The long-term behaviours of the pulsation and Blazhko periods of RR Lyr are investigated by means of Kepler and ground-based observations. The difficulties in detecting additional modes in the Cepheids monitored with CoRoT are discussed.
Though FM Del has been considered as a RR Lyr star by Preston et al. in 1959 (following discovery by Huth, 1957), Huth (1960) eventually changed his mind by showing that it is in fact a cepheid of W Vir type of period of 3.95452 days. Various authors
since then have considered it as a cepheid indeed, with the exception of Wils et al. (2006) who list this star in their RR Lyr catalog with a period of 0.79688 days. On this basis, FM Del was added to Tarot RR Lyr program. We present here these observations which confirm the cepheid type.
We present the results of collaborative observations of three RR Lyrae stars (CX Lyr, NU Aur and VY CrB) which have a strong Blazhko effect. This work has been initiated and performed in the framework of the GEOS RR Lyr Survey (Groupe Europeen dObser
vations Stellaires). From the measured light curves, we have determined the times and the magnitudes at maximum. The times of maxima have been compared to ephemerides to obtain the (O-C) values and from a period analysis of these (O-C) values, the Blazhko period is derived. The Blazhko periods of NU Aur (114.8 days) and VY CrB (32.3 days) are reported here for the first time and a more accurate period for CX Lyr (68.3 days) has been obtained. The three stars are subject to strong Blazhko effect, but this effect has different characteristics for each of them. When we compare the variations of magnitude at maximum and variations of (O-C) values with respect to the Blazhko phase, these variations are either in phase, in opposition, or even in quadrature.
The Blazhko effect in CX Lyr has been reported for the first time by Le Borgne et al. (2007). The authors have pointed out that the Blazhko period was not evaluated accurately due to dataset scarcity. The possible period values announced were 128 or
227 days. A newly conducted four-month observing campaign in 2008 (fifty-nine observation nights) has provided fourteen times of maximum. From a period analysis of measured times of maximum, a Blazhko period of 62 +/- 2 days can be suggested. However, the present dataset is still not densely sampled enough to exclude that the measured period is still a modulation of the real Blazhko period. Indeed the shape of the (O-C) curve does not repeat itself exactly during the campaign duration.
In this paper we compute the singular homology of the space of immersions of the circle into the $n$-sphere. Equipped with Chas-Sullivans loop product these homology groups are graded commutative algebras, we also compute these algebras. We enrich Mo
rse spectral sequences for fibrations of free loop spaces together with loop products, this offers some new computational tools for string topology.
