Disk Radius Research Articles

Long-term Doppler imaging of the star XX Trianguli indicates chaotic non-periodic dynamo

Sunspots are the most well-known manifestations of solar magnetic fields and exhibit a range of phenomena related to the interior dynamo. Starspots are the direct analogs of sunspots on other stars but with the big observational restriction that we usually cannot resolve other star’s surfaces. In this paper we employ an indirect surface imaging technique called Doppler imaging and present 99 independent Doppler images of the star XX Trianguli. The star was selected because it had shown a gigantic star spot in a previous study and was thus well suited for a long-term monitoring effort. We combine the Doppler images into a movie visualizing the star’s surface spot evolution for the past 16 years. Stellar-disk photocenter displacements of up to 24 μas, or about 10% of the stellar disk radius, are reconstructed, but do not show the typical solar-like periodic behavior that could be interpreted as an activity cycle. It suggests a mostly chaotic, likely unperiodic, dynamo. These rotation-induced stellar photocenter variations pose an intrinsic limitation for astrometric exoplanet catches.

Calibration and experiments of discrete element flexible model parameters for kiwifruit stalk

A method combining experimental and simulation optimization was used to calibrate parameters to enhance the accuracy of discrete element model parameters during kiwifruit stem separation. First, physical experiments were conducted to determine the intrinsic and contact parameters of kiwifruit stalk. Second, the mechanical parameters of the kiwifruit stalks were determined using three-point bending and shear tests. On this basis, simulation tests were conducted on kiwifruit stalks by combining the Hertz-Mindlin model with a bonding model, and the optimal combination of bonding parameters was confirmed using the bending strength and maximum shear force. Finally, a discrete element model of the kiwifruit was built with the determined bonding parameters and simulated, and the reliability of the model was verified through mechanical tests. The results showed that the density was 867.5 kg/m3, Poisson's ratio was 0.26, the modulus of elasticity was 3.25 × 108 Pa, the recovery coefficient between the fruit stalks and steel parts was 0.365, and the average values of the static and dynamic friction coefficients between the kiwifruit stalks and steel parts were 0.268 and 0.152, respectively. The kiwifruit stem bonding parameters were normal stiffness per unit area kn=7.201×1011 N/m3, shear stiffness per unit area kt=2.379×1011 N/m3, critical normal stress σmax=5.937×108 Pa, critical shear stress tmax = 2.354×109 Pa, and bonded disc radius Rj=0.164 mm. Compared with the results of the mechanical tests, the relative errors of the bending strength and maximum shear of the discrete element model were 2.13% and 2.84%, respectively. The results showed that the discrete element model improves the simulation of the bending and shearing processes of kiwifruit stalks and is capable of characterizing the physical properties of kiwifruit stalks. The results of this study provide a theoretical foundation for the optimal design of end effectors.

Identification of viscoelastic properties with fluid inertia in a parallel plate with effective mechanical system analyses

Measurement of viscoelastic properties in small amplitude oscillatory shear (SAOS) can be affected by fluid inertia, especially at high frequencies. In this study, we introduce an effective mechanical system approach to address the effects of fluid inertia on the viscoelastic measurement with a SAOS test, employing a parallel plate geometry. In the effective mechanical system approach, viscous, elastic, and inertial properties of a fluid system are modeled systematically by a rotational drag coefficient, a torsional spring constant, and a second moment of inertia, respectively. In this way, we established the analytic solution for the linear viscoelastic behavior of a fluid in the presence of fluid inertia. The shear modulus on the frequency, obtained by the effective mechanical system, reveals that fluid inertia only affects the storage modulus and not the loss modulus. We investigate the behavior of the storage modulus as a function of the gap size, the oscillation frequency, and the disk radius, demonstrating the dependence on the gap size and the frequency. Comparison was made for the shear modulus from the effective mechanical system with viscoelastic flow simulation, employing two viscoelastic (Oldroyd-B and Giesekus) fluid models to validate the accuracy of this approach. The maximum error was found less than 3.3% over the frequency range from 1 to 100 rad/s.

Lack of emission lines in the optical spectra of SAX J1808.4–3658 during reflaring of the 2019 outburst

Aims. We present spectroscopy of the accreting X-ray binary and millisecond pulsar SAX J1808.4–3658. These observations are the first to be obtained during a reflaring phase. We collected spectroscopic data during the beginning of the reflaring of the 2019 outburst and compared them to previous datasets taken at different epochs, both of the same outburst and across the years. To this end, we also present spectra of the source taken during quiescence in 2007, one year before the next outburst. Methods. We made use of data taken by the Very Large Telescope (VLT) X-shooter spectrograph on August 31, 2019, three weeks after the outburst peak. For flux calibration, we used photometric data taken during the same night by the 1m telescopes from the Las Cumbres Observatory network that are located in Chile. We compare our spectra to the quiescent data taken by the VLT-FORS1 spectrograph in September, 2007. We inspected the spectral energy distribution by fitting our data with a multicolored accretion-disk model and sampled the posterior probability density function for the model parameters with a Markov chain Monte Carlo (MCMC) algorithm. Results. We find the optical spectra of the 2019 outburst to be unusually featureless, with no emission lines present despite the high resolution of the instrument. Fitting the UV-optical spectral energy distribution with a disk plus irradiated star model results in a very large value for the inner disk radius of ∼5130 ± 240 km, which could suggest that the disk was emptied of material during the outburst, possibly accounting for the emission-less spectra. Alternatively, the absence of emission lines could be due to a significant contribution of the jet emission at optical wavelengths.

BiLipschitz homogeneous hyperbolic nets

We answer a question of Itai Benjamini by showing there is a \(K< \infty\) so that for any \(\epsilon >0\), there exist \(\epsilon\)-dense discrete sets in the hyperbolic disk that are homogeneous with respect to \(K\)-biLipschitz maps of the disk to itself. However, this is not true for \(K\) close to \(1\); in that case, every \(K\)-biLipschitz homogeneous discrete set must omit a disk of hyperbolic radius \(\epsilon(K)>0\). For \(K=1\), this is a consequence of the Margulis lemma for discrete groups of hyperbolic isometries.

Area functional and majorant series estimates in the class of bounded functions in the disk

In this article, the new inequalities for the weighted sums of coefficients in the class of bounded functions in the disk are obtained. We develop the methods of I.R. Kayumov and S. Ponnusamy, using E. Reich's theorem on the majorization of subordinate functions. The sharp estimates for the area of the image of the disk of radius r under the action of the function which is expanded into a lacunary series of standard form are obtained. Under significantly lower than in [20] restrictions on the initial coefficient, the estimates for the Bohr–Bombieri function of the Hadamard convolution operator are proved. Using the example of the differentiation operator, it is shown that in some cases the new method for calculating the lower bound for the Bohr radius of the Hadamard operator with a fixed initial coefficient is more effective than the known one.

Thermal instability of three-dimensional boundary layer stagnation point flow towards a rotating disc

In this paper, the thermal instability of a three-dimensional boundary layer axisymmetric stagnation point flow towards a heated horizontal rotating disk is considered. A large number of works have been done on stability analysis. However, they did not check the thermal stability of the non-parallel-flow in the face of small disturbances that occur in the vicinity of the heated rotating disk. The governing equations of the basic flow are reduced to three coupled nonlinear partial differ-ential equations, and solved numerically with the fourth-order Runge-Kutta method. Thermal stability is examined by making use of linear stability theory based on the decomposition of the normal mode of Görtler-Hammerlin. The resulting eigenvalue problem is solved numerically using a pseudo-spectral method based on the expansion of Laguerre’s polyno-mials. The obtained results are discussed in detail through multiple configurations. As the main result, for large Prandtl numbers (Pr), the rotation disk parameter (Ω) has a destabilizing effect while for small Pr (around the unity) it tends to stabilize the basic flow. It was found that as the disk radius r→0, the flow is linearly stable, and the disturbances grow rapidly away from the stagnation point. For low values of Pr, the flow becomes more stable, and strong thermal gradients are necessary to destabilize it. However, an increase in Pr leads to a significant expansion of the instability region.

Spindle vibration induced optical performance deterioration and its trans-scale characterization for diamond turned large-aperture optics

In ultra-precision diamond turning of large-aperture optics, the spindle vibration (SV) would cause a deterioration of optical performance. To discuss this issue, the spindle vibration was first excited by a series of designed mass center errors for diamond turning of large-aperture optics. Then, a trans-scale characterization was developed to reveal its dynamic behaviors by combining a white light interferometer and laser interferometer. Next, the amplitude variations were quantitatively evaluated by surface texture parameters and the scale bandwidth was revealed through power spectrum density (PSD). Finally, the point spread function (PSF), encircled energy ratio (EER), and modulation transfer function (MTF) were analyzed and compared. The results indicated that, with the increased SV, Sq and Sz increased and Ssk and Sku showed a transition from skew to normal height distribution. PSD showed that spindle vibration mainly affected the large-scale components rather than the small-scale components. The shape of PSF changed from a standard ring to a dispersed half ring. At the 1 µm radius of the Airy disk, the EER decreased from 82.0% (no SV) to 27.5% (high SV). At the scale of 200mm−1, the MTF decreased from 0.84 (no SV) to 0.44 (high SV). The work provides a fundamental understanding of the evolutionary mechanism of spindle vibration induced optical performance deterioration.

Experimental Verification of Laser Radar Cross Section Model for Complex Targets with Gaussian Beam Irradiation

The reflection of a Gaussian laser beam from a flat Lambert disk is considered theoretically. It was found that the results of experimental measurements of the reflected beam power as a function of the disk radius at various distances from the photodetector to the target are in good agreement with the theoretical model. It was shown that when the radius of the laser beam is greater than the dimensions of the probed complex target this target can be replaced by an equivalent Lambert disk with the same laser radar cross section.

Modeling the Energy-dependent Broadband Variability in the Black Hole Transient GX 339–4 Using AstroSat and NICER

We present a spectro-timing analysis of the black hole X-ray transient GX 339–4 using simultaneous observations from AstroSat and the Neutron Star Interior Composition Explorer (NICER) during the 2021 outburst period. The combined spectrum obtained from NICER, Large Area X-ray Proportional Counter and SXT data is effectively described by a model comprising a thermal disk component, hard Comptonization component, and reflection component with an edge. Our analysis of the AstroSat and NICER spectra indicates the source to be in a low/hard state, with a photon index of ∼1.64. The power density spectra obtained from both AstroSat and NICER observations exhibit two prominent broad features at 0.22 Hz and 2.94 Hz. We generated energy-dependent time lag and fractional root mean square (frms) at both frequencies in a broad energy range of 0.5–30 keV and found the presence of hard lags along with a decrease in variability at higher energy levels. Additionally, we discovered that the correlated variations in accretion rate, inner disk radius, coronal heating rate, and the scattering fraction, along with a delay between them, can explain the observed frms and lag spectra for both features.

Bolometric Corrections for FU Ori Object Accretion Disk Luminosities

The accretion luminosity of an FU Ori disk is a fundamental system parameter, but a challenging one to estimate for all but the most well-studied systems. FU Ori objects are dynamically evolving accretion disks, especially close in time to the outburst epoch. They have a complex multitemperature disk structure that results in distinctly shaped, broad spectral energy distributions (SEDs). Detailed spectroscopic analysis is required for simultaneous constraint on relevant physical parameters such as the central stellar mass, inner disk radius, disk inclination, and disk accretion rate. However, outbursting systems that are deeply embedded and/or distant may be limited to only photometric measurement and over only a narrow range of wavelengths. The bolometric corrections necessary to estimate accretion luminosities are not straightforward and in particular cannot be adopted from existing literature on isotropically radiating stars. We present bolometric corrections specific to astrophysical accretion disks for a variety of filters in ongoing and upcoming all-sky surveys.

Radiation mechanism of twin kilohertz quasi-periodic oscillations in neutron star low-mass X-ray binaries

Context. The connection between quasi-periodic oscillations (QPOs) and magnetic fields has been investigated in various celestial bodies. Magnetohydrodynamic (MHD) waves have been employed to explain the simultaneous upper and lower kilohertz (kHz) QPOs. Nevertheless, the intricate and undefined formation pathways of twin kHz QPOs present a compelling avenue for exploration. This study area holds great interest as it provides an opportunity for deriving crucial parameters related to compact stars. Aims. We strive to develop a self-consistent model elucidating the radiation mechanism of twin kHz QPOs, which we then compare it with observations. Methods. A sample of 28 twin kHz QPOs detected from the X-ray binary 4U 1636–53 was used for a comparison with the results of the Markov chain Monte Carlo calculations based on our model of the radiation mechanism of twin kHz QPOs, which is related to twin MHD waves. Results. We obtained 28 groups of parameters of 4U 1636–53 and a tight exponential fit between the flux and the temperature of seed photons to Compton up-scattering and find that the electron temperature in the corona around the neutron star decreases with increasing seed photon temperature. Conclusions. The origin of twin kHz QPOs are dual disturbances that arise from twin MHD waves that are generated at the innermost radius of an accretion disc. The seed photons can be transported through a high temperature corona and are Compton up-scattered. The photons that vary the frequencies of twin MHD waves lead to the observed twin kHz QPOs.

Dust Drift Timescales in Protoplanetary Disks at the Cusp of Gravitational Instability

Millimeter emitting dust grains have sizes that make them susceptible to drift in protoplanetary disks due to the difference between their orbital speed and that of the gas. The characteristic drift timescale depends on the surface density of the gas. By comparing disk radius measurements from Atacama Large Millimeter/submillimeter Array CO and continuum observations at millimeter wavelengths, the gas surface density profile and dust drift time can be self-consistently determined. We find that profiles which match the measured dust mass have very short drift timescales, an order of magnitude or more shorter than the stellar age, whereas profiles for disks that are on the cusp of gravitational instability, defined via the minimum value of the Toomre parameter, Qmin∼1−2 , have drift timescales comparable to the stellar lifetime. This holds for disks with masses of dust ≳5 M ⊕ across a range of absolute ages from less than 1 Myr to over 10 Myr. The inferred disk masses scale with stellar mass as Mdisk≈M*/5Qmin . This interpretation of the gas and dust disk sizes simultaneously solves two long standing issues regarding the dust lifetime and exoplanet mass budget, and suggests that we consider millimeter wavelength observations as a window into an underlying population of particles with a wide size distribution in secular evolution with a massive planetesimal disk.

High-resolution ALMA Observations of Richly Structured Protoplanetary Disks in σ Orionis

The Atacama Large Millimeter/submillimeter Array (ALMA) has detected substructures in numerous protoplanetary disks at radii from a few to over 100 au. These substructures are commonly thought to be associated with planet formation, either by serving as sites fostering planetesimal formation or by arising as a consequence of planet–disk interactions. Our current understanding of substructures, though, is primarily based on observations of nearby star-forming regions with mild UV environments, whereas stars are typically born in much harsher UV environments, which may inhibit planet formation in the outer disk through external photoevaporation. We present high-resolution (∼8 au) ALMA 1.3 mm continuum images of eight disks in σ Orionis, a cluster irradiated by an O9.5 star. Gaps and rings are resolved in the images of five disks. The most striking of these is SO 1274, which features five gaps that appear to be arranged nearly in a resonant chain. In addition, we infer the presence of gap or shoulder-like structures in the other three disks through visibility modeling. These observations indicate that substructures robustly form and survive at semimajor axes of several tens of au or less in disks exposed to intermediate levels of external UV radiation as well as in compact disks. However, our observations also suggest that disks in σ Orionis are mostly small, and thus millimeter continuum gaps beyond a disk radius of 50 au are rare in this region, possibly due to either external photoevaporation or age effects.

Broadband X-ray spectral and timing properties of the accreting millisecond X-ray pulsar IGR J17498−2921 during the 2023 outburst

We report on the broadband spectral and timing properties of the accreting millisecond X-ray pulsar IGR J17498−2921 during its April 2023 outburst. We used data from NICER (1–10 keV), NuSTAR (3–79 keV), Insight-HXMT (2–150 keV), and INTEGRAL (30–150 keV). We detected significant 401 Hz pulsations across the 0.5–150 keV band. The pulse fraction increases from ∼2% at 1 keV to ∼13% at 66 keV. We detected five type-I X-ray bursts, including three photospheric radius expansion bursts, with a rise time of ∼2 s and an exponential decay time of ∼5 s. The recurrence time is ∼9.1 h, which can be explained by unstable thermonuclear burning of hydrogen-deficient material on the neutron star surface. The quasi-simultaneous 1–150 keV broadband spectra from NICER, NuSTAR and INTEGRAL can be aptly fitted by an absorbed reflection model, relxillCp, and a Gaussian line of instrumental origin. The Comptonized emission from the hot corona is characterized by a photon index Γ of ∼1.8 and an electron temperature kTe of ∼40 keV. We obtained a low inclination angle i ∼ 34°. The accretion disk shows properties of strong ionization, log(ξ/erg cm s−1)∼4.5, over-solar abundance, AFe ∼ 7.7, and high density, log(ne/cm−3)∼19.5. However, a lower disk density with normal abundance and ionization could also be possible. Based on the inner disk radius of Rin = 1.67RISCO and the long-term spin-down rate of −3.1(2)×10−15 Hz s−1, we were able to constrain the magnetic field of IGR J17498−2921 to the range of (0.9 − 2.4)×108 G.

The association between asymmetric stress distribution on the lamina cribrosa and glaucoma progression.

The purpose of this study was to assess the effect of ocular movements on the progression of glaucoma. A total of 118 primary open-angle glaucoma patients were enrolled, comprising 71 patients in the progression group and 47 patients in the non-progression group. Utilizing three geometric parameters-axial length, optic disc radius, and optic cup deepening-a personalized virtual optic nerve head (ONH) model was designed. ONH biomechanical changes during ocular movement were simulated using a finite element analysis. Simulation results were analyzed and compared between the progression and non-progression groups. In both progression and non-progression groups, ONH strains significantly increased with increasing rotation angle. When the eye rotated by 10°, the stress on the anterior surface of the lamina cribrosa on the temporal side was significantly higher in the progression group compared to the non-progression group (16.19 ± 0.90kPa vs. 13.24 ± 3.00 kPa, P < 0.001). The stress ratio, indicating asymmetric stress distribution, was higher in the progression group than in the non-progression group (0.56 ± 0.13 vs. 0.49 ± 0.19, P = 0.018). Stress ratio significantly increased with increasing optic disc radius (standardized β = 0.303, P < 0.001) and optic cup deepening (standardized β = 0.538, P < 0.001). Asymmetric stress distribution with ocular movement was higher in the progression group. This asymmetry was associated with optic disc radius and optic cup deepening. Therefore, ocular movement may contribute to the progression of glaucoma, with ONH geometry playing a role. WHAT IS KNOWN : Ocular movement is considered one of the physical stress factors affecting the optic nerve head. Ocular movement increased the strain on the optic nerve head and resulted in an asymmetric stress distribution on the lamina cribrosa surface. Asymmetric stress distribution on lamina cribrosa with ocular movement was higher in the glaucoma progression group and associated with optic disc radius and optic cup deepening.

Mass-transfer Outbursts Reborn: Modeling the Light Curve of the Dwarf Nova EX Draconis

EX Draconis is an eclipsing dwarf nova that shows outbursts with moderate amplitude (≃2 mag) and a recurrence timescale of ≃20–30 days. Dwarf novae outbursts are explained in terms of either a thermal-viscous instability in the disc or an instability in the mass-transfer rate of the donor star (MTIM). We developed simulations of the response of accretion discs to events of enhanced mass transfer, in the context of the MTIM, and applied them to model the light curve and variations in the radius of the EX Dra disc throughout the outburst. We obtain the first modeling of a dwarf nova outburst by using χ 2 to select, from a grid of simulations, the best-fit parameters to the observed EX Dra outbursts. The observed time evolution of the system brightness and the changes in the radius of the outer disc along the outburst cycle are satisfactorily reproduced by a model of the response of an accretion disc with a viscosity parameter α = 4.0 and a quiescent mass-transfer rate Ṁ2(quiescence)=4.0×1016 g s−1 to an event of width Δt = 6.0 × 105 s (∼7 days) where the mass-transfer rate increases to Ṁ2(outburst)=1.5×1018 g s−1.

Retrieval of Thermally Resolved Water Vapor Distributions in Disks Observed with JWST-MIRI

The mid-infrared water vapor emission spectrum provides a novel way to characterize the delivery of icy pebbles toward the innermost (<5 au) regions of planet-forming disks. Recently, JWST MIRI-MRS showed that compact disks exhibit an excess of low-energy water vapor emission relative to extended multigapped disks, suggesting that icy pebble drift is more efficient in the former. We carry out detailed emission-line modeling to retrieve the excitation conditions of rotational water vapor emission in a sample of four compact and three extended disks within the JWST Disk Infrared Spectral Chemistry Survey. We present two-temperature H2O slab model retrievals and, for the first time, constrain the spatial distribution of water vapor by fitting parametric radial temperature and column density profiles. Such models statistically outperform the two-temperature slab fits. We find a correlation between the observable hot water vapor mass and stellar mass accretion rate, as well as an anticorrelation between cold water vapor mass and submillimeter dust disk radius, confirming previously reported water line flux trends. We find that the mid-IR spectrum traces H2O with temperatures down to 180–300 K, but the coldest 150–170 K gas remains undetected. Furthermore the H2O temperature profiles are generally steeper and cooler than the expected “superheated” dust temperature in passive irradiated disks. The column density profiles are used to estimate icy pebble mass fluxes, which suggest that compact and extended disks may produce markedly distinct inner-disk exoplanet populations if local feeding mechanisms dominate their assembly.

X-ray reverberation modelling of the continuum, optical/UV time-lags in quasars

Extensive, multi-wavelength monitoring campaigns of nearby and higher redshift active galactic nuclei (AGN) have shown that the UV/optical variations are well correlated with time delays which increase with increasing wavelength. Such behaviour is expected in the context of the X-ray thermal reverberation of the accretion disc in AGN. Our main objective is to use time-lag measurements of luminous AGN and fit them with sophisticated X-ray reverberation time-lags models. In this way we can investigate whether X-ray reverberation can indeed explain the observed continuum time lags, and whether time-lag measurements can be used to measure physical parameters such as the X-ray corona height and the spin of the black hole (BH) in these systems. We use archival time-lag measurements for quasars from different surveys, and we compute their rest frame, mean time-lags spectrum. We fit the data with analytical X-ray reverberation models, using $ statistics, and fitting for both maximal and non spinning BHs, for various colour correction values and X-ray corona heights. We found that X-ray reverberation can explain very well the observed time lags, assuming the measured BH mass, accretion rate and X-ray luminosity of the quasars in the sample. The model agrees well with the data both for non-rotating and maximally rotating BHs, as long as the corona height is larger than $ 40$ gravitational radii. This is in agreement with previous results which showed that X-ray reverberation can also explain the disc radius in micro-lensed quasars, for the same corona heights. The corona height we measure depends on the model assumption of a perfectly flat disc. More realistic disc models may result in lower heights for the X-ray corona.

Integral mean estimates of Turán-type inequalities for the polar derivative of a polynomial with restricted zeros

Abstract In this article, we extend inequalities concerning the polar derivative of a polynomial to integral mean for the class of polynomials with s-fold zero at the origin and the remaining zeros inside some closed disk of radius k k for k ≥ 1 k\ge 1 and k ≤ 1 k\le 1 , and we thereby obtain bounds that depend on some coefficients of the underlying polynomial. Our results not only extend some known polynomial inequalities but also reduce some interesting results in particular cases. Furthermore, we provide numerical examples and graphical representations to demonstrate the superior precision of our results compared to previously established results.