2.1 Local intensity profiles

The local photospheric intensity profile is represented by a slowly rotating standard of the same spectral type as the target. Our imaging code uses a two-temperature model and hence requires a local intensity spot profile, represented by a slowly rotating M-dwarf standard. Each pixel on the stellar surface is represented by a combination of pure photospheric and pure spot local intensity profile, scaled according to limb-darkening, foreshortening cosine. The contribution of each local profile in a given pixel to the Doppler-broadened stellar profile is calculated and regularized using the maximum-entropy criterion. An image pixel then takes a value of zero (spot temperature) to unity (immaculate photospheric temperature). For Speedy Mic, the large number of grating settings used precluded use of the same spectral templates. The shape of the stellar profile is, however, dominated by the broadening, so that use of a different local intensity profile of the same spectral type will have negligible effect. The EW of two stars of the same spectral type may also differ slightly due to metallicity differences. Differences in the relative strengths of the spot and photospheric mapping lines will result in only a slightly different spot occupancy. Our Doppler-imaging code also includes the effects of gravity darkening which are, however, small, affecting the range of local flux values by up to 0.84 per cent.

For all grating settings at both sites, we used the K3V standard HD 16160 as the photospheric intensity profile, except for the SAAO July 10 data set where we used HD 125072. All grating settings used the M3V template HD 119850 to represent the spot local intensity profile, except for the AAT/E79 data sets where we used Gl 849 (M3.5V). We corrected all the template spectra to zero velocity by inverting and fitting a Gaussian using the figaro routine emlt.

2.2 Continuum fitting

For a 1k×1k chip, the shape of the continuum in the echelle orders is generally well approximated by a carefully chosen nth-degree polynomial, as approximately only half an order can be recorded across the chip. However, with increasing chip sizes, complete orders can be recorded, and the sinc-function shape of the continuum is not well approximated by a polynomial.

The continua of the slowly rotating photospheric and spot temperature standards can generally be fitted with a spline function. The number of knots required in the spline fit varies from one data set to the next, and in this case eight knots were used on the SAAO data, and 11 knots were used on the AAT data. An object master frame consisting of all the co-added Speedy Mic spectra was divided by the continuum fit to the slowly rotating photospheric standard. This process is similar to that first detailed by Collier Cameron & Unruh (1994). Since the continuum level and shape of Speedy Mic differ slightly from those of the photospheric standard, a low-order (quartic) polynomial was fitted to this divided spectrum to remove residual misfits, and to normalize the spectrum, resulting in a standard or master continuum fit.

Normalization of the Speedy Mic spectra was carried out by dividing each target spectrum by the co-added high S/N ratio master frame, in order to obtain an essentially flat residual. This residual was then fitted with a quartic polynomial to remove residual misfits and any remaining tilt, mainly due to extinction effects throughout the night's observing as the star rises and sets. Slight changes in continuum tilt due to the starspot contribution are also removed in the process. This fit, when multiplied by the master continuum fit, results in the correct continuum for the individual target spectrum in question.

3 Least-Squares Deconvolution

We extract averaged profile information from all lines present in our spectra using our least-squares deconvolution code spdecon, the use of which is documented in Barnes et al. (1998) and Paper I. This technique was developed by Donati et al. (1997) for use with polarimetric Stokes I and V profiles. There are between ∼1000 and ∼3000 photospheric absorption lines available in our SAAO and AAT data sets. We assume that an echelle spectrum contains the same starspot signatures in all the photospheric Doppler-broadened profiles. While the amplitude of the signature may vary from line to line in any given spectrum, the morphology should remain unchanged. Table 2 details the S/N ratio of each data set and the multiplex gain of the deconvolution process. The velocity bin width in the deconvolved profiles is generally set to match the mean velocity bin size of the CCD. In the case of the mitll chip, this corresponds to 1.9 km s⁻¹. Due to the large v sin i of Speedy Mic, and memory constraints imposed by the Doppler-imaging program, the deconvolved profiles for all AAT observations were set to a bin width of 4 km s⁻¹. For the SAAO data sets, a deconvolved profile width of 4.5 km s⁻¹ closely matches the mean CCD pixel width of 4.3 km s⁻¹. Hence the gain values, as quoted in Table 2 for the AAT data sets, are a factor of (4.0/1.9)^1/2 greater than if the CCD mean pixel widths and deconvolved bin width had been matched. For the SAAO data set the effect is small [i.e., (4.5/4.3)^1/2].

Table 2.

Table showing mean input S/N ratio of spectra, output S/N ratio and multiplex gain for least-squares deconvolution. The effective number of lines used for deconvolution is also shown.

4 Derivation of System Parameters

Accurate system parameters, v_rad, v sin i and EW, are required for the purposes of Doppler imaging. As mentioned above, there have been several attempts to measure the v sin i of Speedy Mic, yielding estimates ranging from ∼100 km s⁻¹ to ∼280 km s⁻¹ (including errors). Co-addition of all deconvolved profiles for a given data set reveals a profile asymmetry (even in the SAAO data sets, which afford the greatest degree of phase coverage). This asymmetry is visible in the blue wing of the profiles and fits presented in Fig. 2. There may be some variation in the shape of the asymmetry in the 1998 July 10 data set from the SAAO. This may only be a noise effect, given the poor S/N ratio of the profiles. However, the data sets seem to show little variation in this absorption feature, which always appears at ∼−140 km s⁻¹.

Figure 2.

Profiles and maximum-entropy-regularized fits to data. The profile pixels are approximately equal to the size of the CCD pixels in each case. Left: July 10 and 11 SAAO data, Right: July 11–14 AAT data. The number to the right of each profile is the phase of observation.

It would appear that a background star is contaminating the spectrum. CDS-Catalogue (1999) lists no object within a 4-arcsec radius (the dekker limit, set at the AAT) of Speedy Mic. The galactic coordinates (l=6°.25, b=−38°.25) (CDS-Catalogue 1999) and Hipparcos distance of 44.4±3.2 pc indicate that Speedy Mic is located 27.4 pc below the Galactic plane. The apparently small EW and estimated FWHM of ∼20 km s⁻¹ of the extra absorption feature suggest that it is a star, probably an M dwarf.

Radial velocity corrections for internal shifts of the instruments are made using telluric features (see Collier Cameron 1998 and Paper I). This ensures reasonably accurate radial velocity determinations. There is a slight systematic increase in radial velocity from one data set to the next. Given that different phase ranges are sampled by different data sets taken with different instruments, one would expect some spurious scatter in the radial velocity.

We cannot include the extra absorption feature in the Doppler-imaging process, as it will lead to significant overestimation of the v sin i value. A non-variable feature in the wing of the absorption profile does not make physical sense on a single star, and would result in spurious features in the maximum-entropy reconstructions. As a result, we inflated the size of the error bars in the range −176 to −116 km s⁻¹ on all data sets. This leaves a small amount of continuum blueward of the absorption feature, enabling reliable re-normalization after each maximum-entropy iteration. Since we include a mask which blocks the contribution from the extreme wings of the stellar profile close to the continuum level, nothing blueward of −116 km s⁻¹ contributes to the final image. The rest of the profile appears uncontaminated, but we expect that the resulting images may suffer from slight degradation in latitude discrimination. This will mostly affect features traversing the whole profile (i.e., low-latitude features). However, given the broad nature of the profiles, the spatial resolution and therefore latitude discrimination should not suffer badly from this process.

System parameters which best fit the data are found by minimization of χ² for a range of input test parameters in our Doppler-imaging code dots (see Paper I for full details). Table 3 details the derived system parameters, showing a high degree of consistency between data sets. Given the large spot amplitudes passing through the profiles and the low degree of phase coverage for some data sets, the radial velocity measurements are remarkably consistent. Since we do not always use the same template stars to represent the local intensity profiles, slight variations in the zero-velocity-correction process (see Section 2.1) may also introduce systematic radial velocity differences. Obviously we wish to choose a consistent set of parameters. Combining the complete data set, however, yields υ_rad=−8.0km s−1 and υsin i=128km s⁻¹, in good agreement with the mean values from individual data sets. These values were therefore chosen for image reconstructions.

Table 3.

Best-fitting parameters for each data set. Note that equivalent widths are the least-squares deconvolved EWs of a mean-depth line. A direct comparison can therefore only be made between data sets using either the E79 or the E31 grating (the GIRAFFE set-up is different on both nights). The values are reasonably consistent, given that many of the data sets are incomplete. The main variation in these values is probably a result of distortions of the profiles due to starspots.

Finally, for υsin i=128km s⁻¹, and the appropriate equivalent width for which χ² is minimized, we applied the minimization technique to the axial inclination parameter. This was applied to the combined data sets as shown in Fig. 1. The SAAO July 10 and 11 data gave i=40° although the plot of χ² against inclination shown in Fig. 1 is rather unusual if the inclination is actually 40°. The AAT July 11 and 12 data set give a minimum χ² against inclination curve which is not smooth, making an inclination determination difficult. The SAAO/AAT July 11 and AAT July 13 and 14 data both gave i=55°, and the approximate trend one might expect for a star with a true inclination of ∼55°. Whereas the SAAO data sets are more complete, the S/N ratio of individual profiles is relatively low. The AAT data, on the other hand, suffer from poor phase coverage but have high S/N ratio profiles. The inclination determination from combined dual-site observations is probably dominated by the high S/N data from the AAT.

Figure 1.

Minimum χ² against inclination for various Speedy Mic data sets.

We choose i=55° since the minimized curves are closest to those found from synthetic data sets, and also because the axial rotation period and adopted v sin i values yield an R sin i=0.961. This already indicates a bloated object as Gray (1992) gives a typical main-sequence K3V radius as 0.73 R_⊙. Inclinations of i=45° and 55° lead to radii of 1.36 R_⊙ and 1.17 R_⊙ respectively. In favour of minimizing this exaggerated size, we choose i=55°. Speedy Mic is an extremely rapid rotator, and we caution that a lower inclination is not strictly ruled out. Further, use of the Barnes–Evans relationship in the form given for B−V observations by O'Dell, Hendry & Collier Cameron (1994) yields D sin i=47.618±2.194pc. This in turn yields R=0.90±0.08 R_⊙ and i≥78°. If, however, Speedy Mic is oversized for its age and spectral type, as appears to be the case for PZ Tel (Paper I), the inclination estimate would decrease. An increase in the radius of order 10 per cent would bring the inclination determination into reasonable agreement with the adopted inclination of 55°. Incorrect determination of inclination by ±10° is not generally expected to have serious effects on the positions and morphology of intermediate to low-latitude features. Underestimation of inclination leads to exaggeration of low-latitude spot occupancies, while overestimation of inclination leads to underestimation of the same features. The reverse is true for high-latitude features and polar spots.

5 Results

5.1 Images

Figs 3 and 4 show images of Speedy Mic, formed from the maximum-entropy-regularized inversion of fits to data sets from the SAAO and AAT. Observations were made in conjunction with observations of the 0.94-d-period K0 dwarf PZ Tel (Paper I). As in Paper I, we combined data sets from both sites and also different nights in order to obtain greater phase coverage. Even with the short 0.380-d rotation period of Speedy Mic, phase coverage is not complete in the AAT data sets. There is global similarity between all the images presented here, in that starspots are seen at all latitudes. The surface appears heavily spotted in all maps over the phase ranges of observations. The mean profile from both nights of SAAO data after removal (see below) of the feature in the blue wing, and the immaculate broadened profile, are shown in Fig. 5. A flat-bottomed profile, the hallmark of a strong polar spot, is clearly not present, a fact borne out in the image reconstructions which show no strong polar feature at the time of observations.

Figure 3.

Maximum-entropy-regularized image reconstructions of Speedy Mic from SAAO data. From top to bottom: July 10, July 11 and July 10 and 11 combined. Note that phase runs in the opposite sense to longitude, with phase 0.0 at longitude 360° and phase 1.0 at 0°.

Figure 4.

Maximum-entropy-regularized image reconstructions of Speedy Mic. From top to bottom: July 10 and 11 using SAAO data, July 11 using SAAO and AAT data, ucles with E79 grating, July 11 and 12 using AAT data, ucles with E31 (12th) grating and July 13 and 14 using AAT, ucles with E31 (July 13 and July 14) and E79 (July 14) data. The features cover the same global region on the stellar surface in all images. The same features can be compared in all images, including the reconstruction from the SAAO data alone (tick marks represent the phases of observations).

Figure 5.

Mean profile using all SAAO sepctra with profile in the blue wing removed (see text). Also shown is the immaculate rotationally broadened profile.

There are, however, differences between the maps, which may be partly attributable to the poor S/N ratio of the spectra and lack of phase coverage. Fig. 3 shows reconstructions based upon SAAO data alone which, when compared with the AAT images in Fig. 4, reveal less detail as expected. It is clear that small features of the order of 3° are being resolved in the AAT images. The lower resolution of the SAAO data (GIRAFFE resolution ∼30 000; UCLES resolution ∼50 000) means that some isolated features are not detected, whereas groups of features may be resolved as a single, larger spot (e.g., compare the feature(s) at longitude 30°, latitude 10° in the SAAO and AAT reconstructions). Again, this resolution problem is further compounded by the lower S/N ratio of the SAAO data sets.

It was found that by subtracting the fits to each time series, a residual absorption corresponding to the feature in the blue wing remained. A Gaussian fit to this feature was used to remove it from the time series profiles. The resulting image reconstruction using all the corrected AAT profiles is shown in Fig. 4 (bottom). As expected, the image is consistent with previous reconstructions. It should be mentioned that the use of the complete data (SAAO included) set to form an image at this resolution (i.e., pixel size = 2°×2°) was precluded through lack of sufficient computer memory. Given the lower S/N ratio of the SAAO data sets, it is expected that the AAT data would dominate the reconstruction, still resulting in a sufficient fit to the SAAO data, and little change in the image when compared with Fig. 4 (bottom).

5.2 Differential rotation

In common with previous attempts to measure differential rotation on AB Dor (Donati & Collier Cameron 1997) and PZ Tel (Paper I), we assume solar differential rotation as a function of latitude which can be described as  

1

to first order. For the synodic solar rotation period, the appropriate constants are Ω₀=0.235 d⁻¹ and α=0.052 d⁻¹ (Lang 1992). Donati et al. (2000) showed that by including a solar-type differential rotation model into the imaging code, it is possible to measure the parameters Ω₀ and α by minimizing the fit to the data. Applying a similar technique to the complete set of Speedy Mic data, however, yields inconclusive results. In this case the four different data sets with varying degrees of phase coverage, different S/N ratio spectral data and a masked blue wing appear to bias the goodness of fit to large degrees of differential rotation, both solar and antisolar. It is strongly suspected that simple, single-site data with a relatively consistent S/N ratios are necessary for this technique to yield reliable differential rotation parameters.

The most likely reason for the results obtained here is difficult, if not impossible, to correct for. The deconvolved profile derived from different data sets results in a profile with different mean effective wavelength. Since different numbers of absorption lines are used to derive the profile, it is highly likely that the amplitude of the spot feature differs slightly in each data set. The smearing effect of a spot feature due to differential rotation also changes the width and height of a spot bump over time. The Doppler-imaging code cannot distinguish between a different spot amplitude at a given phase as a result of differential rotational smearing and as a result of comparing different data sets. Also, the choice of local intensity mapping profiles representing the photosphere and spot are arbitrary, and in this case differ from one data set to the next as described in Section 2.1. This is not crucial when combining data sets to form an image, although this effect may result in slightly different spot filling factors being attributed to a given pixel (it is for this reason that Doppler imaging cannot be used to obtain reliable spot coverage estimates) from the different data sets. The correct ratio of these line strengths for each data set should be held, however, if the same template stars are observed for each instrumental set-up as long as the M-dwarf template spectrum accurately matches the starspot contribution to the target spectrum.

Clearly, attempts to determine differential rotation by optimizing the fit to a multi-data-set reconstruction are subject to severe systematic effects. Only the simple (though not without its own systematic effects) method of cross-correlation of constant latitude strips, which relies upon the position of spot features, can be used in this instance. We find that the images are not sufficiently consistent to reliably measure the magnitude of the differential rotation in this way, although the cross-correlation image (Fig. 6, top) clearly rules out extreme values. We therefore resorted to measuring the rms scatter in the the cross-correlation (longitudes 230°−320°) image for the AAT/SAAO July 11 and AAT July 13 and 14 data sets (other cross-correlation ranges between various images yielded larger amounts of scatter). The measured scatter corresponds to an equator-lap-pole time of 59 d for Speedy Mic. This result does not tell us the sign of the differential rotation, although we expect the equator to rotate faster than the poles based upon the solar model, AB Dor and PZ Tel results.

Figure 6.

Cross-correlation images for Speedy Mic image reconstructions. The top image is the cross-correlation performed over longitudes 230°–320° between the AAT/SAAO July 11 image and the AAT July 13/14 image. Although there is reasonable correlation, the images differ sufficiently to allow a reliable estimate of the differential rotation to be made. The bottom plot is the result of cross-correlating the SAAO July 10 and 11 image with the AAT July 11–14 image over all longitudes, demonstrating reasonable consistency of results from both observing sites.

5.3 Prominences

The excess Hα emission from Speedy Mic is clearly very large, with the line being filled nearly to the continuum (Fig. 7), at the times of the observations. As in Paper I, we measured the excess emission using an inactive-standard star subtraction technique following Soderblom, King & Henry (1998). The derived value for the emission EW, after correcting for telluric features in the line is W_»(Hα)=651 mυ. This is derived from the mean profile of frames co-added on July 13 and 14 at the AAT, and may be biased due to incomplete phase coverage. Following the method of Herbig (1985) to determine the ratio of Hα flux to bolometric flux (R_Hα), we find R_Hα=−3.77. A comparison with similar measurements in the Pleiades unsurprisingly shows extremely strong Hα emission, lying near to the peak of the Pleiades distribution at the B−V colour of Speedy Mic (Soderblom et al. 1993).

Figure 7.

Normalized échelle order containing the Hα line. The slowly rotating standard star, HD 16160 was convolved with the mean deconvolved rotation profile from July 13 and 14. The line clearly shows a high degree of chromospheric infilling. The asymmetry in the Hα profile is due to incomplete phase coverage.

Prominences, being relatively cool and diffuse circumstellar clouds, may be visible as absorption transients in low-excitation lines such as Hα. They are visible only if they form in front of the stellar disc, in the observers line of sight. The Hα time series shown in Fig. 8 show a number of transients at the time of observations. This confirms the presence of prominences as reported by Jeffries (1993). Although the S/N ratio in the SAAO data is not high, prominence features which appear on July 10 are also visible on July 11. The feature at phase ∼0.75 in the SAAO July 11 data is perhaps also seen in the July 10 data. Also, there is tentative evidence that the feature seen in the short AAT July 12 time series is also visible in the SAAO July 11 data. Unfortunately, the lack of prolonged blocks of phase coverage at the AAT on July 13 and 14 makes identification difficult.

Figure 8.

Time series spectra for Hα profiles (The Hα line was not available with the UCLES E79 grating). Absorption features appear black in the Hα plots. Several features are identifiable, with the same features appearing in the 1998 July 10 and 11 SAAO data sets, indicating stable prominences over two rotation cycles apart.

It is possible through measurement of the straight-line gradient (in a phase versus wavelength grey-scale plot) d»/d(φ/2π) from each absorption feature, to obtain an estimate of ϖR∗. Details of this procedure are given in Paper I. Results for the measurable features are shown in Table 4.

Table 4.

Distance of prominences above rotation axis. Errors are estimated from measured uncertainties in d»/d(φ/2π).

The inclination of Speedy Mic at 55°, and the large distances from the rotation axis at which prominences are seen, imply that the prominences must be at latitudes of around 35° rather than at equatorial latitudes, because they transit the stellar disc. The location of prominences above the equatorial corotation radius (R_c = 1.7R*) indicates that the field is both closed and complex at large axial distances. A dipolar field would result in the formation of slingshot prominences above equatorial regions only, with magnetic foot-points in both hemispheres. This is clearly not the case for the prominences we observe on Speedy Mic, which suggests that the foot-points of magnetic loops are in one hemisphere. Prominence features such as these have been seen on several other stars (Barnes et al. 1998; Collier Cameron & Robinson 1989a,b; Donati et al. 1999, and references therein; Paper I) at inclinations other than 90°. This does not rule out the possibility of prominences at equatorial latitudes which we are not able to observe.

6 Discussion

The distribution of starspots on Speedy Mic is quite different from that seen on other stars, in that it appears to be much more heavily spotted at intermediate and low latitudes. There is nevertheless still evidence of depletion of spots at intermediate latitudes (30°−40°) in most of the images, although the precise location varies from image to image. Most images of rapid rotators tend to show a polar spot, with the exception of the 1989 image of AB Dor (Kürster, Schmitt & Cutispoto 1994). Subsequent images (e.g. Collier Cameron & Unruh 1994; Unruh, Collier Cameron & Cutispoto 1995; Donati & Collier Cameron 1997) of this object at later epochs have always shown a strong polar feature. Additionally, and perhaps contrary to intuition, the long-term mean light curve showed a minimum brightness at the epoch of the Kurster et al. observations. The lack of a polar spot at the time of observations of Speedy Mic may not therefore be permanent but, as the observations of AB Dor seem to suggest, may be a consequence of a stellar activity cycle. Only further spectral observations will confirm or disprove this hypothesis.

The lower latitude structure is more easily identified in different images, albeit with a greater latitudinal uncertainty. The least-squares deconvolution process removes the effects of blends which would be greatest in the profile wings if one were simply to co-add all the spectral lines. As a result, there should be no significant systematic bias in determination of low-latitude features from blends. There are differences in the higher latitude structure from one image to the next, however, even though high latitudes stay in view much longer and with more profiles contributing information to the image. Within a given image, these features possess more well-defined latitudinal positions (i.e., less smearing), but the reason for the variation in structure from one image to the next is less clear. One explanation may be that there is confusion in resolving the numerous high-latitude features which do not pass into the wings of the profile, but remain relatively ‘clustered together’ around the line centre. In contrast, the signatures of the low-latitude features pass through a greater extent of the profile and are located spatially further apart, thereby reducing this problem.

It must also be stressed that we are confident that the data has not been over-fitted, an additional factor which can add spurious surface features. The data reduction process is never perfect and, combined with incomplete phase coverage (and in this case overblown uncertainties in the blue wing), usually has the effect that the corresponding reduced χ² level is in excess of unity. The degree of non-parallelism between the gradient of the χ² statistic and the gradient of the entropy begins to increase rapidly when noise is being fitted in the data. By stopping the iterations before this point, the data are correctly fitted to the level of noise.

Donati & Collier Cameron (1997) found that small-scale features remained sufficiently consistent over a period of 4–5 to allow both the sense and magnitude of the differential rotation rate on AB Dor to be determined. Our present spectroscopic observations at least indicate stability of starspot groups on this time-scale of observations. This confirms previous photometric studies (Cutispoto et al. 1997) which reveal a stable light curve over a 6-d time-scale. It is worth noting that the current results do not rule out significant small-scale starspot evolution over the five nights of observations, in which case the image reconstructed from all AAT data sets should be treated with some caution. If this goes some way to explaining the differences in the images, then latitude-dependent differential rotation is likely to be a difficult parameter to measure on the fastest rotators.

It may be worth examining whether agreement between the determined stellar inclination and hence radius, when compared with the χ² minimization technique, can be achieved. The B − V and hence effective stellar temperature (T = 4984 K from calibrations made by Flower 1996) are well determined. Starspots may result in an underestimation of stellar temperature, but presumably do not contribute significantly. Our derived value of R sin i = 0.961 is also a well-determined parameter. The stellar evolution models of Forestini (1994) reveal that Speedy Mic is a pre-main-sequence object, lying in the region between a 1-M_⊙ and 1.1-M_⊙ star. From the evolution models, we obtain M = 1.0 M_⊙, _R = 1.03 R_⊙, _L = 0.59L_⊙, age ~ 20Myr, i ~ 69°, _Mboi = 5.39, and _M=1.1M_⊙, _R=1.15R_⊙, _L = 0.74L_⊙, age ~ 15Myr, _i ~ 55°, M_bol = 5.12. Finally, a bolometric magnitude of 5.77 ± 0.15 is obtained from the Hipparcos parallax, taking V = 9.3, and assuming a bolometric correction of −0.295 (Flower 1996). There is apparently a large discrepancy between the observed and theoretical bolometric magnitudes. It is this discrepancy which leads to overestimates of the stellar axial inclination by methods such as the Barnes–Evans relation. The situation may be resolved if we take the model M_bol values as lower limits. The difference can then be explained by the unspotted V magnitude being, for example, 9.0 rather than 9.3. This implies a 30 per cent spottedness for the 1.0-M_⊙ model, or a 50 per cent spottedness for the 1.1-M_⊙ model. The higher inclination value would perhaps better explain the fact that prominences (Section 5) are observed. It is worth noting, however, that 50 per cent spot coverage has been determined for II Peg from TiO bandhead strengths (O'Neal & Saar 1998). Given the extremely rapid rotation of Speedy Mic and therefore presumed high dynamo efficiency, the radius may indeed be as high as 1.17 R_⊙. This leaves one further discrepancy in that the recovered spot occupancy in the images (Section 4) is approximately 4.5 per cent. If spot occupancies of an order of magnitude greater are to be achieved, it can only be assumed that a global uniform distribution of starspots exists, below the resolution Doppler imaging techniques.

The very fast rotation and moderately late spectral type at K3V may mean that comparisons of surface distribution even with other rapid rotators is difficult. Doppler images for single stars of later spectral type than K0V are rare. To date, there are images only for the K2 dwarf LQ Hya (Rice & Strassmeier 1998; Donati 1999) and the K5 dwarf BD +22° 4409 (LO Peg) (Lister, Collier Cameron & Bartus 1999), which fit this criterion. Both these stars are similar to many other earlier type stars in that they exhibit low-latitude/equatorial features and a polar cap, but a relative paucity of spots at some intermediate latitude. Only further images will reveal whether a more distinct and lower latitude band is ever present. If not, the high degree of spottedness may simply be due to extreme magnetic activity due to the short rotation period.

The upper limit placed on the differential rotation shear is not entirely inconsistent with other differential rotation measurements found for rapidly rotating (pre-) main-sequence dwarfs. Without knowledge of the exact magnitude of the differential rotation rate, it is difficult to say whether it is consistent with the Sun, AB Dor (Donati & Collier Cameron 1997), PZ Tel (Paper I) and the theoretical predictions of Kitchatinov & Rüdiger (1999). Donati et al. (2000) measured the latitude-dependent differential rotation rate on RX J1508.6-4423 using pairs of Doppler images. This post-T Tauri star with a period of 0.31 d was found to exhibit an equator–pole lap time of 50 ± 10 d, less than half the solar value. At this age in the evolution of a 1-M_⊙ star, the time-scale for the decrease in moment of inertia is much shorter than the time-scale for the loss of angular momentum through the action of a magnetically coupled stellar wind (see, e.g., Bouvier, Forestini & Allain 1997). The change in the moment of inertia is, however, accompanied by more rapid changes in the stellar radius at this age. The form of internal differential rotation resulting from the redistribution of angular momentum is unknown, and may be different when the star reaches the main sequence.

There have been attempts to measure the differential rotation rate in a number of late-type stars, as discussed briefly in Paper I. Donahue, Saar & Baliunas (1996) have measured the modulation of Caii H and K fluxes in a number of late-type dwarfs. Several observations per week over a 10-yr period have yielded a range of periods for some objects. If the active regions causing the Caii H and K emission occur at different stellar latitudes throughout the stellar magnetic cycle, the corresponding change in the period is due to differential rotation. The range of the observed period, ΔP, thus represents a lower limit to the surface differential rotation. Donahue et al. find that the mass-independent relation holds, where 〈P〉 is the mean seasonal rotation period of the star. In terms of the angular velocity,  

2

which can be written as  

3

In terms of rotation period this is  

4

The results of Donahue et al. yield n = 0.7 ± 0.1, whereas the differential rotation measurements from Doppler images and directly from the Sun with n ≈ 0 are reasonably consistent with those of Hall (1991), where n = 0.15 for RS CVn binaries. The power index, n, in equation (3) is not in fact constant, as shown by the models of Kitchatinov & Rüdiger (1999). For a G dwarf, it is found to vary from a value of −0.56 at the solar rotation rate to a value of 0 at a rotation period of 1 d, with a mean value of n = −0.15. Similarly, for a K5 star Kitchatinov & Rüdiger find values of n = −0.21, 0.05 and −0.04 respectively. The difference of the mean power law for the observed data of Donahue et al. may be due to the fact that in the sample the slowest rotators are represented by K dwarfs, whereas the fastest rotators are mainly G and F dwarfs. Given that the differential rotation results only give an upper limit, the results for Speedy Mic are not inconsistent with results from other Doppler imaging studies. Clearly, a larger sample of reliable differential rotation estimates is needed.

7 Conclusions

Speedy Mic is a highly active star, as evinced by various observations. It exhibits a high degree of coronal activity, as indicated by a (L_x/L_bol) = −3.07 (Singh et al. 1999), this being close to the X-ray saturation limit found for rapid rotators in the Pleiades (Stauffer et al. 1994) and α Persei (Randich et al. 1996) clusters. While the Hα chromospheric emission level is also near the peak of the Pleiades distribution Soderblom et al. (1993), the Doppler images reveal a high degree of photospheric spot coverage. All these observations demonstrate a high degree of magnetic activity, which is perhaps not surprising given the relative youth and rapid rotation of this object.

Speedy Mic has attracted much attention because it is a relatively nearby dwarf with a high projected rotation velocity and short axial rotation period. Since equivalent width is approximately conserved as v sin i varies, the mean profile depth is small. Even with such extreme stellar parameters, our spectral deconvolution code spdecon performs well. Despite the low S/N ratio of the co-added pairs of spectra from 300-s exposures at the Sutherland 1.9-m Telescope/GIRAFFE (SAAO), the multiplex gains of ∼25 produced by least-squares deconvolution allow detection of starspot signatures in the relatively shallow, rotationally broadened profiles. Least-squares deconvolution has allowed us to determine a v sin i measurement to within a precision of ∼1 km s⁻¹, whereas previous measurements of v sin i varied (including errors) from 100 to 280 km s⁻¹. This error is derived from the spread of values found in Table 3 (i.e., 127.8 ± 1.2 km s⁻¹). The level in each parabolic fit yields an error of ∼0.3 km s⁻¹.

The surface maps at once show similarities, and uniqueness, when compared with other Doppler images. This demonstrates the need for the study of a greater sample of stars before any firm conclusions or reasonable models for the latitude dependency of spots can be determined. As such, there is a lack of images for stars of spectral types later than mid-K, with no images of M dwarfs. This restriction is due to the faintness of these objects, and hence the size of telescopes and efficiency of instrumentation. At present, least-squares deconvolution offers the only means to reliably probe later spectral types.

Acknowledgments

JRB thanks Y. C. Unruh (Fond zur Förderung der wissenschaftlichen Forschung, grant number S7302-AST) for help with modifications to our Doppler-imaging code, dots. This paper is based on data collected with GIRAFFE at the Sutherland 1.9-m Telescope (SAAO) and UCLES at the AAT. The data reductions and image reconstructions were carried out at the St Andrews node of the PPARC Starlink Project and the Centro de Astrofisica da Universidade do Porto. JRB was funded by a PPARC research studentship during the course of this work.