6 Discussion

  
6.1 The XLF of cTTS and wTTS

We have reanalysed the XLF for cTTS and wTTS in Taurus-Auriga, first presented by N95, increasing the sensitivity with respect to the RASS by $\sim$2 orders of magnitude. Our pointed PSPC observations confirm that in Taurus-Auriga wTTS are on average more X-ray luminous than cTTS. This is in contrast to studies of Cha I and $\rho$ Oph (Feigelson et al. 1993; Casanova et al. 1995; Grosso et al. 2000), where no difference was found between the two sub-classes of TTS concerning their X-ray emission level. In a study of the Orion Nebula region with the ROSAT HRI Gagné & Caillault (1995) found slightly lower median $L_{\rm x}$ and $L_{\rm x}/L_{\rm bol}$ values for stars with massive accretion disks, i.e. cTTS. Alcalá et al. (1997) have found higher X-ray luminosities for ROSAT discovered wTTS in the outer parts of the Cha I and Cha II regions. This seems to indicate that samples of wTTS may be biased towards strong X-ray emitters, and that discrepancies can arise from the different spatial distribution of the cTTS and wTTS sample.

We have ruled out such an X-ray selection bias for our sample, by comparing the XLF for wTTS discovered by means of their X-ray emission to those which have been identified in other ways. XLF constructed for a coeval subgroup of cTTS and wTTS located in a central portion of the Taurus-Auriga complex, the L1495E cloud, show the same disagreement. Therefore, the difference does not seem to be related to the wide spatial extension (hence large age spread) of the Taurus star forming region. In addition this test shows that the disagreement is not caused by the different sensitivities (due to different exposure times) of the various combined PSPC observations.

Further effects, like different spectral type distribution, the specific choice of the $W_{\rm H\alpha}$ boundary between cTTS and wTTS, or our way of splitting the X-ray emission on all components in multiples, can not explain the observed discrepancies between the cTTS and wTTS XLF. To investigate whether the high number of upper limits in the cTTS sample affects the shape of the XLF we have also computed XLF neglecting all upper limits. (Grosso et al. 2000 have not included upper limits in their XLF of $\rho$ Oph.) The structure of the XLF, however, remains unaffected.

We conclude that there is an intrinsic difference in X-ray emission from cTTS and wTTS in Taurus. Besides the extinction effect discussed above the different evolutionary state of TTS in different star forming regions may contribute to the observed discrepancies. It should be noted that the subsamples of cTTS and wTTS in Taurus with known $T_{\rm eff}$ and $L_{\rm bol}$ occupy the same region in the H-R diagram, i.e. the difference in $L_{\rm x}$ seems not to be a direct age effect.

The correlation between the X-ray luminosity and $P_{\rm rot}$ we found for all examined samples suggests that the X-ray emission level may be governed by rotation. To check this hypothesis we have computed separate XLF for fast rotating wTTS ( $v \sin{i} > 22~{\rm km\,s^{-1}}$, the mean ${v \sin{i}}$ for wTTS), and slowly rotating wTTS ( $v \sin{i} < 12~{\rm km\,s^{-1}}$). Indeed, the slow rotators are characterized by lower X-ray luminosity ( $\log{L_{\rm x,mean}} = 29.54 \pm 0.13$versus $30.00 \pm 0.11$ for the fast group). This explains some but not all of the discrepancy between the XLF of Fig. 3. From the mean rotation rate of cTTS and wTTS and the mean $\log{L_{\rm x}}$ values derived from the KME analysis the slope in Fig. 9 would be expected to be much steeper. But note, that only a small fraction of TTS has measured rotation periods, and the large spread in the observed rotation-activity relation may be due to mixing of stars with different mass.

If, indeed, rotation is the major parameter that determines the amount of X-rays emitted by a given star then cTTS and wTTS in Taurus-Auriga are expected to have different $L_{\rm x}$ because the wTTS are on average faster rotators (see Bouvier et al. 1993 and our Fig. 9). Different distributions of rotation periods are also found in other star forming regions, e.g. Lupus (Wichmann et al. 1998b). Only in Orion cTTS and wTTS are found to rotate at the same speed (Stassun et al. 1999). The rotational state of the PMS stars in Cha I and $\rho$ Oph has not yet been investigated in detail. We suspect that most of the wTTS in Taurus-Auriga (including those in L1495E) have spent a longer time than those in Cha I and $\rho$ Oph since they have dispersed their disks, and therefore have had more time to spin up, and consequently should drive a more powerful dynamo. This implies that the disk lifetimes depend on the local condition in the star forming region. We remark that this hypothesis can only be tested after more measurements of rotational velocities in these different regions are available. In a later paper we will compare the XLF in different star forming regions in more detail.

  
6.2 Spectral type and age dependence of the X-ray emission

We have compared the XLF of TTS in Taurus-Auriga, the Pleiades, and the Hyades. Following early studies by the EO the XLF of Pleiades and Hyades had been examined with the improved sensitivity of ROSAT (see e.g. Hodgkin et al. 1995; Micela et al. 1996; Pye et al. 1994; Stern et al. 1995). However, all studies of X-ray luminosity on these young clusters were based on smaller data sets than the one presented here.

In lack of the knowledge about individual masses we take account of the known mass dependence of the X-ray luminosity by regarding G, K, and M stars separately. For all spectral type groups wTTS are found to be the strongest X-ray emitters, and the Hyades show the lowest level of X-ray emission. The difference between $\langle L_{\rm x} \rangle$ of the Pleiades and the Hyades is small for G stars where the spread in the mass distribution is largest, but large for M stars which have more uniform masses. This suggests that the decline in the X-ray emission is mostly an age effect. The XLF of cTTS and the Pleiades intersect each other, because the Pleiades are characterized by a much steeper distribution indicating less spread in $L_{\rm x}$. This difference may be a result of the uniform distance assumed for all stars in a given group (except the Hyades for which individual Hipparcos parallaxes were used). If the extension in the direction along the line-of-sight is comparable to the observed spatial dispersion, the TTS in Taurus-Auriga should be subject to a distance spread of $\sim$50 pc. Consequently the luminosities of some stars are underestimated while others are overestimated, thus leading to a larger spread in $L_{\rm x}$ and a flattening of the XLF. For the more compact Pleiades region instead the assumption of uniform distance may be adequate.

The XLF of Hyades K stars show a substructure appearing as an edge at $\log{L_{\rm x}} \sim 28.7$. In order to explain this feature we have divided the K star Hyades into two subgroups of $\log{L_{\rm x}}$ larger/smaller than 28.7. No differences between these two samples were found concerning the distribution of effective temperature, distances, and location on the sky. Only few of the Hyades K stars have measured ${v \sin{i}}$ or rotation period. Therefore, the hypothesis that the high-luminosity tail is composed of the fast rotators can not be tested. Note, that the edge in the slope is seen in both single and binary stars (see Fig. 8), but seems to be more pronounced for single stars. We suggest, that the effect is due to as yet undiscovered multiples among the K type Hyades.

We have extended our investigation of the dependence of the X-ray emission on spectral type by direct examination of correlations between these parameters (see Fig. 7). This investigation reveals differences between TTS, Pleiades, and Hyades which we suppose are related to the different ages of these groups. For stars on the MS $T_{\rm eff}$ corresponds to mass, and mass is related to the depth of the convection zone. The observed anti-correlation between ${\log{(L_{\rm x}/L_{\rm bol})}}$ and ${\log{T_{\rm eff}}}$ from Fig. 7 therefore demonstrates the importance of convection for X-ray activity. Although there is a tendency of ${\log{(L_{\rm x}/L_{\rm bol})}}$ being larger for cooler stars, the absolute amount of X-rays emitted is smaller (see Figs. 6 and 7). In the Pleiades $L_{\rm x}$ does not strongly depend on spectral type, although ${\log{(L_{\rm x}/L_{\rm bol})}}$ decreases with increasing $T_{\rm eff}$. This is most likely due to the shorter time the latest type stars in the Pleiades have spent on the MS. Most of the late K and M type Pleiads did not spin down to loose their high initial activity level, yet. The PMS TTS show no correlation between ${\log{(L_{\rm x}/L_{\rm bol})}}$ and ${\log{T_{\rm eff}}}$. This may be due to the large age spread in the TTS sample (10^5..7 yrs).

The most active stars of all groups are characterized by ${\log{(L_{\rm x}/L_{\rm bol})}}$ $\sim -3$, the canonical value for late-type stars. This behavior is been referred to as "saturation'', and has been described in the literature; see e.g. Fleming et al. (1989), Feigelson et al. (1993), Micela et al. (1996), Randich et al. (1996), Stauffer et al. (1997), Micela et al. (1999). A common explanation is that all saturated stars have reached their highest possible level of X-ray activity, e.g. by coverage of the full surface with active regions. The stellar radius rather than rotation would then determine the X-ray emission level (see Fleming et al. 1989). The correlation between $L_{\rm x}$ and spectral type in TTS may be understood in terms of such a saturation effect: Fig. 7 suggests that many TTS regardless of their spectral type have reached the saturation level. However, the more luminous the stars, the larger they are, and the higher the saturation level for $L_{\rm x}$. Therefore, for given $L_{\rm bol}$ the X-ray luminosity is limited by a value that corresponds to saturation, and which is lower for later spectral types.

The dispersion of $\log{L_{\rm x}}$ for given spectral type can be regarded from two points of view: (a) all stars of given spectral type show intrinsically similar amounts of X-ray emission, and the spread in $L_{\rm x}$is caused by variability of individual stars, or (b) the dispersion reflects different activity levels of the stars. Our analysis of the longterm X-ray behavior of these stars (to be presented in a subsequent paper; Stelzer et al. in prep.) suggests little variability on long timescales making the former hypothesis improbable. The distribution of $L_{\rm x}$ within stars of homogeneous spectral type thus more likely reflects the variety of X-ray emission from individual stars.

  
6.3 Are Hyades binaries overluminous?

Pye et al. (1994) have examined the XLF of Hyades stars combining 11 ROSAT PSPC observations. In their sample they found that Hyades dK binaries are overluminous in X-rays: all binary dK stars analysed by Pye et al. (1994) were brighter than any of the single dK stars. This result was confirmed by Stern et al. (1995) on a larger sample of Hyades drawn from the RASS.

In our analysis of the XLF in the Hyades we have treated binary stars in two ways: (A) in the same way as singles, i.e. without taking account of the multiplicity (sample "b1''), and (B) dividing the observed luminosity by two to account for X-rays from both components (sample "b2''). We find a probability of $\sim$10-15% for the null-hypothesis that the distributions of singles ("s'') and "b2'' among the Hyades K stars are drawn from the same parent distribution. For Hyades M stars (not examined by Pye et al. 1994 due to lack of statistics but found to display a similar though less pronounced divergence between single and binary XLF in the study of Stern et al. 1995) we find a similar probability for the rejection of the null-hypothesis that "s'' and "b2'' are drawn from the same parent distribution. However, the sample of M star binaries in the Hyades is very small (9 stellar systems). For all other pairs of "s'' - "b2'' distributions, i.e. those of Hyades G stars, Pleiades, and TTS, there is no statistical evidence for differences. The agreement between the XLF of single ("s'') and binary ("b2'') stars is expected if the components in binaries have no mutual influence on their activity, and if indeed the distribution of the observed X-ray emission equally on all components conforms with the real situation. This seems likely because binaries with very high mass ratio, i.e. largely different $L_{\rm x}$, are more difficult to detect than equal mass ratio binaries.

When compared to the distributions "b1'', singles are fainter in all cases (probability for the distributions being similar <10%). This is in agreement with the study of Pye et al. (1994) and Stern et al. (1995) who have examined samples of type "b1''.

This results emphasize that it is important to consider the binary character when analysing XLF of double stars. Splitting the X-ray emission onto the components significantly decreases the difference between single and binary XLF. However, some discrepancy for the Hyades K and M stars remains unexplained. A proper treatment of binary stars is also important in correlation studies, as it decreases the spread.

  
6.4 The age-activity-rotation connection

We have shown that the rotation period and various measures for the X-ray activity (i.e. luminosity, surface flux, and $L_{\rm x}/L_{\rm bol}$-ratio) are correlated for all examined age groups. The steepness of the activity-rotation relation is very different for TTS, Pleiades, and Hyades, with the largest slope for the TTS, e.g. slow rotators in the Pleiades have much higher surface flux than TTS with similar periods (see Figs. 9 to 11). We think that these differences can be explained by the particular distribution of spectral types: In Fig. 12 we show the $\log{F_{\rm s}} - \log{P_{\rm rot}}$diagrams with plotting symbols scaled according to $T_{\rm eff}$.

Figure 12: X-ray surface flux versus rotation period for TTS, Pleiades, and Hyades indicating the distribution of effective temperatures (plotting symbols are scaled to $T_{\rm eff}$). Note, that most of the slow rotators in the TTS sample are cool objects. Open circles are upper limits for undetected objects.

In the TTS sample we observe a clear clustering of cooler stars at slow rotation periods. For given $L_{\rm bol}$ and $L_{\rm x}$ cooler stars have larger radius and therefore smaller surface flux. This results in a steeper slope for the TTS sample.

Fast rotators are found at all spectral types in the Pleiades and among the TTS. Indeed, the fastest rotators form the upper envelope to the ${\log{(L_{\rm x}/L_{\rm bol})}}$- ${\log{T_{\rm eff}}}$ diagram (Fig. 7). At the age of the Hyades most stars (regardless of spectral type) have slowed down their rotation, such that the range of measured periods is limited, and definitive statements about the activity-rotation connection for the Hyades are difficult.

We have examined the mean level of X-ray surface flux for each age group in order to infer a decay law. In Fig. 13 the mean $F_{\rm s}$ is plotted for cTTS,

Figure 13: Time evolution of the X-ray surface flux for TTS, Pleiades, and Hyades for three spectral type groups (plotting symbols for G and M stars for clarity with a small offset on the age-scale). The thick solid line represents a fit to the mean of $F_{\rm s}$ obtained by combining G, K, and M stars from the wTTS, Pleiades, and Hyades sample. The slope of this exponential decay is $-2.0 \pm 0.1$ in agreement with earlier estimates for smaller samples of stars from the same region (see text).

wTTS, Pleiades, and Hyades, each being split into G, K, and M type stars. The X-ray flux increases from cTTS to wTTS as mentioned by N95. (Only one cTTS has spectral type of G.) An exponential fit to the combined G + K + M sample from the wTTS to the Hyades age is overlaid, and provides a slope of $-2.01 \pm 0.09$. This compares well with the result by Walter & Barry (1991) who found a decrease of $F_{\rm s}$ with $-2.20 \pm 0.21$ for a sample composed of Einstein detected naked TTS, Pleiades and Hyades.

Acknowledgements

We made use of the Open Cluster Database, compiled by C. F. Prosser and J. R. Stauffer. R.N. wishes to acknowledge financial support from the Bundesministerium für Bildung und Forschung through the Deutsche Zentrum für Luft- und Raumfahrt e.V. (DLR) under grant number 50 OR 0003. The ROSAT project is supported by the Max-Planck-Gesellschaft and Germany's federal government (BMBF/DLR). We would like to thank the referee T. Montmerle for helpful comments and stimulating discussions.