If we want to estimate the completeness of the discovered TTS population of TTS in Lupus, we have to take into account first that not all TTS within the region of interest are detected by ROSAT as X-ray sources, and second that not all of the detected X-ray sources in the region of interest have been spectroscopically studied as yet.
Although spatially complete, the RASS is flux limited. Therefore, in order to estimate the fraction of TTS that escaped detection, ideally we have to compare the X-ray luminosity function (XLF) of the RASS-discovered WTTS with an unbiased XLF of WTTS, thus determining which fraction of this unbiased XLF is sampled by the RASS in Lupus.
For the construction of the XLF of the newly discovered
WTTS we followed the procedure described in detail in previous papers
(Neuhäuser et al. 1995b; Wichmann et al. 1996).
We calculate luminosities 
for our new WTTS as
where Z is the broadband count rate,
r the distance to the Lupus SFR, taken
to be 140pc (Hughes et al. 1993),
while ECF denotes the energy conversion
factor. ECF was calculated individually for each TTS of our sample
by fitting Raymond-Smith spectra (Raymond & Smith 1977)
to the observed X-ray hardness ratios in the way described in
Neuhäuser et al. (1995b).
Since photometry is available for many of our new WTTS
(Wichmann et al. 1997), we were able to calculate
for these
stars, thus in these cases the only free parameter for the fit was 
. For stars with no known 
, fits were done
with two free parameters (temperature 
, and hydrogen
column density 
). The X-ray data for all ROSAT-discovered TTS are
given in Table 10, the fit results for the X-ray luminosity in
Table 11, respectively.
Figure 1: X-ray luminosity functions of RASS-discovered WTTS (solid line) and
WTTS discovered by pointed ROSAT observations (dotted line) in Lupus,
as compared with X-ray luminosity functions of Lupus CTTS
(left panel, broken line) and optically discovered
Taurus WTTS (right panel, broken line). Data for Taurus WTTS were taken from
Neuhäuser et al. (1995b)
Table 4: X-ray luminosities of new Lupus WTTS (a: RASS-discovered,
b: discovered by pointed observations), Lupus CTTS in the Lupus 1-3 clouds,
and (for comparison) Taurus WTTS.
Data for Taurus WTTS from Neuhäuser et al. (1995b).
Due to the large number of upper limits, no
reliable estimate for 
is possible for
the Lupus CTTS
X-ray luminosities for TTS known prior to ROSAT
are given in Table 12, as
obtained from the pointed observations listed
in Table 1 (click here) to 3 (click here), with
calculated from published values of
the visual extinction 
(Hughes et al. 1994).
For the conversion from 
to 
we used the relation
following the detailed investigation of
absorption in the local environment and of TTS by Paresce (1984)
and Vrba & Rydgren (1985).
The best available estimate of
an unbiased XLF of WTTS
is presumably given by
the XLF of WTTS that originally were optically
discovered, i.e.
by means of 
or CaHK surveys or by proper motion surveys.
A large sample of such
WTTS in the Taurus-Auriga star forming region
has recently been studied by Neuhäuser et al. (1995b).
As found by Neuhäuser et al. (1995b), the mean X-ray
luminosity of CTTS is significantly lower than that of WTTS.
A large fraction of the previously known (i.e. optically discovered)
CTTS in Lupus have been observed in our pointed ROSAT observations
(see Table 12).
We obtain a mean X-ray luminosity of 
for the Lupus CTTS, significantly below the mean X-ray luminosity
of 
determined by
Neuhäuser et al. (1995b) for the (optically discovered) Taurus
WTTS (the number of previously
known WTTS in Lupus is too low for a meaningful comparison with CTTS).
This result agrees well with that of Neuhäuser et al. (1995b), who found
for Taurus that the CTTS are significantly less X-ray luminous than the WTTS.
We conclude that the (absorption corrected) mean X-ray luminosity of
CTTS is intrinsically lower than that of the WTTS.
In Fig. 1 (click here) we show the XLF of RASS-discovered WTTS (without WTTS discovered in pointed observations) in comparison with the XLFs of previosly known Lupus CTTS and optically discovered Taurus WTTS, respectively. Also shown is the XLF of new WTTS discovered by pointed observations in Lupus 1-3. The derived mean and median luminosities for these four samples are given in Table 4 (click here).
From Fig. 1 (click here) as well as from the data given in Table 4 (click here) we see that the mean X-ray luminosity of RASS-discovered WTTS is much higher than that one of the optically discovered Taurus WTTS, due to the bias introduced by the flux limit of the RASS. On the other hand, the XLF of the WTTS discovered by means of pointed observations in the Lupus 1-3 clouds is indistiguishable from that of the optically discovered Taurus WTTS. Thus in the Lupus 1-3 clouds, with our deep pointed observations presumably nearly all WTTS are detected as X-ray sources.
The XLF of our new WTTS has a value of 
for
,
i.e. 
of our new WTTS show an X-ray luminosity as large or
larger than this value.
However, only 
of WTTS in the
unbiased comparison sample have 
, i.e.
an X-ray unbiased sample is
complete
only to 
for an X-ray luminosity, which is exceeded by
about 80% of our RASS-detected sample of new WTTS.
We estimate therefore, that the fraction of previously unknown WTTS,
which are sampled by the RASS in Lupus, is 
.
(We use the particular value of 
,
because it lies well within both the XLFs of the new
WTTS and our comparison sample).
Here we assume, that the WTTS outside the clouds have an XLF similar to WTTS found in the regions of active star formation, like the Lupus clouds or those regions in Taurus-Auriga where WTTS have been found by optical surveys. If, however, the RASS-discovered WTTS are typically older than those of the comparison sample, as might be indicated by their spatial position far from dense clouds, then from theoretical grounds (e.g. Bouvier et al. 1996) their mean X-ray luminosity might be different. Recent models suggest, that only after dissipation of circumstellar material TTS will spin up and their activity could rise accordingly. This might also be the explanation for the generally higher X-ray luminosity of WTTS as compared with CTTS. If this holds true, it would reduce the bias introduced by X-ray selection. However, up to now little is known about the importance of other factors like, e.g., the depth of the convection zone, which decreases during the PMS evolution. Thus, it is not clear how the evolution of the XLF during the PMS phase really looks like.
Next, we discuss the incompleteness of our optical follow-up observations,
i.e. we estimate, what fraction of the WTTS detected as X-ray sources
in the RASS have been identified by our survey already and how much WTTS
are to be expected among those sources not observed as yet.
Based on the RASS data on Taurus TTS, Neuhäuser et al. (1995a)
found a selection criterium for WTTS based on the X-ray
hardness ratios HR1 and HR2, defined as
defined as
where 
, 
, 
, and 
denote the count rates
in the energy bands 0.1 to 0.4keV, 0.5 to 2.1keV, 0.5 to 0.9keV and
0.9 to 2.1keV, respectively.
86% of all Taurus WTTS known prior to ROSAT, as well as 78% of all
WTTS discovered in Taurus by follow-up observations of RASS sources
fall in the region defined by
in the HR1 - HR2 plane.
As no selection based on hardness ratios has been used for our follow-up
observations of ROSAT sources in Lupus, we can test this criterium
a posteriori with our new Lupus WTTS. As can be seen from
Fig. 2 (click here), in fact the majority of our new WTTS occupy
the region given by Eq. (4 (click here)). Of 126 sources identified with WTTS,
74% are found inside this box, while
the percentage of WTTS among those investigated
sources located within the selection box is 67%.
Figure 2: Hardness ratios for RASS-discovered WTTS in Lupus (left panel)
as compared with hardness ratios of sources where no TTS could be found
(right panel, solid squares indicate stars dMe/dKe stars, open squares
other/no identification). The lines mark the box defined by
Neuhäuser et al. (1995a) for selection of TTS candidates
Of 437 X-ray sources in the RASS, 238 are situated within the region given by Eq. (4 (click here)). 105 of those are TTS or other sources of known nature, while 133 are sources of unknown nature. From the results quoted above, we would expect about 67% of the latter, i.e., 89 sources, to be WTTS. Moreover, these 89 WTTS should represent about 74% of all hitherto unidentified WTTS in the RASS, regardless of their hardness ratios. Thus we would expect some 120 WTTS in the RASS not yet identified.
However, in our survey we have restricted ourselves to sources where at
least one stellar object brighter than 
can be found within
the error circle. Thus, the fractions of sources inside/outside the HR box
only pertain to that subsample of sources which fullfill this optical
selection criterium. Also the number of 120 more WTTS should be regarded as an
upper limit for WTTS brighter than 
, as at least
some of the sources not yet investigated will not fullfill this optical
selection criterium. We are not able to draw any conclusions about the number
of WTTS fainter than 
or about sources where only objects
fainter than this limit can be found within the error circle. However, there
seems to be a limit on the ratio 
of X-ray fluxes
and optical
fluxes 
, which implies that WTTS fainter than 
would not be detected by the RASS anyway.
We conclude, that we have identified as yet about 
(83/203) of
the WTTS detected as X-ray sources in the RASS (where the number of 203
is the addition of the 83 WTTS yet discovered and the 120 more WTTS estimated
among the yet unidentified RASS sources), and that the WTTS which
are RASS sources represent about 
of all WTTS in Lupus.
Thus in total about 650 WTTS should be present in the Lupus SFR,
including those already found by us. In contrast, from optical surveys
(Thé 1962; Schwartz 1977) only some 48 CTTS are known
in this SFR.
Therefore, for the whole area studied, we obtain a WTTS/CTTS ratio of about 13, while for the dark clouds, where the CTTS are concentrated, the ratio is about unity. A similar variation of the WTTS/CTTS ratio has been found for the Taurus SFR (Wichmann et al. 1996; Neuhäuser et al. 1995a). This large difference is due to the completely different spatial distribution of WTTS and CTTS.