Binary Plane Research Articles

Photo-dynamical Analysis of Circumbinary Multi-planet System TOI-1338: A Fully Coplanar Configuration with a Puffy Planet

TOI-1338 is the first circumbinary planet (CBP) system discovered by TESS. It has one transiting planet at P ∼ 95 days and an outer nontransiting planet at P ∼ 215 days complemented by radial velocity (RV) observation. Here we present a global photodynamical modeling of the TOI-1338 system that self-consistently accounts for the mutual gravitational interactions between all known bodies in the system. As a result, the three-dimensional architecture of the system can be established by comparing the model with additional data from TESS Extended Mission and published HARPS/ESPRESSO RV data. We report an inconsistency of binary RV signal between HARPS and ESPRESSO, which could be due to the contamination of the secondary star. According to stability analysis, the RV data via ESPRESSO are preferred. Our results are summarized as follows: (1) The inner transiting planet is extremely coplanar to the binary plane ΔI b ∼ 0.°12, making it a permanently transiting circumbinary planet at any nodal precession phases; we updated the future transit ephemerides with improved precisions. (2) The outer planet, despite its untransiting nature, is also coplanar with the binary plane by ΔIc=9.°1−4.°8+6.°0 (22° for the 99% upper limit). (3) The inner planet could have an extremely low density of 0.137 ± 0.026 g cm−3. With a TESS magnitude of 11.45, TOI-1338 b is an optimal circumbinary planet CBP for ground-based follow-up and transit spectroscopy.

AC Her: Evidence of the First Polar Circumbinary Planet

We examine the geometry of the post–asymptotic giant branch (AGB) star binary AC Her and its circumbinary disk. We show that the observations describe a binary orbit that is perpendicular to the disk with an angular momentum vector that is within 9° of the binary eccentricity vector, meaning that the disk is close to a stable polar alignment. The most likely explanation for the very large inner radius of the dust is a planet within the circumbinary disk. This is therefore both the first reported detection of a polar circumbinary disk around a post-AGB binary and the first evidence of a polar circumbinary planet. We consider the dynamical constraints on the circumbinary disk size and mass. The polar circumbinary disk feeds circumstellar disks with gas on orbits that are highly inclined with respect to the binary orbit plane. The resulting circumstellar disk inclination could be anywhere from coplanar to polar depending upon the competition between the mass accretion and binary torques.

Circumbinary Accretion: From Binary Stars to Massive Binary Black Holes

We review recent works on the dynamics of circumbinary accretion, including time variability, angular momentum transfer between the disk and the binary, and the secular evolution of accreting binaries. These dynamics impact stellar binary formation/evolution, circumbinary planet formation/migration, and the evolution of (super)massive black hole binaries. We discuss the dynamics and evolution of inclined/warped circumbinary disks and connect with observations of protoplanetary disks. A special kind of circumbinary accretion involves binaries embedded in big disks, which may contribute to the mergers of stellar-mass black holes in AGN disks. Highlights include the following: ▪Circumbinary accretion is highly variable, being modulated at P b (the binary period) or ∼5P b, depending on the binary eccentricity e b and mass ratio q b.▪The inner region of the circumbinary disk can develop coherent eccentric structure, which may modulate the accretion and affect the physical processes (e.g., planet migration) taking place in the disk.▪Over long timescales, circumbinary accretion steers binaries toward equal masses, and it does not always lead to binary orbital decay. The secular orbital evolution depends on the binary parameters (e b and q b) and on the thermodynamic properties of the accreting gas.▪A misaligned disk around a low-eccentricity binary tends to evolve toward coplanarity due to viscous dissipation. But when e b is significant, the disk can evolve toward “polar alignment,” with the disk plane perpendicular to the binary plane.

Fertilitopes

We introduce tools from discrete convexity theory and polyhedral geometry into the theory of West’s stack-sorting map s. Associated to each permutation pi is a particular set mathcal V(pi ) of integer compositions that appears in a formula for the fertility of pi , which is defined to be |s^{-1}(pi )|. These compositions also feature prominently in more general formulas involving families of colored binary plane trees called troupes and in a formula that converts from free to classical cumulants in noncommutative probability theory. We show that mathcal V(pi ) is a transversal discrete polymatroid when it is nonempty. We define the fertilitope of pi to be the convex hull of mathcal V(pi ), and we prove a surprisingly simple characterization of fertilitopes as nestohedra arising from full binary plane trees. Using known facts about nestohedra, we provide a procedure for describing the structure of the fertilitope of pi directly from pi using Bousquet-Mélou’s notion of the canonical tree of pi . As a byproduct, we obtain a new combinatorial cumulant conversion formula in terms of generalizations of canonical trees that we call quasicanonical trees. We also apply our results on fertilitopes to study combinatorial properties of the stack-sorting map. In particular, we show that the set of fertility numbers has density 1, and we determine all infertility numbers of size at most 126. Finally, we reformulate the conjecture that sum _{sigma in s^{-1}(pi )}x^{textrm{des}(sigma )+1} is always real-rooted in terms of nestohedra, and we propose natural ways in which this new version of the conjecture could be extended.

Evidence for Multiple Shocks from the γ-Ray Emission of RS Ophiuchi

In 2021 August, the Fermi Large Area Telescope, H.E.S.S., and MAGIC detected GeV and TeV γ-ray emission from an outburst of recurrent nova RS Ophiuchi. This detection represents the first very high-energy γ-rays observed from a nova, and it opens a new window to study particle acceleration. Both H.E.S.S. and MAGIC described the observed γ-rays as arising from a single, external shock. In this paper, we perform detailed, multi-zone modeling of RS Ophiuchi’s 2021 outburst, including a self-consistent prescription for particle acceleration and magnetic field amplification. We demonstrate that, contrary to previous work, a single shock cannot simultaneously explain RS Ophiuchi’s GeV and TeV emission, in particular the spectral shape and distinct light-curve peaks. Instead, we put forward a model involving multiple shocks that reproduces the observed γ-ray spectrum and temporal evolution. The simultaneous appearance of multiple distinct velocity components in the nova optical spectrum over the first several days of the outburst supports the presence of distinct shocks, which may arise either from the strong latitudinal dependence of the density of the external circumbinary medium (e.g., in the binary equatorial plane versus the poles) or due to internal collisions within the white dwarf ejecta (which power the γ-ray emission in classical novae).

Precession and polar alignment of accretion discs in triple (or multiple) stellar systems

ABSTRACTWe investigate the mechanism of polar alignment for accretion discs in hierarchical systems (HSs) with more than two stars. In eccentric binary systems, low-mass discs that are sufficiently tilted to the binary orbit align in a polar configuration with respect to the binary plane by aligning their angular momentum to the binary eccentricity vector. In HSs, secular evolution of the orbital parameters makes the eccentricity vector of the system precess with time. This precession undermines the stability of the polar orbit for accretion discs hosted in HSs. We analytically show that the binary criteria for polar alignment derived in the literature are necessary but not sufficient conditions for polar alignment in HSs. Then, we derive an analytical criterion for polar alignment in HSs. In general, we find that discs orbiting the innermost level of an HS can go polar. Conversely, radially extended discs orbiting the outer levels of an HS cannot polarly align and evolve as orbiting around a circular binary. We confirm our findings through detailed numerical simulations. Also, our results are compatible with the observed distribution of disc–orbit mutual inclination. Finally, we compare the observed distribution of disc inclinations in the binary and in the HS populations. Binaries host mainly coplanar discs, while HSs show a wide range of disc inclinations. We suggest that the wider range of inclinations in HSs results from the secular oscillation of their orbital parameters (such as Kozai–Lidov oscillations), rather than from a different initial condition or evolution between HSs and binaries.

The Orbital Architecture of Qatar-6: A Fully Aligned Three-body System?

The evolutionary history of an extrasolar system is, in part, fossilized through its planets’ orbital orientations relative to the host star’s spin axis. However, spin–orbit constraints for warm Jupiters—particularly in binary star systems, which are amenable to a wide range of dynamical processes—are relatively scarce. We report a measurement of the Rossiter–McLaughlin effect, observed with the Keck/HIRES spectrograph, across the transit of Qatar-6 A b—a warm Jupiter orbiting one star within a binary system. From this measurement, we obtain a sky-projected spin–orbit angle λ = 0.°1 ± 2.°6. Combining this new constraint with the stellar rotational velocity of Qatar-6 A that we measure from TESS photometry, we derive a true obliquity —consistent with near-exact alignment. We also leverage astrometric data from Gaia DR3 to show that the Qatar-6 binary star system is edge-on (), such that the stellar binary and the transiting exoplanet orbit exhibit line-of-sight orbit–orbit alignment. Ultimately, we demonstrate that all current constraints for the three-body Qatar-6 system are consistent with both spin–orbit and orbit–orbit alignment. High-precision measurements of the projected stellar spin rate of the host star and the sky-plane geometry of the transit relative to the binary plane are required to conclusively verify the full 3D configuration of the system.

Final stage of merging binaries of supermassive black holes: observational signatures

ABSTRACT There are increasing interests in binary supermassive black holes (SMBHs), but merging binaries with separations smaller than $\sim 1\,$ light-days ($\sim 10^{2}\,$ gravitational radii for 108 M⊙), which are rapidly evolving under control of gravitational waves, are elusive in observations. In this paper, we discuss fates of mini-discs around component SMBHs for three regimes: (1) low rates (advection-dominated accretion flows: ADAFs); (2) intermediate rates; (3) super-Eddington accretion rates. Mini-discs with intermediate rates are undergoing evaporation through thermal conduction of hot corona forming a hybrid radial structure. When the binary orbital periods are shorter than sound propagation time-scales of the evaporated mini-discs, a new instability, denoted as sound instability, arises because the discs will be highly twisted so that they are destroyed. We demonstrate a critical separation of Acrit(∼102Rg) from the sound instability of the mini-discs and the cavity is full of hot gas. For those binaries, component SMBHs are accreting with Bondi mode in the ADAF regime, showing periodic variations resulting from Doppler boosting effects in radio from the ADAFs due to orbital motion. In the mean while, the circumbinary discs (CBDs) are still not hot enough (ultraviolet deficit) to generate photons to ionize gas for broad emission lines. For slightly super-Eddington accretion of the CBDs, Mg ii line appears with decreases of UV deficit, and for intermediate super-Eddington Balmer lines appear, but C iv line never unless CBD accretion rates are extremely high. Moreover, if the CBDs are misaligned with the binary plane, it is then expected to have optical periodical variations with about ten times radio periods.

Counting Embeddings of Rooted Trees into Families of Rooted Trees

An embedding of a rooted tree $S$ into another rooted tree $T$ is a mapping of the vertex set of $S$ into the vertex set of $T$ that is order-preserving in a certain sense, depending on the chosen tree family. Equivalently, $S$ and $T$ may be interpreted as tree-like partially ordered sets, where $S$ is isomorphic to a subposets of $T$. A good embedding is an embedding where the root of $S$ is mapped to the root of $T$.
 We investigate the number of good and the number of all embeddings of a rooted tree $S$ into the family of all trees of given size $n$ of a certain family of trees. The tree families considered are binary plane trees (the order of descendants matters), binary non-plane trees and rooted plane trees. We derive the asymptotic behaviour of the number of good and the number of all embeddings in all these cases and prove that the ratio of the number of good embeddings to that of all embeddings is of the order $\Theta(1/\sqrt{n})$ in all cases, where we provide the exact constants as well. Furthermore, we prove some monotonicity properties of this ratio. Finally, we comment on the case where $S$ is disconnected.

Infrared spectroscopy of the 2019 eruption of the recurrent nova V3890 Sgr: Separation into equatorial and polar winds revealed

ABSTRACT We present infrared spectroscopy of the 2019 eruption of the recurrent nova V3890 Sgr, obtained over the period of 5.1–46.3 d after the eruption. The spectrum of the red giant became more prominent as the flux declined, and by day 46.3 dominated the spectrum. Hydrogen and helium emission lines consisted of a narrow component superposed on a broad pedestal. The full width at half-maximum of the narrow components declined with time t as the eruption progressed, as t−0.74, whereas those of the broad components remained essentially constant. Conversely, the line fluxes of the narrow components of Pa β remained roughly constant, while those of the broad components declined by a factor ∼30 over a period of ≲ 25 d. The behaviour of the broad components is consistent with them arising in unencumbered fast-flowing ejecta perpendicular to the binary plane, in material that was ejected in a short ∼3.3-d burst. The narrow components arise in material that encounters the accumulated circumstellar material. The outburst spectra were rich in coronal lines. There were two coronal line phases, one that originated in gas ionized by supersoft X-ray source, the other in shocked gas. From the relative fluxes of silicon and sulphur coronal lines on day 23.4 – when the emitting gas was shocked – we deduce that the temperature of the coronal gas was 9.3 × 105 K, and that the abundances are approximately solar.

Bit level color image encryption using Logistic-Sine-Tent-Chebyshev (LSTC) map

The paper presents a bit-level chaos based color image encryption technique using Logistic-Sine-Tent-Chebyshev (LSTC) map. The color image is first decomposed into red, blue, and green color image components. Each color image component is transformed to an 8-bit binary plane. Mutual diffusion of two sequences is used to scramble two binary elements using the LSTC map, cyclic shifts, and the XOR operation. The binary element confusion is performed using a chaos map and transformed into binary bit planes. With the help of the chaos map, the binary element is swapped and transformed into another binary bit plane. Individual cipher text image components are obtained by combining the binary bit planes. Finally, the encrypted image component is combined to generate the color cipher text image. The proposed scheme experimental results show excellent resistance to statistical attack, differential attack, and brute-force attack with a single round of encryption. As a result, the proposed scheme is secure and reliable for transmitting color images over the internet.

Troupes, cumulants, and stack-sorting

In several cases, a sequence of free cumulants that counts certain binary plane trees corresponds to a sequence of classical cumulants that counts the decreasing versions of the same trees. Using two new operations on binary plane trees that we call insertion and decomposition, we prove that this surprising phenomenon holds for families of trees that we call troupes. We give a simple characterization of troupes, showing that they are plentiful. Troupes provide a broad framework for generalizing several of the results that are known about West's stack-sorting map s. Indeed, we give new proofs of some of the main theorems underlying techniques that have been developed recently for understanding s; these new proofs are far more conceptual than the original ones, explain how the objects called valid hook configurations arise very naturally, and generalize to the context of troupes. To illustrate these general techniques, we enumerate 2-stack-sortable and 3-stack-sortable alternating permutations of odd length and 2-stack-sortable and 3-stack-sortable permutations whose descents are all peaks.The unexpected connection between troupes and cumulants provides a powerful new tool for analyzing the stack-sorting map that hinges on free probability theory. We give numerous applications of this method. For example, we show that if σ∈Sn−1 is chosen uniformly at random and des denotes the descent statistic, then the expected value of des(s(σ))+1 is(3−∑j=0n1j!)n. Furthermore, the variance of des(s(σ))+1 is asymptotically (2+2e−e2)n. We obtain similar results concerning the expected number of descents of postorder readings of decreasing binary plane trees of various types. We also obtain improved estimates for |s(Sn)| and an improved lower bound for the degree of noninvertibility of s:Sn→Sn. The combinatorics of valid hook configurations allows us to give two novel formulas that convert from free to classical (univariate) cumulants. The first formula is given by a sum over noncrossing partitions, and the second is given by a sum over 231-avoiding valid hook configurations. We pose several conjectures and open problems.

Inspiraling corrugation-induced quantum effects on neutron star binary plane

We use the path-integral formula and investigate some dynamical quantum effects induced by the inspiraling lateral corrugation of orbital plane in gravitationally bound neutron star (NS) binaries, with orbital separation of 109 m. Based on Dewitt's approach, we calculate the gravitational Casimir energy cost of the binary plane, which consists of statically gravitational effects and deformation-induced effects. It is found that the static effects include a term coming from the self-gravity of the orbital plane and the contribution of Newtonian gravitational potential of the binary system. While the deformation-induced effect also results from two parts, i.e. the instability of orbital binding energy, scaling as 1(R−r)2, and the dynamically Casimir energy cost of the orbital binding energy, decaying as 1(R−r)4. The dynamically gravitational Casimir phenomena and the corresponding energy cost modify the spiral-in orbital motion of the binary and thus the frequency of released gravitational waves (GWs). We consider the mechanical response of two NS components and qualitatively study the corrections to the orbital motion of the system and the GW frequencies. It is found that the dynamical Casimir effects exert a dissipative force on the binary plane, depending on the frequency of GWs. The resultant dissipation may enhance with the decaying separation and increasing GW frequencies, which subsequently accelerates the orbital decay of the binary. However, the dissipation rate just has an order of 10−70 eV/s. So the corrections to the dynamics of NS binaries are very marginal, by considering the wide separation, the cosmological coalescence time, and low-frequency GWs of the system.

A Novel Medical Image Encryption Using R鰏sler System

The technological advances made possible by the Internet, coupled with the unforeseen critical circumstances set in motion by the Covid-19 pandemic, have greatly increased the generation and transmission of medical images every day. Medical image transmission over an unsecured public network threatens the privacy of sensitive patient information. We have, in this paper, designed a new secure color medical image encryption algorithm based on binary plane decomposition, DNA (deoxyribonucleic acid) computing, and the chaotic Rössler dynamical system. At first, a bit-by-bit swap is performed on twenty four binary planes of the input image and encoded using DNA encoding rules. Thereafter, the Rössler system is used to modify the pixel values of the encoded image, which is subsequently decoded. Finally, the ciphered image is obtained by pixel-by-pixel permutation using position sequences. An innovative approach is used to compute keys from the color components of the input image. Extensive performance experiments of the proposed technique is conducted with metrics such as key sensitivity, key space, correlation coefficients (horizontal, diagonal and vertical directions), histograms, information entropy, number of pixel changes rate (NPCR), information entropy, unified average changing intensity (UACI), and encryption time. Comparative analyses have demonstrated that the proposed algorithm is fast, robust and competitive.

Variations of the Catalan numbers from some nonassociative binary operations

We investigate certain nonassociative binary operations that satisfy a four-parameter generalization of the associative law. From this we obtain variations of the ubiquitous Catalan numbers and connections to many interesting combinatorial objects such as binary trees, plane trees, lattice paths, and permutations.

A novel retinal image segmentation using rSVM boosted convolutional neural network for exudates detection

Retinal image analysis is an emerging research field in ophthalmological disease diagnosis since falsely detected optic disc, fovea, and blood vessels have become essential levels for automated diagnosis practices. In this article, we introduce a novel retinal image segmentation based on ranking support vector machine (rSVM) with convolutional neural network in deep learning field for the detection of diabetic retinopathy. Firstly, the spatial features of the retinal images have been extracted from RGB channel and mapped into a single binary features plane by the computing of pixel by pixel score using rSVM. Thereafter, we have designed a deep convolutional neural network for the retinal image segmentation followed by automatic anomaly detection using morphological operations. The rSVM computes a score function which is more suitable for multi-level classification to binary features classification in order to reduce the overall execution time in the segmentation task. The CNN has been designed with rSVM to define a consistent feature label in the network that reduces the number of channels in the CNN which lead to fast convergence. As a consequence, we have achieved good segmentation accuracy such as 96.4%, 97% and 98.2% for three different databases through post processing steps in comparison with other existing model.

Steganography Technique Inspired by Rook

A steganographic technique inspired by rook is presented in this paper to ensure privacy and secrecy. In this approach, the cover image is partitioned into n × 1 pixel blocks and converted equivalent n × 8 binary bit planes. Then the functional output of each block is calculated on the basis of the number of rook positions, which are attacked by opponent rooks. The rook is a chess piece that moves only forward and backward in a straight line. In binary bit plane, 0 and 1 are considered as a black and white opponent rook, respectively. The secret information is considered as stream of binary bits. The binary bits of secret information are compared with the functional output of the corresponding block. If it is equal to the functional output of the corresponding block, then nothing needs to be done. In case of inequality, the small number of bits needs to be flipped in such a way that the functional output of the corresponding block becomes equal to the corresponding secret binary bits and the distortion of the cover is minimized.

The morphology of the X-ray afterglows and of the jetted GeV emission in long GRBs

ABSTRACT We recall evidence that long gamma-ray bursts (GRBs) have binary progenitors and give new examples. Binary-driven hypernovae (BdHNe) consist of a carbon–oxygen core (COcore) and a neutron star (NS) companion. For binary periods ∼5 min, the COcore collapse originates the subclass BdHN I characterized by (1) an outstanding supernova (SN; the ‘SN-rise’); (2) a black hole (BH), born from the NS collapse by SN matter accretion, leading to a GeV emission with luminosity $L_{\rm GeV} = A_{\rm GeV}\, t^{-\alpha _{\rm GeV}}$, observed only in some cases; and (3) a new NS (νNS), born from the SN, originating from the X-ray afterglow with $L_\mathrm{ X} = A_{\rm X}\, t^{-\alpha _{\rm X}}$, observed in all BdHN I. We record 378 sources and present for four prototype GRBs 130427A, 160509A, 180720B, and 190114C: (1) spectra, luminosities, SN-rise duration; (2) AX, αX = 1.48 ± 0.32, and (3) the νNS spin time evolution. We infer (i) AGeV, αGeV = 1.19 ± 0.04 and (ii) the BdHN I morphology from time-resolved spectral analysis, three-dimensional simulations, and the GeV emission presence/absence in 54 sources within the Fermi-Large Area Telescope boresight angle. For 25 sources, we give the integrated and time-varying GeV emission, 29 sources have no GeV emission detected and show X/gamma-ray flares previously inferred as observed along the binary plane. The 25/54 ratio implies the GeV radiation is emitted within a cone of half-opening angle ≈60° from the normal to the orbital plane. We deduce BH masses of 2.3–8.9 M⊙ and spin of 0.27–0.87 by explaining the GeV emission from the BH rotational energy extraction, while their time evolution validates the BH mass–energy formula.

An image encryption scheme in bit plane content using Henon map based generated edge map

At present times the topic of Chaos gain a lot of attention for the encryption/decryption methodology, yet we didn’t settled to get a good difference between conventional counterparts. Several chaotic maps can be considered sensitivity dependence to seed values. Taking into consideration for this property, In this paper, the author have presented an image encryption technique employing a 2-dimensional chaotic Henon map, initially it implemented the confusion scheme using chaotic sequence obtained by several iterations using chaotic map approach. In the subsequent stage Edge Maps, generated by edge detection filters and binary bit plane decomposition is applied to perform further confusion using a bit-xor operation to get a cipher image. It is more secure and robust, experimental analysis and simulation is performed to get required results which better revealed that the encrypted images are secured and tolerant to different attacks.

Shock-powered radio precursors of neutron star mergers from accelerating relativistic binary winds

ABSTRACT During the final stages of a compact object merger, if at least one of the binary components is a magnetized neutron star (NS), then its orbital motion substantially expands the NS’s open magnetic flux – and hence increases its wind luminosity – relative to that of an isolated pulsar. As the binary orbit shrinks due to gravitational radiation, the power and speed of this binary-induced inspiral wind may (depending on pair loading) secularly increase, leading to self-interaction and internal shocks in the outflow beyond the binary orbit. The magnetized forward shock can generate coherent radio emission via the synchrotron maser process, resulting in an observable radio precursor to binary NS merger. We perform 1D relativistic hydrodynamical simulations of shock interaction in the accelerating binary NS wind, assuming that the inspiral wind efficiently converts its Poynting flux into bulk kinetic energy prior to the shock radius. This is combined with the shock maser spectrum from particle-in-cell simulations, to generate synthetic radio light curves. The precursor burst with a fluence of ∼1 Jy·ms at ∼GHz frequencies lasts ∼1–500 ms following the merger for a source at ∼3 Gpc (Bd/1012 G)8/9, where Bd is the dipole field strength of the more strongly magnetized star. Given an outflow geometry concentrated along the binary equatorial plane, the signal may be preferentially observable for high-inclination systems, that is, those least likely to produce a detectable gamma-ray burst.