Astron. Astrophys. 359, 113-130 (2000)

4. X-ray luminosities of the HRI -detected T Tauri stars

4.1. Derivation from source count rates

We assume a fiducial TTS X-ray spectrum (see Montmerle 1996) having =1 keV plasma, with cosmic abundances, and Raymond-Smith line emissivities, and with interstellar absorption based on Morrison & McCammon (1983) cross sections. We use the relation given by Ryter (1996) to estimate the hydrogen column density, , from the visual extinction, , determined from IR data ⁵: cm^-2. The intrinsic (i.e., extinction corrected) X-ray luminosities in the full ROSAT energy band (0.1-2.4 keV), , were calculated for classified sources from source count rates for pc using EXSAS, and are given in Cols. 10-13 of Table B1. The intrinsic X-ray luminosities span the range - erg s^-1. (For X-ray sources without extinction estimates we label the detection exposure with a question mark.)

4.2. Luminosity functions of HRI -detected Class II and Class III sources

We here compare the extinction corrected X-ray luminosities of the Class II and Class III sources detected by the HRI in the ISOCAM field ⁶ in order to evaluate the contribution of the circumstellar disk to the X-ray absorption, or to the X-ray emission (for instance by magnetic reconnection between the star and the disk; see Montmerle et al. 2000).

Fig. 3 shows the cumulative X-ray luminosity distribution functions for these two populations, estimated using the ASURV statistical software package (rev. 1.2; ⁷ Lavalley et al. 1992), which takes upper limits into account. These distributions are mathematically identical to the maximum likelihood Kaplan-Meier estimator (Feigelson & Nelson 1985). Their mean X-ray luminosities (in erg s^-1) are given by for Class II sources, and for Class III sources. We used nonparametric two-sample tests implemented in ASURV - Gehan's generalized Wilcoxon test, Logrank test, Peto & Peto generalized Wilcoxon test, Peto & Prentice generalized Wilcoxon test - to see whether the difference between the two luminosity functions is significant. These tests gave a high probability (46-72 ) that they are statistically indistinguishable. This result agrees with previous deep studies of the Oph main cloud (CMFA) and Chamaeleon I (Feigelson et al. 1993; Lawson et al. 1996) YSO populations.

Fig. 3. Cumulative normalized X-ray luminosity functions of Class II and Class III sources detected with the HRI in the Oph cloud. The dashed (dotted) histogram shows the Class II (Class III) source integral X-ray luminosity functions. The solid histogram shows the total cumulative X-ray luminosity functions. The straight line shows the fit for the total cumulative X-ray luminosity functions. The left scale gives the Kaplan-Meier estimator. The right scale gives the cumulative number of X-ray sources.

In contrast, Neuhäuser et al. (1995) found in the Taurus-Auriga star-forming region that Class III sources are more X-ray luminous than Class II sources. Neuhäuser et al. (1995) used the ROSAT   All Sky Survey (RASS ) to cover a large area of the Taurus-Auriga ( square degrees), including dense cores, but also away from this star-forming region. This shallow survey and large area must be compared to our deep pointed observations, where our field of interest covers 0.5 square degrees. In our observations we focus only on the dense cores, studying a younger population of YSO. Contamination of the T Tauri star sample by a more evolved, wide-spread, and older Class III source population, may explain the discrepancy with the result of Neuhäuser et al. (1995). ⁸

Thus, we confirm that the contribution of the disk of Class II sources to their X-ray emission, or to X-ray absorption, must be small.

Next, we combine the X-ray luminosity distributions of Class II and Class III sources to obtain the cumulative X-ray luminosity distribution function of all TTS detected by the HRI . For between 29.7 () and 31.3 (), the distribution is loglinear: . For , the distribution shows a downwards trend, which is due to our lower efficiency to detect weak X-ray emitting TTS. We deduce from this linear relation the total X-ray luminosity emitted by the X-ray sources with X-ray luminosity between and (an arbitrary value): . Thus, the total X-ray luminosity of this group of X-ray sources is dominated by the brightest sources (with ), and is very weakly dependent on the loglinear fit. For , we find erg s^-1. This value is close to the asymptotic value erg s^-1 obtained taking , thus future detections of new X-ray emitting TTS with low X-ray luminosity will not greatly affect this result.

4.3. HRI source variability

We present in Appendix C a study of the variability of the X-ray sources which were observed both by the HRI and the PSPC , and we show that some sources were in a high X-ray state during the HRI or the PSPC observations. Here, we study the variability of the Core F HRI sources.

Core F observations comprise three time-separated observations, which allow us to reiterate the "Christmas tree" luminosity study made with Einstein Observatory by Montmerle et al. (1983). The idea suggested by the similarity between Class II sources and Class III sources in X-rays was to assume that all the X-ray sources are basically one single type of X-ray object, seen in different states. The result was that the distribution of the flux variations could be approximated by a power-law with an index .

We have estimated whenever possible for each Core F HRI source the X-ray flux variations from the observed high/low luminosity ratio, , based on the three observations. This yields 27 values including 11 lower limits. The integral distribution for a given ratio is estimated using the maximum likelihood Kaplan-Meier estimator (see Fig. 4). We find a power-law distribution: , with an index . This implies that the differential distribution follows a power-law distribution of slope .

Fig. 4. Distribution of X-ray luminosity variations. We have estimated whenever possible for each X-ray source of core F the X-ray variability amplitude with the ratio high- on low-observed luminosity during the three observations. The frequency distribution has been estimated using the maximum likelihood Kaplan-Meier estimator. We find a power-law distribution: , with , consistent with a variability due to stellar flares, which supports the analogy with the solar magnetic activity.

We suggest following Montmerle et al. (1983) that this power-law behavior, may be explained in terms of variability due to stellar flares, if interpreted in terms of stochastic relaxation phenomenon (Rosner & Vaiana 1978), and dominating the X-ray activity of the underlying stars. Such a power-law behavior is seen in the solar flares in radio, optical, soft and hard X-ray emission with the power-law index =1.1-3.0 (see review in Aschwanden et al. 1998). For soft X-ray emission =1.7-1.9, which is consistent with our result, and supports the analogy with the solar magnetic activity.

© European Southern Observatory (ESO) 2000

Online publication: June 30, 2000
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