The latitude distribution of star-spots on He 699 (original) (raw)

Abstract

In this paper, the latitude distribution of star-spots is analysed for the rapidly rotating G dwarf He 699. An image has been reconstructed from data taken with the William Herschel Telescope on La Palma on 2000 October 8. The predominant magnetic field structure is a decentred polar spot at high latitude, with smaller low-latitude features also present. This result is verified by independent reconstructions using even- and odd-numbered spectra. This work confirms and extends that of Barnes et al., and provides further evidence that there is a correlation between the presence of low-latitude features and the amplitude of the photometric light curve. It is also a further step in the search for activity cycles on young G dwarfs.

1 Introduction

Star-spots are the most easily observed form of magnetic activity on cool stars with an outer convective zone. Using modern indirect imaging techniques such as Doppler imaging, combined with high-precision optical photometry, it is possible to measure the lifetimes, latitude distributions, local rotation rates and surface brightnesses of stellar spots, and any changes in these properties as the stellar magnetic cycle progresses.

The stars that display such activity are rapidly rotating, young, main-sequence stars. In general their rotational periods are less than 1 d, and half of the known population are G and K dwarfs in open clusters less than 100 Myr old. For example, in the Pleiades open cluster G and K dwarfs can exhibit up to 15 per cent photometric modulation because of spots, implying that up to 30 per cent of the stellar surface is spotted (Stauffer et al. 1984).

α Persei is a young open cluster around the star of the same name which is also its brightest member. The distance to α Per is 180–187 pc (O'Dell, Hendry & Collier Cameron 1994), and from main-sequence fitting it has an age of 50 Myr (Soderblom et al. 1993). The distance given by the Hipparcos parallax is 181.5±22.1 pc, while Dzervitis, Paupers & Vansevicius (1994) estimate its distance to be 180±3 pc by using main-sequence fitting to photometry in the Vilnius system. As it is a young cluster, it has many late-type stars with high rotation period typically of the order of 0.5 d (Prosser 1991). It has been of particular interest in the past for both photometric and spectroscopic observations, which have shown that the cluster has a large population of rapidly rotating stars (v sin _i_=90 km s−1) on its lower main sequence (Stauffer et al. 1985; Stauffer, Hartmann & Jones 1989). This rapid rotation is present in α Per in early G to early K dwarfs.

It is only with the advent of multi-line profile cross-correlation techniques, such as least-squares deconvolution, that Doppler imaging can be used to image such faint stars. Barnes et al. (1998) first applied least-squares deconvolution to the α Per G dwarfs He 699 and 520. The image reconstructions from this analysis demonstrate that both stars have high-latitude and/or polar spots and low-latitude features.

In this paper the work of Barnes et al. (1998, 2001) is extended by studying the star-spot distribution on the α Per member He 699, four years after the original observations. He 699 is a rapidly rotating G dwarf with a rotation period of 0.49 d, an equatorial v sin _i_=93.5 km s−1 and an inclination of 52°.5 (Barnes et al. 2001). In Section 2, the principles of Doppler imaging are outlined. In Section 3 the spectroscopic and photometric data, which are the basis of the final images (Section 4), are presented.

2 Doppler Imaging

Doppler imaging is a powerful tool for investigating the distributions and evolution of long-lived stellar surface features. It is important for spot mapping as it has the ability to separate the effects of finite spot lifetimes from those of differential rotation.

Deutsch (1958, 1970) first proposed the usage of line profiles to map the stellar surface. Goncharsky et al. (1977) developed the first inversion technique with minimization, but it was Vogt & Penrod (1983) who coined the term ‘Doppler imaging’. The principles of this technique are well explained in the literature (e.g. Rice, Wehlau & Khokhlova 1989; Collier Cameron 1999).

The underlying principle of Doppler imaging, as described by Vogt & Penrod (1983), is that there is a relation between the wavelength shift within a Doppler-broadened profile and the spatial position on the stellar disc, making it possible to reconstruct an image of the star showing the locations, sizes and shapes of its star-spots.

The effectiveness of the technique of Doppler imaging primarily depends on the ratio of the rotational broadening of the spectral line to the intrinsic linewidth. This imposes a lower limit on the required rotational velocity. Most stars that satisfy this criteria are fast rotators having high activity levels, as rotation is a significant factor in the dynamo process that generates the activity.

An upper velocity limit is imposed by the conservation of equivalent width. As the velocity increases, the lines become shallower which reduces the ‘bumps’ to the point where they become lost in the noise beyond a certain v sin i. In general stars with rotational velocities in the range 20–100 km s−1 are suitable candidates (Bruls, Solanki & Schüssler 1998).

3 Observations

3.1 Combination of spectroscopy and photometry

To attain the best possible reconstruction of the stellar image, it is necessary to combine both spectroscopic and photometric data sets.

In general the photometric light curve of a single star can have one or two minima. The implications of these features for spot modelling have been described by Berdyugina (1998). The deepest minimum in the light curve is caused by the largest activity regions on the stellar surface, for example a large group of star-spots. If a secondary minimum is present, it indicates that there is another smaller active region separated from the primary minimum by ∼180° in longitude.

The main information that can be derived from the photometric light curve is the passage of active regions at low latitudes across the visible hemisphere of the star. It is less sensitive to high-latitude features that are higher than the inclination of the star as these features will be constantly in view. However, without Doppler-imaged spectroscopic data it is impossible to obtain reliably any information on the structure, shape, area or latitude of the star-spots. Photometric light curves do not contain high-order Fourier components required to resolve such fine stellar features because of the effects of limb darkening (Collier Cameron & Hilditch 1997). Unruh & Collier Cameron (1997) noted that the spectroscopic reconstructions have poor latitude discrimination at latitudes 30°.

3.1.1 Spectroscopy

He 699 was observed on the night of 2000 October 8 with the Utrecht Echelle Spectrograph on the 4.2-m William Herschel Telescope at the Roque de los Muchachos Observatory on La Palma.

The detector was an array of two EEV CCDs, each with 2048×4096 13.5-μm pixels. The CCD was centred at wavelength 5000 Å in order 27 of the 31.6 line mm−1 echelle grating. This enabled 61 orders to be extracted giving a wavelength coverage of 4026–7295 Å. The velocity increment per pixel at the detector was 1.6 km s−1, and the full width at half-maximum (FWHM) intensity of the thorium–argon arc calibration spectra was 2.93 pixels, giving a resolving power _R_=63 300.

Table 1 shows the record of observations. A total of 47 spectra of He 699 were obtained on this night, each of 600-s duration. The CCD was exposed to a maximum count of 6000 ADU per pixel in the brightest parts of the image. The 600-s exposure time compares favourably with the 53-s read-out time for the dual EEV CCD in terms of observing efficiency, i.e. the fraction of the time spent collecting photons is above 92 per cent. Following extraction, the signal-to-noise ratio in the continuum of the central order, 114, is 14 per pixel.

Table 1.

Observations of He 699 on 2000 October 8.

3.1.2 Photometry

The light curves were obtained in the V band on the 0.93-m James Gregory Telescope at St Andrews using a Wright Instruments CCD camera mounted at the Cassegrain focus. Observations were made on 2000 October 14, with 60-s exposures. Light cloud was present towards the end of the night. The field of view containing the target and reference stars is shown in Fig. 1.

Figure 1.

Finding chart showing the object and comparison star. Differential photometry was carried out with respect to the star marked 1, while the star marked 2 served as a check. The reference stars are the same as those used in Barnes et al. (1998). The field size is approximately 17×11 arcmin2.

3.2 Data reduction

The one-dimensional echelle spectra were extracted using the Starlink echomop (Mills 1994) and figaro reduction packages through the automated pipeline routine. Pixel-to-pixel variations were removed using flat-field exposures taken with an internal tungsten reference lamp.

Orders were extracted using the echomop implementation of the extraction algorithm developed by Horne (1986). Wavelength calibration was carried out in echomop using thorium–argon arc frames, which were treated in a similar manner to the object and standard frames. Error statistics, based on the readout and photon noise, were propagated through the reduction process by echomop.

Because of the integration time of 600 s, the raw spectra contains many cosmic ray events. Cosmic ray rejection was efficiently implemented before extraction through the use of the figarobclean command, with the rejection threshold set to 10_σ_. The occurrence of hot pixels was deemed to be insignificant and these are accounted for in later stages of this analysis, i.e. in the process of deconvolution.

The automated extraction procedure then subtracted the bias from each frame, cropped each frame, determined the form and location of the stellar profile on each image relative to the trace, subtracted a linear fit to the scattered light background across the spatial profile and performed an optimal (profile and inverse variance weighted) extraction of the order across the full spatial extent of the object-plus-sky region. 61 orders were extracted from each exposure. The blue CCD recorded order number 140 at the blue end of the chip to order number 115 at the red end of the chip, giving wavelength coverage of 402.6 to 501.2 nm with substantial wavelength overlap between orders. On the red chip orders 113 to 79 were recorded, covering the wavelength range of 497.5 to 7295 nm also with good inter-order overlap. Order 114 was positioned on the gap between the two CCDs, but there was no loss in wavelength coverage, because of the inter-order overlap, which can be noted from the wavelength coverage of each chip.

The photometric data were reduced using jgtphot, a software package developed for use with the James Gregory Telescope at St Andrews (Bell, Hilditch & Edwin 1993). The resulting light curves are plotted as differential magnitude values with respect to the marked stars.

4 Image Reconstruction

Careful preparation of the observations is essential to attain the best possible results using Doppler imaging. The steps that have been employed in this analysis are described in the subsequent text of this section.

4.1 Continuum fitting

The general shape of the continuum in the echelle orders is generally well approximated by careful selection of the number of spline knots. Following Collier Cameron & Unruh (1994), a continuum was fitted to the spectrum of a slowly rotating star of similar spectral type, in this analysis HR 6847. This approach has the advantage that the lines do not suffer from rotational broadening, giving a greater number of continuum windows. For least-squares deconvolution the best possible fit to all orders is required. A spline fit with 11 knots was considered to be the best fit for the standard star used.

4.2 The local specific intensity profiles

The spotted star is considered to have two temperatures, one for the cooler spotted stellar surface and one for the non-spotted photospheric part of the stellar surface. Two template stellar spectra were used: an M1 dwarf (HD 1326) with a photospheric temperature _T_=3500 K for the spots, and a G2 V dwarf (HR 6847) with _T_=5750 K for the photosphere. These were deconvolved, using the method of least-squares deconvolution, in the same manner using the same scaled continuum frame, ensuring correct equivalent width.

4.3 Limb-darkening coefficient

The weighted mean wavelength (498.8 nm) was calculated from lines in the line list such that it was weighted with respect to both the line strength and the variance from the standard fit used in spdecon. Linear interpolation was used to obtain a value for the limb darkening from Kurucz (1993a,b) local thermodynamic equilibrium (LTE) models. The limb-darkening coefficients are 0.6336 and 0.6659 for the respective spot and photospheric temperatures of 3500 and 5750 K. In this analysis 10 limb angles were used.

4.4 Least-squares deconvolution

Since He 699 is too faint (m _v_=11.5 and signal-to-noise ratio to apply the conventional technique of Doppler imaging, it is necessary to use least-squares deconvolution.

The least-squares deconvolution method (Donati et al. 1997) can be used to combine the information content of many weak and intermediate-strength photospheric absorption lines in an optimal way, by computing average profiles from thousands of spectral lines simultaneously.

The least-squares deconvolution process can be simplistically described as solving the vector equation

(1)

where

(2)

Here z n represents the best-fitting composite profile which, when convolved with a pattern of line positions and strengths encoded in the transformation matrix α, yields an optimal fit to the observed spectrum. A more detailed mathematical explanation is given by Donati et al. (1997) and Collier Cameron (2001).

A composite profile was deconvolved that was slightly wider than the stellar rotation profile. This allows enough continuum in the least-squares profile to allow an empirical measurement of the signal-to-noise ratio in the adjacent continuum. The maximum improvement in the signal is proportional to the square root of the number of line images used. In this analysis 3550 lines were used. The gain in this analysis is calculated empirically to be approximately 44, representing a substantial improvement in the signal-to-noise ratio.

Telluric (H2O and O2) lines are numerous in the red part of the spectrum and can affect some photospheric lines. In order to minimize the influence of the telluric lines on the deconvolved profile, the line list was edited to mask out the worst affected wavelength ranges. Absorption lines close to Na i D were also removed, along with lines that were very close to the end of each order to minimize edge effects.

The time-series spectra that were produced using least-squares deconvolution are shown in Fig. 2. In the time-series spectra it is possible to identify low-latitude spots and a more slowly varying asymmetry in the line profile which is indicative of a large, off-centred structure at high latitude. This high-latitude structure crosses the disc centre at approximately phase 0.25 to 0.3, coinciding closely with the photometric minimum.

Figure 2.

Time-series spectra for He 699, with the mean profile subtracted. The vertical lines are at the v sin i of He 699, 935.

4.5 Final image reconstruction

Surface images of He 699 were recovered from the spectroscopic line profiles and photometric light curves using the dots surface imaging code (Collier Cameron 1997; Collier Cameron, Jeffery & Unruh 1992). dots is a maximum entropy code for the Doppler tomography of stellar surfaces which is based on the memsys algorithm of Skilling & Bryan (1984). The stellar surface geometry model and integration scheme are described by Collier Cameron (1997).

In this analysis a restricted form of the entropy is used, combining the entropy of the spot image f i and of the photospheric image (1-f i):

(3)

Here m i is the default value that a pixel will have when there are no other constraints imposed by the data. To construct the final image, the values for the spot and photospheric f i are iteratively adjusted to maximize

(4)

This is equivalent to maximizing the entropy S over the surface of a hyper-ellipsoid, of constant _χ_2, in image space. This is bounded by the constraint surface at some fixed value of _χ_2. The Lagrange multiplier, λ, is set so that the final solution lies on a surface with χ_2≃_M, M being the number of measurements in the data set. A more detailed explanation of this and other methods is given by Collier Cameron (2001).

As discussed by Collier Cameron & Unruh (1994), an incorrect treatment of fine-tuning parameters can lead to spurious features. Reconstructions using dots were carried out by varying the values of the radial velocity and equivalent width, while keeping previously established values constant [i.e. _v_ sin _i_ and the rotation period (Barnes et al. 2001)], to minimize the goodness of fit (as measured by _χ_2) to the data. The parameters v sin i and equivalent width are correlated and so a grid containing various combinations of these parameters must be examined.

The spectroscopic and photometric data sets and the resulting maximum entropy reconstructed images are plotted in Figs 3, 4 and 5. The final image is a combination of the spectroscopic and photometric data sets. Independent reconstructions from the even- and odd-numbered spectra are plotted in Figs 6 and 7. The image reconstructions used a stellar surface grid with 90 latitude bands.

Figure 3.

Spectroscopic data fits and maximum entropy fits for He 699, for the observations made on 2000 October 8.

Figure 4.

Maximum entropy image reconstructions for He 699, for the observations of 2000 October 8. Right-hand panel: the mean fractional spot occupancy of the image as a function of latitude. Note: phase runs in reverse to longitude.

Figure 5.

Photometric light curve and maximum entropy fit for He 699, for the observations of 2000 October 8. Top: profile fits; bottom: light-curve fit. The drop-out of data points is a result of the presence of light cloud towards the end of the night.

Figure 6.

Maximum entropy image reconstructions for He 699, for the observations of 2000 October 8 (even-numbered spectra).

Figure 7.

Maximum entropy image reconstructions for He 699, for the observations of 2000 October 8 (odd-numbered spectra).

Included in dots is a weighting factor, β to determine on which data set, spectroscopic or photospheric, higher emphasis should be placed. This weighting factor can be set to between 0 and 1, where 0 implies 100 per cent photometric data and 1 implies 100 per cent spectroscopic data. The value for β for which the _χ_2s of both data sets converge simultaneously was set to 0.97 with a _χ_2=1.25. As discussed by Unruh, Collier Cameron & Cutispoto (1995) and in Section 3.1 of this analysis, the spectroscopic reconstructions have poor latitude discrimination within ∼30° of the stellar equator. However, the converse is true for the photometric light curve, which is particularly sensitive to the structure that is present at low latitudes, although at much lower resolution. The value selected for β has the effect on He 699 of emphasizing the low-latitude structure. The final values for _χ_2 are (for the spectroscopy) and (for the photometry) .

5 Results and Discussion

A maximum entropy image reconstruction of the spot distribution on He 699 is shown in Fig. 4. The mean fractional spot occupancy as a function of latitude is also plotted, clearly showing high latitudes as the main regions of spot coverage.

The lower latitude features are predominantly at a latitude 30° and are elongated in latitude. The reasoning behind this vertical structure is that _v˙_∝cos (latitude) is insensitive to small changes in latitude at the equator. The entropy criterion expresses the uncertainty in latitude by smearing the image north–south at low latitudes.

The observed presence of low-latitude features is in disagreement with the convective overshoot dynamo models which predict the emergence of the magnetic field to be at intermediate to high latitudes (Granzer et al. 2000).

There are also some mid-latitude features present on the left-hand side of the image at approximately a latitude of 60°. These long horizontal features are considered to be an artefact of the imaging process, possibly introducing some smearing between two spots at either end of the distribution. The smearing occurs as a result of incomplete observations at this phase range.

The image obtained by the cross-correlation of even- and odd-numbered data sets (Figs 6 and 7) is shown in Fig. 8. The central vertical band in this plot signifies that there is correlation between the two data sets. The width of the cross-correlation function peak gives the longitude resolution. The cross-correlation plot implies that there is more low-latitude structure present on the surface of He 699 than is shown in Fig. 4. Features that are not in the centre of the image are considered to be spurious features that occur during the incomplete phase coverage of the spectroscopic data. The image that has been reconstructed in this analysis is in good agreement with previous studies of the same star by Barnes et al. (1998, 2001). Barnes et al. (2001) reconstructed surface images using the same methods as in this analysis for data obtained in 1996 October and November. These images show a polar spot and a decenterd polar spot respectively for each of the observations, comparing well with the results of this analysis. An interesting point of comparison between the image reconstructions is present in the low-latitude spot coverage. Whereas the 1996 data sets have significant low-latitude features, there are few present in the current data set. This contrast is also present in the amplitude of the photometric light curve, with the amplitude of the 1996 data set being of a factor of 2 greater than the amplitude of the current data set. The significance of this further verifies that there is a correlation between the presence of low-latitude features and the amplitude of the photometric light curve.

Figure 8.

Image obtained from the cross-correlation of the even- and odd-numbered spectra.

Acknowledgments

This paper is based on data from the William Herschel Telescope and the James Gregory Telescope at St Andrews. The data reductions and image reconstructions were carried out at the St Andrews node of the PPARC Starlink Project. JRB acknowledges support from the PPARC-funded astrotomography rolling grant at St Andrews. SVJ acknowledges support from a PPARC research studentship and the University of St Andrews.

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