  We conducted a 12-month monitoring campaign of 33 T Tauri stars (TTS) in
Taurus. Our goal was to monitor objects that possess a disk but have a weak
Halpha line, a common accretion tracer for young stars, to determine whether
they host a passive circumstellar disk. We used medium-resolution optical
spectroscopy to assess the objects' accretion status and to measure the Halpha
line. We found no convincing example of passive disks; only transition disk and
debris disk systems in our sample are non-accreting. Among accretors, we find
no example of flickering accretion, leading to an upper limit of 2.2% on the
duty cycle of accretion gaps assuming that all accreting TTS experience such
events. Combining literature results with our observations, we find that the
reliability of traditional Halpha-based criteria to test for accretion is high
but imperfect, particularly for low-mass TTS. We find a significant correlation
between stellar mass and the full width at 10 per cent of the peak (W10%) of
the Halpha line that does not seem to be related to variations in free-fall
velocity. Finally, our data reveal a positive correlation between the Halpha
equivalent width and its W10%, indicative of a systematic modulation in the
line profile whereby the high-velocity wings of the line are proportionally
more enhanced than its core when the line luminosity increases. We argue that
this supports the hypothesis that the mass accretion rate on the central star
is correlated with the Halpha W10% through a common physical mechanism.
