Observed Rotation Rates Research Articles

Evolution of Stellar Rotation in Open Clusters

Understanding stellar rotation and the role of magnetic braking remains a major outstanding problem in astrophysics. In this paper, stellar rotation of the young open cluster Blanco 1 is investigated and compared with other clusters with ages ranging from ∼35 Myr to ∼950 Myr and star masses in the range 0.2 < M⊙ < 1.4. It is proposed that rotation rates of stars in young open clusters are determined by the early angular momentum acquired during formation and not by magnetic braking effects, which operate on longer time scales. On the convective C Sequence, for lighter stars, the early angular velocity is related directly to the moment of inertia. However, for the interface or I Sequence, differential rotation exists and observed rotation rates are essentially the rotation rates of the outer convection zone. It is estimated that the convection zone can rotate at over 10× the rate of the inner radiative zone for heavier stars. This differential rotation process can drive saturated interface dynamos that lead to large rotational mass dependences which can be described by a simple energy transfer model. Comparing with clusters of different ages magnetic braking outlines the evolution of older clusters from young clusters. For old clusters such as Praesepe the majority of stars have experienced spin down, that can be described by a simple model based on an additional momentum loss proportional to the angular momentum of the early cluster, which for the I Sequence is consistent with the well known Skumanich relation.

Super slowly spinning stars in close binaries

ABSTRACT Stars in short-period binaries typically have spins that are aligned and synchronized with the orbit of their companion. In triple systems, however, the combination of spin and orbital precession can cause the star’s rotation to evolve to a highly misaligned and sub-synchronous equilibrium known as a Cassini state. We identify a population of recently discovered stars that exhibit these characteristics and which are already known to have tertiary companions. These third bodies have a suitable orbital period to allow the inner binary to evolve into the sub-synchronous Cassini state, which we confirm with orbital evolution models. We also compute the expected stellar obliquity and spin period, showing that the observed rotation rates are often slower than expected from equilibrium tidal models. However, we show that tidal dissipation via inertial waves can alter the expected spin–orbit misalignment angle and rotation rate, potentially creating the very slow rotation rates in some systems. Finally, we show how additional discoveries of such systems can be used to constrain the tidal physics and orbital evolution histories of stellar systems.

The s process in rotating low-mass AGB stars

Aims. We investigate the s-process during the AGB phase of stellar models whose cores are enforced to rotate at rates consistent with asteroseismology observations of their progenitors and successors. Methods. We calculated new 2 M⊙, Z = 0.01 models, rotating at 0, 125, and 250 km s−1 at the start of main sequence. An artificial, additional viscosity was added to enhance the transport of angular momentum in order to reduce the core rotation rates to be in agreement with asteroseismology observations. We compared rotation rates of our models with observed rotation rates during the MS up to the end of core He burning, and the white dwarf phase. Results. We present nucleosynthesis calculations for these rotating AGB models that were enforced to match the asteroseismic constraints on rotation rates of MS, RGB, He-burning, and WD stars. In particular, we calculated one model that matches the upper limit of observed rotation rates of core He-burning stars and we also included a model that rotates one order of magnitude faster than the upper limit of the observations. The s-process production in both of these models is comparable to that of non-rotating models. Conclusions. Slowing down the core rotation rate in stars to match the above mentioned asteroseismic constraints reduces the rotationally induced mixing processes to the point that they have no effect on the s-process nucleosynthesis. This result is independent of the initial rotation rate of the stellar evolution model. However, there are uncertainties remaining in the treatment of rotation in stellar evolution, which need to be reduced in order to confirm our conclusions, including the physical nature of our approach to reduce the core rotation rates of our models, and magnetic processes.

The YORP effect on the GOES 8 and GOES 10 satellites: A case study

The Yarkovsky-O’Keefe-Radzievskii-Paddack (YORP) effect is a proposed explanation for the observed rotation behavior of inactive satellites in Earth orbit. This paper further explores the YORP effect for highly asymmetric inactive satellites. Satellite models are developed to represent the GOES 8 and GOES 10 satellites, both of which are currently inactive in geosynchronous Earth orbit (GEO). A simple satellite model for the GOES 8 satellite is used to analyze the short period variations of the angular velocity and obliquity as a result of the YORP effect. A more complex model for the rotational dynamics of the GOES 8 and GOES 10 satellites are developed to probe their sensitivity and to match observed spin periods and states of these satellites. The simulated rotation periods are compared to observations for both satellites. The comparison between YORP theory and observed rotation rates for both satellites show that the YORP effect could be the cause for the observed rotational behavior. The YORP model also predicts a novel state for the GOES 8 satellite, namely that it could periodically fall into a tumbling rotation state. Recent observations of this satellite are consistent with this prediction.

Implications of the generation of internal gravity waves by penetrative convection for the internal rotation evolution of low-mass stars

Due to the space-borne missions CoRoT and Kepler , noteworthy breakthroughs have been made in our understanding of stellar evolution, and in particular about the angular momentum redistribution in stellar interiors. Indeed, the high-precision seismic data provide with the measurement of the mean core rotation rate for thousands of low-mass stars from the subgiant branch to the red giant branch. All these observations exhibit much lower core rotation rates than expected by current stellar evolution codes and they emphasize the need for an additional transport process. In this framework, internal gravity waves (herefater, IGW) could play a signifivative role since they are known to be able to transport angular momentum. In this work, we estimate the effciency of the transport by the IGW that are generated by penetrative convection at the interface between the convective and the radiative regions. As a first step, this study is based on the comparison between the timescale for the waves to modify a given rotation profile and the contraction/expansion timescale throughout the radiative zone of 1.3M⊙ stellar models. We show that IGW, on their own, are ineffcient to slow down the core rotation of stars on the red giant branch, where the radiative damping becomes strong enough and prevent the IGW from reaching the innermost layers. However, we find that IGW generated by penetrative convection could effciently modify the core rotation of subgiant stars as soon as the amplitude of the radial differential rotation between the core and the base of the convective zone is high enough, with typical values close to the observed rotation rates in these stars. This result argues for the necessity to account for IGW generated by penetrative convection in stellar modeling and in the angular momentum redistribution issue.

Angular momentum redistribution by mixed modes in evolved low-mass stars

Seismic observations by the space-borne mission \emph{Kepler} have shown that the core of red giant stars slows down while evolving, requiring an efficient physical mechanism to extract angular momentum from the inner layers. Current stellar evolution codes fail to reproduce the observed rotation rates by several orders of magnitude, and predict a drastic spin-up of red giant cores instead. New efficient mechanisms of angular momentum transport are thus required. In this framework, our aim is to investigate the possibility that mixed modes extract angular momentum from the inner radiative regions of evolved low-mass stars. To this end, we consider the Transformed Eulerian Mean (TEM) formalism, introduced by Andrews \& McIntyre (1978), that allows us to consider the combined effect of both the wave momentum flux in the mean angular momentum equation and the wave heat flux in the mean entropy equation as well as their interplay with the meridional circulation. In radiative layers of evolved low-mass stars, the quasi-adiabatic approximation, the limit of slow rotation, and the asymptotic regime can be applied for mixed modes and enable us to establish a prescription for the wave fluxes in the mean equations. The formalism is finally applied to a $1.3 M_\odot$ benchmark model, representative of observed CoRoT and \emph{Kepler} oscillating evolved stars. We show that the influence of the wave heat flux on the mean angular momentum is not negligible and that the overall effect of mixed modes is to extract angular momentum from the innermost region of the star. A quantitative and accurate estimate requires realistic values of mode amplitudes. This is provided in a companion paper.

The rotation rates of massive stars

Context: Rotation plays a key role in the life cycles of stars with masses above 8 Msun. Hence, accurate knowledge of the rotation rates of such massive stars is critical for understanding their properties and for constraining models of their evolution. Aims: This paper investigates the reliability of current methods used to derive projected rotation speeds v sin i from line-broadening signatures in the photospheric spectra of massive stars, focusing on stars that are not rapidly rotating. Methods: We use slowly rotating magnetic O-stars with well-determined rotation periods to test the Fourier transform (FT) and goodness-of-fit (GOF) methods typically used to infer projected rotation rates of massive stars. Results: For our two magnetic test stars with measured rotation periods longer than one year, i.e., with v sin i < 1 km/s, we derive v sin i ~ 40-50 km/s from both the FT and GOF methods. These severe overestimates are most likely caused by an insufficient treatment of the competing broadening mechanisms referred to as microturbulence and macroturbulence. Conclusions: These findings warn us not to rely uncritically on results from current standard techniques to derive projected rotation speeds of massive stars in the presence of significant additional line broadening, at least when v sin i <~ 50 km/s. This may, for example, be crucial for i) determining the statistical distribution of observed rotation rates of massive stars, ii) interpreting the evolutionary status and spin-down histories of rotationally braked B-supergiants, and iii) explaining the deficiency of observed O-stars with spectroscopically inferred v sin i ~ 0 km/s. Further investigations of potential shortcomings of the above techniques are presently under way.

LOW-FREQUENCY OBSERVATIONS OF POLARIZED EMISSION FROM LONG-LIVED NON-THERMAL RADIO SOURCES IN THE SOLAR CORONA

We report observations of circularly polarized emission from the solar corona at 77 MHz during the periods 2006 August 11–18, 2006 August 23–29, and 2007 May 16–22 in the minimum phase between the sunspot cycles 23 and 24. The observations were carried out with the east–west one-dimensional radio polarimeter at the Gauribidanur observatory located about 100 km north of Bangalore. Two-dimensional imaging observations at 77 MHz during the same period with the radioheliograph at the same observatory revealed that the emission region co-rotated with the Sun during the three aforementioned periods. Their rotation rates, close to the central meridian on the Sun, are 4. 6, 5. 2, and 4. 9 ± 0. 5 per day, respectively. We derived the radial distance of the region from the above observed rotation rates and the corresponding values are ≈1.24 ± 0.03 R� (2006 August 11–18), ≈1.40 ± 0.03 R� (2006 August 23–29), and ≈1.32 ± 0.03 R� (2007 May 16–22). The estimated lower limit for the magnetic field strength at the above radial distances and periods are ≈1.1, 0.6, and 0.9 G, respectively.

The effect of stellar rotation on colour–magnitude diagrams: on the apparent presence of multiple populations in intermediate age stellar clusters

Abstract A significant number of intermediate age clusters (1–2 Gyr) in the Magellanic Clouds appear to have multiple stellar populations within them, derived from bimodal or extended main-sequence turn-offs. If this is interpreted as an age spread, the multiple populations are separated by a few hundred million years, which would call into question the long-held notion that clusters are simple stellar populations. Here, we show that stellar rotation in stars with masses between 1.2 and 1.7 M⊙ can mimic the effect of a double or multiple population, whereas in actuality only a single population exists. The two main causes of the spread near the turn-off are the effects of stellar rotation on the structure of the star and the inclination angle of the star relative to the observer. Both effects change the observed effective temperature, hence colour, and flux of the star. In order to match observations, the required rotation rates are 20–50 per cent of the critical rotation, which are consistent with observed rotation rates of similar mass stars in the Galaxy. We provide scaling relations which can be applied to non-rotating isochrones in order to mimic the effects of rotation. Finally, we note that rotation is unlikely to be the cause of the multiple stellar populations observed in old globular clusters, as low-mass stars (&amp;lt;1 M⊙) are not expected to be rapid rotators.

Temperature Dependence of Single Molecule Rotation of the Escherichia coli ATP Synthase F1 Sector Reveals the Importance of γ-β Subunit Interactions in the Catalytic Dwell

The temperature-dependent rotation of F1-ATPase gamma subunit was observed in V(max) conditions at low viscous drag using a 60-nm gold bead (Nakanishi-Matsui, M., Kashiwagi, S., Hosokawa, H., Cipriano, D. J., Dunn, S. D., Wada, Y., and Futai, M. (2006) J. Biol. Chem. 281, 4126-4131). The Arrhenius slopes of the speed of the individual 120 degrees steps and reciprocal of the pause length between rotation steps were very similar, indicating a flat energy pathway followed by the rotationally coupled catalytic cycle. In contrast, the Arrhenius slope of the reciprocal pause length of the gammaM23K mutant F1 was significantly increased, whereas that of the rotation rate was similar to wild type. The effects of the rotor gammaM23K substitution and the counteracting effects of betaE381D mutation in the interacting stator subunits demonstrate that the rotor-stator interactions play critical roles in the utilization of stored elastic energy. The gammaM23K enzyme must overcome an abrupt activation energy barrier, forcing it onto a less favored pathway that results in uncoupling catalysis from rotation.

STELLAR ROTATION AND PLANET INGESTION IN GIANTS

We investigate the expected increase in the rotation rate of post-main-sequence stars as they expand and ingest orbiting planets. This phenomenon is expected to occur when the stellar radius becomes larger than the planet's periastron distance. We calculate the expected frequency of planet ingestion during the red giant, horizontal branch (HB), and early asymptotic giant branch phases for planets of mass . We also calculate the probability of observing anomalous rotation rates in a population of solar metallicity giants as a function of stellar mass and evolutionary stage. Planet ingestion is most easily detectable in a solar mass HB star, with a probability of about 1% for solar-neighborhood metallicity. Our analysis is based on the observed distribution of mass, eccentricity, semimajor axis for extrasolar planets around solar-type main-sequence stars, on stellar evolution models, and on the typical observed rotation rates observed in a sample of solar-neighborhood giants.

Diurnal Variations in Summertime Surface Wind upon Japanese Plains: Hodograph Rotation and Its Dynamics

This study investigates diurnal variations in surface wind in Japan during June-August of 1992-2006 using data from the Automated Meteorological Data Acquisition System (AMeDAS) and the Sapporo City Multisensor (MULTI). Harmonic analysis and hodograph analysis are employed to investigate the rotation direction and rotation rate of the wind vector at about 1000 stations. An analysis of six major plains in Japan reveals distinct clockwise and anticlockwise hodograph regions within each plain. The rotation direction is attributed to two lagged pressure-gradient forces of contrasting orientations: one between the land and sea, and another between the plain and adjacent mountains. An analysis of the linearized equations of motion reveals that rotation of the wind vector is mainly controlled by the balance between the pressure gradient force and the frictional force, with a small but non-negligible contribution by the Coriolis force, particularly near the coast. The observed rotation rates of the hodographs show a brief stagnation during the mid-afternoon and a longer stagnation during the nighttime. This irregular rotation rate is well explained by taking into account the semidiurnal component of the wind. The linearized equations of motion indicate that this semidiurnal component results from the semidiurnal component of the pressure gradient force, which is generated by non-sinusoidal solar heating over the course of a day.

Internal Rotation of Subdwarf B Stars: Limiting Cases and Asteroseismological Consequences

Observations of the rotation rates of horizontal branch (HB) stars show puzzling systematics. In particular, cooler HB stars often show rapid rotation (with velocities in excess of 10 km s-1), while hotter HB stars (those with Teff in excess of 11,000 K) typically show much smaller rotation velocities of 8 km s-1 or less. Simple models of angular momentum evolution of stars from the main sequence through the red giant branch fail to explain these effects. Assuming solid body rotation throughout produces models that rotate much too slowly. On the other hand, assuming local conservation of angular momentum, but with solid body rotation in the convective regions, produces HB models that also rotate too slowly at all Teff but preserve a rapidly rotating core. In these cases, the observed angular velocities of HB stars require that some of the angular momentum stored in the core reaches the surface. Models that assume constant specific angular momentum in the surface convection zone have faster rotation in the envelope; while the predictions of these models match the observed rotation rates of the cooler HB stars, hot HB stars rotate more slowly than the models. Thus, while there is not yet a coherent explanation of the trends of rotation on the HB, evolutionary models in all cases preserve a rapidly rotating core. To test the idea that HB stars contain such a core, one can appeal to detailed computations of trace element abundances and rotational mixing. However, a more direct probe is available to test these limiting cases of angular momentum evolution. Some of the hottest horizontal branch stars are members of the pulsating sdB class. They frequently show rich pulsation spectra characteristic of nonradially pulsating stars. Thus, their pulsations probe the internal rotation of these stars and should show the effects of rapid rotation in their cores. Using models of sdB stars that include angular momentum evolution, we explore this possibility and show that some of the sdB pulsators may indeed have rapidly rotating cores.

Differential rotation and meridional flow in the solar supergranulation layer: Measuring the eddy viscosity

We measure the eddy viscosity in the outermost layers of the solar convection zone by comparing the rotation law computed with the Reynolds stress resulting from f-plane simulations of the angular momentum transport in rotating convection with the observed differential rotation pattern. The simulations lead to a negative vertical and a positive horizontal angular momentum transport. The consequence is a subrotation of the outermost layers, as it is indeed indicated both by helioseismology and the observed rotation rates of sunspots. In order to reproduce the observed gradient of the rotation rate a value of about 1.5 x 10^{13} cm/s for the eddy viscosity is necessary. Comparison with the magnetic eddy diffusivity derived from the sunspot decay yields a surprisingly large magnetic Prandtl number of 150 for the supergranulation layer. The negative gradient of the rotation rate also drives a surface meridional flow towards the poles, in agreement with the results from Doppler measurements. The successful reproduction of the abnormally positive horizontal cross correlation (on the northern hemisphere) observed for bipolar groups then provides an independent test for the resulting eddy viscosity.

The helium content and age of the Hyades:

We compare the accurate empirical mass-luminosity (M-L) relation based on five Hyades binary systems to predictions of stellar models calculated with various input parameters (helium, metallicity and age) or physics (mixing-length ratio, model atmosphere, equation of state and microscopic diffusion). Models based on a helium content inferred from the enrichment law are more than 3σ beyond the observations, suggesting that the Hyades initial helium abundance is lower than expected from its supersolar metallicity. With the photometric metallicity ( = dex, Grenon [CITE]) we derive . Because of the (Y, ) degeneracy in the M-L plane, the uncertainty grows to if the metallicity from spectroscopy is adopted ( = dex, Cayrel de Strobel et al. [CITE]). We use these results to discuss the Hertzsprung-Russell (HR) diagram of the Hyades, in the (MV, ) plane, based on the very precise Hipparcos dynamical parallaxes. Present models fit the tight observed sequence very well except at low temperatures. We show that the HR diagram does not bring further constraints on the helium abundance or metallicity of the cluster. In the low mass region of the HR diagram sensitive to the mixing-length parameter (), the slope of the main sequence (MS) suggests that could decrease from a solar (or even supersolar) value at higher mass to subsolar values at low mass, which is also supported by the modeling of the vB22 M-L relation. We find that the discrepancy at low temperatures (() ) remains, even if an improved equation of state or better model atmospheres are used. Finally, we discuss the positions of the stars at turn-off in the light of their observed rotation rates and we deduce that the maximum age of the Hyades predicted by the present models is ~650 Myr.

Fireball flickering: the case for indirect measurement of meteoroid rotation rates

Data collected during the Meteorite Observation and Recovery Program (MORP) indicate that 4% of bright fireballs show a periodic variation or flickering in brightness. The observed flickering frequencies vary from a few Hz to as high as 500 Hz. We interpret the flickering phenomenon in terms of meteoroid rotation. The MORP data does not reveal any apparent correlation between the flickering frequency and the properties of the meteoroid or the atmospheric flow conditions under which ablation is taking place. It is argued that the most likely cause of the flickering phenomenon is the rotational modulation of the cross-section area presented by the meteoroid to the on-coming airflow. A study is made of the Peekskill fireball and it is concluded that the meteoroid was spun-up during its long flight through the Earth's atmosphere, and that its initial brake up was due to rotational bursting. We also argue that the Peekskill event provides the best observational evidence that the flickering phenomenon is truly related to the rotation rate of the impinging meteoroid. We find that the observed rotation rates of the MORP fireballs are clustered just below the allowed limit set by rotational bursting, but argue that this is due to an observational selection effect that mitigates against the detection of low-frequency flickering.

Spectra and Line Profiles of FU Orionis Objects: Comparisons between Boundary Layer Models and Observations

We present solutions for the accretion disks and boundary layers in pre-main-sequence stars undergoing FU Orionis outbursts. These solutions differ from earlier disk solutions in that they include a self-consistent treatment of the boundary layer region. In a previous paper (Popham 1996), we showed that these stars should stop accreting angular momentum once they spin up to modest rotation rates. Here we show that for reasonable values of $\alpha$, these low angular momentum accretion rate solutions fit the spectra and line profiles observed in FU Orionis objects better than solutions with high rates of angular momentum accretion. We find solutions which fit the observations of FU Orionis and V1057 Cygni. These solutions have mass accretion rates of 2 and $1 \times 10^{-4} \msyr$, stellar masses of 0.7 and $0.5 \msun$, and stellar radii of 5.75 and $5.03 \rsun$, respectively. They also have modest stellar rotation rates $8-9 \xss$, comparable to the observed rotation rates of T Tauri stars, and angular momentum accretion rates of zero. This supports our earlier suggestion that FU Orionis outbursts may regulate the rotation rates of T Tauri stars.

Can FU Orionis Outbursts Regulate the Rotation Rates of T Tauri Stars?

We propose that FU Orionis outbursts may play an important role in maintaining the slow rotation of classical disk-accreting T Tauri stars. Current estimates for the frequency and duration of FU Orionis outbursts and the mass accretion rates of T Tauri and FU Orionis stars suggest that more mass may be accreted during the outbursts than during the T Tauri phases. If this is the case, then the outbursts should also dominate the accretion of angular momentum. During the outbursts, the accretion rate is so high that the magnetic field of the star should not disrupt the disk, and the disk will extend all the way in to the stellar surface. Standard thin disk models then predict that the star should accrete large amounts of angular momentum, which will produce a secular spinup of the star. We present boundary layer solutions for FU Orionis parameters which show that the angular momentum accretion rate drops below zero for stellar rotation rates which are always substantially below breakup, but depend on the mass accretion rate and on the adopted definition of the stellar radius. When the angular momentum accretion rate drops close to zero, the star will stop spinning up. Faster stellar rotation rates will produce negative angular momentum accretion which will spin the star down. Therefore, FU Orionis outbursts can keep the stellar rotation rate close to some equilibrium value for which the angular momentum accretion rate is small. We show that this equilibrium rotation rate may be similar to the observed rotation rates of T Tauri stars; thus we propose that FU Orionis outbursts may be responsible for the observed slow rotation of T Tauri stars. This mechanism is independent of whether the disk is disrupted by the stellar magnetic field during the T Tauri phase.

Gravitational waves from wobbling pulsars

The prospects for detection of gravitational waves from precessing pulsars have been considered by constructing fully relativistic rotating neutron star models and evaluating the expected wave amplitude $h$ from a galactic source. For a "typical" neutron matter equation of state and observed rotation rates, it is shown that moderate wobble angles may render an observable signal from a nearby source once the present generation of interferometric antennas becomes operative.

Solar Rotation over Solar Cycle 21

Abstract Having measured the rotation rate of sunspots through solar cycle 21, from 1977 to 1983, we have found that the mean differential rotation averaged over this seven year record is similar to the grand average differential rotation determined by Howard et al. (1984) over the period 1921-1982. However, the rotation rate does change from year to year. These changes are evidenced by a steepening or a flattening of the mean differential rotation profile, as well as significant changes in the equatorial rate. The presence of a time-dependent pattern of azimuthal rolls inferred from the meridional circulation pattern of the sunspots offers a qualitative explanation of the observed rotation rates. The amplitude of the changes is almost one order of magnitude larger than that of the torsional oscillations found by Howard and LaBonte (1981).