Outer Disk Radius Research Articles

Multiwavelength characterization of the accreting millisecond X-ray pulsar and ultracompact binary IGR J17062–6143

ABSTRACT IGR J17062–6143 is an ultracompact X-ray binary (UCXB) with an orbital period of 37.96 min. It harbours a millisecond X-ray pulsar that is spinning at 163 Hz and and has continuously been accreting from its companion star since 2006. Determining the composition of the accreted matter in UCXBs is of high interest for studies of binary evolution and thermonuclear burning on the surface of neutron stars. Here, we present a multiwavelength study of IGR J17062–6143 aimed to determine the detailed properties of its accretion disc and companion star. The multi-epoch photometric UV to near-infrared spectral energy distribution (SED) is consistent with an accretion disc Fν ∝ ν1/3. The SED modelling of the accretion disc allowed us to estimate an outer disc radius of $R_{\rm out} = 2.2^{+0.9}_{-0.4} \times 10^{10}$ cm and a mass-transfer rate of $\dot{m} = 1.8^{+1.8}_{-0.5}\times 10^{-10}$ M⊙ yr−1. Comparing this with the estimated mass-accretion rate inferred from its X-ray emission suggests that ≳90 per cent of the transferred mass is lost from the system. Moreover, our SED modelling shows that the thermal emission component seen in the X-ray spectrum is highly unlikely from the accretion disc and must therefore represent emission from the surface of the neutron star. Our low-resolution optical spectrum revealed a blue continuum and no emission lines, i.e. lacking H and He features. Based on the current data we cannot conclusively identify the nature of the companion star, but we make recommendations for future study that can distinguish between the different possible evolution histories of this X-ray binary. Finally, we demonstrate how multiwavelength observations can be effectively used to find more UCXBs among the LMXBs.

L1 Stream Deflection and Ballistic Launching at the Disk Bow Shock: An Absorption-line Velocity Analysis in Semi-detached Binaries

Abstract Observations of semi-detached interacting binaries reveal orbital modulation in the optical, UV, and X-ray bands, indicating the presence of absorbing material obscuring the disk and accreting primary star at specific orbital phases consistent with L1 stream material overflowing the disk edge. We simulate the L1 stream interaction with the disk using tests particles within the context of the Roche model in the restricted three-body problem. At the disk bow shock the L1 stream particles are deflected and launched onto ballistic trajectories above the disk (as would normally occurs at the front of a detached shock in the hypersonic flow past a blunt body). At a given scale height, the material is assumed to continue without being affected by the disk, while at lower altitude it is being launched at an increasing elevation, as well as gradually being dragged by the Keplerian flow. Near the disk midplane (z ≪ H) the material is assumed to become part of the disk. We follow the stream material ballistic trajectories over the disk surface, where they reach a maximum height z/r at a binary phase Φ ∼ 0.75 and land on the disk at a smaller radius around phase Φ ∼ 0.5. The phase of the maximum height, the phase of the landing site, and the phase of the hot spot itself, all decrease significantly with decreasing radius. The radial velocity for each L1 stream ballistic trajectory along the line of sight (of the observer) to the hot inner parts of the disk is computed as a function of the orbital phase for a binary configuration matching the dwarf nova U Geminorum. The computed velocity amplitudes, phases, and pattern match the observed velocity offsets of the metal lines in the FUSE spectrum of U Gem during outburst. As ballistic trajectories are much easier to compute than realistic 3D hydrodynamical simulations, we propose the use of the L1 stream deflection and ballistic launching as a way to analyze the absorption-line orbital variability in semi-detached binaries and to assess or confirm, with some limitations, system parameters such as the mass ratio, inclination, and disk outer radius.

The shape of Fe Kα line emitted from relativistic accretion disc around AGN black holes

The relativistically broadened Fe K[Formula: see text] line, originating from the accretion disc in a vicinity of a super massive black hole, is observed in only less than 50% of type 1 Active Galactic Nuclei (AGN). In this study, we investigate could this lack of detections be explained by the effects of certain parameters of the accretion disc and black hole, such as the inclination, the inner and outer radius of disc and emissivity index. In order to determine how these parameters affect the Fe K[Formula: see text] line shape, we simulated about 60,000 Fe K[Formula: see text] line profiles emitted from the relativistic disc. Based on simulated line profiles, we conclude that the lack of the Fe K[Formula: see text] line detection in type 1 AGN could be caused by the specific emitting disc parameters, but also by the limits in the spectral resolution and sensitivity of the X-ray detectors.

Optimization of Axial Magnetic Bearing Actuators for Dynamic Performance

Axial magnetic bearing actuators often lack the bandwidth necessary to achieve the desired closed loop performance due to their nonlaminated construction. Since bandwidth can be directly related to actuator material and geometric properties, an opportunity exists to improve closed loop performance through the optimization of these properties. This prospect is exploited herein, both to demonstrate the improvements that can be obtained and to illustrate the relationship between various parameters and dynamic performance. For the latter, Pareto-optimal curves are generated exploring the influence that disk outer radius, peak force, axial gap, and magnetic permeability have upon actuator bandwidth.

Long-lived Protoplanetary Disks in Multiple Systems: The VLA View of HD 98800

The conditions and evolution of protoplanetary disks in multiple systems can be considerably different from those around single stars, which may have important consequences for planet formation. We present Very Large Array (VLA) 8.8 mm (34 GHz) and 5 cm (6 GHz) observations of the quadruple system HD 98800, which consists of two spectroscopic binary systems (Aa-Ab, Ba-Bb). The Ba-Bb pair is surrounded by a circumbinary disk, usually assumed to be a debris disk given its $\sim$10 Myr age and lack of near infrared excess. The VLA 8.8 mm observations resolve the disk size (5-5.5 au) and its inner cavity ($\approx$3 au) for the first time, making it one of the smallest disks known. Its small size, large fractional luminosity, and millimeter spectral index consistent with blackbody emission support the idea that HD 98800 B is a massive, optically thick ring which may still retain significant amounts of gas. The disk detection at 5 cm is compatible with free-free emission from photoionized material. The diskless HD 98800 A component is also detected, showing partial polarization at 5 cm compatible with non-thermal chromospheric activity. We propose that tidal torques from Ba-Bb and A-B have stopped the viscous evolution of the inner and outer disk radii, and the disk is evolving via mass loss through photoevaporative winds. This scenario can explain the properties and longevity of HD 98800 B as well as the lack of a disk around HD 98800 A, suggesting that planet formation could have more time to proceed in multiple systems than around single stars in certain system configurations.

Warping a protoplanetary disc with a planet on an inclined orbit

Recent observations of several protoplanetary discs have found evidence of departures from flat, circular motion in the inner regions of the disc. One possible explanation for these observations is a disc warp, which could be induced by a planet on a misaligned orbit. We present three-dimensional numerical simulations of the tidal interaction between a protoplanetary disc and a misaligned planet. For low planet masses we show that our simulations accurately model the evolution of inclined planet orbit (up to moderate inclinations). For a planet massive enough to carve a gap, the disc is separated into two components and the gas interior and exterior to the planet orbit evolve separately, forming an inner and outer disc. Due to the inclination of the planet, a warp develops across the planet orbit such that there is a relative tilt and twist between these discs. We show that when other parameters are held constant, the relative inclination that develops between the inner and outer disc depends on the outer radius of the total disc modelled. For a given disc mass, our results suggest that the observational relevance of the warp depends more strongly on the mass of the planet rather than the inclination of the orbit.

Orbital alignment of circumbinary planets that form in misaligned circumbinary discs: the case of Kepler-413b

Although most of the circumbinary planets detected by the Kepler spacecraft are on orbits that are closely aligned with the binary orbital plane, the systems Kepler-413 and Kepler-453 exhibit small misalignments of $\sim 2.5^\circ$. One possibility is that these planets formed in a circumbinary disc whose midplane was inclined relative to the binary orbital plane. Such a configuration is expected to lead to a warped and twisted disc, and our aim is to examine the inclination evolution of planets embedded in these discs. We employed 3D hydrodynamical simulations that examine the disc response to the presence of a modestly inclined binary with parameters that match the Kepler-413 system, as a function of disc parameters and binary inclinations. The discs all develop slowly varying warps, and generally display very small amounts of twist. Very slow solid body precession occurs because a large outer disc radius is adopted. Simulations of planets embedded in these discs resulted in the planet aligning with the binary orbit plane for disc masses close to the minimum mass solar nebular, such that nodal precession of the planet was controlled by the binary. For higher disc masses, the planet maintains near coplanarity with the local disc midplane. Our results suggest that circumbinary planets born in tilted circumbinary discs should align with the binary orbit plane as the disc ages and loses mass, even if the circumbinary disc remains misaligned from the binary orbit. This result has important implications for understanding the origins of the known circumbinary planets.

Hints for Small Disks around Very Low Mass Stars and Brown Dwarfs∗

Abstract The properties of disks around brown dwarfs and very low mass stars (hereafter VLMOs) provide important boundary conditions on the process of planet formation and inform us about the numbers and masses of planets than can form in this regime. We use the Herschel Space Observatory PACS spectrometer to measure the continuum and [O i] 63 μm line emission toward 11 VLMOs with known disks in the Taurus and Chamaeleon I star-forming regions. We fit radiative transfer models to the spectral energy distributions of these sources. Additionally, we carry out a grid of radiative transfer models run in a regime that connects the luminosity of our sources with brighter T Tauri stars. We find that VLMO disks with sizes 1.3–78 au, smaller than typical T Tauri disks, fit well the spectral energy distributions assuming that disk geometry and dust properties are stellar mass independent. Reducing the disk size increases the disk temperature, and we show that VLMOs do not follow previously derived disk temperature–stellar luminosity relationships if the disk outer radius scales with stellar mass. Only 2 out of 11 sources are detected in [O i] despite a better sensitivity than was achieved for T Tauri stars, suggesting that VLMO disks are underluminous. Using thermochemical models, we show that smaller disks can lead to the unexpected [O i] 63 μm nondetections in our sample. The disk outer radius is an important factor in determining the gas and dust observables. Hence, spatially resolved observations with ALMA—to establish if and how disk radii scale with stellar mass—should be pursued further.

First evidence of external disc photoevaporation in a low mass star forming region: the case of IM Lup

Abstract We model the radiatively driven flow from IM Lup – a large protoplanetary disc expected to be irradiated by only a weak external radiation field (at least 104 times lower than the ultraviolet field irradiating the Orion Nebula Cluster proplyds). We find that material at large radii (>400 au) in this disc is sufficiently weakly gravitationally bound that significant mass-loss can be induced. Given the estimated values of the disc mass and accretion rate, the viscous time-scale is long (∼10 Myr) so the main evolutionary behaviour for the first Myr of the disc's lifetime is truncation of the disc by photoevaporation, with only modest changes effected by viscosity. We also produce approximate synthetic observations of our models, finding substantial emission from the flow that can explain the CO halo observed about IM Lup out to ≥1000 au. Solutions that are consistent with the extent of the observed CO emission generally imply that IM Lup is still in the process of having its disc outer radius truncated. We conclude that IM Lup is subject to substantial external photoevaporation, which raises the more general possibility that external irradiation of the largest discs can be of significant importance even in low mass star forming regions.

Creep Analysis in Functionally Graded Rotating Disc Using Tresca Criterion and Comparison with Von-Mises Criterion

A mathematical model is developed to analyse steady state creep stresses and strain rates in a variable thickness rotating FGM disc that yields according to Tresca criterion. The results obtained are compared with those estimated using Von-Mises criterion. The radial stress (except for region towards the outer disc radius) and tangential stress (except for some portion towards the inner and outer disc radii) estimated using Von-Mises yield criterion are observed to be slightly higher than those obtained using Tresca criterion. The Tresca criterion estimates higher values of effective stress throughout as compared to Von-Mises criterion. The strain rates estimated using Tresca criterion, as compared to Von-Mises criterion, are also higher throughout the disc, with the maximum difference noticed at the inner disc radius. Thus, the design of rotating FGM disc, undergoing creep, based on Tresca yield criterion would be much safer as compared to design based on Von-Mises criterion.

MASS RATIO DETERMINATION FROM Hα LINES IN BLACK HOLE X-RAY TRANSIENTS

ABSTRACT We find that the mass ratio q in quiescent black hole (BH) X-ray transients is tightly correlated with the ratio of the double-peak separation (DP) to the full width half maximum (FWHM) of the H α emission line, log q = − 6.88 − 23.2 log ( DP / FWHM ) . This correlation is explained through the efficient truncation of the outer disk radius by the 3:1 resonance with the companion star. This is the dominant tidal interaction for extreme mass ratios q = M 2 / M 1 ≲ 0.25 , the realm of BH (and some neutron star) X-ray transients. Mass ratios can thus be estimated with a typical uncertainty of ≈32%, provided that the H α profile used to measure DP/FWHM is an orbital phase average. We apply the DP/FWHM–q relation to the three faint BH transients XTE J1650–500, XTE J1859+226, and Swift J1357–0933 and predict q = 0.026 − 0.007 + 0.038 , 0.049 − 0.012 + 0.023 and 0.040 − 0.005 + 0.003 , respectively. This new relation, together with the FWHM – K 2 correlation presented in Paper I, allows the extraction of fundamental parameters from very faint targets and, therefore, the extension of dynamical BH studies to much deeper limits than was previously possible. As an example, we combine our mass ratio determination for Swift J1357–0933 with previous reported values to yield a BH mass of 12.4 ± 3.6 M ⊙. This confirms Swift J1357–0933 as one of the most massive BH low-mass X-ray binaries in the Galaxy.

Trigonal warping, pseudodiffusive transport, and finite-system version of the Lifshitz transition in magnetoconductance of bilayer graphene Corbino disks

Using the transfer matrix in the angular-momentum space we investigate the impact of trigonal warping on magnetotransport and scaling properties of a ballistic bilayer graphene in the Corbino geometry. Although the conductivity at the charge-neutrality point and zero magnetic field exhibits a one-parameter scaling, the shot-noise characteristics, quantified by the Fano factor $\mathcal{F}$ and the third charge-transfer cumulant $\mathcal{R}$, remain pseudodiffusive. This shows that the pseudodiffusive transport regime in bilayer graphene is not related to the universal value of the conductivity but can be identified by higher charge-transfer cumulants. For Corbino disks with larger radii ratios the conductivity is suppressed by the trigonal warping, mainly because the symmetry reduction amplifies backscattering for normal modes corresponding to angular-momentum eigenvalues $\pm{}2\hbar$. Weak magnetic fields enhance the conductivity, reaching the maximal value near the crossover field $B_L=\frac{4}{3}\sqrt{3}\,({\hbar}/{e})\,t't_\perp\!\left[{t_0^2a(R_{\rm o}-R_{\rm i})}\right]^{-1}$, where $t_0$ ($t_\perp$) is the nearest-neighbor intra- (inter-)layer hopping integral, $t'$ is the skew-interlayer hopping integral, and $R_{\rm o}$ ($R_{\rm i}$) is the outer (inner) disk radius. For magnetic fields $B\gtrsim{}B_L$ we observe quasiperiodic conductance oscillations characterized by the decreasing mean value $\langle\sigma\rangle-\sigma_0\propto{}B_L/B$, where $\sigma_0=(8/\pi)\,e^2/h$. The conductivity, as well as higher charge-transfer cumulants, show beating patterns with an envelope period proportional to $\sqrt{B/B_L}$. This constitutes a qualitative difference between the high-field ($B\gg{}B_L$) magnetotransport in the $t'=0$ case (earlier discussed in Ref. [1]) and in the $t'\neq{}0$ case, providing a finite-system analog of the Lifshitz transition.

Study of infrared excess from circumstellar disks in binaries with Spitzer/IRAC

Abstract The presence of excess emission in the 3.6–8.0 μm region was investigated in a sample of 27 binary star systems located in two nearby star-forming regions, Taurus and Ophiuchus, by using Spitzer/Infrared Array Camera (IRAC) archival data. Angular (Projected) separations of the binaries are greater than 2″ (∼ 280 au), which enables us to perform spatially resolved photometry of individual primary and secondary sources. The measured occurrence of infrared excess suggests that binarity plays a role in the evolution of circumstellar disks, even at such wide binary separations. Most of the binaries have excess emission from both the circumprimary and circumsecondary disks, or show photospheric levels for both components at all four wavelengths of IRAC. On the other hand, four binary systems ($17^{+11}_{-8}$%, designated by “mixed” systems) exhibit the excess emission from a single binary component. This ratio is significantly smaller than that predicted by the random pairing of single stars, suggesting that circumprimary and circumsecondary disks are synchronously dispersed. In addition, the excess frequencies (EFs) of primary and secondary sources with a projected distance of ap ≃ 280–450 au are $100^{+0}_{-17}$% and $91^{+8}_{-18}$%, respectively, and significantly higher than that of single stars (70% ± 5%). We made a simple model describing the EF distribution as a function of the disk outer radius, Rout. Comparisons with observations using the Kolmogorov–Smirnov test show that the observational data are consistent with the model when the EF ≃ 100% region is found at Rout ∼ 30–100 au. This disk radius is smaller than that typically estimated for single stars. The high EF of circumstellar disks with these radii may indicate a prolonged lifetime of dust in binary systems, possibly because the smaller disks counteract mass loss by photoevaporation.

Reprocessing model for the optical quasi-periodic oscillations in black hole binaries

A number of black hole X-ray transients show quasi-periodic oscillations (QPOs) in the optical (ultraviolet) and X-ray bands at the same frequency, which challenge models for production of radiation at these wavelengths. We propose a model where the optical radiation is modulated by the oscillating X-ray flux resulting in varying irradiation of the outer parts of the accretion disc. The proposed QPO mechanism inevitably takes place in the systems with sufficiently small ratio of the outer disc radius to the QPO period. We show that, unlike in the case of the aperiodic variability, it is not possible to obtain the optical QPO profiles from those observed in the X-rays through the transfer function, because of different X-ray signals seen by the disc and by the observer. We demonstrate that with the increasing QPO frequency, occurring at the rising phase of the X-ray outburst, the rms should be constant for sufficiently low frequencies, then to increase reaching the peak and finally to drop substantially when the QPO period becomes comparable to the light-crossing time to the outer disc. We predict that the QPO rms in this model should increase towards shorter wavelengths and this fact can be used to distinguish it from other QPO mechanisms.

HALL EFFECT CONTROLLED GAS DYNAMICS IN PROTOPLANETARY DISKS. II. FULL 3D SIMULATIONS TOWARD THE OUTER DISK

We perform 3D stratified shearing-box MHD simulations on the gas dynamics of protoplanetary disks threaded by net vertical magnetic field Bz. All three non-ideal MHD effects, Ohmic resistivity, the Hall effect and ambipolar diffusion are included in a self-consistent manner based on equilibrium chemistry. We focus on regions toward outer disk radii, from 5-60AU, where Ohmic resistivity tends to become negligible, ambipolar diffusion dominates over an extended region across disk height, and the Hall effect largely controls the dynamics near the disk midplane. We find that around R=5AU, the system launches a laminar/weakly turbulent magnetocentrifugal wind when the net vertical field Bz is not too weak, as expected. Moreover, the wind is able to achieve and maintain a configuration with reflection symmetry at disk midplane. The case with anti-aligned field polarity (Omega. Bz<0) is more susceptible to the MRI when Bz drops, leading to an outflow oscillating in radial directions and very inefficient angular momentum transport. At the outer disk around and beyond R=30AU, the system shows vigorous MRI turbulence in the surface layer due to far-UV ionization, which efficiently drives disk accretion. The Hall effect affects the stability of the midplane region to the MRI, leading to strong/weak Maxwell stress for aligned/anti-aligned field polarities. Nevertheless, the midplane region is only very weakly turbulent. Overall, the basic picture is analogous to the conventional layered accretion scenario applied to the outer disk. In addition, we find that the vertical magnetic flux is strongly concentrated into thin, azimuthally extended shells in most of our simulations beyond 15AU. This is a generic phenomenon unrelated to the Hall effect, and leads to enhanced zonal flow. Observational and theoretical implications, as well as future prospects are briefly discussed.

Magnetorotational instability in decretion disks of critically rotating stars and the outer structure of Be and Be/X-ray disks

Evolutionary models of fast-rotating stars show that the stellar rotational velocity may approach the critical speed. Critically rotating stars cannot spin up more, therefore they lose their excess angular momentum through an equatorial outflowing disk. The radial extension of such disks is unknown, partly because we lack information about the radial variations of the viscosity. We study the magnetorotational instability, which is considered to be the origin of anomalous viscosity in outflowing disks. We used analytic calculations to study the stability of outflowing disks submerged in the magnetic field. The magnetorotational instability develops close to the star if the plasma parameter is large enough. At large radii the instability disappears in the region where the disk orbital velocity is roughly equal to the sound speed. The magnetorotational instability is a plausible source of anomalous viscosity in outflowing disks. This is also true in the region where the disk radial velocity approaches the sound speed. The disk sonic radius can therefore be roughly considered as an effective outer disk radius, although disk material may escape from the star to the insterstellar medium. The radial profile of the angular momentum-loss rate already flattens there, consequently, the disk mass-loss rate can be calculated with the sonic radius as the effective disk outer radius. We discuss a possible observation determination of the outer disk radius by using Be and Be/X-ray binaries.

Magnetoconductance of the Corbino disk in graphene: chiral tunneling and quantum interference in the bilayer case

Quantum transport through an impurity-free Corbino disk in bilayer graphene is investigated analytically, using the mode-matching method to give an effective Dirac equation, in the presence of uniform magnetic fields. Similarly as in the monolayer case (see Rycerz 2010 Phys. Rev. B 81 121404; Katsnelson 2010 Europhys. Lett. 89 17001), conductance at the Dirac point shows oscillations with the flux piercing the disk area ΦD characterized by the period Φ0 = 2 (h/e) ln(Ro/Ri), where Ro(Ri) is the outer (inner) disk radius. The oscillation magnitude depends either on the radii ratio or on the physical disk size, with the condition for maximal oscillations being Ro/Ri ≃ [ Rit⊥/(2ℏvF) ]4/p (for Ro/Ri ≫ 1), where t⊥ is the interlayer hopping integral, vF is the Fermi velocity in graphene, and p is an even integer. Odd-integer values of p correspond to vanishing oscillations for the normal Corbino setup, or to oscillation frequency doubling for the Andreev–Corbino setup. At higher Landau levels, magnetoconductance behaves almost identically in the monolayer and bilayer cases. A brief comparison with the Corbino disk in a two-dimensional electron gas is also provided in order to illustrate the role of chiral tunneling in graphene.

Numerical Analysis of Head Disk Interface Response During Operational Shock With Disk-Ramp Contact

In hard disk drives (HDDs), the ramp load/unload (LUL) technology has proved to be a better alternative to the contact start-stop approach due to the advantages of increasing areal density and greater durability. However, the application of the LUL ramps in HDDs introduces the possibility of collisions between the disk and ramps since the ramps must slightly overlap the disk's outer radius. Therefore, it is important to study the ramp effects on the HDDs response during a shock. A reduced model of a deformable ramp is developed and implemented into a multi-body operational shock model. Numerical analyses using three different ramp models (no ramp, rigid ramp, and deformable ramp) are carried out to study the HDDs failure dependence on the different ramp models.

ChandraX-ray spectroscopy of a clear dip in GX 13+1

The source GX 13+1 is a persistent, bright Galactic X-ray binary hosting an accreting neutron star. It shows highly ionized absorption features, with a blueshift of $\sim$ 400 km s$^{-1}$ and an outflow-mass rate similar to the accretion rate. Many other X-ray sources exhibit warm absorption features, and they all show periodic dipping behavior at the same time. Recently, a dipping periodicity has also been determined for GX 13+1 using long-term X-ray folded light-curves, leading to a clear identification of one of such periodic dips in an archival Chandra observation. We give the first spectral characterization of the periodic dip of GX 13+1 found in this archival Chandra observation performed in 2010. We used Chandra/HETGS data (1.0-10 keV band) and contemporaneous RXTE/PCA data (3.5-25 keV) to analyze the broadband X-ray spectrum. We adopted different spectral models to describe the continuum emission and used the XSTAR-derived warm absorber component to constrain the highly ionized absorption features. The 1.0-25 keV continuum emission is consistent with a model of soft accretion-disk emission and an optically thick, harder Comptonized component. The dip event, lasting $\sim$ 450 s, is spectrally resolved with an increase in the column density of the neutral absorber, while we do not find significant variations in the column density and ionization parameter of the warm absorber with respect to the out-of-dip spectrum. We argue that the very low dipping duty-cycle with respect to other sources of the same class can be ascribed to its long orbital period and the mostly neutral bulge, that is relatively small compared with the dimensions of the outer disk radius.

On the Strength Calculation of the Rotating parts

The existing solutions of differential equations of equilibrium of an infinitesimal element of the rotating parts of an isotropic elastic solid known as the Navier equilibrium equations are considered. Examples of the flat disk calculation by solving the differential equilibrium equations by the sweep method and the finite element method in the modern program “Autodesk Simulation Multiphysics” are represented; paradoxical changes of radial and hoop stresses are revealed. An original method of derivation formulas based only on the principle of d’Alembert to calculate radial and hoop stresses in parts that operate under centrifugal (inertial) forces is proposed. The solution for rotating disks of any profile that corrects unnatural classical solutions is obtained. Analysis of the obtained new formulas for calculating stresses shows that it is necessary to reject the concept of “equal-strength disk” because of the inability to provide the equality of the hoop and radial stress in all sections of the disk. A new method of the optimum strength disk profile calculation, which requires a restriction of outer radius disk, is suggested. In designing of optimum strength rotating parts is recommended to limit outer disk radius of ▪ where [σ] − the allowable stress, ρ − density of the disk material; ω − angular velocity of disk rotation.