*Astron. Astrophys. 332, L53-L56 (1998)*
## 4. The PL relation and LMC distance modulus
The PL relation of Miras can be used to determine the distance
modulus to LMC (van Leeuwen et al. 1997). Here, we calculate the
slopes and zero-points of the mean PL relation for Sample 1. Some care
is needed since gaussian parallax errors propagate into non-gaussian
errors in distances or absolute magnitudes and a bias may result
(Smith & Eichhorn 1996). To avoid this, one can write:
where
and The estimated true
annual parallax of the star, in mas, is taken
from Table 1. The mean (variations) dereddened apparent magnitude
is , the mean (stat.) absolute magnitude is
that a 1 day-period star would have, and
*s* is the slope of the PL relation. A non-linear fit of Eq. (1)
was computed from the E04HFF routine of the NAG software to
minimize:
where the are the data weights. We have used
successively (unweighted) and
where K is a constant, which is the usual
choice. Having derived *a* and *b*, the corresponding
*s* -value is replaced in:
and the absence of correlation between the computed right hand side
and is checked for. The best results were
obtained from weighted data and the corresponding values of *s*
and are given in Table 2. Fits in Fig. 1b
(C-LPVs from references in Sect. 3.1) and from Reid et al. (1995, O-
and C-LPVs) are also given which show nearly identical *s*
-slopes for the Galaxy and LMC. It is thus advisable to deduce the LMC
distance modulus by difference of the intercepts. We obtain
. No correction was applied for metallicity as
suggested by current evidence from various stellar systems (Feast et
al. 1996). The modulus quoted in Table 2 would otherwise be a
lower limit. The slopes of the upper limit (ul in Fig. 1) were
similarly calculated (Figs. 1a: 22 stars including 14 with appreciable
weight and 1b: 13 stars). Values of -4.85 in the Galaxy and -4.72 in
the LMC were found. No estimate of the distance modulus is attempted
here.
**Table 2.** The PL-relation of galactic and LMC carbon LPVs (*s* is the slope, the intercept and *n* the number of stars). Eq. (3): slope vs. , intercept and correlation coefficient.
© European Southern Observatory (ESO) 1998
Online publication: March 30, 1998
helpdesk.link@springer.de |