Inclination Of Rotation Axis Research Articles

Survey of extended main-sequence turn-offs in galactic open clusters: stellar rotations from Gaia RVS spectra

ABSTRACT The origin of extended main-sequence turn-offs (eMSTO) in star clusters younger than 2 Gyr still challenges our current understanding of stellar evolution. Exploiting data from Gaia Data Release 3 (DR3), we investigate eMSTOs in a large sample of 32 Galactic open clusters younger than 2.4 Gyr. We first validate Gaia rotational velocities from radial velocity spectrometer spectra by comparing them with literature values and assessing their correlation with magnetic activity measurements from LAMOST spectra. We detect a general positive correlation between turn-off colour and projected stellar rotation, with slow-rotating stars predominantly found on the bluer side of the turn-off. Comparing our observations with theoretical models, we find that the eMSTO morphology is well reproduced by a single population formed with a high rotation rate, and observed with rotation axis inclination ranging between 0° (pole-on) and 90° (edge-on). This contrasts with observations of Magellanic Cloud clusters, where a population of non-rotating stars appears to be ubiquitous in clusters younger than 700 Myr. However, we note that our interpretation, while successfully explaining the overall eMSTO morphology, cannot fully explain the observed projected rotational velocities. Additionally, two young clusters, NGC 3532 and NGC 2287, exhibit moderate evidence of a split-main sequence in colour and rotation, suggesting a possible small spread in the initial rotation rate. Finally, we advise caution in determining the ages of young clusters from non-rotating isochrones, as neglecting the effects of stellar rotation can impact the isochrone dating by up to factors of 5–20 per cent.

From convective stellar dynamo simulations to Zeeman-Doppler images

Context. Zeeman-Doppler imaging (ZDI) is used to reconstruct the surface magnetic field of late-type stars from high-resolution spectropolarimetric observations. The results are usually described in terms of characteristics of the field topology, such as poloidality versus toroidality and axisymmetry versus non-axisymmetry, in addition to the field strength. Aims. In this study, we want to test how well these characteristics are preserved when applying the ZDI method to simulated data. We are particularly interested in how accurately the field topology is preserved and to what extent stellar parameters, such as projected rotation velocity and rotation axis inclination, influence the reconstruction. Methods. For these tests, we used published magnetic field vector data from direct numerical magnetohydrodynamic simulations taken near the surface of the simulation domain. These simulations have variable rotation rates and therefore represent different levels of activity of an otherwise Sun-like setup with a convective envelope of solar thickness. Our ZDI reconstruction is based on spherical harmonics expansion. By comparing the original values to those of the reconstructed images, we study the ability to reconstruct the surface magnetic field in terms of various characteristics of the field. Results. In general, the ZDI method works as expected. The main large-scale features are reasonably well recovered, but the strength of the recovered magnetic field is just a fraction of the original input. The quality of the reconstruction shows clear correlations with the data quality. Furthermore, there are some spurious dependencies between stellar parameters and the characteristics of the field. Conclusions. Our study uncovers some limits of ZDI. Firstly, the recovered field strength will generally be lower than the ‘real’ value, as smaller structures with opposite polarities will be blurred in the inversion. This is also seen in the relative distribution of magnetic energy in terms of the angular degree ℓ. Secondly, the axisymmetry is overestimated. The poloidality versus toroidality is better recovered. The reconstruction works better for a stronger field and faster rotation velocity. Still, the ZDI method works surprisingly well even for a weaker field and slow rotation provided the data have a high signal-to-noise ratio and good rotation phase coverage.

Detecting active latitudes of Sun-like stars using asteroseismic a-coefficients

Aims. We introduce a framework to measure the asphericity of Sun-like stars using a1, a2, and a4 coefficients and constrain their latitudes of magnetic activity. Methods. We evaluated systematic errors on the inferred coefficients in function of key physical and seismic parameters (inclination of rotation axis, average rotation, height-to-noise ratio of peaks in power spectrum). The measured a-coefficients account for rotational oblateness and the effect of surface magnetic activity. We used a simple model that assumes a single latitudinal band of activity. Results. Using solar SOHO, VIRGO, and SPM data, we demonstrate the capability of the method to detect the mean active latitude and its intensity changes between 1999 and 2002 (maximum of activity) and 2006 and 2009 (minimum of activity). We further applied the method to study the solar-analogue stars 16 Cyg A and B using Kepler observations. In 16 Cyg A, we detected an equatorial band of activity exhibiting an intensity that could be comparable to that of the Sun. However, 16 Cyg B exhibits a bimodality in a4 that is challenging to explain. We suggest that this could be a manifestation of the transition between a quiet and an active phase of activity. Validating or invalidating this hypothesis may require new observations.

Photometric determination of rotation axis inclination, rotation rate, and mass of rapidly rotating intermediate-mass stars

Context. Intermediate-mass stars are often fast rotators, and hence are centrifugally flattened and notably affected by gravity darkening. To analyse this kind of stars properly, one must resort to 2D models to compute the visible radiative flux and to take the geometrical effect of the star inclination into account. Aims. Assuming a given stellar age and chemical composition, our aim is to derive the mass and rotation rates of main sequence fast rotating stars, along with their inclination, from photometric quantities influenced by gravity darkening. Methods. We chose three observables that vary with mass, rotation, and inclination: the temperature derived by the infrared flux method TIRFM, the Strömgren c1 index, and a second index c2 built in the same way as the c1 index, but sensitive to the UV side of the Balmer jump. These observables are computed from synthetic spectra produced with the PHOENIX code and rely on a 2D stellar structure from the ESTER code. These quantities are computed for a grid of models in the range 2–7 M⊙, and rotation rates from 30% to 80% of the critical rate. Then, for any triplet (TIRFM, c1, c2), we try to retrieve the mass, rotation rate, and inclination using a Levenberg-Marquardt scheme, after a selection step to find the most suitable starting models. Results. Hare-and-hound tests showed that our algorithm can recover the mass, rotation rate, and inclination with a good accuracy. The difference between input and retrieved parameters is negligible for models lying on the grid and is less than a few percent otherwise. An application to the real case of Vega showed that the u filter is located in a spectral region where the modelled and observed spectra are discrepant, and led us to define a new filter. Using this new filter and subsequent index, the Vega parameters are also retrieved with satisfactory accuracy. Conclusions. This work opens the possibility to determine the fundamental parameters of rapidly rotating early-type stars from photometric space observations.

X-ray polarimetry of X-ray pulsar X Persei: another orthogonal rotator?

ABSTRACT X Persei is a persistent low-luminosity X-ray pulsar of period of ≈ 835 s in a Be binary system. The field strength at the neutron star surface is not known precisely, but indirect signs indicate a magnetic field above 1013 G, which makes the object one of the most magnetized known X-ray pulsars. Here we present the results of observations X Persei performed with the Imaging X-ray Polarimetry Explorer (IXPE). The X-ray polarization signal was found to be strongly dependent on the spin phase of the pulsar. The energy-averaged polarization degree in 3–8 keV band varied from several to ∼20 per cent over the pulse with a phase dependence resembling the pulse profile. The polarization angle shows significant variation and makes two complete revolutions during the pulse period, resulting in nearly nil pulse-phase averaged polarization. Applying the rotating vector model to the IXPE data we obtain the estimates for the rotation axis inclination and its position angle on the sky, as well as for the magnetic obliquity. The derived inclination is close to the orbital inclination, reported earlier for X Persei. The polarimetric data imply a large angle between the rotation and magnetic dipole axes, which is similar to the result reported recently for the X-ray pulsar GRO J1008−57. After eliminating the effect of polarization angle rotation over the pulsar phase using the best-fitting rotating vector model, the strong dependence of the polarization degree with energy was discovered, with its value increasing from 0 at ∼2 keV to 30per cent at 8 keV.

The ESO-VLT MIKiS Survey Reloaded: Velocity Dispersion Profile and Rotation Curve of NGC 1904* *Based on observations collected at the European Southern Observatory, Cerro Paranal (Chile), under proposal 193.D-0232 (PI: Ferraro) and 0104.D-0636 (PI: Ferraro).

We present an investigation of the internal kinematic properties of M79 (NGC 1904). Our study is based on radial velocity measurements obtained from the ESO-VLT Multi-Instrument Kinematic Survey (MIKiS) of Galactic globular clusters for more than 1700 individual stars distributed between ∼0.″3 and 770″ (∼14 three-dimensional half-mass radii) from the center. Our analysis reveals the presence of ordered line-of-sight rotation with a rotation axis almost aligned along the east–west direction and a velocity peak of 1.5 km s−1 at ∼70″ from the rotation axis. The velocity dispersion profile is well described by the same King model that best fits the projected density distribution, with a constant central plateau at σ 0 ∼ 6 km s−1. To investigate the cluster rotation in the plane of the sky, we have analyzed the proper motions provided by the Gaia EDR3, finding a signature of rotation with a maximum amplitude of ∼2.0 km s−1 at ∼80″ from the cluster center. Analyzing the three-dimensional velocity distribution for a subsample of 130 stars, we confirm the presence of systemic rotation and find a rotation axis inclination angle of 37° with respect to the line of sight. As a final result, the comparison of the observed rotation curves with the results of a representative N-body simulation of a rotating star cluster shows that the present-day kinematic properties of NGC 1904 are consistent with those of a dynamically old system that has lost a significant fraction of its initial angular momentum.

Polarimetric detection of non-radial oscillation modes in the β Cephei star β Crucis

Here we report the detection of polarization variations due to nonradial modes in the beta Cephei star beta Crucis. In so doing we confirm 40-year-old predictions of pulsation-induced polarization variability and its utility in asteroseismology for mode identification. In an approach suited to other beta Cep stars, we combine polarimetry with space-based photometry and archival spectroscopy to identify the dominant nonradial mode in polarimetry, f2, as l = 3, m = -3 (in the m-convention of Dziembowski) and determine the stellar axis position angle as 25 (or 205) +/- 8 deg. The rotation axis inclination to the line of sight was derived as approx. 46 deg. from combined polarimetry and spectroscopy, facilitating identification of additional modes and allowing for asteroseismic modelling. This reveals a star of 14.5 +/- 0.5 Solar masses and a convective core containing approx. 28% of its mass -- making beta Crucis the most massive star with an asteroseismic age.

Digging into the Interior of Hot Cores with ALMA (DIHCA). I. Dissecting the High-mass Star-forming Core G335.579-0.292 MM1

Abstract We observed the high-mass star-forming region G335.579–0.292 with the Atacama Large Millimeter/submillimeter Array (ALMA) at 226 GHz with an angular resolution of 0.″3 (∼1000 au resolution at the source distance). G335.579–0.292 hosts one of the most massive cores in the Galaxy (G335–MM1). The continuum emission shows that G335–MM1 fragments into at least five sources, while molecular line emission is detected in two of the continuum sources (ALMA1 and ALMA3). We found evidence of large- and small-scale infall in ALMA1 revealed by an inverse P-Cygni profile and the presence of a blueshifted spot at the center of the first moment map of the CH3CN emission. In addition, hot gas expansion in the innermost region is unveiled by a redshifted spot in the first moment map of HDCO and (CH3)2CO (both with E u > 1100 K). Our modeling reveals that this expansion motion originates close to the central source, likely due to reversal of the accretion flow induced by the expansion of the H ii region, while infall and rotation motions originate in the outer regions. ALMA3 shows clear signs of rotation, with a rotation axis inclination with respect to the line of sight close to 90°, and a system mass (disk + star) in the range of 10–30 M ☉.

Discovery of rotation axis alignments in Milky Way globular clusters

There is an increasing number of recent observational results that show that some globular clusters exhibit internal rotation while they travel along their orbital trajectories around the Milky Way center. Based on these findings, we searched for any relationship between the inclination angles of the globular cluster orbits with respect to the Milky Way plane and those of their rotation. We discovered that the relative inclination, in the sense of inclination of the rotation axis to orbit axis, is a function of the orbit inclination of the globular cluster. Rotation and orbit axes are aligned for an inclination of ∼56°, while the rotation axis inclination is far from the orbit inclination between ∼20° and −20° when the latter increases from 0° up to 90°. We further investigated the origin of this linear relationship and found no correlation with the semimajor axes and eccentricities of the globular cluster orbits, nor with the internal rotation strength, the globular cluster sizes, actual and tidally disrupted masses, or half-mass relaxation times, among others. The uncovered relationship will affect the development of numerical simulations of the internal rotation of globular clusters, our understanding of the interaction of globular clusters with the gravitational field of the Milky Way, and the observational campaigns made to increase the number of globular clusters with detected internal rotation.

Internal and Imagined External Foci of Attention Do Not Influence Pirouette Performance in Ballet Dancers

ABSTRACT Ballet dancers need to constantly improve their performance. Several studies show that an internal focus (on body movements) leads to inferior motor performance relative to an external focus of attention (on the movement effects), but the majority of dancers usually adopt an internal focus. It is not clear if the benefits of an external focus are relevant for form-based tasks performed in a ballet. Purpose: Test whether an imagined external focus of attention can improve ballet dancers’ performance of a form-based task, the en dehors double pirouette (EDDP). Method: 23 experienced amateurs and 17 professional dancers between 18 and 35 years old performed three EDDP under each of three attentional focus instruction conditions (No Focus, Internal, Imagined External). Order of presentation of Internal and Imagined External focus instructions was blocked and balanced across participants. Movement quality was assessed by three experts with a customized observational scale. Movement kinematics were measured by the angle of inclination of the trunk and inclination of the rotation axis with respect to the global vertical during the EDDP. Results: Movement quality and trunk inclination were significantly different between amateurs and professionals, but the rotation axis inclination was not. No quantitative or qualitative effects of focus were found for the performance of the EDDP across focus conditions. Conclusions: There appears to be no differential effects of using an internal or imagined external focus on the immediate performance of the EDDP for amateur and professional ballet dancers. Personal and task factors might account for the lack of effects.

Analysis of satellite data on dynamics of the extent of sea ice due to insolation contrast

On the basis of theoretical calculations of insolation and Earth remote sensing data on the dynamics of the sea ice area in the Arctic Ocean, a close relationship between long-term changes in the sea ice area and annual insolation contrast in the Northern hemisphere was determined. The change in insolation contrast was generalized (in terms of the source and sink of heat) reflects the change in the meridional insolation gradient that regulates the meridional heat transfer in the ocean - atmosphere system. The regression model was used to make an estimated forecast of changes in the area of sea ice in the Arctic Ocean. According to our estimates, the reduction of the average annual sea ice extent in the Arctic Ocean in 2050 will be 18.3% relative to 2018. The Maximum area (March) will be reduced by 10.1%, and the Minimum area (September) by 60.3%. The decrease in the area of sea ice is associated with an increase in the meridional gradient of insolation and meridional heat transfer resulting from a decrease in the inclination of the Earth's rotation axis in the present epoch.

Star–disc (mis-)alignment in Rho Oph and Upper Sco: insights from spatially resolved disc systems with K2 rotation periods

The discovery of close in, giant planets (hot Jupiters) with orbital angular momentum vectors misaligned with respect to the rotation axis of their host stars presents problems for planet formation theories in which planets form in discs with angular momentum vectors aligned with that of the star. Violent, high eccentricity migration mechanisms purported to elevate planetary orbits above the natal disc plane predict populations of proto-hot Jupiters which have not been observed with Kepler. Alternative theories invoking primordial star-disc misalignments have recently received more attention. Here, the relative alignment between stars and their protoplanetary discs is assessed for the first time for a sample of 20 pre-main-sequence stars. Recently published rotation periods derived from high quality, long duration, high cadence K2 light curves for members of the $\rho$ Ophiuchus and Upper Scorpius star forming regions are matched with high angular resolution observations of spatially resolved discs and projected rotational velocities to determine stellar rotation axis inclination angles which are then compared to the disc inclinations. Ten of the fifteen systems for which the stellar inclination could be estimated are consistent with star-disc alignment while five systems indicate potential misalignments between the star and its disc. The potential for chance misalignment of aligned systems due to projection effects and characteristic measurement uncertainties is also investigated. While the observed frequency of apparent star-disc misalignments could be reproduced by a simulated test population in which 100% of systems are truly aligned, the distribution of the scale of inferred misalignment angles could not.

The GJ 504 system revisited

Context. The G-type star GJ504A is known to host a 3–35 MJup companion whose temperature, mass, and projected separation all contribute to making it a test case for planet formation theories and atmospheric models of giant planets and light brown dwarfs. Aims. We aim at revisiting the system age, architecture, and companion physical and chemical properties using new complementary interferometric, radial-velocity, and high-contrast imaging data. Methods. We used the CHARA interferometer to measure GJ504A’s angular diameter and obtained an estimation of its radius in combinationwith the HIPPARCOS parallax. The radius was compared to evolutionary tracks to infer a new independent age range for the system. We collected dual imaging data with IRDIS on VLT/SPHERE to sample the near-infrared (1.02–2.25 μm) spectral energy distribution (SED) of the companion. The SED was compared to five independent grids of atmospheric models (petitCODE,Exo-REM, BT-SETTL, Morley et al., and ATMO) to infer the atmospheric parameters of GJ 504b and evaluate model-to-model systematic errors. In addition, we used a specific model grid exploring the effect of different C/O ratios. Contrast limits from 2011 to 2017 were combined with radial velocity data of the host star through the MESS2 tool to define upper limits on the mass of additional companions in the system from 0.01 to 100 au. We used an MCMC fitting tool to constrain the companion’sorbital parameters based on the measured astrometry, and dedicated formation models to investigate its origin. Results. We report a radius of 1.35 ± 0.04 R⊙ for GJ504A. The radius yields isochronal ages of 21 ± 2 Myr or 4.0 ± 1.8 Gyr for the system and line-of-sight stellar rotation axis inclination of 162.4−4.3+3.8 degrees or 186.6−3.8+4.3 degrees. We re-detect the companion in the Y2, Y3, J3, H2, and K1 dual-band images. The complete 1–4 μm SED shape of GJ504b is best reproduced by T8-T9.5 objects with intermediate ages (≤ 1.5Gyr), and/or unusual dusty atmospheres and/or super-solar metallicities. All atmospheric models yield Teff = 550 ± 50 K for GJ504b and point toward a low surface gravity (3.5–4.0 dex). The accuracy on the metallicity value is limited by model-to-model systematics; it is not degenerate with the C/O ratio. We derive log L∕L⊙ = −6.15 ± 0.15 dex for the companion from the empirical analysis and spectral synthesis. The luminosity and Teff yield masses of M = 1.3−0.3+0.6 MJup and M = 23−9+10 MJup for the young and old age ranges, respectively. The semi-major axis (sma) is above 27.8 au and the eccentricity is lower than 0.55. The posterior on GJ 504b’s orbital inclination suggests a misalignment with the rotation axis of GJ 504A. We exclude additional objects (90% prob.) more massive than 2.5 and 30 MJup with semi-major axes in the range 0.01–80 au for the young and old isochronal ages, respectively. Conclusions. The mass and semi-major axis of GJ 504b are marginally compatible with a formation by disk-instability if the system is 4 Gyr old. The companion is in the envelope of the population of planets synthesized with our core-accretion model. Additional deep imaging and spectroscopic data with SPHERE and JWST should help to confirm the possible spin-orbit misalignment and refine the estimates on the companion temperature, luminosity, and atmospheric composition.

The Solar Twin Planet Search

It is still unclear how common the Sun is when compared to other similar stars in regards to some of its physical properties, such as rotation. Considering that gyrochronology relations are widely used today to estimate ages of stars in the main sequence, and that the Sun is used to calibrate it, it is crucial to assess if these procedures are acceptable. We analyze the rotational velocities -- limited by the unknown rotation axis inclination angle -- of an unprecedented large sample of solar twins in order to study the rotational evolution of Sun-like stars, and assess if the Sun is a typical rotator. We use high-resolution ($R = 115000$) spectra obtained with the HARPS spectrograph and ESO's 3.6 m telescope at La Silla Observatory. The projected rotational velocities for 82 solar twins are estimated by line profile fitting with synthetic spectra. Macroturbulence velocities are inferred from a prescription that accurately reflects their dependence with effective temperature and luminosity of the stars. Our sample of solar twins include some spectroscopic binaries with enhanced rotational velocities, and we do not find any non-spectroscopic binaries with unusually high rotation velocities. We verified that the Sun does not have a peculiar rotation, but the solar twins exhibit rotational velocities that depart from the Skumanich relation. The Sun is a regular rotator when compared to solar twins with a similar age. Additionally, we obtain a rotational braking law that better describes the stars in our sample ($v \propto t^{-0.6}$) in contrast to previous, often-used scalings.

Estimating the angle of inclination of the Earth's rotational axis: a potentially meaningful practical activity for astronomy education

This article describes a practical activity to estimate the angle of inclination of the Earth's rotation axis as a teaching resource with potential to promote the meaningful learning on topics related to astronomy and Earth science. Some topics of interest for carrying out the activity as the apparent movement of the sun, the angle of incidence of sunlight throughout the year and the seasons are discussed. The procedures and materials used in measuring the length of the shadow of a gnomon, the collected data, and the estimating of the angle of inclination of the rotation axis are presented. The article ends with a reflection on the implementation of this activity in elementary and high school level. http://dx.doi.org/10.18226/23185279.v3iss1p36

Model-based cross-correlation search for gravitational waves from Scorpius X-1

We consider the cross-correlation search for periodic GWs and its potential application to the LMXB Sco X-1. This method coherently combines data from different detectors at the same time, as well as different times from the same or different detectors. By adjusting the maximum time offset between a pair of data segments to be coherently combined, one can tune the method to trade off sensitivity and computing costs. In particular, the detectable signal amplitude scales as the inverse fourth root of this coherence time. The improvement in amplitude sensitivity for a search with a coherence time of 1hr, compared with a directed stochastic background search with 0.25Hz wide bins is about a factor of 5.4. We show that a search of 1yr of data from Advanced LIGO and Advanced Virgo with a coherence time of 1hr would be able to detect GWs from Sco X-1 at the level predicted by torque balance over a range of signal frequencies from 30-300Hz; if the coherence time could be increased to 10hr, the range would be 20-500Hz. In addition, we consider several technical aspects of the cross-correlation method: We quantify the effects of spectral leakage and show that nearly rectangular windows still lead to the most sensitive search. We produce an explicit parameter-space metric for the cross-correlation search in general and as applied to a neutron star in a circular binary system. We consider the effects of using a signal template averaged over unknown amplitude parameters: the search is sensitive to a combination of the intrinsic signal amplitude and the inclination of the neutron star rotation axis, and the peak of the expected detection statistic is systematically offset from the true signal parameters. Finally, we describe the potential loss of SNR due to unmodelled effects such as signal phase acceleration within the Fourier transform timescale and gradual evolution of the spin frequency.

WIDEBAND DYNAMIC RADIO SPECTRA OF TWO ULTRA-COOL DWARFS

A number of radio-loud ultra cool dwarf stars (UCD) exhibit both continuous broadband and highly polarized pulsed radio emission. In order to determine the nature of the emission and the physical characteristics in the source region, we have made multi-epoch, wideband spectral observations of TVLM 0513-46 and 2M 0746+20. We combine these observations with archival radio data to fully characterize both the temporal and spectral properties of the radio emission. The continuum spectral energy distribution can be well modeled using gyrosynchrotron emission from mildly relativistic electrons in a dipolar field. The pulsed emission exhibits a variety of time-variable characteristics, including frequency drifts, frequency cutoffs, and multiple pulses per period. For 2M 0746+20 we determine a pulse period consistent with previously determined values. We modeled locations of pulsed emission using an oblique rotating magnetospheric model with beamed electron cyclotron maser (ECM) sources. The best-fit models have narrow ECM beaming angles aligned with the local source magnetic field direction, except for one isolated burst from 2M 0746+20. For TVLM 0513-46, the best-fit rotation axis inclination is nearly orthogonal to the line of sight. For 2M 0746+20 we found a good fit using a fixed inclination i=36 deg, determined from optical observations. For both stars the ECM sources are located near feet of magnetic loops with radial extents 1.2Rs-2.7 Rs and surface fields 2.2 - 2.5 kG. These results support recent suggestions that radio over-luminous UCDs have a global `weak field' non-axisymmetric magnetic topologies.

Результаты экспериментальных исследований ротационного конического рабочего органа в почвенном канале

The article presents the results of experimental research of the rotary conical tillage working unit in the soil canal. The authors established a functional dependence of driving force and the rotation speed of the conical working unit from the angles of attack α and inclination to the horizontal level β, as well as the depth of tillage a. The rational value of angles of attack α and inclination of rotation axis to the horizon β was determined, which is providing the minimum driving force or the maximum speed of rotation of working unit. At the same time the extreme points on the tractive effort and the rotational speed are different. Therefore, the rational value of angles α and β can be chosen only as a compromise for different depths of soil treatment are in the following ranges. For а=8 cm: 44 ≤α ≤48, 25 ≤ β ≤28; for а=10 cm: 39 ≤α ≤44, 30 ≤ β ≤31; for а=12 cm: 34 ≤α ≤40, 33 ≤ β ≤37. When operating a conical working unit, we can recommend the following. The angle of inclination of the axis of rotation to the horizontal β and the angle of attack α need to be changed, depending on the processing conditions of the soil. During autumn tillage, you must install the angles α and β to provide the least traction so that to reduce fuel consumption. In spring, when preparing the fields for sowing, in the first place it is placed the quality of the soil, which increases with increasing ω. Therefore, it is necessary to set the angles α and β so, as to maximize the speed of rotation of the working unit.

Material Flow in Rotary Drums

The experimental investigation of material flow in non-flight rotary drums is studied in a pilot scale apparatus. Contrary to the other published references that have used granular materials, the novelty of this work is that fine particles were used in the experiments. The objective of the paper is to declare the errors of steady-state model of material flow in such devices. The operating conditions during experiments were conducted in the range of slumping, rolling and cascading regimes of material flow inside rotary drums. To keep with such conditions the rotation speed, axis inclination and feeding flow rate were considered within the range of 3.33 to 7.00 (rpm), 0.00 to 3.00 (deg.) and 6.80 to 13.60 (g/s), respectively in a drum of 14 cm diameter.The obtained experimental data reveals that the model does not describe well the material flow in feeding zone as well as in the discharge zone. However, it is reasonably well for application in the intermediate sections.

Beyond the diffraction limit of optical/IR interferometers

Context. Spectrally resolved long-baseline optical/IR interferometry of rotating stars opens perspectives to investigate their fundamental parameters and the physical mechanisms that govern their interior, photosphere, and circumstellar envelope structures.Aims. Based on the signatures of stellar rotation on observed interferometric wavelength-differential phases, we aim to measure angular diameters, rotation velocities, and orientation of stellar rotation axes.Methods. We used the AMBER focal instrument at ESO-VLTI in its high-spectral resolution mode to record interferometric data on the fast rotator Achernar. Differential phases centered on the hydrogen Br γ line (K band) were obtained during four almost consecutive nights with a continuous Earth-rotation synthesis during ~5 h/night, corresponding to ~60° position angle coverage per baseline. These observations were interpreted with our numerical code dedicated to long-baseline interferometry of rotating stars.Results. By fitting our model to Achernar’s differential phases from AMBER, we could measure its equatorial radius R eq = 11.6 ± 0.3 R ⊙ , equatorial rotation velocity V eq = 298 ± 9 km s-1 , rotation axis inclination angle i = 101.5 ± 5.2°, and rotation axis position angle (from North to East) PArot = 34.9 ± 1.6°. From these parameters and the stellar distance, the equatorial angular diameter ⌀eq of Achernar is found to be 2.45 ± 0.09 mas, which is compatible with previous values derived from the commonly used visibility amplitude. In particular, ⌀eq and PArot measured in this work with VLTI/AMBER are compatible with the values previously obtained with VLTI/VINCI.Conclusions. The present paper, based on real data, demonstrates the super-resolution potential of differential interferometry for measuring sizes, rotation velocities, and orientation of rotating stars in cases where visibility amplitudes are unavailable and/or when the star is partially or poorly resolved. In particular, we showed that differential phases allow the measurement of sizes up to ~4 times smaller than the diffraction-limited angular resolution of the interferometer.