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.
RR Lyr is one of the most studied variable stars. Its light curve has been regularly monitored since the discovery of the periodic variability in 1899. Analysis of all observed maxima allows us to identify two primary pulsation states defined as puls
ation over a long (P0 longer than 0.56684 d) and a short (P0 shorter than 0.56682 d) primary pulsation period. These states alternate with intervals of 13-16 yr, and are well defined after 1943. The 40.8 d periodical modulations of the amplitude and the period (i.e. Blazhko effect) were noticed in 1916. We provide homogeneous determinations of the Blazhko period in the different primary pulsation states. The Blazhko period does not follow the variations of P0 and suddenly diminished from 40.8 d to around 39.0 d in 1975. The monitoring of these periodicities deserved and deserves a continuous and intensive observational effort. For this purpose we have built dedicated, transportable and autonomous small instruments, Very Tiny Telescopes (VTTs), to observe the times of maximum brightness of RR Lyr. As immediate results the VTTs recorded the last change of P0 state in mid-2009 and extended the time coverage of the Kepler observations, thus recording a maximum O-C amplitude of the Blazhko effect at the end of 2008, followed by the historically smallest O-C amplitude in late 2013. This decrease is still ongoing and VTT instruments are ready to monitor the expected increase in the next few years.
We used the GEOS database to study the Blazhko effect of galactic RRab stars. The database is continuously enriched by maxima supplied by amateur astronomers and by a dedicated survey by means of the two TAROT robotic telescopes. The same value of th
e Blazhko period is observed at different values of the pulsation periods and different values of the Blazhko periods are observed at the same value of the pulsation period. There are clues suggesting that the Blazhko effect is changing from one cycle to the next. The secular changes in the pulsation and Blazhko periods of Z CVn are anticorrelated. The diagrams of magnitudes against phases of the maxima clearly show that the light curves of Blazhko variables can be explained as modulated signals, both in amplitude and in frequency. The closed curves describing the Blazhko cycles in such diagrams have different shapes, reflecting the phase shifts between the epochs of the brightest maximum and the maximum O-C. Our sample shows that both clockwise and anticlockwise directions are possible for similar shapes. The improved observational knowledge of the Blazhko effect, in addition to some peculiarities of the light curves, have still to be explained by a satisfactory physical mechanism.
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.
The theory of stellar evolution can be more closely tested if we have the opportunity to measure new quantities. Nowadays, observations of galactic RR Lyr stars are available on a time baseline exceeding 100 years. Therefore, we can exploit the possi
bility of investigating period changes, continuing the pioneering work started by V. P. Tsesevich in 1969. We collected the available times of maximum brightness of the galactic RR Lyr stars in the GEOS RR Lyr database. Moreover, we also started new observational projects, including surveys with automated telescopes, to characterise the O-C diagrams better. The database we built has proved to be a very powerful tool for tracing the period variations through the ages. We analyzed 123 stars showing a clear O-C pattern (constant, parabolic or erratic) by means of different least-squares methods. Clear evidence of period increases or decreases at constant rates has been found, suggesting evolutionary effects. The median values are beta=+0.14 day/Myr for the 27 stars showing a period increase and beta=-0.20 day/Myr for the 21 stars showing a period decrease. The large number of RR Lyr stars showing a period decrease (i.e., blueward evolution) is a new and intriguing result. There is an excess of RR Lyr stars showing large, positive $beta$ values. Moreover, the observed beta values are slightly larger than those predicted by theoretical models.
