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MNRAS 446, 4205­4219 (2015)

doi:10.1093/mnras/stu2398

A multiwavelength study of the M dwarf binary YY Geminorum
C. J. Butler,1 < N. Erkan,2 E. Budding,3 J. G. Doyle,1 B. Foing,4 G. E. Bromage,5 B. J. Kellett,6 M. Frueh,7 J. Huovelin,8 A. Brown9 andJ.E.Neff10
1 2

Armagh Observatory, College Hill, Armagh BT61 9DG, UK Physics Department, Canakkale Onsekiz Mart University, TR-17020, Canakkale, Turkey ¸ ¸ 3 Carter Observatory; and School of Chemical and Physical Sciences, Victoria University, Wellington 6140, New Zealand 4 ESA, Postbus 299, NL-2200 AG Nordwijk, the Netherlands 5 Jeremiah Horrocks Institute, University of Central Lancashire, Preston, PR1 2HE, UK 6 Space Science and Technology Department, STFC Rutherford Appleton Laboratory, Oxon, OX11 0QX, UK 7 McDonald Observatory, 3640 Dark Sky Drive, TX 79734, USA 8 Division of Geophysics and Astronomy, Department of Physics, P.O. Box 48, 00014 University of Helsinki, Finland 9 Center for Astrophysics and Space Astronomy, University of Colorado, Boulder, CO 80303-0593, USA 10 Department of Physics and Astronomy, College of Charleston, Charleston, SC 29424, USA

Accepted 2014 November 11. Received 2014 November 11; in original form 2013 December 5

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ABSTRACT

We review the results of the 1988 multiwavelength campaign on the late-type eclipsing binary YY Geminorum. Observations include: broad-band optical and near-infrared photometry, simultaneous optical and ultraviolet (IUE) spectroscopy, X-ray (Ginga) and radio (VLA) data. From models fitted to the optical light curves, fundamental physical parameters have been determined together with evidence for transient maculations (spots) located near quadrature longitudes and intermediate latitudes. Eclipses were observed at optical, ultraviolet and radio wavelengths. Significant drops in 6 cm radio emission near the phases of both primary and secondary eclipse indicate relatively compact radio emitting volumes that may lie between the binary components. IUE observations during secondary eclipse are indicative of a uniform chromosphere saturated with Mg II emission and an extended volume of Ly emission. Profile fitting of high-dispersion H spectra confirms the chromospheric saturation and indicates significant H opacity to heights of a few per cent of the photospheric radius. There is evidence for an enhanced H emission region visible near phase 0.25­0.35 which may be associated with a large spot on the primary and with two small optical flares which were also observed at other wavelengths: one in microwave radiation and the other in X-rays. For both flares, LX /Lopt is consistent with energy release in closed magnetic structures. Key words: stars: activity ­ binaries: eclipsing ­ stars: flare ­ starspots.

1 I NTR O DUCTION YY Geminorum (BD +32 1582, SAO 60199, Gliese 278c) is a short period (19.54 h) eclipsing binary with two almost identical dM1e (flare star) components. The close binary is a subsystem of the nearby Castor multiple star (YY Gem = Castor C), at a distance of 14.9 pc. The binary nature was discovered in 1916 (Adams & Joy 1917) and the first spectroscopic orbits were given by Joy & Sanford (1926). As the brightest known eclipsing binary of the dMe type, YY Gem is an important fundamental standard for defining the low-mass main-sequence mass­luminosity and mass­radius relationships (Torres & Ribas 2002). However, it was clear already from Kron's (1952) pioneer study that there are significant sur-

E-mail: cjb@arm.ac.uk

face inhomogeneities (starspots) affecting the observed brightness of both components, likely to complicate data analysis. YY Gem was the first star, after the Sun, in which such maculation effects were demonstrated. Before we can accurately define the intrinsic luminosities of such stars we need to clarify the scale of these effects. This is also significant for comparing the photometric parallax with direct measurements, such as that from Hipparcos (Budding, Rhodes & Sullivan 2005). The system was reviewed by Torres & Ribas (2002) and Qian et al. (2002), the latter concentrating mainly on apparent variations of the orbital period. Torres & Ribas (2002) gave revised values for the mean mass and radius of the very similar components as (solar units) M = 0.5992 ± 0.0047, R = 0.6191 ± 0.0057, with mean effective temperature T = 3820 ± 100 K, as well as an improved parallax for the system of 66.90 ± 0.63 mas. From such results, Torres & Ribas argued that there had been a tendency to adopt

C 2014 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society


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Table 1. Multiwavelength observations of YY Gem, 1988 March. Institute ISAS-Tokyo VILSPA-ESA Mauna Kea Mauna Kea McDonald Obs. JILA Boulder Crimea Obs. Observer Bromage Foing Butler Doyle/Butler Frueh Brown Tuominen Facility GINGA IUE UKIRT 0.6 m 0.9 MCD VLA 2.6 m Shajn Range ME X-rays UV IR UBVRI UBVRI 5 and 1.4 GHz UBVRI + H

systematically erroneous parameters for dwarf stars comparable to YY Gem, with wider implications for low-mass stars in general. Determination of the precise structure of these stars, in view of the absence of definitive information on their intrinsic, spot-free, luminosities, is still rather an open question. Torres & Ribas (2002) and Qian et al. (2002) revised the work of Chabrier & Baraffe (1995), giving radiative core radii of about 70 per cent, leaving the outer 30 per cent to account for the convective zone. The strong subsurface convective motions give rise to large-scale magnetic fields that produce large starspots (cf. Bopp & Evans 1973). Moffet first reported large flare events, and, in subsequent studies, YY Gem has been shown to be very active (Lacy, Moffett & Evans 1976; Moffett & Barnes 1979; Doyle & Butler 1985; Doyle & Mathioudakis 1990; Doyle et al. 1990). Doyle et al. (1990) have previously described photometric observations of repetitive, apparently periodic, flares on YY Gem which were observed during this programme. More recently, Gao et al. (2008) modelled such periodicity effects on the basis of magnetic reconnection between loops on the two stars generating interbinary flares. Fast magnetoacoustic waves in plasma trapped in the space between the two components are thought to modulate the magnetic reconnection, producing a periodic behaviour of the flaring rate. Doyle et al. (1990) had previously suggested filament oscillations. Several authors (see Vrsnak et al. 2007) have subsequently reported solar filament oscillations of similar duration to those suggested on YY Gem. Multiwavelength observations of flare activity on YY Gem were initiated by Jackson, Kundu & White (1989) using radio data from the VLA (see also, Gary 1986). Stelzer et al. (2002)usedthe Chandra and XMM­Newton satellites in simultaneous observations of the X-ray spectrum, while Saar & Bookbinder (2003) carried out far-ultraviolet observations. Impulsive UV and X-ray phenomena, taken to be essentially flare-like, were shown to be orders of magnitude stronger than those occurring on the Sun (Haisch et al. 1990). Tsikoudi & Kellett (2000), reviewing X-ray and UV observations of the Castor system, reported a large (EXOSAT) flare event with total X-ray emission estimated as 7 ± 1 â 1033 erg. Their comparison of X-ray and bolometric heating rates pointed to strong magnetic activity within hot coronal components. In this article, we concentrate on the multiwavelength campaign initiated from the Armagh Observatory in 1988 (Butler 1988). Our general aim is to bring together results of some work, previously reported (e.g. Tuominen et al. 1989; Doyle et al. 1990;Butleretal. 1994; Butler, Doyle & Budding 1995; Budding et al. 1996) with contemporaneous satellite and radio observations thereby allowing an overview of the campaign. One specific intention concerns the various light curves and their analyses in terms of standard eclipsing binary models that include photospheric inhomogeneities. In addition, we present hitherto unpublished ultraviolet (IUE), radio (VLA) and X-ray (Ginga) data, which should be relevant to subsequent studies. A number of optical flares were observed but only two of these were seen at other wavelengths, one in X-rays by Ginga and the other in the microwave region by the VLA. 2 T HE 1988 MUL T IWAVELENGTH CAMP AIGN ON YY GEMINOR UM In late February to early March of 1988, YY Gem was the object of a coordinated multiwavelength campaign to observe the star simultaneously in radio, near-infrared, X-rays, UV and optical radiation (Butler 1988). The principal objectives of this programme were: (i) to provide multicolour photometry of the light curve in MNRAS 446, 4205­4219 (2015)

order to establish (a) the distribution of surface inhomogeneities (starspots), and (b) the temperature difference of these inhomogeneous regions from the normal photosphere. (ii) To provide high time resolution photometry in V and K during the eclipses in order to check on possible surface inhomogeneities by `eclipse imaging' ­ i.e. examining any small disturbances observed in the light curve during eclipses. (iii) To use optical spectroscopy, X-ray and radio monitoring to probe the outer atmospheres of the components and assess any topographical connection between photospheric spots and bright chromospheric or coronal regions. (iv) To monitor flares on YY Gem in as many separate wavebands as possible in order to check their energy distribution and constrain models. The programme involved the facilities and observations given in Table 1. Several other organizations offered support to the campaign, but unfortunately a number of these were unable to provide useful data due to poor observing conditions. In Fig. 1,weshowthe overlap between observing facilities that were successful in obtaining data. Seven major facilities provided the most relevant data and six of these were operative on March 5 and 6, with a few hours of overlap on those two days; and to a lesser extent on March 4.

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3 UBVRIK PHO T OMETR Y 3.1 Photometric techniques To achieve the photometric aims, we required broad-band photometry covering as much of the optical and infrared regions as possible. We therefore operated two telescopes simultaneously: the University of Hawaii 0.6 m telescope on Mauna Kea and the neighbouring 3.8 m United Kingdom Infrared Telescope (UKIRT). Some additional observations were contributed by Marion Frueh of McDonald Observatory, Texas. All observers were alerted to a particular problem associated with photometry of YY Gem, namely that the close proximity (separation 71 arcsec) to YY Gem of the bright star Castor (A2 type, V 1.6) makes it difficult to obtain repeatable and consistent sky background measurements, particularly in the U and B bands, where YY Gem is weak and Castor bright. Kron (1952) commented that, in the vicinity of YY Gem, 30 per cent of the monitored blue light originated with Castor and only 70 per cent with YY Gem itself (Budding & Kitamura 1974). For this campaign, in order to reduce the errors associated with scattered light, observers were requested to take the mean of two adjacent sky areas, one to the east and another to the west of YY Gem. Frequent reference to three nearby comparison stars: BD 32 1577, BD 31 1611 and BD 31 1627, together with standard transformation equations and mean extinction coefficients allowed a photometric accuracy 0.01 mag to be achieved. Lists of the standards used, the colour equations derived and the reduced photometric observations are given in the supplementary electronic tables (http://star.arm.ac.uk/preprints/2014/654/).


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Figure 1. Time-line of various facilities used in the multiwavelength campaign of 1988.

3.2 UBVRIK photometry from the 0.6 m telescope on Mauna Kea The UBVRI photometry, from the 0.6 m telescope and Tinsley Photometer, was standardized to the Johnson UBV and Cape/Kron RI systems using equatorial and Southern hemisphere standards from Cousins (1980, 1984). The following mean extinction coefficients were adopted: U = 0.22, B = 0.16, V = 0.12, R = 0.10 and I = 0.07. Due to the manual operation of the Tinsley photoelectric photometer, time resolution for a single complete UBVRI set of measurements was restricted to several minutes. This was satisfactory for the slower variations associated with eclipse effects and the rotational modulation of spots, but unsuitable for flare monitoring. Therefore, two modes of observation were used on this telescope: (1) UBVRI photometry, with low time resolution ( t 2 m) during eclipses and approximately once per hour at other phases, and (2) continuous U band monitoring at (mainly) out-of-eclipse phases. Some of the latter data were reported on by Doyle et al. (1990). Because the 0.6 m telescope was set manually it seems likely that small errors in positioning of the background comparison region could be responsible for some of the scatter in the U and B light curves which increases at shorter wavelengths. However, small, unrecognized, flares would also contribute to the scatter. In Fig. 2, we show the UBVRI light curves for YY Gem from the combined data obtained on 1988 March 2­7 with the 0.6 m telescope.

3.3 BVK photometry with UKIRT on Mauna Kea The UKIRT was scheduled to observe on four half-nights, during which two primary and two secondary eclipses occurred. Continuous monitoring in the K band simultaneously with V or B was made possible with a dichroic filter and visual photometer (VISPHOT), a photoelectric photometer set up to monitor the reflected optical beam. A nodding secondary mirror provided rapid and repeatable background correction. As spot modulation effects are relatively more prominent in V and flare effects in B, it was decided to monitor

Figure 2. Hawaii 0.6 m UBVRI light curves of YY Gem.

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Figure 3. UKIRT-BVK light curves of YY Gem.

in K and V during eclipses and in K and B at out-of-eclipse phases. Useful coverage of the out-of-eclipse phases by UKIRT turned out to be quite limited, however. The autoguider was not functional at this time, resulting in occasional guiding errors. We used the mean atmospheric extinction coefficients given above in carrying out the differential reductions (see also Krisciunas et al. 1987). A selection of standards suitable for both optical and infrared photometry was made for the determination of the colour equations. One of these (Gleise 699, Barnard's star) was believed to be in the declining stage of a flare during observation on 1988 March 4. Further details are given in the supplementary electronic tables. In Fig. 2, discrepancies can be seen at some phases in the B light curves, but there is generally good agreement in V. This is consistent with the greater influence of background irregularities and small flares at shorter wavelengths. In Fig. 3, we show the UKIRT B, V and K observations. The two broad-band photometric data sets (Hawaii 0.6 m and UKIRT) are comparable over common phase intervals, although the less-scattered UKIRT data have poorer phase coverage. The cool-spot hypothesis receives support from the smaller amplitude of the out-of-eclipse variation at the longer wavelengths. This is quite noticeable in the UKIRT K band, but less so in the 0.6 m I-band data.

data for similar reasons). Transformations to the Johnson UBVRI system relied on observations of 17 stars listed by Moffat & Barnes (1979) and the three local standards listed in Section 3.1 (Butler 1988). The following mean extinction coefficients were employed: U = 0.57, B = 0.29, V = 0.17, R = 0.12 and I = 0.09. As at Mauna Kea, we had transformed to the Kron/Cousins R,I system, rather than Johnson's, the McDonald data were further transformed to the Kron/Cousins system using equations formulated by Bessell (1979). The UBVRI observations of YY Gem on the three nights 1988 March 4­6 are listed in the supplementary electronic tables. Though no very large optical flares were recorded at McDonald during this campaign, a flare of approximately 0.6 ma in U was observed simultaneously with a substantial increase in the 6-cm microwave flux recorded by the VLA.

4 M ODELLING THE M A U N A KEA V LIGHT CUR VES The idea of large-scale inhomogeneities in the local surface brightness of stars is not new, and, after a period of dormancy, was revived in the mid-twentieth century, particularly after discussion of possible causes of stellar brightness variation by the careful photometrist Kron (1947, 1950, 1952). Subsequently, evidence has accumulated from across the electromagnetic spectrum of magnetodynamic activity effects on cool stars of a few orders of magnitude greater scale than that known for the Sun. These effects include large areas of the photosphere (spots) with cooler than average temperature. This subject formed the theme of IAU Symposium 176 (Strassmeier & Linsky 1996), and was reviewed in chapter 10 of Budding & Demircan (2007), which outlines the methodology pursued in this paper. Of course, the use of uniform circular areas to model maculation effects is a physical oversimplification, but it is a computational device that allows an easily formulated fitting function to match the data to the available photometric resolution. Even with the highest signal-to-noise ratio (S/N) data currently available, a macula less than about 5 in angular mean radius produces light-curve losses only at the millimagnitude level. Whether a given maculation

3.4 UBVRI photometry from McDonald Observatory In order to increase the probability of obtaining simultaneous optical photometry with radio, X-ray or ultraviolet observations of flares, YY Gem was placed on the schedule for the 0.91 m telescope at McDonald Observatory, Texas on 1988 March 4­6. The photoelectric McD photometer was equipped with a cooled EMI 9658A photomultiplier. With sequential exposures through U, B, V, R and I filters of the Johnson system, a time resolution in each waveband of approximately 20 s was obtained. Unfortunately, a computer crash caused the loss of the electronically recorded data and it was necessary to manually type in the raw photon counts from the printed output (as had also been necessary for the UKIRT MNRAS 446, 4205­4219 (2015)


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region's shape is circular, or of uniform intensity is unfortunately not recoverable. Other indications on surface structure however, such as come from the more detailed Zeeman Doppler Imaging techniques for example (Donati et al. 2003), tend to support somewhat simple and uniform structures to maculae, and there are supporting theoretical arguments, related to magnetic loop parameters. But it is also true that different data sources (e.g. spectroscopy and photometry) and analysis techniques (e.g. minimum entropy or information limit) do not always lead to one clear and consistent picture (Strassmeier 1992; Radick et al. 1998; Petit et al. 2004; Baliunas 2006). Even if real maculae are neither circular nor uniform, there will be certain mean values that can represent their (differential) effect to the available accuracy. Such mean values, as used in sunspot statistical studies, have validity in tracking and relating data to other activity indicators. So while the surface structure of active cool stars may well be more complicated than we can presently discern, the approximations available can summarize observational findings and stimulate efforts towards more detailed future studies. Note that the differential maculation variation, that historically caught the attention of observers, should not cause the steady background component to be disregarded. The latter, coming from a simultaneously extant, uniform, distribution of maculae, can have quite a significant effect, as noted by Popper (1998) and Semeniuk (2000), who derived systematic differences between the distance estimates of certain cool close binaries, obtained photometrically, with those from the Hipparcos satellite. They found that the mean surface flux of such cool binaries was too low to allow them to fit with the normal correlation from their B - V colour indices and concluded that a uniform distribution of dark spots could account for the difference. Budding et al. (2005) confirmed these results and estimated that the mean surface flux could be underestimated up to a level of about 30 per cent in cases of close binaries similar to YY Gem (see also Torres & Ribas 2002). Computer programs that model the light curves of eclipsing variables with surface inhomogeneities were discussed by Budding & Zeilik (1987). This software was developed into a user-friendly format by M. Rhodes, available as WINFITTER from http://home.comcast.net/michael.rhodes/. The adopted technique is an iterative one that progressively defines parameters affecting light curves, beginning with those relating to the binary orbit, and subsequently including those controlling the extent and position of surface spots. The procedure involves a Marquardt­Levenberg strategy for reducing 2 values corresponding to the given fitting function with an assigned trial set of parameters. If an advantageous direction for simultaneous optimization of a group of parameters is located then that direction can be followed in the iteration sequence (`vector search'), otherwise the search proceeds by optimizing each parameter in turn. For a linear problem, 2 minimization is equivalent to the familiar least-squares method (cf. Bevington 1969), but the parameters in our fitting function are not in a linear arrangement, preventing an immediate inversion to the optimal parameter set. However, the 2 Hessian is calculated numerically for a location in parameter space corresponding to the found minimum. If the location is a true minimum with all Hessian's eigenvalues positive, useful light on the determinacy of each individual parameter is thrown. An important issue is the specification of errors. Photometric data sets usually permit data errors to be assigned from the spread of differences between comparison and check stars. We have adopted representative errors based on the observation that the great majority of data points for YY Gem are within 20 per cent of the mean. Uniform error assignment weights the fitting at the bottom
Table 2. Parameters used in or derived from the solution for the V light curve. 0.6 m V light curve model Ratio of luminosities Ratio of masses Ratio of radii Coeff. limb dark. Radius of primary Orbital inclination ( ) L1 /L2 M1 /M2 R1 /R2 u1, 2 R1 /A i 1.02 ± 0.005 1.0 1.0 ± 0.008 0.88 0.154 ± 0.001 86.0 ± 0.11 Temp. decr. 0.84 0.84 1.13 0.01 1.26

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Three-spot model for V light curve Long. 94 8 . 250 0 . 342 7 . Lat. -16 4 5 2 1


Radius 16 4 . 10 0 . 12 3 .

Datum error l Goodness of fit 2 /

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of the minima more highly which is beneficial in fixing the main parameters as these regions of the light curve have relatively highinformation content. A check on the validity of such error estimates comes from the corresponding optimal 2 values. The ratios 2 / , where is the number of degrees of freedom of the fitting, can be compared with those in standard tables of the 2 variate (e.g. Pearson & Hartley 1954) and a confidence level for the given model with the adopted error estimates obtained. If 2 / is quite different from unity, we can be confident that either the data errors are seriously incorrect, or (more often), the derived model is producing an inadequate representation for the available precision. This relates to another well-known aspect of optimization problems, i.e. that while a given model can be adequate to account for a given data set, we cannot be sure that it is the only such model. This is sometimes called the `uniqueness' problem, and, in its most general form, is insoluble. However, if we confine ourselves to modelling with a limited set of parameters and the Hessian at the located 2 minimum remains positive definite for that set with the 2 / ratio also within acceptable confidence limits, then the results are significant within the context. If either of these two conditions fail, then there are reasonable grounds for doubting the representation. Provided the conditions are met, the Hessian can be inverted to yield the error matrix for the parameter set. The errors listed in Tables 2 and 3 were estimated in this way. To speed up a full examination of parameter space, the data can be binned to form normal points with phase intervals typically 0.5 per cent of the period. The residuals from the eclipse model were first fitted with a simple two-spot model (for procedural details see Zeilik et al. 1988), but this was later revised in a fitting that included a bright plage visible near primary minimum, on the basis of additional evidence. The high orbital inclination of YY Gem (86 ) results in poor accuracy for the spot latitude determination. Spots of a given size at the same longitudes but in opposite latitude hemispheres would generally show similar light-curve effects. Attempts to derive a full spot parameter specification simultaneously tend to run into determinacy problems: a low-latitude spot might be moved towards the pole in the modelling, but a quite similar pattern of variation could then be reproduced by a corresponding decrease in size at the same latitude. On the other hand, spot longitudes were always fairly well defined. MNRAS 446, 4205­4219 (2015)


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Table 3. Relative intensities of dark spots in V, R, I, K and the derived temperature difference between the spots and the photosphere. Filter eff (å) 5550 6800 8250 22 000 Limb-darkening coefficient 0.88 0.73 0.60 0.33 Mean intensity 0.20 0.24 ± 0.04 0.73 ± 0.04 0.30 ± 0.08 Spot temp. diff. (K) TP - TS Method 1 Method 2

V RC IC K

630 200 1000

420 280 1320

We adopted the following procedure. (1) Fit the eclipses for the 0.6 m V light curve by adjusting the main geometrical parameters, using the photospheric temperatures listed by Budding & Demircan (2007, table 3.2). A normalization constant also appears as a free parameter for any given light curve. An initial value is usually adopted from setting the highest measured flux to a nominal value of unity. Subsequent optimization will yield a better representation for this. (2) Specify initial values for the longitudes, latitudes and radii of spots, as in Zeilik et al. (1988). (3) Estimate the relative intensity of spots in the V band (compared to the unspotted photosphere). We assigned a preliminary value of 0.2, assuming blackbody emission and an approximate mean temperature difference of 500 K between spots and photosphere Tp - Ts . The low value of entails that the spot size is not so sensitive to the adopted temperature decrement for the V light curve. Since the V spectral region lies some way to the short-wavelength side of the Planckian peak at the adopted temperature (3770 K), only in the infrared will light curves start to show a noticeably decreased maculation amplitude. This could be simulated by a smaller spot, but that would not be consistent, of course, with radii of the same feature obtained in V. In other words, the weight of information in the shorter wavelength photometry goes towards fixing the spot size: at the longer wavelengths it goes towards determining the temperature. (4) Optimize first spot longitudes, then radii and (possibly) latitudes, using CURVEFIT. (5) Retrofit the eclipse curve for the stellar parameters with the spot modulation removed. Final parameters from this procedure are given in Table 2. Adopting the radial velocity analysis of Torres & Ribas (2002) and the standard use of Kepler's third law leads to a separation of the two mass-centres as 3.898 R , or that the radius of either star is some 0.601 R . This is slightly less than the value Torres & Ribas calculated due to the difference in the two light-curve fitting results. Our masses (0.600 M ) however are in almost exact agreement with those of Torres & Ribas, with our own (slightly lower) value for the orbital inclination, i.e. the two sets of results are within their error limits of each other. The inclination listed in Table 2 derives from the fit to the binary light curve, however, in the separate fitting that allows spot parameters to be estimated, a mean value for the inclination has been adopted. This allows the full weight of the difference curve data to go into the determination of the geometrical parameters of the starspots. The final value of 2 / given at the bottom of Table 2 is a little high for the adopted accuracy of the data, as mentioned above. The photometric modelling of these V data, taken in isolation, should then be regarded as a feasible or coarse representation of reality. None the less, it is in keeping with the other results discussed in the following sections, and the combination of evidence gives added significance to the model. Note that this modelling alone cannot distinguish between spots on the primary and secondary components, particularly in the present case with an essentially identical pair. A given spot can be situated on the primary at the longitude indicated in Table 2, or on

the secondary at that longitude ± 180 . The longitudes of the darkened regions are about 5 and 20 from quadrature, i.e. they reach their maximum visibility when the two stars are not too far from greatest elongation. This recalls Doyle & Mathioudakis' (1990) finding that flares tend to occur close to quadrature phases, which, in turn, suggests a topological connection between flaring regions and cool photospheric spots.
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5 M ODELS FOR T HE B , R , I AND K LIGHT CUR VES AND TEMPERAT URES O F S PO TS Following the determination of basic parameters for the V light curve, we processed the light curves from the other filters, assuming the same geometry. We verified that the B, R, I and K light curves could all be fitted by eclipses having closely similar numerical values of the main parameters to those of the V. The large scatter of the U-band (0.6 m) data prevented their detailed analysis in this way. In our final-spot models for the B, R, I and K data, we adopted longitudes, radii and latitudes of the spots which were the same as for the V, and assumed that only the limb-darkening and mean surface brightness of the spots, relative to the unspotted photosphere, differed. At a given wavelength the optimized value of corresponds to a spot mean temperature through the implicit relation (1). The photometric information content thus directs us towards the temperature estimate. With limb-darkening coefficients at the mean wavelength of the Cape/Kron R, I and Johnson B and K bands taken from van Hamme (1993), we determined the relative surface brightness of the spots in the different photometric bands using CURVEFIT. We could then estimate the difference in temperature of the spotted regions from the unspotted photosphere. The mean surface brightness becomes adjustable in the fitting of the infrared light curves. The geometrical parameters are held constant to allow the fitting to concentrate only on the flux ratio for the infrared data sets. Th