Owing to this new set of observations we can first update the
V magnitude of the brightest maximum and the faintest minimum of the
twelve Miras reported
in Table 1 (click here). We indeed observed 11 new extrema that are given
in Table 3 (click here). The new values differ most of the
time by about 
mag but larger discrepancies occur for
some new faintest minima.
Figure 3: Correlation between the B, 
and 
amplitudes with
respect to the V one
Complete visible and colour lightcurves have been reconstructed for all
the Miras except for R Cha, RY Hyi and RU Oct for which the minimum
of luminosity was not precisely observed. For several stars the minimum is found
after 
(W Hyi, X Hyi, R Oct, T Oct and RT Oct).
For these stars the rising branch is indeed
steeper than the declining one. However the minimum
is found at 
for W Cha and V Oct and at 
for V Cha and U Tuc.
Finally the visible lightcurves are rather normal in the sense that no
double maxima or large humps are observed.
The amplitudes of the light-curves are always decreasing
with wavelength from the B filter to 
.
The largest amplitude is indeed found in B (except for
W Cha, X Hyi and RT Oct where it is found in U) while the smallest one
is always found in 
.
A clear relation also exists between the
B, 
or 
amplitudes and the V amplitude (see Fig. 3 (click here)).
A Mira with a large amplitude in the V band (
) also exhibits
large 
, 
and 
. No such relation is
found between 
and 
since the U lightcurve looks
very irregular.
As for the period of the lightcurves they are constant in each colours.
No clear correlation were found between the amplitudes in the five
filters and the period.
The shape of the colour index variations can differ strongly from one colour
to another and from star to star.
The (B-V) colour index generally increases when the star becomes
fainter and decreases when it becomes brighter. For some stars
(R Cha, RY Hyi, RU Oct and U Tuc) (B-V) is almost constant over the whole
cycle (
mag). Larger (B-V) varations are found for
V Cha and R Oct, the two stars in our sample with a period larger
than 400 days. The (U-B) colour
exhibits much more irregular variations than the other ones.
It seems however that a small phase shift
might exist between V and (U-B) (
and (U-B)
is in advance).
The flux emitted in U and B is extremely
low for stars that reach late spectral types. For this reason the Miras
lacking (U-B) and/or (B-V) are most of the time stars close to their
minimum of luminosity. Finally
(V-
) and (V-
) vary both in phase but contrarily to the V magnitude.
The stars are redder around their minimum of luminosity.
No lag is detected between visual and redder light-curves.
As for the colour amplitudes (V-
) reaches a range of 1.8 mag from 0.63
to 2.44, conversely (V-
) has a range with the same amplitude
from 1.13 to 2.99. The (B-V) and (U-B) ranges are 1.6
(from 0.4 to 2.0) and 1.5 (0.3 to 1.8) respectively.
Finally it is interesting to note that the (U-B) colour index
might be negative at some phases.
This colour is even almost always negative for V Cha (except twice
around the maximum of luminosity). However it stayed positive for
W Cha, RY Hyi, T Oct, RT Oct and RU Oct.
A larger flux in U than in B has already been observed by Eggen (1975a)
and Celis (1986a). The spectrum of a Mira variable can thus be very
far from a blackbody distribution in this spectral interval.
Celis proposed that this phenomenon could be the signature of some emission
lines. But we mainly observed negative (U-B) around the
minimum of luminosity. It is known that very few
emission lines are observed
at such phases in Mira spectra (see Querci 1986b, for instance).
Furthermore these lines are very narrow with respect to the width of
the filters and very huge emissions (never observed around 
)
should be present in the spectrum to increase sufficiently the flux in U.
Therefore this might be in contradiction with the Celis proposition.
We did not find any criteria (period or other characteristics) to separate
the Miras with negative (U-B) at some phases and the other ones.
However all these events (39 in all) occured when
the derived spectral types of the stars are between M6 and M8 (except one case
for W Hyi at M5.2) although all the Miras with such spectral types do not
exhibit negative (U-B).
Furthermore Celis (1986a) observed 11 negative (U-B) in five Miras which
spectral types were in the range 
. Similarly )eggen75a reported such facts for R Leo around 
, R Car
at 
, R Oct at 
and RR Sgr at
. The spectral type
of these stars at these phases is known to be also in the range 
(Kholopov et al. 1985).
We thus propose that negative (U-B) colour indexes could be related to
opacity effects occuring around spectral types 
.
This should however be confirmed spectroscopically
and/or with model atmospheres of LPV.
Although the main shape (i.e. period, asymmetry, etc.) of the
light-curves appears reproducible from cycle-to-cycle, variations as large
as 0.5-1 mag in the V filter can occur between successive cycles.
Larger and more frequent cycle-to-cycle scatters are observed in (U-B) than
in the other colours.
It is even sometimes difficult to define a regular variation in this
colour (see RY Hyi for instance).
These large cycle-to-cycle variations of short-wavelength observations argue
that this spectral domain is not a good one to use for establishing the
intrinsic properties of Miras.
However the (V-
) and (V-
) lightcurves are
much more regular from cycle-to-cycle. This smaller scatter of the red
light-curves leads
to rather small cycle-to-cycle variations of the derived spectral types as it
will be shown in the next subsection.
Some of the larger scatters are found around the maximum of luminosity.
For instance a deviation larger than 1.5 mag is observed in all the filters at
between the third and fifth observed cycles of T Oct.
The maximum of luminosity of RU Oct was also hardly defined.
The V maximum of the n = 1 and n = 4 observed cycles are very close
while the maximum of the second cycle seems to be half a magnitude fainter.
Furthermore the third cycle is also fainter and the shape of the lightcurve
is much flatter. Similar cycle-to-cycle variations are also observed in
all the other filters for this Mira.
Such large scatters at maximum visual light from one cycle to another
could explain the range of periods suggested for some stars. For instance
Bateson & Goltz (1991) proposed for W Cha a shorter period (3 days less)
than Kholopov et al. (1985). It is however difficult to confirm this
shorter period with our data.
On the other hand Eggen (1975b) pointed out that the main variations from
cycle-to-cycle are on the rising branch whereas the decreasing branch is less
changed. Our set of data seems to follow the same trend.
Around 
a 1-mag variation has been detected in the
visual lightcuve of R Cha between the first and two later cycles
(the second and the fourth ones). Several observed points confirm that this
event is real. The ascending branch of the first cycle is well sampled
with four observations and three points have been collected in the
n = 2 and n = 4 cycles.
It is interesting to note that this cycle-to-cycle
variation is not observed in the other filters or at least with a much smaller
amplitude. Another example has been recorded around 
in
V Cha, one of the only star exhibiting a rather smooth
lightcurve. The minimum of its n = 3 cycle seems to have been much fainter
and also much redder than the first one.
The star was also too faint in U and B to
be measured at that time. However the following maximum seems entirely normal.
Some ``odd" variations occuring during a cycle have also been recorded.
For instance, just before the third observed maximum of R Oct,
a sudden drop in V has been recorded. Its visual magnitude increased normally
around V = 8 during two consecutive nights at JD = 2449669 and then ten
days later at V = 7.76. The following night (JD = 2449680)
we recorded V = 10.03, i.e.
a sudden decline of more than 2.2 mag. The star seemed again normal
20 days later. We have checked that this ``odd" measurement was real by comparing
the observations of the other Miras at the same time. R Oct was the only
star exhibiting such a variation that given night.
Furthermore the two consecutive nights
when this event occurred were very good photometrically speaking.
Since the (U-B) and (B-V) colours were constant during these two nights
a variation with a similar amplitude also occured in the B and V filters.
Unfortunately no measurements were made in 
and 
during the first night.
But (V-
) and (V-
) recorded during the second night are coherent with
the ones collected at similar phase.
Another example of a similar variation has been recorded just around the
fourth recorded maximum of luminosity of RY Hyi. At JD = 2449603 the
star was close to 
with V = 10.6. Three weeks later
we recorded V = 11.2 and then V = 10.1 ten days later. This Mira thus had a
``odd" decline with an amplitude of 1 mag around its maximum of luminosity.
Similar variations were also recorded for this star
through the other filters at that time.
All these ``odd" events are characterized by short-term (compared to the
period of the stars) variations in
magnitude. They can be close to the LPV rapid variations reported by
Maffei & Tosti (1995). These authors indeed observed several LPV variations
in the B and I filters with amplitudes larger than 0.5 mag and durations
ranging from one day to one month.
Mennessier et al. (1995) also reported the probable detection of similar
short-term variations by the Hipparcos satellite.
Such events were actually suspected in the past
in Miras and semi-regular variables (see Querci 1986a, and
Schaefer 1991).
We thus report two new events confirming the presence of short-term
variations in oxygen-rich Miras.
Figure 4: The derived spectral type variations of the twelve Miras during
their cycle.
The different symbols correspond to the succesive cycles observed
(same as Fig. 2 (click here))
Owing to the Celis method (cf. Sect. 2) the spectral type variations can be derived and then studied over the whole cycle. We actually give for the first time these variations for several Miras with a rather good sampling in phase. However let's note that M giants are usually embedded in circumstellar envelopes and their spectrum may thus be reddened. This could affect the derived spectral types. This phenomenon is neglected in this work but might be important in some stars as X Hyi and R Cha around which IRAS detected oxygen-rich envelopes.
One can see in Fig. 4 (click here) that the derived spectral type of all the
selected Miras varies strongly during the cycle (from 1.3 to 4.5 subtypes).
We report in Table 3 (click here) the new
spectral type extrema for the Miras of our sample (updating the
previously known given in Table 1 (click here)).
We also give in this Table 3 (click here) the amplitude of the spectral
type variations.
Let's recall that the lightcurves of R Cha, RY Hyi and RU Oct are not
well sampled around 
. The derived spectral type amplitude of these
stars is thus underestimated. In another respect
since the spectral types are calculated from the (V-
) and (
)
colour indexes they vary in phase with them and contrarily to the
V magnitude. This thus leads to earlier
derived spectral types around the maximum of the cycle than around the
minimum as it is well known.
Furthermore the derived spectral types at maximum are most of the time
earlier than M6
while the ones at minimum are later than M7.7.
Therefore all the Miras in our
sample exhibit a cycle of formation/dissociation of the VO molecule.
The derived spectral type versus phase curves are nearly regular for most
of the Miras of our sample. Except for W Cha the cycle-to-cycle variations at a
given phase are indeed smaller than half a subtype. This is directly related
to the smaller variations recorded in the red filters than in the bluer ones:
the lightcurves are indeed very regular in (V-
) and (V-
).
The case of W Cha is interesting. All the spectral types derived during
a specific cycle vary regularly but strong cycle-to-cycle variations are
detected. They reach more than one subtype from one cycle to another.
A few other odd variations have also been detected. For instance,
the derived spectral type of RT Oct changes from M6.8 to M5.2 in less than
two weeks
in November 1991 and from M4.1 to M2.8 in 20 days in December 1995.
However the regularity of the derived spectral type variations is most of
the time well verified for the other stars.
Table 4: Derived visual absolute magnitude at maximum light and distance of
the observed Mira variables
The distance of the studied stars can be estimated from their
UBVRI photometry.
Celis (1986b, Eq. (5)) indeed showed that the visual absolute magnitude at
maximum light (
) of Miras can be determined from
their period and their spectral type at 
.
We prefered to use this method than the ones proposed
by Celis (1995) because the dependence of 
with respect to the period
of the star is explicitely taken into account in agreement with all other
methods.
From our observed 
and the corresponding derived
spectral type we then report in Table 4 (click here) the
and the distance of
all the Miras of our sample.
The interstellar extinction (
) was estimated by using the results
of Arenou et al. (1992). They compared their model of galactic
interstellar extinction with previous works
and conclude that their estimates of 
are very good for regions
having 
mag (case for all the Miras of our sample).
Finally let's note that the deduced distances might be slightly
overestimated because the actual maximum of the cycle (and hence its
derived spectral type) has perhaps not been observed.
It is interesting to see how distances derived from these relations and
our data compare with those derived by other methods. Let's first
point out that the best distances come from infrared magnitudes
for Miras in the LMC (disregarding parallaxes because the sample
is so small).
We found eight stars in our sample with previously known
distances (Celis 1981;
Jura & Kleinmann 1992 or
Celis 1995).
They are compared in Table 5 (click here).
Celis (1981) derived the distance
from his (
, P, 
) relation while
Jura & Kleinmann (1992) used the (P, 
) relation of Feast et al. (1989) modified by
Wood (1990). Finally
Celis (1995) used purely photometric
and/or spectral-photometric methods.
Except for X Hyi and one previous estimate of R Oct our derived distances
are consistent with
those found in the literature (the mean difference is less than 22%).
The large discrepancy found between our distance estimate of
X Hyi and the Jura & Kleinmann's one can not be explained easily.
The maximum we observed is rather well defined and no large cycle-to-cycle
variations are found for this star. But we can not exclude a-priori
that the cycles we observed were not peculiar.
Furthermore X Hyi is known to have an oxygen-rich envelope (see its
LRS spectral classification). This might affect strongly the
colours we observed and thus the derived spectral types and distance.
On the other hand Jura & Kleinmann
did not find any photometry of X Hyi in the K band. They
deduced its distance by estimating its K magnitude from the IRAS flux
at 12 
m and the Two Micron Sky Survey flux at
2 
m.
However the K-magnitude may be poorly estimated from the 2 and
12 
m fluxes because of the circumstellar envelope surrounding this
star. This peculiar
Mira thus differs from a ``normal" star and should be treated
more carefully. As for R Oct our distance determination is
larger than the Celis's ones and than the distance
deduced from the period-infrared luminosity relation
derived by Feast et al. (1989). The K magnitude of R Oct
has been found
in Catchpole et al. (1979). Our estimate is certainly
the worst one
since the observed visible maximum of this star varies strongly
from one cycle
to another (up to 
mag). The actual maximum is therefore badly
defined. This could also explain the discrepancy reported
in Table 5 (click here) for RU Oct.
In order to confirm that this method could actually lead to rather good distance
estimates we also compare in Table 5 (click here) the distance
of some other Miras calculated with this method
and previous independent determinations. The main difficulty
was to find UBVRI observations at 
.
We only found such observations of o Cet around its maximum of luminosity in
Mendoza (1967) and R Leo was observed by
Eggen (1975a) at 
.
Some other Miras were also observed by Eggen (1975a) around 
.
The 
data of Mendoza and the 
data of Eggen were
converted into the Cousins system using the colours transformations derived
by Bessel (1983) and
Bessel & Weis (1987) respectively. Finally
Celis (1986b) also reported for some Miras 
and 
calculated with the same method as the one we use in the present paper.
The previously known distances of these
stars were found in Jura & Kleinmann (1992);
Celis (1995)
and Haniff et al. 1995 (who used the (P, 
) relation
of Feast et al. 1989). o Cet and R Leo are the only Miras for
which trigonometric
parallaxes exist and direct estimate of their distance can be made
(Jenkins 1952 and Gatewood 1992 respectively).
We do not report the distances deduced by Eggen himself (1975b) because
they differ to a great extent from ours and more recent ones
(this was first pointed out by Celis 1981).
Eggen actually deduced his period-luminosity relation
from a correlation found between the period and the (R-I) colour at 
derived with nine stars only. Our data do not fit his (P, R-I) relation
transformed into the Cousins system using Bessel & Weis
(1987). We therefore question
this relation and that could explain
why Eggen derived distances in disagreement with all other estimates.
Finally the distance
we deduced for o Cet is in good agreement with its parallax and other
estimations but a difference of 
and sometimes larger with respect to
other works is found for R Leo. This discrepancy
could easily be explained by the lack of UBVRI data at the real maximum
of luminosity of this star.
A rather large departure is also found between our derived distance
of R Hya and the one of Celis (1995) whereas it is quite close to the
two other previous determinations. However the agreement between our
distance determinations and the previous ones is actually rather
good for all the other stars (mean departure smaller than 
).
The photometric method proposed by Celis leads thus to rather good distance estimates IF UBVRI data at the REAL maximum of luminosity are available. The mean departure with respect to other determinations is actually close to their own error bars. However we have already pointed out that the lightcurve of some Miras exhibits strong cycle-to-cycle variations especially around their maximum of luminosity. Since we derived their distance from their magnitude and colours at that time it actually might not be very accurate and several maxima should be observed to increase the accuracy of the method.