L. Jetsu

Surface imaging of HD 199178 (V1794 Cygni)

We present surface temperature maps for the FK Comae-type star HD 199178 (V1794 Cygni) calculated from high resolution spectra obtained in 1994 and 1995. The spot pattern evolves, but all maps reveal a large cool spot remaining nearly at the same high latitude. The main spot is 1200-1600 K cooler than the mean surface temperature. The observed slightly flat bottomed absorption lines would usually be interpreted as evidence for a large cool polar spot. We argue that antisolar surface differential rotation offers a better explanation for the box like shape of the line profiles. However, we do not find conclusive evidence for antisolar differential rotation and note that there are still other possible explanations for the slightly flat bottomed line profiles.

Flip-flops of FK Comae Berenices

Context. FK Comae Berenices is a rapidly rotating magnetically active star, the light curve of which is modulated by cool spots on its surface. It was the first star where the “flip-flop” phenomenon was discovered. Since then, flip-flops in the spot activity have been reported in many other stars. Follow-up studies with increasing length have shown, however, that the phenomenon is more complex than was thought right after its discovery. Aims. Therefore, it is of interest to perform a more thorough study of the evolution of the spot activity in FK Com. In this study, we analyse 15 years of photometric observations with two different time series analysis methods, with a special emphasis on detecting flip-flop type events from the data. Methods. We apply the continuous period search and carrier fit methods on long-term standard Johnson-Cousins V-observations from the years 1995−2010. The observations were carried out with two automated photometric telescopes, Phoenix-10 and Amadeus T7 located in Arizona. Results. We identify complex phase behaviour in 6 of the 15 analysed data segments. We identify five flip-flop events and two cases of phase jumps, where the phase shift is Δ φ 0.031. Conclusions. The flip-flop cannot be interpreted as a single phenomenon, where the main activity jumps from one active longitude to another. In some of our cases the phase shifts can be explained by differential rotation: two spot regions move with different angular velocity and even pass each other. Comparison between the methods show that the carrier fit utility is better in retrieving slow evolution especially from a low amplitude light curve, while the continuous period search is more sensitive in case of rapid changes.

Spot activity of LQ Hydra from photometry between 1988 and 2011

Aims. We investigate the spot activity of the young magnetically active main sequence star LQ Hya. Our aims are to identify possible active longitudes, estimate the differential rotation, and study long and short term changes in the activity. Methods. Our analysis is based on 24 years of Johnson V-band photometry of LQ Hya obtained with the T3 0.4 m Automated Telescope at the Fairborn Observatory. We use the previously published continuous period search (CPS) method to model the evolution of the light curve of LQ Hya. The CPS fits a Fourier series model to short overlapping subsets of data. This enables us to monitor the evolution of the light curve and thus the spot configuration of the star with a higher time resolution. Results. We find seasonal variability in the mean level and amplitude of the light curve of LQ Hya. The variability of the light curve amplitude seems not to be cyclic, but the long-term variations in the mean magnitude may be indicative of an approximately 13 year cycle. However, because of the limited length of the observed time series, it is not yet possible to determine whether this structure really represents an activity cycle. Based on fluctuations of the light curve period, we estimate the differential rotation of the star to be small, and the star is potentially very close to a rigid rotator. We search for active longitudes from the inferred epochs of the light curve minima. We find that on time scales up to six months there are typically one or two relatively stable active areas on the star with limited phase migration. On the other hand, on time scales longer than one year, no stable active longitudes have been present except for the period between 2003 and 2009 and possibly also some time before 1995. Neither do we find any signs of flip-flops with a regular period. The mean time scale of change of the light curve during the observation period is determined to be of the same order of magnitude as the estimated convective turnover time for the star.

The continuous period search method and its application to the young solar analogue HD 116956

Aims. We formulate an improved time series analysis method for the analysis of photometry of active stars. This new continuous period search (CPS) method is applied to 12 years of V band photometry of the young solar analogue HD 116956 (NQ UMa). Methods. The new method is developed from the previous three stage period analysis (TSPA) method. Our improvements are the use of a sliding window in choosing the modelled datasets, a criterion applied to select the best model for each dataset and the computation of the time scale of change of the light curve. We test the performance of CPS with simulated and real data. Results. The CPS has a much improved time resolution which allows us to better investigate fast evolution of stellar light curves. We can also separate between the cases when the data is best described by periodic (i.e. rotational modulation of brightness) and aperiodic (e.g. constant brightness) models. We find, however, that the performance of the CPS has certain limitations. It does not determine the correct model complexity in all cases, especially when the underlying light curve is constant and the number of observations too small. Also the sensitivity in detecting two close light curve minima is limited and it has a certain amount of intrinsic instability in its period estimation. Using the CPS, we find persistent active longitudes in the star HD 116956 and a “flip-flop” event that occurred during the year 1999. Assuming that the surface differential rotation of the star causes observable period variations in the stellar light curve, we determine the differential rotation coefficient to be |k| > 0.11. The mean timescale of change of the light curve during the whole 12 year observing period was T C = 44.1 d, which is of the same order as the predicted convective turnover time of the star. We also investigate the presence of activity cycles on the star, but do not find any conclusive evidence supporting them.

Multiperiodicity, modulations and flip-flops in variable star light curves - II. Analysis of II Pegasus photometry during 1979–2010

Aims. According to previously published Doppler images of the magnetically active primary giant component of the RS CVn binary II Peg, the surface of the star was dominated by one single active longitude that was clearly drifting in the rotational frame of the binary system during 1994-2002; later imaging for 2004–2010, however, showed decreased and chaotic spot activity, with no signs of the drift pattern. Here we set out to investigate from a more extensive photometric dataset whether this drift is a persistent phenomenon, in which case it could be caused either by an azimuthal dynamo wave or be an indication that the binary system’s orbital synchronization is still incomplete. On a differentially rotating stellar surface, spot structures preferentially on a certain latitude band could also cause such a drift, the disruption of which could arise from the change of the preferred spot latitude. Methods. We analyzed the datasets using the carrier fit (CF) method, which is especially suitable for analyzing time series in which a fast clocking frequency (such as the rotation of the star) is modulated with a slower process (such as the stellar activity cycle). Results. We combined all collected photometric data into one single data set and analyzed it with the CF method. We confirm the previously published results that the spot activity has been dominated by one primary spotted region almost through the entire data set and also confirm a persistent, nearly linear drift. Disruptions of the linear trend and complicated phase behavior are also seen, but the period analysis reveals a rather stable periodicity with Pspot = 6. d 71054 ± 0. 00005. After removing the linear trend from the data, we identified several abrupt phase jumps, three of which are analyzed in more detail with the CF method. These phase jumps closely resemble what is called a flip-flop event, but the new spot configurations do not persist for longer than a few months in most cases. Conclusions. There is some evidence that the regular drift without phase jumps is related to the high state, while the complex phase behavior and disrupted drift pattern are related to the low state of magnetic activity. The most natural explanation of the drift is weak anti-solar (pole rotating faster than the equator) differential rotation with a coefficient k ≈ 0.002 combined with the preferred latitude of the spot structure.

Did the Ancient Egyptians Record the Period of the Eclipsing Binary Algol?The Raging One?

The eclipses in binary stars give precise information of orbital period changes. Goodricke discovered the 2.867 day period in the eclipses of Algol in the year 1783. The irregular orbital period changes of this longest known eclipsing binary continue to puzzle astronomers. The mass transfer between the two members of this binary should cause a long-term increase of the orbital period, but observations over two centuries have not confirmed this effect. Here, we present evidence indicating that the period of Algol was 2.850 days three millennia ago. For religious reasons, the ancient Egyptians have recorded this period into the Cairo Calendar (CC), which describes the repetitive changes of the Raging one. CC may be the oldest preserved historical document of the discovery of a variable star.

Spot activity of the RS Canum Venaticorum star σ Geminorum

Aims. We model the photometry of RS CVn star σ Geminorum to obtain new information on the changes of the surface starspot distribution, that is, activity cycles, differential rotation, and active longitudes. Methods. We used the previously published continuous period search (CPS) method to analyse V-band differential photometry obtained between the years 1987 and 2010 with the T3 0.4 m Automated Telescope at the Fairborn Observatory. The CPS method divides data into short subsets and then models the light-curves with Fourier-models of variable orders and provides estimates of the mean magnitude, amplitude, period, and light-curve minima. These light-curve parameters are then analysed for signs of activity cycles, differential rotation and active longitudes. Results. We confirm the presence of two previously found stable active longitudes, synchronised with the orbital period Porb = 19. 60, and found eight events where the active longitudes are disrupted. The epochs of the primary light-curve minima rotate with a shorter period Pmin,1 = 19. d 47 than the orbital motion. If the variations in the photometric rotation period were to be caused by differential rotation, this would give a differential rotation coefficient of α ≥ 0.103. Conclusions. The presence of two slightly different periods of active regions may indicate a superposition of two dynamo modes, one stationary in the orbital frame and the other one propagating in the azimuthal direction. Our estimate of the differential rotation is much higher than previous results. However, simulations show that this may be caused by insufficient sampling in our data.

Evidence of Periodicity in Ancient Egyptian Calendars of Lucky and Unlucky Days

This article presents an experiment in time series analysis, specifically the Rayleigh Test, applied to the ancient Egyptian calendars of lucky and unlucky days recorded in papyri P. Cairo 86637, P. BM 10474 and P. Sallier IV. The Rayleigh Test is used to determine whether the lucky and unlucky days are distributed randomly within the year, or whether they exhibit periodicity. The results of the analysis show beyond doubt that some of the lucky days were distributed according to a lunar calendar. The cycles of the moon thus played an important role in the religious thinking of the Egyptians. Other periods found using the Rayleigh Test are connected to the civil calendar, the mythological symbolism of the twelfth hour of the day and possibly the period of variation of the star Algol.

Detection of real periodicity in the terrestrial impact crater record: quantity and quality requirements

Aims. To determine the quantity and quality requirements for the terrestrial impact crater data which would allow reliable detection of real periodicity. Methods. Artificial impact crater data samples of different size and accuracy are simulated. Erosion is considered, as well as the effect of the unknown ratio between periodic and aperiodic impacts. The probabilities for detecting real and false periodicities are solved with the Rayleigh test from these simulated data. Results. Reliable detection of real periodicity is currently impossible – unless all impacts on Earth have been periodic.

Shifting Milestones of Natural Sciences: The Ancient Egyptian Discovery of Algol's Period Confirmed.

The Ancient Egyptians wrote Calendars of Lucky and Unlucky Days that assigned astronomically influenced prognoses for each day of the year. The best preserved of these calendars is the Cairo Calendar (hereafter CC) dated to 1244–1163 B.C. We have presented evidence that the 2.85 days period in the lucky prognoses of CC is equal to that of the eclipsing binary Algol during this historical era. We wanted to find out the vocabulary that represents Algol in the mythological texts of CC. Here we show that Algol was represented as Horus and thus signified both divinity and kingship. The texts describing the actions of Horus are consistent with the course of events witnessed by any naked eye observer of Algol. These descriptions support our claim that CC is the oldest preserved historical document of the discovery of a variable star. The period of the Moon, 29.6 days, has also been discovered in CC. We show that the actions of Seth were connected to this period, which also strongly regulated the times described as lucky for Heaven and for Earth. Now, for the first time, periodicity is discovered in the descriptions of the days in CC. Unlike many previous attempts to uncover the reasoning behind the myths of individual days, we discover the actual rules in the appearance and behaviour of deities during the whole year.