PSR J1614-2230 Research Articles

Bayesian inference of multi-messenger astrophysical data: Joint and coherent inference of gravitational waves and kilonovae

Context. Multi-messenger observations of binary neutron star mergers can provide information on the neutron star’s equation of state (EOS) above the nuclear saturation density by directly constraining the mass-radius diagram. Aims. We present a Bayesian framework for joint and coherent analyses of multi-messenger binary neutron star signals. As a first application, we analyze the gravitational-wave GW170817 and the kilonova (kN) AT2017gfo data. These results are then combined with the most recent X-ray pulsar analyses of PSR J0030+0451 and PSR J0740+6620 to obtain new EOS constraints. Methods. We extend the bajes infrastructure with a joint likelihood for multiple datasets, support for various semi-analytical kN models, and numerical-relativity (NR)-informed relations for the mass ejecta, as well as a technique to include and marginalize over modeling uncertainties. The analysis of GW170817 used the TEOBResumS effective-one-body waveform template to model the gravitational-wave signal. The analysis of AT2017gfo used a baseline multicomponent spherically symmetric model for the kN light curves. Various constraints on the mass-radius diagram and neutron star properties were then obtained by resampling over a set of ten million parameterized EOSs, which was built under minimal assumptions (general relativity and causality). Results. We find that a joint and coherent approach improves the inference of the extrinsic parameters (distance) and, among the intrinsic parameters, the mass ratio. The inclusion of NR-informed relations marks a strong improvement over the case in which an agnostic prior is used on the intrinsic parameters. Comparing Bayes factors, we find that the two observations are better explained by the common source hypothesis only by assuming NR-informed relations. These relations break some of the degeneracies in the employed kN models. The EOS inference folding-in PSR J0952-0607 minimum-maximum mass, PSR J0030+0451 and PSR J0740+6620 data constrains, among other quantities, the neutron star radius to R1.4TOV = 12.30− 0.56+ 0.81 km(R1.4TOV = 13.20− 0.90+ 0.91 km) and the maximum mass to MmaxTOV = 2.28− 0.17+ 0.25M⊙(MmaxTOV = 2.32− 0.19+ 0.30M⊙), where the ST+PDT (PDT-U) analysis of Vinciguerra et al. (2024, ApJ, 961, 62) for PSR J0030+0451 was employed. Hence, the systematics on the PSR J0030+0451 data reduction currently dominate the mass-radius diagram constraints. Conclusions. We conclude that bajes delivers robust analyses in line with other state-of-the-art results in the literature. Strong EOS constraints are provided by pulsars observations, albeit with large systematics in some cases. Current gravitational-wave constraints are compatible with pulsar constraints and can further improve the latter.

Modeling Compact Object Mergers GW190814 and GW200210 and Other Self-bound Compact Stars with Dark Matter Induced by Gravitational Decoupling and Its Significance to the Mass Gap

We present a rigorous study of compact objects within f(Q) gravity where electrical fields and dark matter are studied and provide novel mass–radius relations with models falling in the mass gap of the events GW190814 and GW200210. After formulating the basic equations and finding their relevant solutions, we impose the boundary conditions on the system under treatment. The decoupled solution for the strange stellar model with the dark matter density profile is obtained. The distribution patterns of the effective energy density and the radial as well as the tangential pressure and anisotropy in the system are intensively examined. The stability properties of the stellar configuration and the influence of dark matter are studied. The recent observations of supermassive compact star candidates such as PSR J1614–2230 and PSR J0952–0607 with observed masses greater than or equal to 2 M ⊙ have been employed in our study. Interestingly, the present study predicts the constraints on mass–radius measurements of the observed stars satisfying the equation of state based on the MIT bag model and employing the condition of mimicking, i.e., ρ θ = χ1ρPI in f(Q) gravity. Our graphical results exhibit that for a particular M–R curve with fixed values of the parameters, neutron stars having mass less than M max exist with larger radii within the context of the f(Q) formalism.

Stellar Modeling via the Tolman IV Solution: The Cases of the Massive Pulsar J0740+6620 and the HESS J1731-347 Compact Object

We model compact objects of known stellar mass and radius made of isotropic matter within Einstein’s gravity. The interior solution describing hydrostatic equilibrium we are using throughout the manuscript corresponds to the Tolman IV exact analytic solution obtained a long time ago. The three free parameters of the solutions are determined by imposing the matching conditions for objects of known stellar mass and radius. Finally, using well established criteria, it is shown that, contrary to the Kohler Chao solution, the Tolman IV solution is compatible with all requirements for well-behaved and realistic solutions, except for the relativistic adiabatic index that diverges at the surface of stars. The divergence of the index Γ may be resolved, including a thin crust assuming a polytropic equation of state, which is precisely the case seen in studies of neutron stars. To the best of our knowledge, we model here for the first time the recently discovered massive pulsar PSR J0740+6620 and the strangely light HESS compact object via the Tolman IV solution. The present work may be of interest to model builders as well as a useful reference for future research.

Modeling compact objects with quark matter and dark energy: A comparative study of the radial oscillation modes of HESS J1731-347 and PSR J0740+6620

We model the massive pulsar J0740+6620 and the light HESS J1731-347 compact object assuming (i) quark matter and (ii) dark energy stars. Within Einstein’s General Relativity, and assuming objects made of isotropic matter, we adopt analytic equations-of-state for both matter contents. Although the inner composition of the objects is very different in each case, both equations-of-state imply qualitatively very similar mass-to-radius relationships. We compute the spectra of radial equations for all four cases and the corresponding wave functions as well as the large frequency separations. A comparison between the different matter contents is made as well.

The NANOGrav 15 yr Data Set: Chromatic Gaussian Process Noise Models for Six Pulsars

Abstract Pulsar timing arrays (PTAs) are designed to detect low-frequency gravitational waves (GWs). GWs induce achromatic signals in PTA data, meaning that the timing delays do not depend on radio frequency. However, pulse arrival times are also affected by radio-frequency-dependent “chromatic” noise from sources such as dispersion measure (DM) and scattering delay variations. Furthermore, the characterization of GW signals may be influenced by the choice of chromatic noise model for each pulsar. To better understand this effect, we assess if and how different chromatic noise models affect the achromatic noise properties in each pulsar. The models we compare include existing DM models used by the North American Nanohertz Observatory for Gravitational waves (NANOGrav) and noise models used for the European PTA Data Release 2 (EPTA DR2). We perform this comparison using a subsample of six pulsars from the NANOGrav 15 yr data set, selecting the same six pulsars as from the EPTA DR2 six-pulsar data set. We find that the choice of chromatic noise model noticeably affects the achromatic noise properties of several pulsars. This is most dramatic for PSR J1713+0747, where the amplitude of its achromatic red noise lowers from log 10 A RN = − 14.1 − 0.1 + 0.1 to − 14.7 − 0.5 + 0.3 , and the spectral index broadens from γ RN = 2.6 − 0.4 + 0.5 to γ RN = 3.5 − 0.9 + 1.2 . We also compare each pulsar's noise properties with those inferred from the EPTA DR2, using the same models. From the discrepancies, we identify potential areas where the noise models could be improved. These results highlight the potential for custom chromatic noise models to improve PTA sensitivity to GWs.

Self-bound isotropic models in [formula omitted] gravity and effect of [formula omitted] parameter on mass–radius relation and stability of compact objects

The present article investigates the effect of f(Q) parameters on two classes of exact spherically symmetric self-bound isotropic solutions for compact objects. The field equation in f(Q) gravity is solved using Korkina–Orlyanskii and Buchdahl models. The physical validity of both models has been verified using regularity, stability, and hydrostatic equilibrium tests. We have also shown the effect of f(Q) gravity parameter α on the stability and mass–radius relation. We predicted the radii of observable compact objects GW 190814, PSR J0740+6620 PSR J1614, 2230, Cen X-3, and LMC X-4. In the absence of β, the massive neutron star GW 190814 is detected at greater values of α=1.5 and 1.2 for models I and II respectively. The corresponding estimated radii for both models are 15.30−0.29+0.18km and 15.03−0.25+0.17km. Additionally, as the non-metricity scalar α increases, the mass–radius decreases, and when β increases with fix α, the reverse scenario arises. Our finding indicates that a lower mass−gap can be achieved in f(Q) gravity theory as compared to the standard theory of gravity.

Geometrically Deformed Charged Anisotropic Models in f(Q, T) Gravity

AbstractIn this study, the geometrically deformed compact objects in the f(Q, T) gravity theory under an electric field through gravitational decoupling via minimal geometric deformation (MGD) technique are developed for the first time. The decoupled field equations are solved via two different mimic approaches and through the Karmarkar condition. Physical viability tests are conducted on our models and examine how decoupling parameters affect the physical qualities of objects. The obtained models are compared with the observational constraints for neutron stars PSR J1810+174, PSR J1959+2048, and PSR J2215+5135, including GW190814. Particularly, by modifying parameters α and n, the occurrence of a “mass gap” component is accomplished. The resulting models exhibit stable, well‐behaved mass profiles, regular behavior and no gravitational collapse, as verified by the Buchdahl–Andréasson's limit. Furthermore, a thorough physical analysis that is based on two parameters: n (f(Q, T)–coupling parameter) and α (decoupling parameter) is provided. This work extends our current understanding of compact star configurations and sheds light on the behavior of compact objects in the f(Q, T) gravity.

Constraining the Dense Matter Equation of State with New NICER Mass–Radius Measurements and New Chiral Effective Field Theory Inputs

Pulse profile modeling of X-ray data from the Neutron Star Interior Composition Explorer is now enabling precision inference of neutron star mass and radius. Combined with nuclear physics constraints from chiral effective field theory (χEFT), and masses and tidal deformabilities inferred from gravitational-wave detections of binary neutron star mergers, this has led to a steady improvement in our understanding of the dense matter equation of state (EOS). Here, we consider the impact of several new results: the radius measurement for the 1.42 M ⊙ pulsar PSR J0437−4715 presented by Choudhury et al., updates to the masses and radii of PSR J0740+6620 and PSR J0030+0451, and new χEFT results for neutron star matter up to 1.5 times nuclear saturation density. Using two different high-density EOS extensions—a piecewise-polytropic (PP) model and a model based on the speed of sound in a neutron star (CS)—we find the radius of a 1.4 M ⊙ (2.0 M ⊙) neutron star to be constrained to the 95% credible ranges 12.28−0.76+0.50 km ( 12.33−1.34+0.70 km) for the PP model and 12.01−0.75+0.56 km ( 11.55−1.09+0.94 km) for the CS model. The maximum neutron star mass is predicted to be 2.15−0.16+0.14 M ⊙ and 2.08−0.16+0.28 M ⊙ for the PP and CS models, respectively. We explore the sensitivity of our results to different orders and different densities up to which χEFT is used, and show how the astrophysical observations provide constraints for the pressure at intermediate densities. Moreover, we investigate the difference R 2.0 − R 1.4 of the radius of 2 M ⊙ and 1.4 M ⊙ neutron stars within our EOS inference.

Anisotropic pressure effect on central EOS of PSR J0740+6620 in the light of dimensionless TOV equation

Abstract It is generally agreed upon that the pressure inside a neutron star is isotropic. However, a strong magnetic field or superfluidity suggests that the pressure anisotropy may be a more realistic model. We derived the dimensionless TOV equation for anisotropic neutron stars based on two popular models, namely the BL model and the H model, to investigate the effect of anisotropy. Similar to the isotropic case, the maximum mass $M_{max}$ and its corresponding radius $R_{Mmax}$ can also be expressed linearly by a combination of radial central pressure $p_{rc}$ and central energy density $\varepsilon_{c}$, which is insensitive to the equation of state (EOS). We also found that the obtained central EOS would change with different values of $\lambda_{BL}$ ($\lambda_{H}$), which controls the magnitude of the difference between the transverse pressure and the radial pressure. Combining with observational data of PSR J0740+6620 and comparing to the extracted EOS based on isotropic neutron star, it is shown that in the BL model, for $\lambda_{BL}$ = 0.4, the extracted central energy density $\varepsilon_{c}$ changed from 546 -- 1056 MeV/fm$^{3}$ to 510 -- 1005 MeV/fm$^{3}$, and the extracted radial central pressure $p_{rc}$ changed from 87 -- 310 MeV/fm$^{3}$ to 76 -- 271 MeV/fm$^{3}$. For $\lambda_{BL}$ = 2, the extracted $\varepsilon_{c}$ and $p_{rc}$ changed to 412 -- 822 MeV/fm$^{3}$ and 50 -- 165 MeV/fm$^{3}$, respectively. In the H model, for $\lambda_{H}$ = 0.4, the extracted $\varepsilon_{c}$ changed to 626 -- 1164 MeV/fm$^{3}$, and the extracted $p_{rc}$ changed to 104 -- 409 MeV/fm$^{3}$. For $\lambda_{H}$ = 2, the extracted $\varepsilon_{c}$ decreased to 894 -- 995 MeV/fm$^{3}$, and the extracted $p_{rc}$ changed to 220 -- 301 MeV/fm$^{3}$.

When the Anomalistic, Draconitic and Sidereal Orbital Periods Do Not Coincide: The Impact of Post-Keplerian Perturbing Accelerations

In a purely Keplerian picture, the anomalistic, draconitic and sidereal orbital periods of a test particle orbiting a massive body coincide with each other. Such degeneracy is removed when post-Keplerian perturbing acceleration enters the equations of motion, yielding generally different corrections to the Keplerian period for the three aforementioned characteristic orbital timescales. They are analytically worked out in the case of the accelerations induced by the general relativistic post-Newtonian gravitoelectromagnetic fields and, to the Newtonian level, by the oblateness of the central body. The resulting expressions hold for completely general orbital configurations and spatial orientations of the spin axis of the primary. Astronomical systems characterized by extremely accurate measurements of orbital periods like transiting exoplanets and binary pulsars may offer potentially viable scenarios for measuring such post-Keplerian features of motion, at least in principle. As an example, the sidereal period of the brown dwarf WD1032 + 011 b is currently known with an uncertainty as small as ≃10−5s, while its predicted post-Newtonian gravitoelectric correction amounts to 0.07s; however, the accuracy with which the Keplerian period can be calculated is just 572 s. For double pulsar PSR J0737–3039, the largest relativistic correction to the anomalistic period amounts to a few tenths of a second, given a measurement error of such a characteristic orbital timescale as small as ≃10−6s. On the other hand, the Keplerian term can be currently calculated just to a ≃9 s accuracy. In principle, measuring at least two of the three characteristic orbital periods for the same system independently would cancel out their common Keplerian component, provided that their difference is taken into account.

Timing irregularities and glitches from the pulsar monitoring campaign at IAR

Pulsars have a very stable rotation overall. However, sudden increases in their rotation frequency, known as glitches, perturb their evolution. While many observatories commonly detect large glitches, small glitches are harder to detect because of the lack of daily cadence observations over long periods of time (years). We aim to explore and characterise the timing behaviour of young pulsars on daily timescales, looking for small glitches and other irregularities, in order to further our comprehension of the real distribution of glitch sizes. Our findings have consequences for the theoretical modelling of the glitch mechanism. We observed six pulsars with up to daily cadence between December 2019 and January 2024 with the two antennas of the Argentine Institute of Radio Astronomy (IAR). We used standard pulsar timing tools to obtain the times of arrival of the pulses and to characterise the pulsar's rotation. We developed an algorithm to look for small timing events in the data and calculate the changes in the frequency (nu ) and its derivative ($ at those epochs. We find that the rotation of all pulsars in this dataset is affected by small step changes in nu and $ Among them, we find three new glitches that have not been reported before: two glitches in PSR J1048$-$5832 with relative sizes of $ $ and $ $, and one glitch in the Vela pulsar with a size of $ $. We also report new decay terms on the 2021 Vela giant glitch, and on the 2022 giant glitches in PSR J0742$-$2822 and PSR J1740$-$3015, respectively. In addition, we find that the red noise contribution significantly diminished in PSR J0742$-$2822 after its giant glitch in 2022. Our results highlight the importance of high-cadence monitoring with an exhaustive analysis of the residuals to better characterise the distribution of glitch sizes and to deepen our understanding of the mechanisms behind glitches, red noise, and timing irregularities.

Relativistic Brueckner–Hartree–Fock Calculations for Cold and Hot Neutron Stars

This study investigates the properties of symmetric and asymmetric nuclear matter using the relativistic Brueckner–Hartree–Fock formalism, examining both zero and finite temperatures up to 70 MeV. Employing the full Dirac space, we incorporate three Bonn potentials (A, B, and C), which account for meson masses, coupling strengths, cutoff parameters, and form factors. The calculated properties of asymmetric nuclear matter form the basis for constructing equation-of-state (EOS) models tailored for neutron stars. These models, in turn, enable the computation of bulk properties for nonrotating, uniformly rotating, and differentially rotating neutron stars. Notably, the EOS models studied in this paper are sufficiently versatile to accommodate the mass of the most massive neutron star ever detected, PSR J0952–0607, estimated to be 2.35 ± 0.17 M ⊙. Furthermore, they yield masses and radii for PSR J0030+451 that align with the confidence intervals established for this pulsar.

Astrophysical Equation-of-State Constraints on the Color-Superconducting Gap.

We demonstrate that astrophysical constraints on the dense-matter equation of state place an upper bound on the color-superconducting gap in dense matter above the transition from nuclear matter to quark matter. Pairing effects in the color-flavor locked quark matter phase increase the pressure at high density, and if this effect is sufficiently large then the requirements of causality and mechanical stability make it impossible to reach such a pressure in a way that is consistent with what is known at lower densities. The intermediate-density equation of state is inferred by considering extensions of chiral effective field theory to neutron star densities, and conditioning these using current astrophysical observations of neutron star radius, maximum mass, and tidal deformability (PSR J0348+0432, PSR J1624-2230, PSR J0740+6620, GW170817). At baryon number chemical potential μ=2.6 GeV we find a 95% upper limit on the color-flavor locked pairing gap Δ of 457MeV using overly conservative assumptions and 216MeV with more reasonable assumptions. This constraint may be strengthened by future astrophysical measurements as well as by future advances in high-density QCD calculations.

Analysis of Neutron Star f-mode Oscillations in General Relativity with Spectral Representation of Nuclear Equations of State

We study quasi-normal f-mode oscillations in neutron star (NS) interiors within a linearized general relativistic formalism. We utilize approximately 9000 nuclear equations of state (EOSs) using spectral representation techniques, incorporating constraints on nuclear saturation properties, chiral effective field theory for pure neutron matter, and perturbative quantum chromodynamics for densities pertinent to NS cores. The median values of the f-mode frequency, ν f (damping time, τ f ) for NSs with masses ranging from 1.4 to 2.0 M ⊙ lie between 1.80 and 2.20 kHz (0.13–0.22 s) for our entire EOS set. Our study reveals a weak correlation between f-mode frequencies and individual nuclear saturation properties, prompting the necessity for more intricate methodologies to unveil multiparameter relationships. We observe a robust linear relationship between the radii and f-mode frequencies for different NS masses. Leveraging this correlation alongside NICER observations of PSR J0740+6620 and PSR J0030+0451, we establish constraints that exhibit partial and minimal overlap for observational data from Riley et al. and Miller et al., respectively, with our nucleonic EOS data set. Moreover, NICER data align closely with the radius and frequency values for a few hadron–quark hybrid EOS models. This indicates the need to consider additional exotic particles such as deconfined quarks at suprasaturation densities. We conclude that future observations of the radius or f-mode frequency for more than one NS mass, particularly at the extremes of the viable NS mass scale, would either rule out nucleon-only EOSs or provide definitive evidence in its favor.

Measuring a Gravitomagnetic Effect with the Triple Pulsar PSR J0337+1715

Measuring a Gravitomagnetic Effect with the Triple Pulsar PSR J0337+1715

Bulk Properties of PSR J0030+0451 Inferred with the Compactness Measurement of NICER

In 2019, the Neutron star Interior Composition ExploreR (NICER) mission released its findings on the mass and radius of the isolated neutron star (INS) PSR J0030+0451, revealing a mass of approximately 1.4 solar masses (M ⊙) and a radius near 13 km. However, the recent reanalysis by the NICER collaboration suggests that the available data primarily yield a precise inference of the compactness for this source while the resulting mass and radius are strongly model-dependent and diverse (the 68.3% credible regions just overlap slightly for the ST+PDT and PDT-U models). By integrating this compactness data with the equation of state (EOS) refined by our latest investigations, we have deduced the mass and radius for PSR J0030+0451, delivering estimates of M=1.48−0.10+0.09M⊙ and R=12.38−0.70+0.51km for the compactness found in the ST+PDT model, alongside M=1.47−0.20+0.14M⊙ and R=12.37−0.69+0.50km for the compactness in the PDT-U model. These two groups of results are well consistent with each other and the direct X-ray data inference within the ST+PDT model seems to be favored. Additionally, we have calculated the tidal deformability, moment of inertia, and gravitational binding energy for this neutron star. Furthermore, employing these refined EOS models, we have updated mass–radius estimates for three INSs with established gravitational redshifts.

The Relativistic Spin Precession in the Compact Double Neutron Star System PSR J1946+2052

Abstract We observe systematic profile changes in the visible pulsar of the compact double neutron star system PSR J1946+2052 using observations with the Five-hundred-meter Aperture Spherical radio Telescope (FAST). The interpulse of PSR J1946+2052 changed from a single-peak to a double-peak shape from 2018–2021. We attribute this evolution as the result of the relativistic spin precession of the pulsar. With the high sensitivity of FAST, we also measure significant polarization for the first time, allowing us to model this with the precessional rotating vector model. Assuming, to the first order, a circular hollow-cone-like emission beam pattern and taking the validity of general relativity (GR), we derive the binary’s orbital inclination angle ( 63 ∘ − 3 ∘ + 5 ∘ ) and pulsar’s spin geometry. The pulsar’s spin vector and the orbital angular momentum vector are found to be only slightly misaligned ( 0. ∘ 21 − 0. ∘ 10 + 0. ∘ 28 ). The quoted uncertainties do not reflect the systematic uncertainties introduced by our model assumptions. By simulating future observations of profile and polarization evolution, we estimate that we could constrain the precession rate within a 43% uncertainty in 9 yr. Hence, we suggest that the system’s profile evolution could be combined with precise pulsar timing to test GR in the future.

High-cadence Timing of Binary Pulsars with CHIME

We performed near-daily observations of the binary pulsars PSR J0218+4232, PSR J1518+4904, and PSR J2023+2853 with the Canadian Hydrogen Intensity Mapping Experiment (CHIME). For the first time, we detected the Shapiro time delay in all three pulsar binary systems, using only 2–4 yr of CHIME/Pulsar timing data. We measured the pulsar masses to be 1.49−0.20+0.23 M ⊙, 1.470−0.034+0.030 M ⊙, and 1.50−0.38+0.49 M ⊙, respectively. The companion mass to PSR J0218+4232 was found to be 0.179−0.016+0.018 M ⊙. We constrained the mass of the neutron star companion of PSR J1518+4904 to be 1.248−0.029+0.035 M ⊙, using the observed apsidal motion as a constraint on the mass estimation. The binary companion to PSR J2023+2853 was found to have a mass of 0.93−0.14+0.17 M ⊙; in the context of the near-circular orbit, this mass estimate suggests that the companion to PSR J2023+2853 is likely a high-mass white dwarf. By comparing the timing model obtained for PSR J0218+4232 with previous observations, we found a significant change in the observed orbital period of the system of Pḃ=0.14(2)×10−12 ; we determined that this variation arises from “Shklovskii acceleration” due to the relative motion of the binary system, and used this measurement to estimate a distance of d = (6.7 ± 1.0) kpc to PSR J0218+4232. This work demonstrates the capability of high-cadence observations, enabled by the CHIME/Pulsar system, to detect and refine general-relativistic effects of binary pulsars over short observing timescales.

Anisotropic Durgapal–Fuloria neutron stars in f(ℛ,T2) gravity

The main purpose of this paper is to obtain physically stable stellar models coupled with anisotropic matter distribution in the context of [Formula: see text] theory. For this, we consider a static spherical geometry and formulate modified field equations containing various unknowns such as matter determinants and metric potentials. We then obtain a unique solution to these equations by employing Durgapal–Fuloria ansatz possessing a constant doublet. We also use matching criteria to calculate the values of these constants by considering the Schwarzschild exterior spacetime. Two different viable models of this modified theory are adopted to analyze the behavior of effective matter variables, anisotropy, energy conditions, compactness and redshift in the interiors of Her X-1, PSR J0348-0432, LMC X-4, SMC X-1, Cen X-3, and SAX J 1808.4-3658 star candidates. We also check the stability of these models by using three different physical tests. It is concluded that our considered stars satisfy all the physical requirements and are stable in this modified gravity for the considered parametric values.

Physical properties and maximum allowable mass-radius relation of complexity-free compact stellar objects within modified gravity formalism* *The authors MKJ and SKM acknowledge that this work is carried out under TRC Project (BFP/RGP/CBS/22/014). This study is also supported via funding from Prince Sattam bin Abdulaziz University project number (PSAU/2024/R/1445). The authors are thankful to the Deanship of Graduate Studies and Scientific

This paper investigates the physical properties and predicted radii of compact stars generated by the Tolman-IV complexity-free model within the background of modified gravity theory, particularly the -gravity theory, under complexity formalism for a spherically symmetric spacetime proposed by L. Herrera [Phys Rev D 97: 044010, 2018]. By solving the resulting set of differential equations, we obtain the explicit forms of the energy-momentum (EM) tensor components, including the density, radial pressure, and tangential pressure. The influence of the parameter χ on various physical properties of the star is thoroughly investigated. The model undergoes a series of rigorous tests to determine its physical relevance. The findings indicate that the model exhibits regularity, stability, and a surface with vanishing pressure. The boundary of this surface is determined by carefully selecting the parameter space. The complexity method employed in gravity offers an interesting approach for developing astrophysical models that are consistent with observable events as demonstrated by recent experiments. In this regard, we use observational data from the GW190814 event, detected by the LIGO and Virgo observatories, to investigate the validity of the Tolman-IV model in gravity. The analysis includes comparing the model's predictions with the observed characteristics of the compact object involved in the merger. In addition, data from two-millisecond pulsars, PSR J1614-2230 and PSR J0952-0607, are incorporated to further constrain the theoretical theories. However, we present a diagram depicting the relationship between the total mass and radius of the compact object candidates for different values of χ.