arXiv subjects

Zs. Regaly

Publications and source records attributed to Zs. Regaly.

At least 19 recordsLinked to original sources

arXiv2026

Rings Around Non-Spherical Worlds: Sub-mm Dust Retention Around Triaxial Small Bodies in the Solar System

We investigated the millennial-scale evolution of narrow innermost rings composed of pebble-sized to sub-millimeter particles around the four known ring-bearing small bodies Chiron, Chariklo, Quaoar, and Haumea. Using a GPU-accelerated 8th-order Hermite integrator, we modeled the combined effects of solar radiation pressure (RP), shadowing of the rings by the host body, heliocentric motion, and the non-axisymmetric gravitational field of the rotating triaxial central body. The calculations compare spherical and triaxial-body models, as well as coplanar and inclined ring configurations. In spherical models, solar RP excites particle eccentricities, leading to accretion onto the central body above a critical RP parameter. This effect is strongest for the lower-mass systems, Chiron and Chariklo, where particles with relatively modest radiation forcing are rapidly removed. In contrast, when the triaxial shape of the host body is included, rapid apsidal precession suppresses RP-driven eccentricity growth and prevents material loss from the ring over the simulated interval. The triaxial models also suppress the previously identified Sun-facing reorientation of highly inclined rings and instead produce moderate vertical broadening. Strongly confined rings persist for RP parameters corresponding to particle sizes larger than about 7-40 micrometers, depending on composition. Their characteristic radial widths are about 10 km for Chiron and Chariklo and about 40-70 km for Quaoar and Haumea. The vertical thicknesses of the rings are estimated to be on the order of 1 km for Chiron and Chariklo, and only several hundred meters for Quaoar and Haumea. Our results suggest that narrow rings around triaxial small bodies in the Solar System can plausibly retain sub-millimeter particles over dynamically relevant timescales shorter than Poynting-Robertson drag.

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arXiv2026

Beyond solar metallicity: How enhanced solid content in disks re-shape low-mass planet torques

The migration of low-mass planets is tightly controlled by the torques exerted by both gas and solids in their natal disks. While canonical models assume a solar solid-to-gas mass ratio (epsilon=0.01) and neglect the back-reaction of solid component of the disk, recent work suggests that enhanced metallicity can radically alter these torques. We quantify how elevated metallicities (epsilon=0.03 and epsilon=0.1) modify the gas and solid torques, test widely used linear scaling prescriptions, and identify the regimes where solid back-reaction becomes decisive. We performed global, 2D hydrodynamic simulations that treat solid material as a pressureless fluid fully coupled to the gas through drag and include the reciprocal back-reaction force. The planet was maintained on a fixed circular orbit, thus we computed static torques. The Stokes number was varied from 0.01 to 10, three surface-density slopes (p=0.5, 1.0, and 1.5) and three accretion efficiencies (eta=0, 10, and 100%) were explored. Torques, obtained by rescaling canonical epsilon=0.01 results, were compared with direct simulations. Solid torques scale linearly with epsilon, but gas torques deviate by 50-100% and can even reverse sign for St<=1 in epsilon=0.1 disks. These are due to strong, feedback-driven, asymmetric gas perturbations in the co-orbital region, amplified by rapid planetary accretion. Solid back-reaction in high-metallicity environments can dominate the migration torque budget of low-mass planets. Simple metallicity rescalings are therefore unreliable for St<=2, implying that precise migration tracks - particularly in metal-rich disks -- require simulations that fully couple solid and gas dynamics. These results highlight metallicity as a key parameter in shaping the early orbital architecture of planetary systems.

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arXiv2025

SN 2023ixf in M101: physical parameters from bolometric light curve modeling

We present new photometric observations of the core-collapse supernova SN 2023ixf occurred in M101, taken with the RC80 and BRC80 robotic telescopes in Hungary. The initial nickel mass from the late-phase bolometric light curve extending up to 400 days after explosion, is inferred as $M_{\rm Ni} = 0.046 \pm 0.007$ M$_\odot$. The comparison of the bolometric light curve with models from hydrodynamical simulations as well as semi-analytic radiative diffusion codes reveals a relatively low-mass ejecta of $M_{\rm ej} \lesssim 9$ M$_\odot$, contrary to SN~2017eaw, another H-rich core-collapse event, which had $M_{\rm ej} \gtrsim 15$ M$_\odot$.

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arXiv2025

Celestial sunflowers -- Survival of rings around small planetary bodies under solar radiation pressure

Context: Rings around giant planets are a common feature of the solar system. Even though solar radiation pressure is known to destabilize rings by exciting the orbital eccentricity of its particles, the Centaur Chariklo (and possibly Chiron), the dwarf planet Haumea, and trans-Neptunian object Quaoar also host rings of solid material. Aims: We explore the dynamical evolution of rings around spherical Chariklo and Haumea analogs, assuming different particle sizes and tilt angles with respect to the planetary orbital plane of the ring. Methods: The ring dynamics were studied using a GPU-based N-body integrator with an 8th-order Hermite scheme for several thousand years, corresponding to 10 solar orbits. The simulations took into account the gravitational effects of the planet and the Sun, radiation pressure, and the shadow cast by the planet. Results: Two families of rings have been identified depending on the ring tilt angle. Slightly tilted rings (<=40 deg) are unstable under a critical particle size. Highly tilted rings (>=50 deg), however, show instability only for a range of particle sizes that spans 1-10 times the critical size. The planetary shadow reduces the critical size by a factor of five and extends the instability region to 0.1-10 times this newly identified critical size. Conclusions: The stabilization of highly inclined rings occurs because the plane of the ring is forced to be perpendicular to the Solar radiation. As a result, the plane of the ring rotates as the planetary bodies revolves: always facing the sun, like a celestial sunflower. Rings which are closely aligned to the orbital plane of the host planet, such as Haumea and Quaoar, presumably consist of particles with a size at least 1-4 um. However, particles in the rings which are highly tilted, like that around Chariklo and Chiron, should consist of particles <=2.5-15 um or >=60-300 um.

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arXiv2023

Mitigating potentially hazardous asteroid impacts revisited

Context: Potentially hazardous asteroids (PHA) in Earth-crossing orbits pose a constant threat to life on Earth. Several mitigation methods have been proposed, and the most feasible technique appears to be the disintegration of the impactor and the generation of a fragment cloud by explosive penetrators at interception. However, mitigation analyses tend to neglect the effect of orbital dynamics on the trajectory of fragments. Aims: We aim to study the effect of orbital dynamics of the impactor's cloud on the number of fragments that hit the Earth, assuming different interception dates. We investigate the effect of self-gravitational cohesion and the axial rotation of the impactor. Methods: We computed the orbits of 10^5 fragments with a high-precision direct N-body integrator of the eighth order, running on GPUs. We considered orbital perturbations from all large bodies in the Solar System and the self-gravity of the cloud fragments. Results: Using a series of numerical experiments, we show that orbital shear causes the fragment cloud to adopt the shape of a triaxial ellipsoid. The shape and alignment of the triaxial ellipsoid are strongly modulated by the cloud's orbital trajectory and, hence, the impact cross-section of the cloud with respect to the Earth. Therefore, the number of fragments hitting the Earth is strongly influenced by the orbit of the impactor and the time of interception. A minimum number of impacts occur for a well-defined orientation of the impactor rotational axis, depending on the date of interception. Conclusions: To minimise the lethal consequences of an PHA's impact, a well-constrained interception timing is necessary. A too-early interception may not be ideal for PHAs in the Apollo or Aten groups. Thus, we find that the best time to intercept PHA is when it is at the pericentre of its orbit.

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arXiv2023

Planetary nurseries: vortices formed at smooth viscosity transition

Excitation of Rossby wave instability and development of a large-scale vortex at the outer dead zone edge of protoplanetary discs is one of the leading theories that explains horseshoe-like brightness distribution in transition discs. Formation of such vortices requires a relatively sharp viscosity transition. Detailed modelling, however, indicates that viscosity transitions at the outer edge of the dead zone is relatively smooth. In this study, we present 2D global, non-isothermal, gas-dust coupled hydrodynamic simulations to investigate the possibility of vortex excitation at smooth viscosity transitions. Our models are based on a recently postulated scenario, wherein the recombination of charged particles on the surface of dust grains results in reduced ionisation fraction and in turn the turbulence due to magnetorotational instability. Thus, the alpha-parameter for the disc viscosity depends on the local dust-to-gas mass ratio. We found that the smooth viscosity transitions at the outer edge of the dead zone can become Rossby unstable and form vortices. A single large-scale vortex develops if the dust content of the disc is well coupled to the gas, however, multiple small-scale vortices ensue for the case of less coupled dust. As both type of vortices are trapped at the dead zone outer edge, they provide sufficient time for dust growth. The solid content collected by the vortices can exceed several hundred Earth masses, while the dust-to-gas density ratio within often exceeds unity. Thus, such vortices function as planetary nurseries within the disc, providing ideal sites for formation of planetesimals and eventually planetary systems.

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arXiv2020

On the oligarchic growth in a fully interacting system

Protoplanets develop via collisions between planetesimals and planetary embryos in the final assembly stage of planet formation. The efficiency of the planet formation can be defined by the mass ratio between formed protoplanets and the initial mass of embryos and planetesimals. In final assembly planet formation models, the gravitational interactions between planetesimals are usually neglected due to computational difficulties, namely, computations require fewer resources in this way. We investigated the effect of this simplification via modeling the planet formation efficiency in a circumstellar belt of embryos and self-interacting or non-self-interacting planetesimals. We used our own developed GPU-based direct N-body integrator, HIPERION, for the simulations. We found that planet formation efficiency is higher if the planetesimal self-interaction is taken into account in models that contain the commonly used 100 embryos. The observed effect can be explained by the damping of planetesimal eccentricities by their self-gravity. The non-self-interacting and self-interacting models show qualitatively the same results if the initial number of embryos is above 200.

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arXiv2017

On the cavity of a debris disc carved by a giant planet

One possible explanation of the cavity in debris discs is the gravitational perturbation of an embedded giant planet. Planetesimals passing close to a massive body are dynamically stirred resulting in a cleared region known as the chaotic zone. Theory of overlapping mean-motion resonances predicts the width of this cavity. To test whether this cavity is identical to the chaotic zone, we investigate the formation of cavities by means of collisionless N-body simulations assuming a 1.25-10 Jupiter mass planet with eccentricities of 0-0.9. Synthetic images at millimetre wavelengths are calculated to determine the cavity properties by fitting an ellipse to 14 percent contour level. Depending on the planetary eccentricity, e_pl, the elliptic cavity wall rotates as the planet orbits with the same (e_pl<0.2) or half (e_pl>0.2) period that of the planet. The cavity centre is offset from the star along the semi-major axis of the planet with a distance of d=0.1q^-0.17e_pl^0.5 in units of cavity size towards the planet's orbital apocentre, where q is the planet-to-star mass ratio. Pericentre (apocentre) glow develops for e_pl<0.05 (e_pl>0.1), while both are present for 0.05<=e_pl<=0.1. Empirical formulae are derived for the sizes of the cavities: da_cav=2.35q^0.36 and da_cav=7.87q^0.37e_pl^0.38 for e_pl<=0.05 and e_pl>0.05, respectively. The cavity eccentricity, e_cav, equals to that of the planet only for 0.3<=e_pl<=0.6. A new method based on ALMA observations for estimating the orbital parameters and mass of the planet carving the cavity is also given.

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arXiv2017

Interpreting Brightness Asymmetries in Transition Disks: Vortex at Dead Zone or Planet Carved Gap Edges?

Recent sub-millimeter observations show non-axisymmetric brightness distributions with a horseshoe-like morphology for more than a dozen transition disks. The most accepted explanation for the observed asymmetries is the accumulation of dust in large-scale vortices. Protoplanetary disks vortices can form by the excitation of Rossby-wave instability in the vicinity of a steep pressure gradient, which can develop at the edges of a giant planet carved gap or at the edges of an accretionally inactive zone. We studied the formation and evolution of vortices formed in these two distinct scenarios by means of two-dimensional locally isothermal hydrodynamic simulations. We found that the vortex formed at the edge of a planetary gap is short-lived, unless the disk is nearly inviscid. In contrast, the vortex formed at the outer edge of a dead zone is long-lived. The vortex morphology can be significantly different in the two scenarios: the vortex radial and azimuthal extensions are ~1.5 and ~3.5 times larger for the dead zone edge compared to gap models. In some particular cases, the vortex aspect ratios can be similar in the two scenarios, however, the vortex azimuthal extensions can be used to distinguish the vortex formation mechanisms. We calculate predictions for vortex observability in the sub-millimeter continuum with ALMA. We found that the azimuthal and radial extent of brightness asymmetry correlates with vortex formation process, within the limitations of alpha-viscosity prescription.

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arXiv2017

Vortex stretching in self-gravitating protoplanetary discs

Horseshoe-shaped brightness asymmetries of several transitional discs are thought to be caused by large-scale vortices. Anticyclonic vortices are efficiently collect dust particles, therefore they can play a major role in planet formation. Former studies suggest that the disc self-gravity weakens vortices formed at the edge of the gap opened by a massive planet in discs whose masses are in the range of 0.01<=M_disc/M_*<=0.1. Here we present an investigation on the long-term evolution of the large-scale vortices formed at the viscosity transition of the discs' dead zone outer edge by means of two-dimensional hydrodynamic simulations taking disc self-gravity into account. We perform a numerical study of low mass, 0.001<=M_disc/M_*<=0.01, discs, for which cases disc self-gravity was previously neglected. The large-scale vortices are found to be stretched due to disc self-gravity even for low-mass discs with M_disc/M_*>=0.005 where initially the Toomre Q-parameter was <=50 at the vortex distance. As a result of stretching, the vortex aspect ratio increases and a weaker azimuthal density contrast develops. The strength of the vortex stretching is proportional to the disc mass. The vortex stretching can be explained by a combined action of a non-vanishing gravitational torque caused by the vortex, and the Keplerian shear of the disc. Self-gravitating vortices are subject to significantly faster decay than non-self-gravitating ones. We found that vortices developed at sharp viscosity transitions of self-gravitating discs can be described by a GNG model as long as the disc viscosity is low, i.e. alpha_dz<=10^-5.

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arXiv2017

The circumstellar disk response to the motion of the host star

Grid-based hydrodynamics simulations of circumstellar disks are often performed in the curvilinear coordinate system, in which the center of the computational domain coincides with the motionless star. However, the center of mass may be shifted from the star due to the presence of any non-axisymmetric mass distribution. As a result, the system exerts a gravity force on the star, causing the star to move in response, which can affect the evolution of the circumstellar disk. We aim at studying the effects of stellar motion on the evolution of protostellar and protoplanetary disks. In protostellar disks, a non-axisymmetric distribution of matter in the form of spiral arms or massive clumps can form due to gravitational instability. Protoplanetary disks can also feature non-axisymmetric structures caused by a high-mass planet or a large-scale vortex. We use 2D grid-based hydrodynamic simulations to explore the effect of stellar motion. We adopt a non-inertial polar coordinate system centered on the star, in which the stellar motion is taken into account by calculating the indirect potential caused by the non-axisymmetric disk, a high-mass planet, or a large-scale vortex. We found that the stellar motion has a moderate effect on the evolution history in protostellar disks, reducing somewhat the disk size and mass, while having a profound effect on the collapsing envelope, changing its inner shape from an initially axisymmetric to a non-axisymmetric configuration. Protoplanetary disk simulations show that the stellar motion slightly reduces the width of the gap opened by a high-mass planet, decreases the planet migration rate, and strengthens the large-scale vortices formed at the viscosity transition. We conclude that the inclusion of the indirect potential is recommended in grid-based hydrodynamics simulations of circumstellar disks which use the curvilinear coordinate system.

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arXiv2014

Planet-vortex interaction:How a vortex can shepherd a planetary embryo

Context: Anticyclonic vortices are considered as a favourable places for trapping dust and forming planetary embryos. On the other hand, they are massive blobs that can interact gravitationally with the planets in the disc. Aims: We aim to study how a vortex interacts gravitationally with a planet which migrates toward it or a planet which is created inside the vortex. Methods: We performed hydrodynamical simulations of a viscous locally isothermal disc using GFARGO and FARGO-ADSG. We set a stationary Gaussian pressure bump in the disc in a way that RWI is triggered. After a large vortex is established, we implanted a low mass planet in the outer disc or inside the vortex and allowed it to migrate. We also examined the effect of vortex strength on the planet migration and checked the validity of the final result in the presence of self-gravity. Results: We noticed regardless of the planet's initial position, the planet is finally locked to the vortex or its migration is stopped in a farther orbital distance in case of a stronger vortex. For the model with the weaker vortex, we studied the effect of different parameters such as background viscosity, background surface density, mass of the planet and different planet positions. In these models, while the trapping time and locking angle of the planet vary for different parameters, the main result, which is the planet-vortex locking, remains valid. We discovered that even a planet with a mass less than 5 * 10^{-7} M_{\star} comes out from the vortex and is locked to it at the same orbital distance. For a stronger vortex, both in non-self-gravitated and self-gravitating models, the planet migration is stopped far away from the radial position of the vortex. This effect can make the vortices a suitable place for continual planet formation under the condition that they save their shape during the planetary growth.

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arXiv2014

Asymmetric fundamental band CO lines as a sign of an embedded giant planet

We investigate the formation of double-peaked asymmetric line profiles of CO in the fundamental band spectra emitted by young (1-5Myr) protoplanetary disks hosted by a 0.5-2 Solar mass star. Distortions of the line profiles can be caused by the gravitational perturbation of an embedded giant planet with q=4.7 10^-3 stellar-to-planet mass ratio. Locally isothermal, 2D hydrodynamic simulations show that the disk becomes globally eccentric inside the planetary orbit with stationary ~0.2-0.25 average eccentricity after ~2000 orbital periods. For orbital distances 1-10 AU, the disk eccentricity is peaked inside the region where the fundamental band of CO is thermal excitated. Hence, these lines become a sensitive indicators of the embedded planet via their asymmetries (both in flux and wavelength). We find that the line shape distortions (e.g. distance, central dip, asymmetry and positions of peaks) of a given transition depend on the excitation energy (i.e. on the rotational quantum number J). The magnitude of line asymmetry is increasing/decreasing with J if the planet orbits inside/outside the CO excitation zone (R_CO<=3, 5 and 7 AU for a 0.5,1 and 2 Solar mass star, respectively), thus one can constrain the orbital distance of a giant planet by determining the slope of peak asymmetry-J profile. We conclude that the presented spectroscopic phenomenon can be used to test the predictions of planet formation theories by pushing the age limits for detecting the youngest planetary systems.

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arXiv2013

Trapping of giant-planet cores - I. Vortex aided trapping at the outer dead zone edge

In this paper the migration of a 10 Earth-mass planetary core is investigated at the outer boundary of the dead zone of a protoplanetary disc by means of 2D hydrodynamic simulations done with the graphics processor unit version of the FARGO code. In the dead zone, the effective viscosity is greatly reduced due to the disc self-shielding against stellar UV radiation, X-rays from the stellar magnetosphere and interstellar cosmic rays. As a consequence, mass accumulation occurs near the outer dead zone edge, which is assumed to trap planetary cores enhancing the efficiency of the core-accretion scenario to form giant planets. Contrary to the perfect trapping of planetary cores in 1D models, our 2D numerical simulations show that the trapping effect is greatly dependent on the width of the region where viscosity reduction is taking place. Planet trapping happens exclusively if the viscosity reduction is sharp enough to allow the development of large-scale vortices due to the Rossby wave instability. The trapping is only temporarily, and its duration is inversely proportional to the width of the viscosity transition. However, if the Rossby wave instability is not excited, a ring-like axisymmetric density jump forms, which cannot trap the 10 Earth-mass planetary cores. We revealed that the stellar torque exerted on the planet plays an important role in the migration history as the barycentre of the system significantly shifts away from the star due to highly non-axisymmetric density distribution of the disc. Our results still support the idea of planet formation at density/pressure maximum, since the migration of cores is considerably slowed down enabling them further growth and runaway gas accretion in the vicinity of an overdense region.

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arXiv2011

Possible planet-forming regions on submillimetre images

Submillimetre images of transition discs are expected to reflect the distribution of the optically thin dust. Former observation of three transition discs LkHa330, SR21N, and HD1353444B at submillimetre wavelengths revealed images which cannot be modelled by a simple axisymmetric disc. We show that a large-scale anticyclonic vortex that develops where the viscosity has a large gradient (e.g., at the edge of the disc dead zone), might be accountable for these large-scale asymmetries. We modelled the long-term evolution of vortices being triggered by the Rossby wave instability. We found that a horseshoe-shaped (azimuthal wavenumber m=1) large-scale vortex forms by coalescing of smaller vortices within 5x10^4 yr, and can survive on the disc life-time (~5x10^6 yr), depending on the magnitude of global viscosity and the thickness of the viscosity gradient. The two-dimensional grid-based global disc simulations with local isothermal approximation and compressible-gas model have been done by the GPU version of hydrodynamic code FARGO (GFARGO). To calculate the dust continuum image at submillimetre wavelengths, we combined our hydrodynamical results with a 3D radiative transfer code. By the striking similarities of the calculated and observed submillimetre images, we suggest that the three transition discs can be modelled by a disc possessing a large-scale vortex formed near the disc dead zone edge. Since the larger dust grains (larger than mm in size) are collected in these vortices, the non-axisymmetric submillimetre images of the above transition discs might be interpreted as active planet and planetesimal forming regions situated far (> 50 AU) from the central stars.

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arXiv2011

Asymmetric transit curves as indication of orbital obliquity: clues from the late-type dwarf companion in KOI-13

KOI-13.01, a planet-sized companion in an optical double star was announced as one of the 1235 Kepler planet candidates in February 2011. The transit curves show significant distortion that was stable over the ~130 days time-span of the data. Here we investigate the phenomenon via detailed analyses of the two components of the double star and a re-reduction of the Kepler data with pixel-level photometry. Our results indicate that KOI-13 is a common proper motion binary, with two rapidly rotating components (v sin i ~ 65--70 km/s). We identify the host star of KOI-13.01 and conclude that the transit curve asymmetry is consistent with a companion orbiting a rapidly rotating, possibly elongated star on an oblique orbit. After correcting the Kepler light curve to the second light of the optical companion star, we derive a radius of 2.2 R_J for the transiter, implying an irradiated late-type dwarf, probably a hot brown dwarf rather than a planet. KOI-13 is the first example for detecting orbital obliquity for a substellar companion without measuring the Rossiter-McLaughlin effect from spectroscopy.

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arXiv2011

Spectral signatures of disk eccentricity in young binary systems: I. Circumprimary case

Star formation occurs via fragmentation of molecular clouds, which means that the majority of stars born are a members of binaries. There is growing evidence that planets might form in circumprimary disks of medium-separation binaries. The tidal forces caused by the secondary generally act to distort the originally circular disk to an eccentric one. To infer the disk eccentricity from high-res NIR spectroscopy, we calculate the fundamental band emission lines of the CO molecule emerging from the atmosphere of the disk. We model circumprimary disk evolution under the gravitational perturbation of the orbiting secondary using a 2D grid-based hydrodynamical code, assuming alpha-type viscosity. The hydrodynamical results are combined with our spectral code based on the double-layer disk model to calculate the CO molecular line profiles. We find that the orbital velocity distribution of the gas parcels differs significantly from the circular Keplerian fashion, thus the line profiles are asymmetric in shape. The magnitude of asymmetry is insensitive to the binary mass ratio, the magnitude of viscosity, and the disk mass. In contrast, the disk eccentricity, thus the level of the line profile asymmetry, is influenced significantly by the binary eccentricity and the disk geometrical thickness. We demonstrate that the disk eccentricity profile in the planet-forming region can be determined by fitting the high-resolution CO line profile asymmetry using a simple 2D spectral model that accounts for the velocity distortions caused by the disk eccentricity. Thus, with our novel approach the disk eccentricity can be inferred with high-resolution near-IR spectroscopy prior to the era of high angular resolution optical or radio direct-imaging. By determining the disk eccentricity in medium-separation young binaries, we might be able to constrain the planet formation theories.

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arXiv2010

Practical suggestions on detecting exomoons in exoplanet transit light curves

The number of known transiting exoplanets is rapidly increasing, which has recently inspired significant interest as to whether they can host a detectable moon. Although there has been no such example where the presence of a satellite was proven, several methods have already been investigated for such a detection in the future. All these methods utilize post-processing of the measured light curves, and the presence of the moon is decided by the distribution of a timing parameter. Here we propose a method for the detection of the moon directly in the raw transit light curves. When the moon is in transit, it puts its own fingerprint on the intensity variation. In realistic cases, this distortion is too little to be detected in the individual light curves, and must be amplified. Averaging the folded light curve of several transits helps decrease the scatter, but it is not the best approach because it also reduces the signal. The relative position of the moon varies from transit to transit, the moon's wing will appear in different positions on different sides of the planet's transit. Here we show that a careful analysis of the scatter curve of the folded light curves enhances the chance of detecting the exomoons directly.

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