Circular Orbit Research Articles

Twenty-three new Heartbeat Star systems discovered based on TESS data

ABSTRACT Heartbeat stars (HBSs) are ideal astrophysical laboratories to study the formation and evolution of binary stars in eccentric orbits and the internal structural changes of their components under strong tidal action. We discover 23 new HBSs based on TESS photometric data. The orbital parameters, including orbital period, eccentricity, orbital inclination, argument of periastron, and epoch of periastron passage of these HBSs, are derived by using a corrected version of Kumar et al.'s model based on the Markov Chain Monte Carlo (MCMC) method. The preliminary results show that these HBSs have orbital periods in the range from 2.7 to 20 d and eccentricities in the range from 0.08 to 0.70. The eccentricity-period relation of these objects shows a positive correlation between eccentricity and period and also shows the existence of orbital circularization. The Hertzsprung–Russell diagram shows that the HBSs are not all located in a particular area. The distribution of the derived parameters suggests a selection bias within the TESS survey towards HBSs with shorter periods. These objects are a very useful source to study the structure and evolution of eccentricity orbit binaries and to extend the TESS HBS catalog.

Stability Analysis of Stable Circular Orbit in Multi-Static Black Hole Spacetime

We herein study the circular orbit stability of a static black hole system composed of multiple Reissner–Nordstrom (RN) black holes. By comparing the circular orbits of two static black holes, three static black holes (TBHs), four static black holes and five static black holes at different spacetime, we find that the continuity of their stable circular orbits changes, i.e., the peaks of the effective potentials are transformed from single-peaked to bi-peaked, and that the distance a between the black holes is the main reason for this change. This characteristic is completely different from the continuity of the stable circular orbit interval of any kind of single black hole in the past. After calculation, we obtain several critical values that lead to the change in circular orbit stability. The three fundamental frequencies (orbital frequency, radial local frequency, and vertical local frequency) are derived and compared for two different spacetimes of double and three black holes. We also analyse the effect of the black hole distance a on the three fundamental frequencies of circular orbits.

Galactic Stellar Black Hole Binaries: Spin Effects on Jet Emissions of High-Energy Gamma-Rays

In the last few decades, galactic stellar black hole X-ray binary systems (BHXRBs) have aroused intense observational and theoretical research efforts specifically focusing on their multi-messenger emissions (radio waves, X-rays, γ-rays, neutrinos, etc.). In this work, we investigate jet emissions of high-energy neutrinos and gamma-rays created through several hadronic and leptonic processes taking place within the jets. We pay special attention to the effect of the black hole’s spin (Kerr black holes) on the differential fluxes of photons originating from synchrotron emission and inverse Compton scattering and specifically on their absorption due to the accretion disk’s black-body radiation. The black hole’s spin (dimensionless spin parameter a*) enters into the calculations through the radius of the innermost circular orbit around the black hole, the RISCO parameter, assumed to be the inner radius of the accretion disk, which determines its optical depth τdisk. In our results, the differential photon fluxes after the absorption effect are depicted as a function of the photon energy in the range 1GeV ≤E≤103GeV. It is worth noting that when the black holes’ spin (α*) increases, the differential photon flux becomes significantly lower.

QPOs and circular orbits around black holes in Chaplygin-like cold dark matter

Understanding the nature of dark energy in the universe is an actual issue in theoretical astrophysics and cosmology. One way to do it is by probing dark fluids with different equations of states (EoS). In the present work, we consider a Schwarzschild black hole (BH) surrounded by a dark fluid with a Chaplygin-like EoS as a generalized version of the Chaplygin EoS. We first investigate the effects of the dark fluid parameters on the horizon properties of the BH. The effective mass of the spacetime is calculated and analyzed under the dark fluid parameters. The scalar invariants of the BH spacetime are also calculated, and it is shown that the spacetime curvature increases as the dark fluid parameter increases. Next, we studied the circular motion of the test particle around the BH. As standard particle motion investigations, we analyze the effective potential of the particles for circular motion, specific energy, and angular corresponding to circular orbits with zero and nonvanishing values of the dark fluid intensity. In addition, we study the innermost stable circular orbits (ISCO). It is observed that there is an outermost stable circular orbit (OSCO) due to the presence of the dark fluid. It also shows that at a critical value of the dark fluid intensity parameter, ISCO and OSCO take the same radius. We calculate the frequency of Keplerian orbits and radial and vertical oscillations of the particles along stable circular orbits. We also applied orbital data from hotspots observed near Sgr A* to obtain upper and lower values for the EoS parameter. Finally, we investigate quasiperiodic oscillations and obtain the mass-to-EoS parameter relations for GRS J1915-105 and XTE 1550-564.

Reachable Set Computation with Terminal Velocity Constraints

This work establishes a general-purpose method for computing the exact boundary of the reachable set in a specified direction, with additional constraints imposed on the terminal velocities. Reachable sets with rest boundary conditions, that is, zero-velocity constraints imposed at initial and final times, are of interest for formation flying and spacecraft rendezvous and docking applications. The rest-to-rest reachability problem is extended to compute reachable neighboring circular orbits and a modified problem formulation is developed to exclusively compute the maximum and minimum reachable circular orbits. Reachable sets are computed by applying classical optimal control techniques to a maximum position optimization problem. A solution method for the optimization problem is outlined, which makes use of a Newton’s method solving schema. Additional constraints are added to the problem to compute maxima along specified directions, allowing for the characterization of the reachable set in as many directions as desired. Example reachable sets are computed to illustrate the use of this method on various systems, including an application to relative motion.

An effective model for the tidal disruption of satellites undergoing minor mergers with axisymmetric primaries

According to the hierarchical formation paradigm, galaxies form through mergers of smaller entities and massive black holes (MBHs), if present at their centers, migrate to the nucleus of the newly formed galaxy, where they form binary systems. The formation and evolution of MBH binaries, and in particular their coalescence timescale, is highly relevant for current and future facilities aimed at detecting the gravitational wave signal produced by the MBHs close to coalescence. While most of the studies targeting this process are based on hydrodynamic simulations, the high computational cost makes a complete parameter space exploration prohibitive. Semianalytic approaches represent a valid alternative, but they require ad hoc prescriptions for the mass loss of the merging galaxies in minor mergers due to tidal stripping, which is not commonly considered or is at best modelled assuming very idealised geometries. In this work we propose a novel, effective model for the tidal stripping in axisymmetric potentials, to be implemented in semi-analytic models. We validated our semi-analytic approach against N-body simulations considering different galaxy sizes, inclinations, and eccentricities, finding only a moderate dependence on the orbit eccentricity. In particular, we find that, for almost circular orbits, our model mildly overestimates the mass loss, and this is due to the adjustment of the stellar distribution after the mass is removed. Nonetheless, the model exhibits a very good agreement with simulations in all the considered conditions, and thus represents an extremely powerful addition to semi-analytic calculations.

Timing and scintillation studies of PSR J1439−5501

Context. PSR J1439−5501 is a mildly recycled pulsar in a 2.12-day circular orbit around a heavy white dwarf. A white dwarf cooling model has estimated the companion mass to be between 1 and 1.3 M⊙ and the inclination angle to be greater than 55°. Such high mass and inclination are expected to induce a Shapiro delay, namely, a relativistic time delay in the signal propagation caused by the curved space-time induced by the companion. Until now, however, no Shapiro delay has been measured in this system. Aims. Our aim is to detect the Shapiro delay and, thus, to independently measure the mass and inclination of PSR J1439−5501 by using data from the Parkes and MeerKAT radio telescopes. Methods. The Shapiro delay parameters were measured through pulsar timing, which coherently accounts for every rotation of the pulsar. These measurements were then used to estimate the masses of the component stars and the inclination angle of the binary. A scintillation analysis was additionally performed by investigating the secondary spectra, which are the Fourier-transformed observed scintillation patterns. The obtained secondary spectral variations were analyzed in terms of the orbital motion and annual variation to estimate the ascending nodes, distance, and the location of the screen. Results. We obtained a highly significant measurement of the Shapiro delay, which allows estimates of the pulsar mass (1.57−0.26+0.30 M⊙), the white dwarf (WD) companion mass (1.27−0.12+0.13 M⊙), and inclination angle, (75(1)° or 105(1)°). These estimates assume that the companion mass cannot exceed the Chandrasekhar mass limit (1.48 M⊙), along with a lower limit of 1.17 M⊙ for NS masses. These results are consistent with previous studies, but the precision of the component masses has been improved significantly. The orbital and spin parameters and the large WD mass make this system very similar to that of PSR J2222−0137 and PSR J1528−3146, thereby suggesting a common evolutionary mechanism. The scintillation analysis suggests that the longitude of the ascending node is 16(7)° or −20(6)°, depending on the sense of the inclination angle. The screen distance is 260 ± 100 pc, potentially associated with the edge of the Local Bubble.

Forming Massive Terrestrial Satellites through Binary-exchange Capture

The number of planetary satellites around solid objects in the inner solar system is small either because they are difficult or unlikely to form or because they do not survive for astronomical timescales. Here we conduct a pilot study on the possibility of satellite capture from the process of collision-less binary exchange and show that massive satellites in the range 0.01–0.1 M ⊕ can be captured by Earth-sized terrestrial planets in a way already demonstrated for larger planets in the solar system and possibly beyond. In this process, one of the binary objects is ejected, leaving the other object as a satellite in orbit around the planet. We specifically consider satellite capture by an “Earth” in an assortment of hypothetical encounters with large terrestrial binaries at 1 au around the Sun. In addition, we examine the tidal evolution of captured objects and show that orbit circularization and long-term stability are possible for cases resembling the Earth–Moon system.

Powered–coasting–powered multi-phase mission reconfiguration method for launch vehicles under power system failures

For the final stage of a launch vehicle with powered–coasting–powered multi-phase flight, this paper investigates the joint reconfiguration method to determine subsequent flight trajectory and degraded orbit after power system failure in the first powered phase. While power system failures due to mass–flow–rate drop have been thoroughly studied in the existing literature, this paper focuses on the more challenging specific impulse drop failures, which result in loss of total launcher energy. This paper aims to design a fault-tolerant guidance method with onboard potential and to analyze the survivability and characteristics of the launcher in the event of such a failure. In the problem modeling, the strong nonlinearity of the orbital elements as terminal constraints is eliminated by analyzing the orbital properties in the orbital coordinate system to establish the primal trajectory optimization problem. For this multi-phase trajectory optimization problem, a joint optimization algorithm for the degradation orbit and the flight trajectory, based on convex optimization and Radau pseudospectral method, is designed to achieve autonomous mission reconfiguration. The algorithm introduces the relaxation–penalization idea, where the terminal constraints are relaxed and penalized in the performance index, allowing the algorithm to adaptively form an optimal degradation circular or elliptical orbit based on the remaining capacity of the launch vehicle. Simulation experiments demonstrate the effectiveness and superiority of the mission reconfiguration algorithm. Finally, the paper presents the first analysis of the optimal allocation of flight time between the first powered phase, the coasting phase, and the second powered phase in a propellant depletion scenario following the launcher power system failure.

Insight-HXMT, NICER, and NuSTAR Views to the Newly Discovered Black Hole X-Ray Binary Swift J151857.0–572147

The systematic properties are largely unknown for the black hole X-ray binary Swift J151857.0–572147 newly discovered in the 2024 outburst. The nature of a black hole can be completely defined by specifying the mass and dimensionless spin parameter. Therefore, accurate measurement of the two fundamental parameters is important for understanding the nature of black holes. The joint spectral fitting of a reflection component with simultaneous observations from Insight-HXMT, NICER, and NuSTAR reveals for the first time a black hole dimensionless spin of 0.84−0.26+0.17 and an inclination angle of 21.1−3.6+4.5 degrees for this system. Monitoring of the soft state by NICER results in disk flux and temperature following Fdisk∝Tin3.83±0.17 . For the standard thin disk, Ldisk≈4πRin2σTin4 , so the relationship between the flux and temperature of the disk we measured indicates that the inner radius of the disk is stable and the disk is in the innermost stable circular orbit. With an empirical relation built previously between the black hole outburst profile and the intrinsic power output, the source distance is estimated as 5.8 ± 2.5 kpc according to the outburst profile and peak flux observed by Insight-HXMT and NICER. Finally, a black hole mass of 3.67 ± 1.79–8.07 ± 4.20M ⊙ can be inferred from a joint diagnostic of the aforementioned parameters measured for this system. This system is also consistent with most black hole X-ray binaries with high spin and a mass in the range of 5–20 M ⊙.

Exploring dark forces with multimessenger studies of extreme mass ratio inspirals

The exploration of dark sector interactions via gravitational waves (GWs) from binary inspirals has been a subject of recent interest. We study dark forces using extreme mass ratio inspirals (EMRIs), pointing out two issues of interest. Firstly, the innermost stable circular orbit (ISCO) of the EMRI, which sets the characteristic length scale of the system and hence the dark force range to which it exhibits enhanced sensitivity, probes force mediator masses that complement those studied with supermassive black hole (SMBH) or neutron star binaries. The LISA mission (the proposed μAres detector) will probe mediators with masses m V ∼ 10-16 eV (m V ∼ 10-18 eV), corresponding to ISCOs of 106 M ⊙ (108 M ⊙) central SMBHs. Secondly, while the sensitivity to dark couplings is typically limited by the uncertainty in the binary component masses, independent mass measurements of the central SMBH through reverberation mapping campaigns or the motion of dynamical tracers enable one to break this degeneracy. Our results therefore highlight the necessity for coordinated studies, loosely referred to as “multimessenger”, between future μHz- mHz GW observatories and ongoing and forthcoming SMBH mass measurement campaigns, including OzDES-RM, SDSS-RM, and SDSS-V Black Hole Mapper.

Exploring a novel feature of ellis spacetime: Insights into scalar field dynamics

We have studied neutral and charged massive particles dynamics in Ellis spacetime in the presence of the external scalar field. Focusing on the circular motion of massive particles, the impact of an external scalar field on the Innermost Stable Circular Orbit (ISCO) position is analyzed, revealing a non-linear relationship with the scalar field parameter. Perturbation techniques are employed to investigate oscillatory motion near stable orbits in the Ellis spacetime, yielding analytical expressions for radial and angular oscillations. The throat of the wormhole has been constrained by comparing theoretical and observational results for fundamental frequencies of particles from quasars. Finally, scalar and gravitational perturbations in the Ellis spacetime have been studied. It is shown that the equation for the scalar profile function is fully independent from the tensor functions and the solution can be represented in terms of the confluent Heun function. However, it has been shown that equations for the tensor profile functions strongly depend on the scalar profile functions in the Ellis spacetime and they are reduced to the Regge–Wheeler–Zerilli equation. Finally, numerical solutions to the Regge–Wheeler–Zerilli equation for the radial functions in the Ellis have been presented.

The Three-phase Evolution of the Milky Way

We illustrate the formation and evolution of the Milky Way over cosmic time, utilizing a sample of 10 million red giant stars with full chemodynamical information, including metallicities and α-abundances from low-resolution Gaia XP spectra. The evolution of angular momentum as a function of metallicity—a rough proxy for stellar age, particularly for high-[α/Fe] stars—displays three distinct phases: the disordered and chaotic protogalaxy, the kinematically hot old disk, and the kinematically cold young disk. The old high-α disk starts at [Fe/H] ≈ −1.0, “spinning up” from the nascent protogalaxy, and then exhibiting a smooth “cooldown” toward more ordered and circular orbits at higher metallicities. The young low-α disk is kinematically cold throughout its metallicity range, with its observed properties modulated by a strong radial gradient. We interpret these trends using Milky Way analogs from the TNG50 cosmological simulation, identifying one that closely matches the kinematic evolution of our galaxy. This halo’s protogalaxy spins up into a relatively thin and misaligned high-α disk at early times, which is subsequently heated and torqued by a major gas-rich merger. The merger contributes a large amount of low-metallicity gas and angular momentum, from which the kinematically cold low-α stellar disk is subsequently born. This simulated history parallels several observed features of the Milky Way, particularly the decisive Gaia–Sausage–Enceladus merger that likely occurred at z ≈ 2. Our results provide an all-sky perspective on the emerging picture of our galaxy’s three-phase formation, impelled by the three physical mechanisms of spinup, merger, and cooldown.

Accreting black holes in dark matter halos

We examine the thin accretion disk behaviors surrounding black holes embedded in cold dark matter halos and scalar field dark matter halos. We first calculate the event horizons and derive the equations of motion and effective potential in black hole geometries with different dark matter halos. We then compute the specific energy, specific angular momentum, and angular velocity of particles moving along circular orbits. We also derive the effective potentials to find the locations of the innermost stable circular orbit (ISCO) and compare them to the Schwarzschild and Kerr black holes without the dark matter halos. We also use the observed ISCO of the supermassive black hole at the Galactic Center of the Milky Way, Sagittarius A*, to constrain the dark matter halos. Published by the American Physical Society 2024

Timing and Scintillation Studies of Pulsars in Globular Cluster M3 (NGC 5272) with FAST

We present the phase-connected timing solutions of all five pulsars in globular cluster M3 (NGC 5272), namely PSRs M3A to F (PSRs J1342+2822A to F), with the exception of PSR M3C, from FAST archival data. In these timing solutions, those of PSRs M3E and F are obtained for the first time. We find that PSRs M3E and F have low-mass companions and are in circular orbits with periods of 7.1 and 3.0 days, respectively. For PSR M3C, we have not detected its signal in all 41 observations. We found no X-ray counterparts for these pulsars in archival Chandra images in the band of 0.2–20 keV. From the autocorrelation function analysis of M3A and M3B’s dynamic spectra, the scintillation timescale ranges from 7.0 ± 0.3 to 60.0 ± 0.6 minutes, and the scintillation bandwidth ranges from 4.6 ± 0.2 to 57.1 ± 1.1 MHz. The measured scintillation bandwidths from the dynamic spectra indicate strong scintillation, and the scattering medium is anisotropic. From the secondary spectra, we captured a scintillation arc only for PSR M3B with a curvature of 649 ± 23 m−1 mHz−2.

Orbit determination for spacecraft with continuous low-thrust using nonsingular Thrust-Fourier-Coefficients and filtering-through approach

Orbit determination using optical survey measurements for cataloging spacecraft encounters new obstacles from mega-constellations. These challenges arise from the sparse observations, and the frequent occurrences of unknown maneuvers which are difficult to model using traditional methods. By utilizing 14 Fourier coefficients, the Thrust-Fourier-Coefficients (TFC) model can effectively represent the averaged variations of orbital elements caused by arbitrary maneuvers. However, this model contains systematic offsets that will reduce the accuracy of orbit determination, and is unsuitable for spacecraft in nearly circular orbits. This paper first replaces the classical Keplerian elements of the previous TFC model with the nonsingular elements. Then detailed analytical expressions for model offsets have been derived based on Kozai’s orbit-averaging method. A process noise covariance matrix related to the model offsets has been added to the iterated extended Kalman filter to compensate for the unmodeled dynamics and enhance the accuracy. Simulations based on this modified method demonstrate that the accuracy of orbit determination for maneuvering satellites can meet the requirements of catalog maintenance even with sparse observations.

Extreme mass-ratio inspiral around the horizonless massive object

In this paper, we calculated the extreme mass-ratio inspiral (EMRI) waveform radiated from a binary composed of a massive horizonless object (MHO) and a compact object (CO), where CO is spiraling on a circular equatorial orbit around the MHO. Due to the absent of horizon, there exist the ingoing and outgoing waves near the reflective surface of MHO, which have significantly influence on the evolution of orbital parameters. We observe that there indeed exist the differences of EMRI trajectories between the massive Kerr black hole and MHO cases. By calculating the mismatch of gravitational wave (GW) waveforms from massive black hole (MBH) and MHO, our result indicates that the space-borne gravitational wave detector could distinguish the modified effect of reflectivities from the BH case, which allows to put an upper constraint on the reflectivity R\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal {R}}$$\\end{document} of MHO, at the level of R≳10-4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal {R}} > rsim 10^{-4}$$\\end{document}.

Dynamics and collision of particles in modified black-bounce geometry

In the present work, we first regularize a black hole spacetime in modified gravity (MOG) in the presence of the scalar-tensor-vector (STV) field, called the Schwarzschild MOG black hole, under the transformation r2→r2+a2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$r^2 \\rightarrow r^2 + a^2$$\\end{document}, known as the Simpson–Visser (SV) spacetime (where a is regularization or black-bounce parameter). The spacetime can represent a black hole and a wormhole. We analyze horizon properties and calculate the effective mass of the spacetime. Also, we find black hole-wormhole regions in black-bounce and MOG parameter spacetime. We also analyze scalar invariants of spacetime, such as the Ricci scalar, the square of the Ricci tensor, and the Kretchmann scalar. We study test particle motion in the SV-MOG spacetime by considering the interaction between the particle and the STV field. We investigate how the STV fields change the innermost stable circular orbits (ISCOs), energy, and angular momentum of the test particle’s ISCO. It is shown that the ISCO decreases in the presence of the black bounce parameter and increases in the STV field. We also study the collisions of test particles and analyze how the MOG and black-bounce parameters influence the critical angular momentum of colliding particles and their center of mass energy.

Geodesics structure and deflection angle of electrically charged black holes in gravity with a background Kalb–Ramond field

This article investigates the geodesic structure and deflection angle of charged black holes in the presence of a nonzero vacuum expectation value background of the Kalb–Ramond field. Topics explored include null and timelike geodesics, energy extraction by collisions, and the motion of charged particles. The photon sphere radius is calculated and plotted to examine the effects of both the black hole charge (Q) and the Lorentz-violating parameter (b) on null geodesics. The effective potential for timelike geodesics is analyzed, and second-order analytical orbits are derived. We further show that the combined effects of Lorentz-violating parameter and electric charge can mimic a Kerr black hole spin parameter up to its maximum values, i.e., a/M∼1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$a/M \\sim 1$$\\end{document} thus suggesting that the current precision of measurements of highly spinning black hole candidates may not rule out the effect of Lorentz-violating parameter. The center of mass energy of colliding particles is also considered, demonstrating a decrease with increasing Lorentz-violating parameter. Circular orbiting particles of charged particles are discovered, with the minimum radius for a stable circular orbit decreasing as both b and Q increase. Results show that this circular orbit is particularly sensitive to changes in the Lorentz-violating parameter. Additionally, a timelike particle trajectory is demonstrated as a consequence of the combined effects of parameters b and Q. Finally, the light deflection angle is analyzed using the weak field limit approach to determine the Lorentz-breaking effect, employing the Gauss–Bonnet theorem for computation. Findings are visualized with appropriate plots and thoroughly discussed.

Inter-Satellite Link Prediction with Supervised Learning Based on Kepler and SGP4 Orbits

Distributed Space Systems (DSS) are gaining prominence in the space industry due to their ability to increase mission performance by allowing cooperation and resource sharing between multiple satellites. In DSS where communication between heterogeneous satellites is necessary, achieving autonomous cooperation while minimizing energy consumption is a critical requirement, particularly in sparse constellations with nano-satellites. In order to minimize the functioning time and energy consumed by the Inter-Satellite Links established for satellite-to-satellite communication, their temporal encounters must be anticipated. This work proposes an autonomous solution based on Supervised Learning that allows heterogeneous satellites in circular polar Low-Earth Orbits to predict their close-approach encounters given the Orbital Elements. The model performance is evaluated and compared in two different scenarios: (1) a simplified scenario assuming Kepler orbits and (2) a realistic scenario assuming Simplified General Perturbations 4 orbital model. The obtained results demonstrate a Balanced Accuracy exceeding 95% when compared to realistic data from an available database. This work represents a promising initial stage in developing an alternative approach within the field of DSS.