A&A 383, 210-217 (2002)
DOI: 10.1051/0004-6361:20011693

On X-ray variability in ROSAT-PSPC observations of F7-K2 stars

A. Marino1 - G. Micela2 - G. Peres1 - S. Sciortino2


1 - Dipartimento di Scienze Fisiche e Astronomiche, Sez. di Astronomia, Università di Palermo,
Piazza del Parlamento 1, 90134 Palermo, Italy
2 - Osservatorio Astronomico G. S. Vaiana, Piazza del Parlamento 1, 90134 Palermo, Italy

Received 27 August 2001 / Accepted 27 November 2001

Abstract
We have analyzed the X-ray variability of dF7-dK2 stars in the solar neighborhood detected with the pointed ROSAT-PSPC observations. Our data base is the sample of all stars listed in the CNS3 catalog (Gliese & Jahrei$\beta$ 1991) having a B-V color between 0.5 and 0.9; it includes 70 pointed observations of 40 distinct stars or multiple systems. We have applied the unbinned Kolmogorov-Smirnov test on all X-ray photon time series of our sample: only 10 observations relative to 8 distinct stars are variable at a confidence level greater than 99$\%$ and 4 of them belong to multiple systems. For the subsample of 9 stars observed both at the beginning and at the end of the mission, we can study the variability on time scale of years and compare amplitude variations at short and long time scales. Our analysis suggests that, for these stars, the X-ray variability is more likely on longer time scale. All the stars variable on long time scale, and not on short time scale, are relatively quiet and similar to the Sun, suggesting that the variations may be due to cycles. The comparison of our results with those previously obtained for dM stars shows that the amplitude of variability of X-ray emission from dF7-dK2 stars is smaller than that observed in dM stars.

Key words: stars: coronae - stars: late-type - X-rays: stars - galaxy: solar neighbourhood


1 Introduction

The Sun is the only star for which X-ray variability is extensively studied on virtually all time scales (e.g. Vaiana et al. 1973; Vaiana & Tucker 1974; Kreplin et al. 1977; Zombeck et al. 1978; Withbroe et al. 1985). The soft X-ray emission of the Sun is highly variable on time scales ranging from minutes to years. Moreover, observations of the Sun have high spatial, spectral and temporal resolution, and span a much longer time interval than stellar observations. Resolving the structure of the solar corona, presently down to $\sim $700 km, allows us to identify directly the sources of X-ray emission and to relate variations of the global solar X-ray flux (e.g. Kreplin et al. 1977; Kahler & Kreplin 1991; Donnelly & Bouwer 1981; Peres et al. 2000; Orlando et al. 2001) to the originating structures on the Sun.

Since no equivalent studies are possible for other stars, X-ray variability studies provide a powerful tool to test the properties of coronae of late-type stars and to infer the presence of solar-like phenomena. We know that magnetic phenomena largely determine the level of solar coronal activity; by analogy, we expect the same to hold for solar-type stars. Solar observations are the benchmark against which to test dynamo models: these models are calibrated on the Sun. While the Sun offers unique observational details and it is a very fruitful test for theory, it suffers the difficulty that relevant stellar parameters that are supposed to affect model prediction cannot be varied. Hence comparing the Sun with late-type stars with different masses, rotation rates and evolutionary states will help us in understanding how the dynamo process depends on basic stellar parameters.

The systematic analysis of the X-ray variability of nearby dM stars as observed with ROSAT-PSPC (Marino et al. 2000, hereafter Paper I), showed that variability is a general property of these stars on all time scales we have explored. The amplitudes of these variations are independent from both stellar X-ray and visual luminosity. Compared to properties of solar X-ray variability our results suggest that the amplitude distribution of X-ray variability in dM stars is consistent with the analogous distribution for solar flares. The comparison of our data with those obtained with Einstein IPC showed that long term variability (on time scales longer than 10 years), if present, must be of smaller amplitudes than the short term variations observed in the ROSAT X-ray light curves (Paper I).

Coronal and chromospheric activity are known to be related (Schrijver et al. 1992). The observations of the Ca II H and K lines has allowed to monitor the chromospheric activity of solar-type stars in detail (Wilson 1978; Baliunas & Vaughan 1985; Baliunas et al. 1995). These data show a variety of behaviors which can be basically reduced to three different types: mostly old quiet stars like the Sun show a cyclic behavior, with periods ranging from about 3 to 15 years or more; young active stars usually show a chaotic behavior with no obvious periodicities; the remaining stars appear to be constant, with no indication at all of an activity cycle. The X-ray emission of the stars in the spectral range dF7-dG9 observed with EINSTEIN Observatory (Maggio et al. 1987) resulted well correlated with their cromospheric Ca II H-K line emission.

In this paper we present a study of X-ray variability of nearby dF7-dK2 stars detected with ROSAT-PSPC (Pfeffermann et al. 1987; Trümper 1992) pointed observations. Since, the sensitivity of ROSAT-PSPC is much higher than that of the Einstein IPC, we can study variability of smaller amplitudes and in more X-ray quiet stars. Furthermore, a better time coverage is reached since the typical observation live times with ROSAT are longer than with Einstein. ROSAT observations (similary to Einstein ones) are fragmented in time segments of typically a few thousand seconds.

Our paper is organized as follows: in Sect. 2 we present our sample of dF7-dK2 stars, the X-ray data, and their analysis. The basic results are given in Sect. 3. In Sect. 4, we draw our conclusions.

2 Observations and data analysis

2.1 The sample

Our sample contains all stars in the spectral range dF7-dK2, listed in the CNS3 catalog, having a (B-V) color between 0.5 and 0.9, detected in ROSAT-PSPC pointed observations. Among these, we have selected all stars detected with more than 40 net counts and having an off-axis angle from the center of the field of view less than 48 arcmin. Our sample consists of 40 stars, for a total of 70 distinct observations. Fifteen of these stars were multiply observed with the ROSAT-PSPC at time intervals typically separated by months; in these cases we can explore variability up to these time scales. Table 1 summarizes the optical characteristics of our sample stars. Columns 1 and 2 provide the stellar names according to the catalogs by Gliese & Jahreiss (1991), Woolley and HD number, while more common names are given in Col. 8. The distances in Col. 5 are from the Hipparcos catalogue (Perryman et al. 1997) for all the stars having Hipparcos measurements, for the only one (GL 663) without Hipparcos measurement we report the CNS3 distance. The other optical data are taken from the CNS3 catalog or SIMBAD database.


   
Table 1: Optical properties of the selected sample.
NameHDSp.B-VDist.SingleOther
  Type (pc)B./T.name

GL5

166K0 Ve0.7513.70S 
GL171581F9 V0.588.59S$\zeta$ Tuc
GL17.31835G2 V0.6620.39SBE Cet
GL192151G2 IV0.577.47S$\beta$ Hyi
GL415015F8 V0.5318.57S 
GL6810476K1 V0.847.47S107 Psc
GL8613445K0 V0.8210.91S 
GL11717925K2 V0.8710.38SEP Eri
GL12419373G0 V0.6010.53S$\tau$ Per
GL13720630G5 Ve0.689.16S$\kappa$ Cet
GL13920794G5 V0.716.06S82 Eri
Wo915828946K10.7926.79S 
GL18933262F7 V0.5211.65S$\zeta$ Dor
GL21137394K1 Ve0.8412.24S 
Wo918939091G1 V0.6018.21S 
GL23143834G5 V0.7210.15S$\propto$ Men
GL31172905G1 V0.6214.27S$\pi^1$ UMa
GL434101501G8 Ve0.729.54S61 UMa
GL449102870F9 V0.5510.90S$\beta$ Vir
GL3715106156G8 V0.7930.96S 
GL475109358G0 V0.598.37SB$\beta$ CVn
GL502114710G0 V0.579.15S$\beta$ Com
GL506115617G6 V0.718.53S61 Vir
GL559A128620G2e V0.641.35B$\alpha^1$ Cen
GL559B128621K0 V0.841.35B$\alpha^2$ Cen
GL559.1129333dG0 e0.6133.94SEK Dra
GL566A131156G8 Ve0.736.70B$\xi$ Boo A
GL566B131156K4 Ve1.166.70B$\xi$ Boo B
GL567131511K2 V0.8411.54SDE Boo
GL575A133640F9 V0.6512.76B44 Boo A
GL575B G2 12.76B44 Boo B
GL598141004G0 V0.6011.75S$\lambda$ Ser
GL620.1A147513G3/5 V0.6312.87B 
GL635A150680G0 IV0.6510.79B$\zeta$ Her A
GL635B K0 V0.7510.79B$\zeta$ Her B
GL641152391G8 V0.7616.94S 
GL663A155886K1 Ve0.855.33B36 OphA
GL663B155885K1 Ve0.865.33B36 OphB
GL691160691G5 V0.7015.28S$\mu$ Ara
GL732.1175225G9 IVa0.8426.10S 
GL744177565G5 IV0.7117.17S 
GL764185144K0 V0.795.77S$\sigma$ Dra
GL779190406G1 V0.6117.67S15 Sge
GJ1255197433K0 V0.8627.65BVW Cep
GL882217014G4 V0.6715.36S51 Peg


   
Table 2: Journal of ROSAT PSPC observations. Asterisks indicate stars observed over at least four temporal segments having more than 30 counts each. In Col. 9, K-S results ``-'' indicate a Confidence Level $\leq $90%.
Name Obs. seq. Exposure Elapsed Time Observing HR Rate $\pm$ Err. $L_{\rm x}$ Results of
    (s) Time (s) Dates   [cnt/s] [erg/s] the K-S test
GL5 200645N00 2575 6308 91/12/20 -0.19 0.859$\pm$ 0.018 29.13 $\geq$99%
GL17 201138N00 2385 1600708 93/05/09-27 -0.85 0.029$\pm$ 0.003 27.03 -
GL17.3* 201470N00 5388 201731 93/06/16-18 -0.17 0.408$\pm$ 0.009 29.15 -
GL19 200071A01 2668 965914 92/11/17-29 -1.00 0.043$\pm$ 0.004 26.98 -
GL19 200071N00 1743 1819 91/04/21-91/05/11 -0.65 0.111$\pm$ 0.008 27.63 -
GL41* 400379N00 5587 65137 93/07/16-17 -0.61 0.059$\pm$ 0.003 28.16 $\geq$99%
GL68 201768N00 3968 24912 93/07/14 -0.54 0.029$\pm$ 0.003 27.09 -
GL86* 701156N00 1723 6464 93/06/09 -0.60 0.097$\pm$ 0.008 27.92 -
GL86* 701157N00 1995 6640 93/06/08 -0.67 0.113$\pm$ 0.008 27.97 -
GL86* 701158N00 1914 6732 93/06/07 -0.57 0.127$\pm$ 0.008 28.04 -
GL86* 701159N00 2400 14822 93/05/28 -0.65 0.098$\pm$ 0.008 27.91 -
GL86* 701160N00 3587 7764 93/05/29 -0.55 0.117$\pm$ 0.006 28.02 -
GL86* 701161N00 1621 1811 93/05/30 -0.54 0.143$\pm$ 0.009 28.11 -
GL86* 701162N00 1335 1472 93/05/31 -0.65 0.129$\pm$ 0.010 28.03 -
GL86* 701163N00 2449 41037 93/06/01 -0.50 0.143$\pm$ 0.008 28.11 -
GL86* 701164N00 1589 1780 93/06/02 -0.53 0.130$\pm$ 0.009 28.07 -
GL86* 701166N00 1036 1154 93/06/04 -0.48 0.111$\pm$ 0.010 28.01 -
GL86* 701167N00 2373 6856 93/06/05 -0.52 0.128$\pm$ 0.007 28.06 -
GL86* 701168N00 2251 6722 93/06/06 -0.49 0.136$\pm$ 0.008 28.09 -
GL117 150055N00 3880 247597 90/07/20-23 -0.19 1.107$\pm$ 0.017 29.00 $\geq$99%
GL124 180169N00 1821 1962 97/02/23 -0.67 0.068$\pm$ 0.006 27.71 -
GL137 201473N00 1588 1676 93/07/27 -0.39 1.115$\pm$ 0.026 28.87 -
GL139 201139N00 1738 333240 92/08/13-17 -0.83 0.024$\pm$ 0.004 26.67 90%-95%
GL189 200644N00 500 529 92/01/30 -0.20 1.476$\pm$ 0.054 29.22 -
GL211 201509N00 5498 224831 92/03/11-12 -0.43 0.432$\pm$ 0.009 28.71 -
GL231* 180172N00 2660 574955 97/02/23-97/03/02 -0.75 0.032$\pm$ 0.003 27.31 -
GL231* 201142N00 2573 29266 92/11/06 -0.84 0.077$\pm$ 0.005 27.62 -
GL311* 200654N00 21730 186681 92/04/25-27 -0.25 0.847$\pm$ 0.006 29.15 95%-99%
GL311* 201472N00 4756 402169 93/10/05-10 -0.19 0.884$\pm$ 0.014 29.18 90%-95%
GL434 201120N00 1956 52782 93/05/18-19 -0.41 0.428$\pm$ 0.015 28.49 -
GL449* 200813N00 7433 99760 92/06/02-03 -0.51 0.449$\pm$ 0.008 28.61 -
GL475* 201141N00 2690 526766 93/05/22-28 -0.89 0.048$\pm$ 0.004 27.19 -
GL475* 900137N00 20537 85622 91/06/01-02 -0.80 0.076$\pm$ 0.002 27.48 $\geq$99%
GL502* 110309N00 904 35777 90/06/28 -0.49 0.384$\pm$ 0.021 28.39 -
GL502* 110315N00 775 46445 90/06/28 -0.51 0.402$\pm$ 0.023 28.41 -
GL502* 110342N00 1217 34744 90/06/27 -0.60 0.476$\pm$ 0.020 28.46 90%-95%
GL502* 140315N00 432 629 90/07/08-09 -0.63 0.364$\pm$ 0.029 28.33 -
GL502* 140316N00 1205 12719 90/07/09 -0.61 0.439$\pm$ 0.019 28.42 -
GL502* 201471N00 8135 71257 93/06/17-18 -0.70 0.359$\pm$ 0.007 28.30 -
GL506 201144N00 3113 506395 92/07/23-29 -0.94 0.021$\pm$ 0.003 26.80 95%-99%
GL559AB* 180025N00 357 374 93/09/14 -0.54 9.958$\pm$ 0.167 28.13 -
GL559AB* 201119N00 3260 98824 92/09/02-03 -0.85 4.693$\pm$ 0.038 27.64 $\geq$99%
GL559.1* 200069N00 7136 26020 91/05/09 0.06 1.290$\pm$ 0.013 30.17 $\geq$99%
GL559.1* 150015A01 5673 108940 93/04/15-16 0.004 0.909$\pm$ 0.013 29.95 $\geq$99%
GL559.1* 201474N00 4891 14552 93/10/19 0.01 0.869$\pm$ 0.013 29.97 $\geq$99%
GL566AB 150090N00 464 486 90/07/22-23 -0.30 2.482$\pm$ 0.073 28.96 90%-95%
GL567 150090N00 391 486 90/07/22-23 -0.52 0.414$\pm$ 0.033 28.62 -
GL567 800294N00 2650 82858 92/08/08-09 -0.46 0.476$\pm$ 0.013 28.69 90%-95%
GL575AB 200841N00 2166 2286 92/06/15 -0.13 3.915$\pm$ 0.043 29.73 -
GL598 180174N00 2726 75869 97/02/21 -0.91 0.091$\pm$ 0.006 27.75 -
GL620.1A 200588A01 1234 1316 93/03/05-06 -0.27 0.816$\pm$ 0.026 29.05 -
GL620.1A 200588N00 1724 1857 92/02/26 -0.24 0.758$\pm$ 0.021 29.02 -
GL635AB 180173N00 1841 1984 97/02/23 -0.86 0.098$\pm$ 0.007 27.76 -
GL635AB 201136N00 7752 9129 94/09/08 -0.72 0.185$\pm$ 0.005 28.14 -
GL641 201371N00 1956 18620 92/09/08 -0.33 0.260$\pm$ 0.012 28.78 -


 
Table 2: continued.
Name Obs. seq. Live-time Elapsed Time Observing HR Rate $\pm$ Err. $L_{\rm x}$ Results of
    (s) (s) Dates   [cnt/s] [erg/s] the K-S test
GL663AB 201373N00 1783 80796 92/09/21 -0.43 1.233$\pm$ 0.026 28.44 $\geq$99%
GL691 201147N00 2894 7346 92/10/04 -0.69 0.023$\pm$ 0.003 27.80 -
GL732.1 200976N00 1842 1983 92/11/01 -0.08 0.916$\pm$ 0.022 29.72 -
GL732.1 201021N00 2110 3597 92/11/28 -0.19 0.584$\pm$ 0.017 29.52 90%-95%
GL744 200494A00 1734 17539 91/10/22 -0.77 0.041$\pm$ 0.005 27.86 -
GL744 200494A01 2891 162161 92/04/15-17 -0.91 0.022$\pm$ 0.003 27.47 -
GL764* 180170N00 1647 2228 97/02/24 -0.74 0.407$\pm$ 0.016 27.93 -
GL764* 201125N00 2684 2916 92/11/03 -0.77 0.189$\pm$ 0.008 27.57 -
GL779 201475N00 5634 77300 93/11/15-16 -0.69 0.064$\pm$ 0.003 28.13 -
GL882 201282N00 11983 100323 92/12/28-29 -1.00 0.008$\pm$ 0.001 26.84 -
GL1255* 201763N00 18523 98300 92/12/28-29 0.00 1.758$\pm$ 0.010 30.06 $\geq$99%
GL3715 700079A00 1966 52925 91/12/16-17 -0.43 0.031$\pm$ 0.004 28.37 95%-99%
Wo9158 700916N00 2905 7161 93/09/02 -0.72 0.018$\pm$ 0.003 27.93 -
Wo9158 700945N00 2331 2516 93/03/06 -0.83 0.018$\pm$ 0.003 27.84 -
Wo9189 999998A01 7107 526765 91/03/05-91/04/24 -0.90 0.016$\pm$ 0.001 27.38 -


   
Table 3: Variability on longer time scale: here we use multiple ROSAT observations separed by at least 6 months. As in Table 2, a ``-'' in K-S results means a Confidence Level $\leq $90%.
name HD ${<}L_{\rm x}{>}$ K-S results K-S results Elapsed time Elapsed time
    range on short-time on long-time of each obs. of all obs.
    [erg/s] scale scale [hours] [months]
GL19 2151 26.98-27.63 - $\geq$99% 0.5-268 18
GL231 43834 27.31-27.62 - $\geq$99% 8-160 52
GL559 128620/1 27.64-28.13 ${\leq} 90\%$- ${\geq} 99\%$ $\geq$99% 0.1-27 12
GL559.1 129333 29.95-30.17 $\geq$99% $\geq$99% 4-7-30 30
GL620.1 147513 29.02-29.05 - - 0.4-0.5 12
GL635 150680 27.76-28.14 - $\geq$99% 0.6-2.5 30
GL744 177565 27.47-27.86 - $\geq$99% 5-45 6
GL764 185144 27.57-27.93 - $\geq$99% 0.6-0.8 50
Wo9158 28946 27.84-27.93 - - 0.7-2 6

2.2 X-ray observations

Table 2 provides a journal of the ROSAT-PSPC observations in our study. Column 1 gives the star's name (as in Table 1), the ROSAT Observation Request (ROR) is listed in Col. 2, and the date of the observation in Col. 5; the esposure-time for each observation is given in Col. 3, while in Col. 4 we provide the total time spanned by the observation. In Col. 6 we give the hardness ratio, defined as $HR= \frac{H-S}{H+S}$, S being the number of photons measured in channels 3-10 (0.11-0.42) keV and H the number of photons recorded in channels 11-30 (0.42-2.4) keV. In Col. 7 we report the count rate in the (0.1-2.4) keV range. The mean X-ray luminosity, computed as explained below, is given in Col. 8 and the results of the Kolmogorov-Smirnov test discussed in Sect. 3 (e.g. Eadie et al. 1971; Siegel 1956) are presented in Col. 9.

For each star we evaluated the number of photon counts in a circular region centered on the average position of the observed photons in the (0.1-2.4) keV range and with a radius R, ranging from 2 arcmin for sources positioned on the optical axis, up to 5 arcmin, for sources at large off-axis positions. Count rates of the off-axis sources were corrected for vignetting. The radius R has been determined as described in Paper I.

2.3 Flux and luminosity determination

The conversion factor from count rate to X-ray flux depends on the instrumental properties, on the interstellar hydrogen column along the line of sight, and on the source spectrum. The X-ray emission was assumed to be produced by a single temperature plasma described by a Raymond-Smith model spectrum (Raymond & Smith 1977). Interstellar absorption has not been included since this effect is negligible in the case of our sample of nearby stars. For these conditions we modeled a conversion factor [erg cm-2/count] as a function of the observed Hardness Ratio HR (as also described in Sect. 2.3 and Fig. 1 of the Paper I).

We computed X-ray luminosities from the obtained fluxes and the distances reported in Table 1. Since each observation consists of a set of temporal segments typically obtained during different satellite orbits we estimated count rate, HR, flux and X-ray luminosity for each temporal segment with at least 30 counts. In Fig. 1 we show the scatter diagram of X-ray luminosity versus B-V. The segments connecting symbols indicate multiple observations of the same star, filled diamonds mark the 10 short-term variable observations with a confidence level >99%, filled circles mark the observations showing variability with confidence level between 90$\%$ and 99$\%$, the position of the Sun is also shown (square symbol), with the range of expected solar luminosities between periods of minimum and maximum activity indicated by a vertical line. There are very few sources with X-ray luminosity similar to that of the solar minimum. This is due to a selection effect because of our choice of selecting the sample as described in Sect. 2.1.

  \begin{figure} \par\includegraphics[width=8.5cm,clip]{h3111f1.ps}\end{figure} Figure 1: Scatter plot of X-ray luminosities vs. B-V. The segments connecting symbols indicate multiple observations of the same star, filled diamonds mark the 10 short-term variable observations with confidence level >99%, filled circles mark observations showing variability with a confidence level between 90$\%$ and 99$\%$, the position and the luminosity variation of the Sun over the solar cycle, is also shown (square symbol). The (statistical) errors of the measured X-ray luminosities are typically $\sim $15%.
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3 Results

3.1 Time variability

For each star in our sample, we obtained light curves in the (0.11-2.4) keV band.

In order to have a statistical evaluation of the X-ray variability we applied the unbinned Kolmogorov-Smirnov (K-S) test on all X-ray photon time series of our sample stars. We used the procedure implemented in the pros.xtiming package of IRAF after having removed data gaps. This method does not allow us to distinguish stochastic variability, or other forms of variability, from periodic ones (see also Collura et al. 1987; Haisch & Schmitt 1994 for a more sophisticated treatment of the gaps), but it can detect variability of any kind.

For each observation, we ran the K-S test on the source counts as well as on the counts detected in the background regions, the latter being carried out to monitor possible background variability. In three cases the background is variable with Confidence Level (CL) >99$\%$; GL 231 (Obs. seq. 180172N00), GL 475 (Obs. seq. 900137N00), GL 1255) however, in these cases, the number of counts in the variable background is much lower than the counts attributed to the source, hence we assume that the test results for these sources are reliable. In Col. 9 of Table 2 we report the results in terms of the confidence level at which we can reject the hypothesis that the source in the given observation is constant. In Table 4 we present a summary of K-S test results. Only during 10 observations relative to 8 distinct stars we have found the emission to be variable at a CL greater than 99%. This finding suggests that X-ray variability on short time scale is not common among these stars.

Furthermore, we have analyzed the K-S results for stars of different X-ray luminosities (see Table 5). The Table suggests that the X-ray variabilty changes with X-ray luminosity level, and in particular that a larger fraction of variable stars are more X-ray luminous. However we show below that this result is very likely due to the different count statistics distribution in the two samples.

 

 
Table 4: Results of the K-S test.
Results of the K-S Number of observations
>99% 10
95%-99% 3
90%-95% 6
$\leq $90% 51


Indeed, to explore the possible presence of a bias due to the statistics of photon counts in our results, in Fig. 2 we show the cumulative X-ray luminosity functions for variable $(CL > 99 \%)$ and not variable ($CL < 90\%$) stars with at least 500 counts. Figure 2 suggests that the high luminosity stars are more variable than the low luminosity ones, but the K-S two-sample test is unable to distinguish the two distributions[*] This result allows us to study the variability of our sample assuming that all nearby dF7-dK2 stars belong to the same population as far as X-ray variability is concerned (Fig. 3, dashed line). We derive the cumulative Time amplitude X-ray Luminosity Distribution (Time XLD) for these stars (dashed line Fig. 3) defined as the cumulative distribution of the ratio between the "instantaneous'' $L_{\rm x}$ and the minimum value observed for each observation. The Time XLD gives the fraction of time that an dF7-dK2 star spends in a state at flux larger than a given factor of its minimum value.

In Fig. 3 we also compare the Time XLD for our sample, having $L_{\rm x} > 27.5$, with the distribution obtained for dM stars (Fig. 4, Paper I). Using K-S two-sample test, we have tested the null hypothesis that the M XLD and the dF7-dK2 XLD are drawn from the same population, finding that, the two distribution are different, with dM stars more variable than dF7-dK2 $(CL > 99 \%)$. This finding may be a strong indication that magnetic activity on dM stars and solar type stars is due to different processes, as it appears to be the case, for example, in Brown Dwarfs as suggested by Berger et al. (2001).


 

 
Table 5: K-S test results for different ranges of log($L_{\rm x}$).
  log($L_{\rm x}$) [erg/s]
         
CL $\leq $27.5 27.5-28.5 28.5-29.5 >29.5
         
>99% 1 3 2 4
95%-99% 1 1 1 0
90%-95% 1 1 3 1
$\leq $90% 8 32 9 2



  \begin{figure} \par\includegraphics[width=8.4cm,clip]{h3111f2.ps}\end{figure} Figure 2: The cumulative X-ray luminosity functions for variable ( $CL > 99 \%$; dashed line) and non variable ($CL < 90\%$; solid line) stars, having at least 500 counts. The two luminosity functions are indistinguishable, according to a K-S two sample test, suggesting that variability is independent on X-ray luminosity.
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  \begin{figure} \par\includegraphics[width=8.8cm,clip]{h3111f3.ps}\end{figure} Figure 3: The dashed line shows the cumulative time X-ray luminosity distribution for dF7-dK2 stars having more than 500 counts and log( $L_{\rm x}) \geq 27.5$; the solid line shows the cumulative time amplitude X-ray luminosity distribution for dM stars with more than 500 counts.
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3.2 X-ray variability on longer time scale

Nine stars of our sample were multiply observed with a similar off-axis, and with a time separation of at least six months. Using a procedure implemented in the pros.xdataio package of IRAF, we applied the K-S test on all available data for each star, just appending the various observations one after the other.

We find indications that the variability increases with the time scales. Five stars, not variable $(CL <90\%)$ on time scales ranging from a few hours to less than 1 week, result variable $(CL > 99 \%)$ on time scales of months (see Table 3). We note that the only two stars, out of the nine stars multiply observed, that show short term variability are: EK Dra, the most active star of our sample, and $\alpha$ Cen, the one observed with the highest statistics. On the contrary the stars that do not show long term variability are Wo9158, observed over a time scale of only 6 months, and GL 620.1, the only star, together with EK Dra, of the subsample observed on long time scale, having $L_{\rm x} > 10^{29}$ erg/s. Below we discuss the evidence that very X-ray luminous G-type stars do not appear variable on longer time scale. The amplitude of the variations ranges between a factor $\sim $2 and $\sim $4 for variable stars on long time scales.

A few stars in our sample have been observed with Einstein-IPC in 1978-1981 allowing the study of possible variability on a time scale comparable with that of the solar cycle. We show in Fig. 4 the log($L_{\rm x}$) measured with the PSPC (one value for each observing time interval) versus log($L_{\rm x}$) measured with the IPC (one value averaged on the IPC observation (Maggio et al. 1987; Barbera et al. 1993). We excluded the upper limit IPC observations consistent with the PSPC observation and the PSPC observations spanning less than 500 s because in this case it is very difficult to disintangle flare emission from quiescent emission. Given the difference of the two instruments and the cross calibration uncertainties, we do not consider as significant any variability within a factor two i.e. inside the region of the plot enclosed by the dotted lines. Long term variability seems to exist for three stars of our sample (GL 86, GL 124, GL 598); we note that these stars have X-ray luminosity similar to the solar one. In literature we found information on cyclic variability only for one of these three stars (GL 598), it is found to have a cyclic period >30 yr (Baliunas et al. 1995). Saar & Brandenburg (1999) find for GL 598 a cyclic period >25 yr.


  \begin{figure} \par\includegraphics[width=8.4cm,clip]{h3111f4NEW.eps}\end{figure} Figure 4: Scatter plot of log($L_{\rm x}$) observed by Einstein-IPC (corrected using hipparcos distances) and ROSAT-PSPC. The solid line represents the line of equality and the dashed line represents variation of factors two.
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  \begin{figure} \par\includegraphics[width=8.3cm,clip]{h3111f5.ps}\end{figure} Figure 5: Scatter plot of X-ray luminosity vs. the Ca II $R'_{\rm HK}$ emission index (Henry et al. 1996; Soderblom 1985; Radick et al. 1998) for the stars in our sample quoted in the same papers. Filled symbols are the stars variable on long time scale but not on short time scale, vertical lines show the range of luminosity spanned by stars having more than one temporal segment, among them the filled crossed symbols are the three stars variable between IPC and PSPC observations and not variable on short term scale (for them, the vertical lines indicate variations between IPC and PSPC observations). Crosses indicate the stars variable on short time scale with a $CL \geq 99\%$, the Sun is shown as a square symbol. For the Sun vertical line spans the luminosity variation over the solar cycle (Peres et al. 2000).
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It is worth noting that stars variable on longer time scales have a solar-like X-ray luminosity, while for the two more luminous stars of our sample there is no long term variability. Studies of stellar X-ray emission at different epochs based on Einstein and ROSAT observations of stars in open clusters (Stern et al. 1995; Gagnè et al. 1995; Micela et al. 1996) as well as of field stars (Schmitt et al. 1995; Fleming et al. 1995) suggest that at least the most active stars do not show long term variability. Some authors have suggested that the lack of strong cyclic activity in active stars indicates that small-scale turbulent magnetic field generation is strongly dominant over the large-scale dynamo that accounts for the Sun's magnetic cycle.

4 X-ray and chromospheric emission

The Ca II H-K fluxes are closely related to magnetic activity in late-type stars (Schrijver et al. 1992) suggesting a common origin for the activity. On the Sun, the Ca II emission varies significantily on several time scales: about 27 days due to rotational modulation; weeks to months due to the growth and decay of active regions; 11 yr due to the activity cycle and longer periods may also modulate the activity cycle. From solar minimum in 1975, to solar maximum in 1980, the intensity of Ca II K3 central emission increased by 30%, while the emission within a 1 A window centered on the K line increased by 18% (White & Livingston 1981).

Stellar magnetic cycles manifest themselves in a long term variability of their chromospheric (Wilson 1978; Baliunas et al. 1995) and possibly also coronal emission (Hempelmann et al. 1996). We therefore studied the relation between X-ray luminosity and Ca II H-K emission as parameterized by the Ca II $R'_{\rm HK}$index ( $R'_{\rm HK}$ measures the intensity of the line corrected for the contribution of the photospheric continuum and scaled for the bolometric flux). Using the Ca II data published by Henry et al. (1996), taken between 1992-1993, integrated with data from Soderblom (1985) and Radick et al. (1998), we show in Fig. 5 the scatter plot of log($L_{\rm x}$) versus $R'_{\rm HK}$ for the stars in our sample mentioned in the same papers. Figure 5 also shows the best fit power-law relation obtained by Maggio et al. (1987). Our data are in good agreement with this relation. The Ca II and X-ray data are not taken symultaneonsly, introducing some spread in the relation; in particular the star GL 449 (see Fig. 5) shows an anomalous value of Ca H-K. In Fig 5 vertical segments show also the spread introduced by X-ray variability Our data indicate that at least at low activity levels ( $L_{\rm x} \leq 10^{28}$) long-term variability can also account for the observed spread.

We have searched information on cyclic variability (Wilson 1978; Baliunas et al. 1995) of the stars in our sample. Chromospheric observations of GL 137 and GL 663 analyzed by Wilson (1978) indicate cyclic variations while GL 434 and GL 502 do not seem to show any cyclical behavior. Baliunas et al. (1995) find indication of long term variations (on time scales longer than about 20 yr) for GL 17.3, GL 137, GL 434, GL 663A; GL 502 analyzed by Baliunas et al. (1995) presents a 16.6 yr activity cycle superposed on a 9.6 yr cycle. GL 598 has rotation and mass similar to the Sun, but weak chromospheric activity and a variation in activity that appears to be longer than 30 yr. Data are too sparse to compare the time scales of variations in calcium and X-ray.

5 Summary and conclusions

Acknowledgements
The authors acknowledge financial support MURST-COFIN 99. This research made use of the Simbad database, operated at CDS. We also thank the anonymous referee for useful comments.

References

 
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