Rotation Period Of Star Research Articles

New Suns in the Cosmos. IV. The Multifractal Nature of Stellar Magnetic Activity in Kepler Cool Stars

Abstract In the present study, we investigate the multifractal nature of a long-cadence time series observed by the Kepler mission for a sample of 34 M dwarf stars and the Sun in its active phase. Using the Multifractal Detrending Moving Average algorithm, which enables the detection of multifractality in nonstationary time series, we define a set of multifractal indices based on the multifractal spectrum profile as a measure of the level of stellar magnetic activity. This set of indices is given by the (A, , C, H)-quartet, where A, , and C are related to geometric features from the multifractal spectrum and the global Hurst exponent H describes the global structure and memorability of time series dynamics. As a test, we measure these indices and compare them with a magnetic index defined as S ph and verify the degree of correlation among them. First, we apply the Poincaré plot method and find a strong correlation between the index and one of the descriptors that emerges from this method. As a result, we find that this index is strongly correlated with long-term features of the signal. From the multifractal perspective, the index is also strongly linked to the geometric properties of the multifractal spectrum except for the H index. Furthermore, our results emphasize that the rotation period of stars is scaled by the H index, which is consistent with Skumanich’s relationship. Finally, our approach suggests that the H index may be related to the evolution of stellar angular momentum and a star’s magnetic properties.

Starspots on WASP-107 and pulsations of WASP-118

By analysing the K2 short-cadence photometry we detect starspot occultation events in the lightcurve of WASP-107, the host star of a warm-Saturn exoplanet. WASP-107 also shows a rotational modulation with a period of 17.5 +/- 1.4 d. Given that the rotational period is nearly three times the planet's orbital period, one would expect in an aligned system to see starspot occultation events to recur every three transits. The absence of such occultation recurrences suggests a misaligned orbit unless the starspots' lifetimes are shorter than the star's rotational period. We also find stellar variability resembling gamma Doradus pulsations in the lightcurve of WASP-118, which hosts an inflated hot Jupiter. The variability is multi-periodic with a variable semi-amplitude of about 200 ppm. In addition to these findings we use the K2 data to refine the parameters of both systems, and report non-detections of transit-timing variations, secondary eclipses and any additional transiting planets. We used the upper limits on the secondary-eclipse depths to estimate upper limits on the planetary geometric albedos of 0.7 for WASP-107b and 0.2 for WASP-118b.

THE ROTATION PERIOD DISTRIBUTIONS OF 4–10 Myr T TAURI STARS IN ORION OB1: NEW CONSTRAINTS ON PRE-MAIN-SEQUENCE ANGULAR MOMENTUM EVOLUTION

ABSTRACT Most existing studies of the angular momentum evolution of young stellar populations have focused on the youngest (≲1–3 Myr) T Tauri stars. In contrast, the angular momentum distributions of older T Tauri stars (∼4–10 Myr) have been less studied, even though they hold key insights to understanding stellar angular momentum evolution at a time when protoplanetary disks have largely dissipated and when models therefore predict changes in the rotational evolution that can in principle be tested. We present a study of photometric variability among 1974 confirmed T Tauri members of various subregions of the Orion OB1 association, and with ages spanning 4–10 Myr, using optical time series from three different surveys. For 564 of the stars (∼32% of the weak-lined T Tauri stars and ∼13% of the classical T Tauri stars in our sample) we detect statistically significant periodic variations, which we attribute to the stellar rotation periods, making this one of the largest samples of T Tauri star rotation periods yet published. We observe a clear change in the overall rotation period distributions over the age range 4–10 Myr, with the progressively older subpopulations exhibiting systematically faster rotation. This result is consistent with angular momentum evolution model predictions of an important qualitative change in the stellar rotation periods starting at ∼5 Myr, an age range for which very few observational constraints were previously available.

WASP-South transiting exoplanets: WASP-130b, WASP-131b, WASP-132b, WASP-139b, WASP-140b, WASP-141b and WASP-142b

We describe seven exoplanets transiting stars of brightness V = 10.1 to 12.4. WASP-130b is a "warm Jupiter" having an orbital period of 11.6 d around a metal-rich G6 star. Its mass and radius (1.23 +/- 0.04 Mjup; 0.89 +/- 0.03 Rjup) support the trend that warm Jupiters have smaller radii than hot Jupiters. WASP-131b is a bloated Saturn-mass planet (0.27 Mjup; 1.22 Rjup). Its large scale height and bright (V = 10.1) host star make it a good target for atmospheric characterisation. WASP-132b (0.41 Mjup; 0.87 Rjup) is among the least irradiated and coolest of WASP planets, having a 7.1-d orbit around a K4 star. WASP-139b is a "super-Neptune" akin to HATS-7b and HATS-8b, being the lowest-mass planet yet found by WASP (0.12 Mjup; 0.80 Rjup). The metal-rich K0 host star appears to be anomalously dense, akin to HAT-P-11. WASP-140b is a 2.4-Mjup planet in an eccentric (e = 0.047 +/- 0.004) 2.2-d orbit. The planet's radius is large (1.4 Rjup), but uncertain owing to the grazing transit (b = 0.93). The 10.4-day rotation period of the K0 host star suggests a young age, and the timescale for tidal circularisation is likely to be the lowest of all known eccentric hot Jupiters. WASP-141b (2.7 Mjup, 1.2 Rjup, P = 3.3 d) and WASP-142b (0.84 Mjup, 1.53 Rjup, P = 2.1 d) are typical hot Jupiters orbiting metal-rich F stars. We show that the period distribution within the hot-Jupiter bulge does not depend on the metallicity of the host star.

The missing magnetic morphology term in stellar rotation evolution

This study examines the relationship between magnetic field complexity and mass and angular momentum losses. Observations of open clusters have revealed a bimodal distribution of the rotation periods of solar-like stars that has proven difficult to explain under the existing rubric of magnetic braking. Recent studies suggest that magnetic complexity can play an important role in controlling stellar spin-down rates. However, magnetic morphology is still neglected in most rotation evolution models due to the difficulty of properly accounting for its effects on wind driving and angular momentum loss. Using state-of-the-art magnetohydrodynamical magnetized wind simulations we study the effect that different distributions of the magnetic flux at different levels of geometrical complexity have on mass and angular momentum loss rates. Angular momentum loss rates depend strongly on the level of complexity of the field but are independent of the way this complexity is distributed. We deduce the analytical terms representing the magnetic field morphology dependence of mass and angular momentum loss rates. We also define a parameter that best represents complexity for real stars. As a test, we use these analytical methods to estimate mass and angular momentum loss rates for $8$ stars with observed magnetograms and compare them to the simulated results. Magnetic field complexity provides a natural physical basis for stellar rotation evolution models requiring a rapid transition between weak and strong spin-down modes.

NEW SUNS IN THE COSMOS. III. MULTIFRACTAL SIGNATURE ANALYSIS

ABSTRACT In the present paper, we investigate the multifractality signatures in hourly time series extracted from the CoRoTspacecraft database. Our analysis is intended to highlight the possibility that astrophysical time series can be members of a particular class of complex and dynamic processes, which require several photometric variability diagnostics to characterize their structural and topological properties. To achieve this goal, we search for contributions due to a nonlinear temporal correlation and effects caused by heavier tails than the Gaussian distribution, using a detrending moving average algorithm for one-dimensional multifractal signals (MFDMA). We observe that the correlation structure is the main source of multifractality, while heavy-tailed distribution plays a minor role in generating the multifractal effects. Our work also reveals that the rotation period of stars is inherently scaled by the degree of multifractality. As a result, analyzing the multifractal degree of the referred series, we uncover an evolution of multifractality from shorter to larger periods.

Magnetic cycles and rotation periods of late-type stars from photometric time series

We investigate the photometric modulation induced by magnetic activity cycles and study the relationship between rotation period and activity cycle(s) in late-type (FGKM) stars. We analyse light-curves spanning up to 9 years of 125 nearby stars provided by the ASAS survey. The sample is mainly conformed by low-activity main sequence late A to mid M-type stars. A search is performed for short (days) and long-term (years) periodic variations in the photometry. We modelled with combinations of sinusoids the light-curves to measure the properties of these periodic signals. To provide a better statistical interpretation of our results we complement them with the results from previous similar works. We have been able to measure long-term photometric cycles of 47 stars. Rotational modulation was also detected and rotational periods measured in 36 stars. For 28 stars we have simultaneous measurements of both, activity cycles and rotational periods, being 17 of them M-type stars. From sinusoidal fits we measured both photometric amplitudes and periods. The measured cycle periods range from 2 up to 14 yr with photometric amplitudes in the range of 5-20 mmag. We have found that the distribution of cycle lengths for the different spectral types is similar. On the other hand the distribution of rotation periods is completely different, trending to longer periods for later type stars. The amplitudes induced by magnetic cycles and rotation show a clear correlation. A trend of photometric amplitudes with rotation period is also outlined in the data. For a given activity index the amplitudes of the photometric variability induced by activity cycles of main sequence GK stars are lower than those of early and mid-M dwarfs. Using spectroscopic data we also provide an update in the empirical relationship between the level of chromospheric activity as given by log(Rhk) and the rotation periods.

Interaction of extra solar planets with their host star

AbstractTransit is the passage of the planet in front of its star. During one of these transits, the planet may occult a spot on the photosphere of the star, causing small variations in its light curve. By detecting the same spot in a later transit, it is possible to estimate the stellar rotation period. The comparison between the rotation period of star at the equator and the planets orbital period showed the existence of resonances between these periods. Two types of mechanisms are proposed in the literature: electromagnetic interaction between the stellar and planetary fields and gravitational interaction. Our results have shown that for planets CoRoT-2b, CoRoT-5b and CoRoT-8b, tidal effects seem to dominate, whereas for planets CoRoT-4b and CoRoT-6b electromagnetic interaction dominates over tidal effects. A distinct characteristic of these last two systems is that the orbital period is larger than the rotation period of the star.

Some aspects of cool main sequence star ages derived from stellar rotation (gyrochronology)

AbstractRotation periods for cool stars can be measured with good precision by monitoring starspot light modulation. Observations have shown that the rotation periods of dwarf stars of roughly solar metallicity have such systematic dependencies on stellar age and mass that they can be used to derive reliable ages, a procedure called gyrochronology. We review the method and show illustrative cases, including recent ground‐ and space‐based data. The age uncertainties approach 10 % in the best cases, making them a valuable complement to, and constraint on, asteroseismic or other ages.

THE IMPACT OF STELLAR ROTATION ON THE DETECTABILITY OF HABITABLE PLANETS AROUND M DWARFS

ABSTRACT Stellar activity and rotation frustrate the detection of exoplanets through the radial velocity technique. This effect is particularly of concern for M dwarfs, which can remain magnetically active for billions of years. We compile rotation periods for late-type stars and for the M dwarf planet-host sample in order to investigate the rotation periods of older field stars across the main sequence. We show that for stars with masses between 0.25 and 0.5 M ⊙ (M4V–M1V), the stellar rotation period typical of field stars coincides with the orbital periods of planets in the habitable zone. This will pose a fundamental challenge to the discovery and characterization of potentially habitable planets around early M dwarfs. Due to the longer rotation periods reached by mid M dwarfs and the shorter orbital period at which the planetary habitable zone is found, stars with masses between 0.1 and 0.25 M ⊙ (M6V–M4V) offer better opportunities for the detection of habitable planets via radial velocities.

Erratum: Rotation periods of late-type dwarf stars from time series high-resolution spectroscopy of chromospheric indicators

Erratum: Rotation periods of late-type dwarf stars from time series high-resolution spectroscopy of chromospheric indicators

A novel period estimation method for X-ray pulsars based on frequency subdivision

Period estimation of X-ray pulsars plays an important role in X-ray pulsar based navigation (XPNAV). The fast Lomb periodogram is suitable for period estimation of X-ray pulsars, but its performance in terms of frequency resolution is limited by data length and observation time. Longer observation time or oversampling can be employed to improve frequency analysis results, but with greatly increased computational complexity and large amounts of sampling data. This greatly restricts real-time autonomous navigation based on X-ray pulsars. To resolve this issue, a new method based on frequency subdivision and the continuous Lomb periodogram (CLP) is proposed to improve precision of period estimation using short-time observation data. In the proposed method, an initial frequency is first calculated using fast Lomb periodogram. Then frequency subdivision is performed near the initial frequency to obtain frequencies with higher precision. Finally, a refined period is achieved by calculating the CLP in the obtained frequencies. Real data experiments show that when observation time is shorter than 135 s, the proposed method improves period estimation precision by 1–3 orders of magnitude compared with the fast Lomb periodogram and fast Fourier transform (FFT) methods, with only a slight increase in computational complexity. Furthermore, the proposed method performs better than efsearch (a period estimation method of HEAsoft) with lower computational complexity. The proposed method is suitable for estimating periods of X-ray pulsars and obtaining the rotation period of variable stars and other celestial bodies.

Rotation periods of late-type dwarf stars from time series high-resolution spectroscopy of chromospheric indicators

We determine rotation periods of a sample of 48 late F-type to mid-M dwarf stars using time-series high-resolution spectroscopy of the Ca II H&K and H-alpha chromospheric activity indicators. We find good agreement between the rotation periods obtained from each of these two indicators. An empirical relationship between the level of chromospheric emission measured by log (R'HK) and the spectroscopic rotation periods is reported. This relation is largely independent of the spectral type and the metallicity of the stars and can be used to make a reliable prediction of rotation periods for late K to mid-M dwarfs with low levels of activity. For some stars in the sample, the measured spectroscopic rotation periods coincide, or are very close, to the orbital periods of postulated planets. In such cases, further studies are needed to clarify whether the associated periodic radial velocity signals reveal the existence of planets or are due to magnetic activity.

Calibrating gyrochronology using Kepler asteroseismic targets

Among the available methods for dating stars, gyrochronology is a powerful one because it requires knowledge of only the star's mass and rotation period. Gyrochronology relations have previously been calibrated using young clusters, with the Sun providing the only age dependence, and are therefore poorly calibrated at late ages. We used rotation period measurements of 310 Kepler stars with asteroseismic ages, 50 stars from the Hyades and Coma Berenices clusters and 6 field stars (including the Sun) with precise age measurements to calibrate the gyrochronology relation, whilst fully accounting for measurement uncertainties in all observable quantities. We calibrated a relation of the form $P=A^n\times(B-V-c)^b$, where $P$ is rotation period in days, $A$ is age in Myr, $B$ and $V$ are magnitudes and $a$, $b$ and $n$ are the free parameters of our model. We found $a = 0.40^{+0.3}_{-0.05}$, $b = 0.31^{+0.05}_{-0.02}$ and $n = 0.55^{+0.02}_{-0.09}$. Markov Chain Monte Carlo methods were used to explore the posterior probability distribution functions of the gyrochronology parameters and we carefully checked the effects of leaving out parts of our sample, leading us to find that no single relation beween rotation period, colour and age can adequately describe all the subsets of our data. The Kepler asteroseismic stars, cluster stars and local field stars cannot all be described by the same gyrochronology relation. The Kepler asteroseismic stars may be subject to observational biases, however the clusters show unexpected deviations from the predicted behaviour, providing concerns for the overall reliability of gyrochronology as a dating method.

Time in powers of ten: natural phenomena and their timescales

With a Foreword by Steven WeinbergIn this richly illustrated book, Nobel Laureate Gerard 't Hooft and Theoretical Physicist Stefan Vandoren describe the enormous diversity of natural phenomena that take place at different time scales.In the tradition of the bestseller Powers of Ten, the authors zoom in and out in time, each step with a factor of ten. Starting from one second, time scales are enlarged until processes are reached that take much longer than the age of the universe. After the largest possible eternities, the reader is treated to the shortest and fastest phenomena known. Then the authors increase with powers of ten, until again the second is reached at the end of the book.At each time scale, interesting natural phenomena occur, spread over all scientific disciplines: orbital and rotation periods of planets and stars, decay times of elementary particles and atoms, biological rhythms and evolution processes, but also the different geological time scales.

OBLIQUITIES OFKEPLERSTARS: COMPARISON OF SINGLE- AND MULTIPLE-TRANSIT SYSTEMS

The stellar obliquity of a transiting planetary system can be constrained by combining measurements of the star's rotation period, radius, and projected rotational velocity. Here we present a hierarchical Bayesian technique for recovering the obliquity distribution of a population of transiting planetary systems, and apply it to a sample of 70 Kepler Objects of Interest. With ~95% confidence we find that the obliquities of stars with only a single detected transiting planet are systematically larger than those with multiple detected transiting planets. This suggests that a substantial fraction of Kepler's single-transiting systems represent dynamically hotter, less orderly systems than the "pancake-flat" multiple-transiting systems.

SOPHIE velocimetry ofKeplertransit candidates XI. Kepler-412 system: probing the properties of a new inflated hot Jupiter

We confirm the planetary nature of Kepler-412b, listed as planet candidate KOI-202 in the Kepler catalog, thanks to our radial velocity follow-up program of Kepler-released planet candidates, which is on going with the SOPHIE spectrograph. We performed a complete analysis of the system by combining the Kepler observations from Q1 to Q15, to ground-based spectroscopic observations that allowed us to derive radial velocity measurements, together with the host star parameters and properties. We also analyzed the light curve to derive the star's rotation period and the phase function of the planet, including the secondary eclipse. We found the planet has a mass of 0.939 $\pm$ 0.085 M$_{Jup}$ and a radius of 1.325 $\pm$ 0.043 R$_{Jup}$ which makes it a member of the bloated giant subgroup. It orbits its G3 V host star in 1.72 days. The system has an isochronal age of 5.1 Gyr, consistent with its moderate stellar activity as observed in the Kepler light curve and the rotation of the star of 17.2 $\pm$ 1.6 days. From the detected secondary, we derived the day side temperature as a function of the geometric albedo and estimated the geometrical albedo, Ag, is in the range 0.094 to 0.013. The measured night side flux corresponds to a night side brightness temperature of 2154 $\pm$ 83 K, much greater than what is expected for a planet with homogeneous heat redistribution. From the comparison to star and planet evolution models, we found that dissipation should operate in the deep interior of the planet. This modeling also shows that despite its inflated radius, the planet presents a noticeable amount of heavy elements, which accounts for a mass fraction of 0.11 $\pm$ 0.04.

ROTATION PERIODS OF 34,030 KEPLER MAIN-SEQUENCE STARS: THE FULL AUTOCORRELATION SAMPLE

We analyzed 3 years of data from the Kepler space mission to derive rotation periods of main-sequence stars below 6500 K. Our automated autocorrelation-based method detected rotation periods between 0.2 and 70 days for 34,030 (25.6%) of the 133,030 main-sequence Kepler targets (excluding known eclipsing binaries and Kepler Objects of Interest), making this the largest sample of stellar rotation periods to date. In this paper we consider the detailed features of the now well-populated period-temperature distribution and demonstrate that the period bimodality, first seen by McQuillan, Aigrain & Mazeh (2013) in the M-dwarf sample, persists to higher masses, becoming less visible above 0.6 M_sun. We show that these results are globally consistent with the existing ground-based rotation-period data and find that the upper envelope of the period distribution is broadly consistent with a gyrochronological age of 4.5 Gyrs, based on the isochrones of Barnes (2007), Mamajek & Hillenbrand (2008) and Meibom et al. (2009). We also performed a detailed comparison of our results to those of Reinhold et al. (2013) and Nielsen et al. (2013), who have measured rotation periods of field stars observed by Kepler. We examined the amplitude of periodic variability for the stars with detected rotation periods, and found a typical range between ~950 ppm (5th percentile) and ~22,700 ppm (95th percentile), with a median of ~5,600 ppm. We found typically higher amplitudes for shorter periods and lower effective temperatures, with an excess of low-amplitude stars above ~5400 K.

Magnetic dipole moment of soft gamma-ray repeaters and anomalous X-ray pulsars described as massive and magnetic white dwarfs

Abstract Anomalous X-ray pulsars (AXPs) and soft gamma-ray repeaters (SGRs) are some of the most interesting groups of pulsars that have been intensively studied in recent years. They are understood as neutron stars (NSs) with super-strong magnetic fields, namely B ≳ 1014 G. However, in the last two years two SGRs with low magnetic fields B ∼ (1012–1013) G have been detected. Moreover, three fast and very magnetic white dwarfs (WDs) have also been observed in recent years. Based on these new pulsar discoveries, we compare and contrast the magnetic fields, magnetic dipole moment, characteristic ages, and X-ray steady luminosities of these two SGRs (in the WD model) with the three fast white dwarfs, to conclude that they show strong similarities corroborating an alternative description of several SGRs/AXPs as very massive and magnetic white dwarfs. We show that the values for m obtained for several SGRs and AXPs are in agreement with the observed range 1034 emu ≤ m ≤ 1036 emu of isolated and polar magnetic white dwarfs. This result, together with the fact that for magnetic white dwarfs B ∼ (106–108) G their magnetic dipole moments are almost independent of the star rotation period (104 s ≲ P ≲ 106 s)—a phenomenology not shared by neutron star pulsars—suggests a possible magnetic white dwarf nature for some SGRs/AXPs that have much smaller periods (P ∼ 10 s). Moreover, since for pulsars the dipole radiation power is proportional only to m and to the rotational star frequency, we can explain in the WD model—considering only the different scales of the magnetic dipole moment for WDs and NSs—why the steady luminosity LX for several SGRs/AXPs (and in particular the low-B SGRs) compared to those of X-ray dim isolated neutron stars (XDINs) and high-B pulsars obeys the ratio LXSGRs/AXPs/LXXDINs ∼ mWD/mNS ∼ 103: all these X-ray sources have essentially the same rotational periods (P ∼ 10 s) and the X-ray luminosity is correlated to the spin-down luminosity, which is equal to the dipole radiation power in the dipole model.

Rotation periods of 12 000 main-sequenceKeplerstars: Dependence on stellar spectral type and comparison withvsiniobservations

Aims: We aim to measure the starspot rotation periods of active stars in the Kepler field as a function of spectral type and to extend reliable rotation measurements from F-, G-, and K-type to M-type stars. Methods: Using the Lomb-Scargle periodogram we searched more than 150 000 stellar light curves for periodic brightness variations. We analyzed periods between 1 and 30 days in eight consecutive Kepler quarters, where 30 days is an estimated maximum for the validity of the PDC_MAP data correction pipeline. We selected stable rotation periods, i.e., periods that do not vary from the median by more than one day in at least six of the eight quarters. We averaged the periods for each stellar spectral class according to B - V color and compared the results to archival vsini data, using stellar radii estimates from the Kepler Input Catalog. Results: We report on the stable starspot rotation periods of 12 151 Kepler stars. We find good agreement between starspot velocities and vsini data for all F-, G- and early K-type stars. The 795 M-type stars in our sample have a median rotation period of 15.4 days. We find an excess of M-type stars with periods less than 7.5 days that are potentially fast-rotating and fully convective. Measuring photometric variability in multiple Kepler quarters appears to be a straightforward and reliable way to determine the rotation periods of a large sample of active stars, including late-type stars.