1 Introduction

The influence of accretion disks surrounding young PMS stars on their observed X-ray activity levels is presently debated. The topic has been investigated many times through imaging X-ray observations of star forming region but contradictory results are reported. Mentioning just a few recent examples, Feigelson et al. (2002) analyze Chandra ACIS-I data finding no indication that the presence of an accretion disk modifies activity levels of Orion Nebula Cluster (ONC) stars. The same negative result, although somewhat controversial, is reported for IC 348 members by Preibisch & Zinnecker (2001,2002), also using Chandra ACIS-I observations; by Lawson et al. (1996) for the Chamaeleon I cloud using ROSAT PSPC data; by Flaccomio et al. (2000) for NGC 2264 using the ROSAT HRI; by Grosso et al. (2000) for $\rho$ Ophiuchi again with the ROSAT HRI; by Getman et al. (2002) for NGC 1333 (ACIS-I).

On the other hand, Classical T-Tauri Stars (CTTS) belonging to the Taurus-Aurigae association are found to be sub-luminous in the X-ray band respect to Weak Lined T-Tauri Stars (WTTS) by both Neuhäuser et al. (1995) and Stelzer & Neuhäuser (2001). Flaccomio et al. (2002b), using Chandra HRC-I data, report a similar result, with high statistical confidence and at odds with Feigelson et al. (2002), for the rich ONC population. Other indications of a difference between CTTS and WTTS have been found in X-ray band variability characteristics and spectra. Namely, Stelzer et al. (2000) in Taurus-Aurigae, Flaccomio et al. (2000) in NGC 2264 and Flaccomio et al. (in preparation) in the ONC, all find that CTTS are more variable than WTTS. Some studies have also indicated that CTTS may have different X-ray spectral characteristics respect to WTTS: Tsujimoto et al. (2002) find that the mean kT for CTTS is about 3 keV, compared to $\sim$1.2 for WTTS. Such a large kT difference may in part be due to a selection effect: in the X-ray selected sample of Tsujimoto et al. (2002) class II sources (CTTS) are significantly more absorbed respect to class III-MS sources (WTTS) and it is therefore possible that only the hardest CTTS have been observed. Other contrasting indications have been also presented: Kastner et al. (2002), using high resolution X-ray spectra of the 10Myr old CTTS TW Hydrae, derive a differential emission measure distribution peaking at $\sim$0.3 keV and propose that the emission mechanism is related to matter accretion. No systematic difference in kT between CTTS and WTTS is observed by Preibisch & Zinnecker (2002) in IC 348 members.

Are these contradictory results due to real differences between different star forming regions or to the different approaches used in analyzing and interpreting data? We will touch upon four important points that can affect the result: 1) accounting for the mass/ $L_{\rm bol}$ dependence of PMS activity; 2) choosing a relevant accretion/disk indicator; 3) avoiding selection effects in the reference stellar sample; 4) converting observed X-ray photon detection rates to X-ray luminosities.

Mass/ $L_{\rm bol}$ dependence.

It is possible that the failure to detect a difference in activity levels between stars with different circumstellar/accretion properties is due to the fact that the activity levels are also influenced by other stellar characteristics, and the various contributions have not been disentangled. In particular a dependence of mean $L_{\rm X}$ on stellar mass (or bolometric luminosity) has been widely found for PMS stellar groups. Most of the studies mentioned above compare the X-ray Luminosity Function (XLF) of CTTS with that of WTTS, both XLFs being computed from stellar samples comprising a wide range of masses. Such a procedure tends to hide possible differences because: 1) the presence and/or magnitude of the effect sought might depend on stellar mass; 2) if a different mass-$L_{\rm X}$ relation holds for these two classes, stars having the same $L_{\rm X}$, but different mass, will contribute to both XLFs. A more sensible approach, in order to eliminate this source of confusion (see e.g. Flaccomio et al. 2002b), is to compare XLFs of stars in restricted mass ranges; this however requires, for meaningful statistical comparisons, sufficiently large samples of well characterized members. To the same effect, considering that the ratio $L_{\rm X}/L_{\rm bol}$ is, for low mass PMS stars ( ${\lesssim} 3~M_\odot$), on average much less dependent from mass than $L_{\rm X}$ (e.g. Flaccomio et al. 2002b), it is also sensible to compare the distributions of this latter parameter for the two classes. As an added advantage, $L_{\rm X}/L_{\rm bol}$ is arguably less sensitive to interstellar extinction corrections (although the newly introduced variable, $L_{\rm bol}$, also carries non-negligible uncertainties). Both of these approaches were successfully followed by Flaccomio et al. (2002b) to establish the difference in activity levels between accreting and non-accreting ONC members.

Disk/accretion indicator.

There is no widespread consensus on which indicator of presence of disk or of accretion is to be used to search for effects on activity levels. Some studies have correlated X-ray data with accretion indicators, such as the H $_{\rm\alpha }$ or Ca II line emission. Others have instead employed circumstellar disk indicators such as near IR excesses (in K or L band). The relation between presence of disks and matter accretion phenomena is not yet fully understood. A statistical correlation between accretion and disk indicators is generally observed but it seems clear that not all IR detected disks are associated with accretion and it is also possible that the presence of accretion is not always related to a near-IR detectable disk (e.g. because of a large inner disk hole that suppress the K band excess or because of the disk view-angle). It is presently unclear whether X-ray emission levels are influenced by one (or both) of the two phenomena. It seems therefore reasonable to explicitly distinguish between the two. As a clarifying example, Preibisch & Zinnecker (2002) find statistically significant evidence that accreting stars in IC 348 have lower $L_{\rm X}$ respect to non accreting ones, but no evidence of a difference between stars with and without K-L color excess (a disk indicator). They consider these two results contradictory, maintain that the infrared excess gives a more realistic picture of the circumstellar properties of the T Tauri stars than the $\rm H_{\alpha}$ emission and attribute the detected difference in X-ray luminosity functions to selection biases. An alternative point of view would be that accretion and not the presence of an IR-detectable disk influences X-ray activity and the two are not simply related. We note that in other cases in which a difference in activity levels is reported the distinction was performed on the basis of accretion indicators: H $_{\rm\alpha }$ in Taurus (e.g. Stelzer & Neuhäuser 2001) and Ca II in the ONC (Flaccomio et al. 2002b).

Parent sample selection.

Ideally, a complete and not-contaminated sample of members of a given SFR should be used to investigate the matter. However, this is in practice hardly possible. Understanding selection biases is therefore crucial: in the case of IC 348 discussed above, Preibisch & Zinnecker (2002) suspect that strong, easily detectable H $_{\rm\alpha }$ emission may favor the inclusion in the reference stellar sample of optically (and X-ray) faint accreting stars and therefore artificially depress the mean $L_{\rm X}$ of CTTS. This, i.e. selecting members on the basis of their circumstellar/accretion properties, or in any other way that favors the selection of faint CTTS over that of WTTS, is indeed the main risk to be avoided, or accounted for, in such a study. Taking the approach of dividing the whole sample in narrow mass ranges (see above), this problem, usually worse for low mass, low $L_{\rm X}$ stars, is reduced for the higher mass ranges. Other member selection methods, are not likely to result in spurious results: selection through sensitivity limited X-ray observations, for example, will sample to the same minimum $L_{\rm X}$ both CTTS and WTTS (assuming similar X-ray spectra and absorptions), so that if the two underlying (i.e. complete) XLFs do not differ, the detection fraction of both classes will be the same and the two distributions of observed $L_{\rm X}$ will not differ either. Inclusion in the reference sample of contaminating non-members, usually low $L_{\rm X}$ stars, will depress the mean activity levels inferred for non accreting/disk-surrounded stars, therefore going in the direction of producing the opposite result respect to the observed one.

X-ray count-rate to $L_{\rm X}$ conversion.

X-ray telescopes detect photons in wide energy ranges. The conversion between detected count-rate and X-ray luminosity depends therefore on the incoming spectra. Given the low statistic of most X-ray sources with present day instruments and/or the lack of spectral resolution of some X-ray detectors, it is necessary to assume a source spectrum. For coronal sources this usually reduces to assuming the kT of a thermal emission spectrum and the hydrogen column density, $N_{\rm H}$, of the absorbing material between the source and the observer. Differences in the way these two parameters are estimated can lead to significantly different conversion factors and therefore affect the result of our search for a difference between CTTS and WTTS. On one hand, systematic differences in the X-ray spectra (kT and $N_{\rm H}$) of CTTS and WTTS might result, if not properly accounted for, in spurious results regarding the different X-ray luminosity of the two classes. On the other hand, significant random errors in the conversion could easily wash out an existing correlation between $L_{\rm X}$ and accretion/disk indicators. In the works of Feigelson et al. (2002) and Getman et al. (2002), for example, the evidence presented against a difference of WTTS and CTTS is obtained using detector plane (non absorption-corrected) X-ray fluxes. Likewise Lawson et al. (1996) and Flaccomio et al. (2000), also obtaining a negative result, assume a single count-rate to flux conversion factor and therefore neglect any difference in absorption between sources. Flaccomio et al. (2002a,b) on the other hand, although assume a single kT for all sources, correct for individual absorption values ( $N_{\rm H} \propto A_{V}$), finding a positive result. Stelzer & Neuhäuser (2001) also correct for absorption (through a low energy hardness ratio) and find a positive result. Is it possible that a peculiarity in the $N_{\rm H}$ vs. A_V relation or in the intrinsic spectra of CTTS and WTTS results in artificially lowering the luminosities derived for CTTS respect to those derived for WTTS? Regarding the relation between X-ray and optical extinction, recent studies correlating $N_{\rm H}$, derived from X-ray medium resolution spectra, and optically derived A_V confirm the relation between the two and do not evidence any such difference (cf. Imanishi et al. 2001; Flaccomio et al. 2002a; Feigelson et al. 2002; Kohno et al. 2002). It is however possible, although presently not still fully established, that CTTS have harder X-ray spectra respect to WTTS (Tsujimoto et al. 2002). We may wonder how a different kT would affect the luminosities we derive. Figure 1 shows the value of the conversion factors for the ROSAT HRI, as a function of kT and $N_{\rm H}$. Qualitatively similar plots are obtained for the ROSAT PSPC and for the Chandra HRC-I, the two other instruments used for the observations discussed later in this paper. We observe that, for a given source $N_{\rm H}$, the difference in kT, if eventually confirmed, will indeed go in the direction of decreasing the inferred $L_{\rm X}$ of lower kT sources respect to high kT ones, thus potentially accounting for part of the observed differences between CTTS and WTTS. However it is also clear that for typical $A_{V} \sim 0.5{-}4.0$ the mistake committed in not accounting for individual source temperatures could be at most of the order of ${\sim} 0.1{-}0.2$ dex, smaller than the difference between CTTS and WTTS found by Flaccomio et al. (2002b) in the ONC. We stress however that even if this effect were to be confirmed, therefore reducing the actual difference in luminosities respect to that inferred assuming a single kT, the difference between the X-ray emission of CTTS and WTTS would be confirmed, and the spectral differences would provide additional clues for the understanding of its physical origin.

In this paper, keeping the above four points in mind, we further discuss and extend the evidence for a role of accretion and/or disk in determining the observed X-ray activity level of ONC members, as already reported by Flaccomio et al. (2002b). In the light of newly available optical/IR data we then critically reanalyze the results obtained by Flaccomio et al. (2000) and Lawson et al. (1996), both of which concluded that stars surrounded by disks, in NGC 2264 and Cha I respectively, have the same activity levels as those that do not have a disk. Here we derive the opposite result.

The structure of this paper is as follows: in Sect. 2 we discuss the new observational evidence for a difference in activity levels between CTTS and WTTS belonging to the ONC. In Sects. 3 and 4 we then discuss the cases of NGC 2264 and the Chamaeleon I cloud. Finally in Sect. 5 we briefly summarize our results.