Radius Of Star Research Articles

Relativistic model for anisotropic compact stars in embedding class-I spacetime

In the present article, we introduce a completely new regular model for static, spherically symmetric celestial fluid spheres in embedding class I spacetime. In this regard, needfully, we propose a new suitable metric potential e λ(r) to generate the present model. The various analyses on energy density, pressure, anisotropic factor, mass, compactness parameter, redshift, and energy condition make sure the model is physically viable on the ground of model stars Vela X-1, Cen X-3, SMC X-4, and LMC X-4. The reported solutions also respect the equilibrium state by satisfying the Tolman–Oppenheimer–Volkoff (TOV) equation and ensure stability by satisfying the causality condition, condition on the adiabatic index, and Harrison–Zeldovich–Novikov condition. The generated M − R graph matches the ranges of masses and radii for the model compact stars. Additionally, this study provides estimates of the moment of inertia based on the I − M graph.

Dark energy effects on surface gravitational redshift and Keplerian frequency of neutron stars

Research on the properties of neutron stars with dark energy is a particularly interesting yet unresolved problem in astrophysics. We analyze the influence of dark energy on the equation of state, the maximum mass, the surface gravitational redshift and the Keplerian frequency for the traditional neutron star and the hyperon star matter within the relativistic mean field theory, using the GM1 and TM1 parameter sets by considering the two flavor symmetries of SU(6) and SU(3) combined with the observations of PSR J1614-2230, PSR J0348+0432, PSR J0030+0451, RX J0720.4-3125, and 1E 1207.4-5209. It is found that the existence of dark energy leads to the softened equations of the state of the traditional neutron star and the hyperon star. The radius of a fixed-mass traditional neutron star (or hyperon star) with dark energy becomes smaller, which leads to increased compactness. The existence of dark energy can also enhance the surface gravitational redshift and the Keplerian frequency of traditional neutron stars and hyperon stars. The growth of the Keplerian frequency may cause the spin rate to speed up, which may provide a possible way to understand and explain the pulsar glitch phenomenon. Specifically, we infer that the mass and the surface gravitational redshift of PSR J1748-2446ad without dark energy for the GM1 (TM1) parameter set are 1.141 M ⊙ (1.309 M ⊙) and 0.095 (0.105), respectively. The corresponding values for the GM1 (TM1) parameter set are 0.901 M ⊙ (1.072M ⊙) and 0.079 (0.091) if PSR J1748-2446ad contains dark energy with α = 0.05. PSR J1748-2446ad may be a low-mass pulsar with a lower surface gravitational redshift under our selected models.

Re-visiting the role of short-range correlations on neutron-star properties

The impact of short-range correlations (SRCs) on neutron star (NS) properties are re-examined across various classes of relativistic mean-field (RMF) models. The coupling strengths of the models are so adjusted that the low-density part of the equation of state (EoS), complemented with saturation properties such as binding energy of symmetric nuclear matter and nuclear symmetry energy responsible for the bulk properties of finite nuclei, remains practically unaffected with the inclusion of SRCs. The EoS for symmetric nuclear matter and the nuclear symmetry energy at supra-saturation densities which governs the EoS for NS matter become softer or stiffer in the presence of the SRCs, depending on the type of RMF model considered. These distinct effects of SRCs are observed to be more significant at higher densities, as expected, when behaviour of the EoS at low densities, which govern the finite nuclei physics, is not compromised. For most of the models with self-couplings of scalar and vector mesons, the EoS of symmetric nuclear matter stiffens, with a slight effect on nuclear symmetry energy with the inclusion of SRCs. Conversely, in the models incorporating cross-couplings between mesons, the addition of SRCs leads to softer symmetry energy, compensating the stiffening effect of the EoS of symmetric nuclear matter. With the inclusion of SRCs, the values of radius and tidal deformability of canonical mass star and maximum mass of NSs for realistic EoSs align well the present constraints on astrophysical observations.

A NICER View of PSR J1231−1411: A Complex Case

Recent constraints on neutron star mass and radius have advanced our understanding of the equation of state (EOS) of cold dense matter. Some of them have been obtained by modeling the pulses of three millisecond X-ray pulsars observed by the Neutron Star Interior Composition Explorer (NICER). Here, we present a Bayesian parameter inference for a fourth pulsar, PSR J1231−1411, using the same technique with NICER and XMM-Newton data. When applying a broad mass-inclination prior from radio timing measurements and the emission region geometry model that can best explain the data, we find likely converged results only when using a limited radius prior. If limiting the radius to be consistent with the previous observational constraints and EOS analyses, we infer the radius to be 12.6 ± 0.3 km and the mass to be 1.04−0.03+0.05 M ⊙, each reported as the posterior credible interval bounded by the 16% and 84% quantiles. If using an uninformative prior but limited between 10 and 14 km, we find otherwise similar results, but Req=13.5−0.5+0.3 km for the radius. In both cases, we find a nonantipodal hot region geometry where one emitting spot is at the equator or slightly above, surrounded by a large colder region, and where a noncircular hot region lies close to southern rotational pole. If using a wider radius prior, we only find solutions that fit the data significantly worse. We discuss the challenges in finding the better fitting solutions, possibly related to the weak interpulse feature in the pulse profile.

Magnetic Field Evolution for Crystallization-driven Dynamos in C/O White Dwarfs

We investigate the evolution of magnetic fields generated by the crystallization-driven dynamo in carbon–oxygen white dwarfs (WDs) with masses ≲1.05 M ⊙. We use scalings for the dynamo to demonstrate that the initial magnetic field strength (B 0) has an upper limit that depends on the initial convection zone size (R out,0) and the WD mass. We solve the induction equation to follow the magnetic field evolution after the dynamo phase ends. We show that the predicted surface magnetic field strength (B surf) differs from B 0 by at least a factor of ∼0.3. This reduction depends on R out,0, where values smaller than half of the star radius give B surf ≲ 0.01 B 0. We implement electrical conductivities that account for the solid phase effect on the ohmic diffusion. We observe that the conductivity increases as the solid core grows, freezing in the magnetic field at a certain point of the evolution and slowing its outward transport. We study the effect of turbulent magnetic diffusivity induced by the convection and find that for a small R out,0, B surf is stronger than the nonturbulent diffusion cases because of the more rapid transport, but still orders of magnitude smaller than B 0. Given these limitations, the crystallization-driven dynamo theory could explain only magnetic C/O WDs with field strengths less than a few megagauss for the mass range 0.45–1.05 M ⊙. Our results also suggest that a buried fossil field must be at least 100 times stronger than observed surface fields if crystallization-driven convection is responsible for its transport to the surface.

Differential rotation in neutron stars at finite temperatures

IntroductionThis paper investigates the impact of differential rotation on the bulk properties and onset of rotational instabilities in neutron stars at finite temperatures up to 50 MeV.MethodsUtilizing the relativistic Brueckner-Hartree-Fock (RBHF) formalism in full Dirac space, the study constructs equation of state (EOS) models for hot neutron star matter, including conditions relevant for high temperatures. These finite-temperature EOS models are applied to compute the bulk properties of differentially rotating neutron stars with varying structural deformations.ResultsThe findings demonstrate that the stability of these stars against bar-mode deformation, a key rotational instability, is only weakly dependent on temperature. Differential rotation significantly affects the maximum mass and radius of neutron stars, and the threshold for the onset of bar-mode instability shows minimal sensitivity to temperature changes within the examined range.DiscussionThese findings are crucial for interpreting observational data from neutron star mergers and other high-energy astrophysical events. The research underscores the necessity of incorporating differential rotation and finite temperature effects in neutron star models to predict their properties and stability accurately.

Optimised use of interferometry, spectroscopy, and stellar atmosphere models for determining the fundamental parameters of stars

Thanks to recent progress in the field of optical interferometry, instrument sensitivities have now reached the level achieved in the domain of new space missions dedicated to exoplanet and stellar studies. Combining interferometry with other observational approaches enables the determination of stellar parameters and helps improve our understanding of stellar physics. In this paper, we aim to demonstrate a new way of using stellar atmosphere models for a joint interpretation of spectroscopic and interferometric observations. Starting from a discrete grid of one-dimensional (1D) stellar atmosphere models, we developed a training algorithm, based on an artificial neural network, capable of estimating the spectrum and intensity profile of a star over a range of wavelengths and viewing angles. A minimisation algorithm based on the trained function allowed for the simultaneous fitting of the observational spectrum and interferometric complex visibilities. As a result, coherent and precise stellar parameters can be extracted. We show the ability of the trained function to match the modelled intensity profiles of stars in the effective temperature range of $4500$ K to $7000$ K and surface gravity range of $3$ to $5$ dex, with a relative precision to the model that is better than $0.05<!PCT!>$. Using simulated interferometric data and actual spectroscopic measurements, we demonstrated the performance of our algorithm on a sample of five benchmark stars. Using this method, we achieved an accuracy within $0.5<!PCT!>$ for the angular diameter, radius, and surface gravity, and within $20$ K for the effective temperature. This paper demonstrates a new method of using interferometric data combined with spectroscopic observations. This approach offers an improved determination of the radius, effective temperature, and surface gravity of stars.

Measuring neutron star radius with second and third generation gravitational wave detector networks

Abstract The next generation of ground-based interferometric gravitational wave detectors will observe mergers of black holes and neutron stars throughout cosmic time. A large number of the binary neutron star merger events will be observed with extreme high fidelity, and will provide stringent constraints on the equation of state of nuclear matter. In this paper, we investigate the systematic improvement in the measurability of the equation of state with increase in detector sensitivity by combining constraints obtained on the radius of a $1.4 \, \mathrm{M}_{\odot}$ neutron star from a simulated source population. Since the measurability of the equation of state depends on its stiffness, we consider a range of realistic equations of state that span the current observational constraints. We show that a single 40km Cosmic Explorer detector can pin down the neutron star radius for a soft, medium and stiff equation of state to an accuracy of 10m within a decade, whereas the current generation of ground-based detectors like the Advanced LIGO-Virgo network would take $\mathcal{O}(10^5)$ years to do so for a soft equation of state. 

Role of local anisotropy in hybrid stars

Using the Bower–Liang model, we discuss how pressure anisotropies affect the microscopic and macroscopic properties of hybrid stars. We find that anisotropies affect the maximum mass, central density, and radius of the canonical stars. Anisotropies also affect the minimum neutron star mass that presents quarks in their core, as well as the total amount of quarks for the maximally massive stars. We also confront our results with standard constraints, such as the radius and the tidal parameter of the canonical star, as well as the mass and radius of the PSR J0740+6620 pulsar. We observe that moderate values for anisotropies could fulfill these constraints simultaneously. On the other hand, within more extreme degrees of anisotropies, more speculative constraints such as black widow pulsars PSR J0952-0607 and the mass-gap object in the GW190814 event can be explained as hybrid stars. We also investigate the role of anisotropies in the neutron stars’ moment of inertia.

Slowly rotating charged Bardeen stellar structure

This paper is devoted to investigating the dynamics of charged stellar structures with Bardeen exterior geometry. For this purpose, firstly a proposed metric coefficient is utilized, which is defined as a=N1+2hr2m/2. Here, h and N are arbitrary constants determined from matching conditions and m is a positive integer. The pressure and density profiles are found to be positive and monotonically decreasing, with maximum values occurring at the center. Furthermore, the energy conditions and causality conditions are satisfied, and the adiabatic index falls within an acceptable range. The second part of the paper focuses on the dynamics of rotating stars. Numerical values for relevant parameters are assumed to obtain the masses and radii of stars within the desired range. Five different compact stars, namely, VelaX−1, CenX−3, 4U1820−30, 4U1608−52, and PSR1903+327, are considered. The behavior of the moment of inertia of the sphere against the solar mass is investigated, revealing an increase in the moment of inertia with an increase in solar mass. Furthermore, the relationships of mass and energy density against the radius of the compact structure exhibit natural behavior, supporting the acceptability of the analysis. Overall, the study supports the existence of realistic charged compact structures with Bardeen exterior geometry.

Axion star condensation around primordial black holes and microlensing limits

We present novel findings concerning the parameter space of axion stars, extended object forming in dense dark matter environments through gravitational condensation. We emphasize their formation within the dense minihalos that potentially surround primordial black holes and in axion miniclusters. Our study investigates the relation between the radius and mass of an axion star in these dense surroundings, revealing distinct morphological characteristics compared to isolated scenarios. We explore the implications of these results when applied to the bound state between a primordial black hole and an axion star and the gravitational microlensing from extended objects, leading to insights on the observational constraints from such “halo” axion stars. We provide a constraint on the fraction of the galactic population of axion stars from their contribution to the microlensing events from the EROS-2 survey, using the numerical resolution of the Schrödinger-Poisson equation.

Discovery of SRGA J144459.2−604207 with the SRG/ART-XC telescope: A well-tempered bursting accreting millisecond X-ray pulsar

We report the discovery of the new accreting millisecond X-ray pulsar SRGA J144459.2−604207 using data of the SRG/ART-XC. The source was observed twice in February 2024 during the declining phase of the outburst. The timing analysis revealed a coherent signal near 447.9 Hz modulated by the Doppler effect due to the orbital motion. The derived parameters for the binary system are consistent with a circular orbit with a period of ∼5.2 h. The pulse profiles of the persistent emission, showing a sine-like part during half a period with a plateau in between, can be well modeled by emission from two circular spots that are partially eclipsed by the accretion disk. Additionally, during our observations with an exposure of 133 ks, we detected 19 thermonuclear X-ray bursts. All bursts have similar shapes and energetics, and none show any signs of an expanding photospheric radius. The burst recurrence times decreases linearly from ∼1.6 h at the beginning of observations to ∼2.2 h at the end and anticorrelate with the persistent flux. The spectral evolution during the bursts is consistent with the models of the neutron star atmospheres that are heated by accretion and implies a neutron star radius of 11–12 km and a distance to the source of 8–9 kpc. We also detected coherent pulsations during the bursts and showed that the pulse profiles differ substantially from those observed in the persistent emission. However, we could not find a simple physical model explaining the pulse profiles detected during the bursts.

The shadow and gamma-ray bursts of a Schwarzschild black hole in asymptotic safety

Abstract The effects and rules of the dimensionless parameter $\xi$ on neutrino annihilation $\nu+\bar{\nu}\to e^{-}+e^{+}$ dominated gamma-ray bursts are analysed and investigated within the context of black holes in asymptotic safety. We also computationally model photon orbits around black holes, as photons and neutrinos have the same geodesic equations near black holes. We show that the black hole shadow radius decreases with increasing $\xi$. Calculations are made to determine the temperature of the accretion disk surrounding the black hole and the ratio $\dot{Q}/\dot{Q}_{Newt}$ of energy deposition per unit time to that of the Newtonian scenario. The accretion disk temperature peaks at a higher temperature due to quantum gravity corrections, which increases the probability of neutrino emission from the black hole. It is interesting to note that larger quantum gravity effects cause the ratio value to significantly decline. In the neutrino-antineutrino annihilation process, the energy deposition rate is sufficient even while the energy conversion is inhibited because of quantum corrections. Gamma-ray bursts might originate from the corrected annihilation process. Additionally, we examine the derivative $\mathrm{d}\dot{Q}/\mathrm{d}r$ about the star radius $r$. The findings demonstrate that the ratio is lowered by the black hole's quantum influence. The neutrino pair annihilation grows weaker the more prominent the influence of quantum gravity is.

Suggested magnetic braking prescription derived from field complexity fails to reproduce the cataclysmic variable orbital period gap

Magnetic wind braking drives the spin-down of low-mass stars and the evolution of most interacting binary stars. A magnetic braking prescription that was claimed to reproduce both the period distribution of cataclysmic variables (CVs) and the evolution of the rotation rates of low-mass stars is based on a relation between the angular momentum loss rate and magnetic field complexity. The magnetic braking model based on field complexity has been claimed to predict a detached phase that could explain the observed period gap in the period distribution of but has never been tested in detailed models of evolution. Here we fill this gap. We incorporated the suggested magnetic braking law in MESA and simulated the evolution of for different initial stellar masses and initial orbital periods. We find that the prescription for magnetic braking based on field complexity fails to reproduce observations of The predicted secondary star radii are smaller than measured, and an extended detached phase that is required to explain the observed period gap (a dearth of non-magnetic with periods sim 2$ and $ sim 3$ hours ) is not predicted. Proposed magnetic braking prescriptions based on a relation between the angular momentum loss rate and field complexity are too weak to reproduce the bloating of donor stars in derived from observations and, in contrast to previous claims, do not provide an explanation for the observed period gap. The suggested steep decrease in the angular momentum loss rate does not lead to detachment. Stronger magnetic braking prescriptions and a discontinuity at the fully convective boundary are needed to explain the evolution of close binary stars that contain compact objects. The tension between braking laws derived from the spin-down of single stars and those required to explain and other close binaries containing compact objects remains.

Bulk properties of nuclear matter in a modified relativistic dirac formalism

In this study, we employ a phenomenologically modified relativistic Dirac framework coupled with the σ - ω quark-meson coupling model to look into the properties of nuclear matter. By combining scalar and vector linear potential forms and incorporating perturbative adjustments for various factors such as centre-of-mass motion, gluonic, and pionic effects, we aim to find the nucleon’s mass in a vacuum. Then, we consider nucleon-nucleon interactions are constructed within a mean-field approximation. Our methodology systematically explores key characteristics of nuclear matter, including equations of state, compressibility, binding energy, and pressure. Furthermore, we compute essential parameters such as the nucleon charge radius, axial-vector coupling constant, pion coupling constant, nuclear sigma term, sensitivity, and potential strengths. And also, we calculate symmetry energy, density slop (L) and incompressibility ( K0 ). In addition, we compute the mass and radius of a neutron star and provide a graphical representation illustrating the relationship between mass and radius. To validate our results, we comprehensively compare them with other theoretical models and quark-meson coupling approaches, confirming the precision and reliability of our theoretical paradigm. Overall, our study enhances our understanding of the fundamental properties of nuclear matter and underscores their relevance in elucidating complex astrophysical phenomena.

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.

Exploring the physical properties of anisotropic compact objects and constraining their mass–radius relations beyond standard limit in [formula omitted]-gravity

The progress in theoretical modeling of compact high-mass stars in the context of alternative gravity has become important in minimizing challenges associated with neutron star (NS) radius measurements. On this basis, we have presented a rigorous study of compact objects beyond the standard limit in gravity F(Q) in particular F(Q)=b1Q+b2 where b1 and b2 are constants. After formulating the basic equations and finding their relevant solutions by assuming a well-behaved ansatz for the metric potential as well as for anisotropy monitored by the parameters μ1,μ2,b1, along with imposing the boundary conditions on the system under treatment, we have developed a stellar model for anisotropic stars. Specifically, we explored the physical properties of these anisotropic stars and provided novel mass–radius (M−R) relations with models falling in the mass gap of the events GW190814 and GW200210, as well as the effects of slow rotation and moment of inertia on these findings. Interestingly, the behavior of the M−R curves represents a polytropic-type equation of state (EOS) for a negative Λ, while a positive Λ corresponds to a quark matter EOS. However, the analysis reveals that the predicted radii of the compact object observed in the GW190814 event, with a mass of 2.5–2.67 M⊙, is approximately 11.4 km for the de Sitter (dS) case and 11.8 km for the anti-de Sitter (AdS) case, assuming a specific value of the parameter b1=1.1. Furthermore, for b1>1.1, the model predicts the existence of more compact stars with a maximum mass of approximately 3M⊙, which is in good agreement with the R2 model of NSs maintaining the Sly EOS. From the I−M curves, it can be observed that higher values of b1 and μ1 in F(Q) gravity can sustain high moments of inertia (I) of stars with high masses. Interestingly, we obtained the range of I for the dS space as [1.92,3.92]×1045gcm2 and for the AdS space as [2.01,4.03]×1045gcm2 for 1.0≤b1≤1.2.

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.

The role of pressure anisotropy on quark stars in gravity’s rainbow

This work is seeking for the existence of stable quark stars (QSs) in the framework of a modified theory of gravity known as gravity’s rainbow. This modification comes from the fact that the geometry of spacetime depends on the energy of the test particle. We solve numerically the modified TOV equations and present the mass–radius (M–R) diagram for quark matter equations of state. To constrain the allowed values of the model parameters, we use current astrophysical measurements of the masses and radii of neutron stars. Finally, we investigate the dynamical stability of the hydrostatic equilibrium equations in gravity’s rainbow by analyzing the static stability, adiabatic index, and sound velocity profiles.

Non-monotonic relations of galaxy star formation, radius, and structure at fixed stellar mass

ABSTRACT We investigate the relation between galaxy structure and star formation rate (SFR) in a sample of $\sim 2.9\times 10^{4}$ central galaxies with $z\lt 0.0674$ and axial ratios $b/a\gt 0.5$. The star-forming main sequence (SFMS) shows a bend around the stellar mass of $M_\ast \le {}M_c=2\times 10^{10}{}{\rm M}_{\odot }$. At $M_\ast \le {}M_c$, the SFMS follows a power-law $\text{SFR}\propto {}M_\ast ^{0.85}$, while at higher masses it flattens. $M_c$ corresponds to a dark matter halo mass of $M_\text{vir}\sim {}10^{11.8}{\rm M}_{\odot }$ where virial shocks occurs. Some galaxy structure (e.g. half-light radius, $R_e$) exhibits a non-monotonic dependence across the SFMS at a fixed $M_\ast$. We find $\text{SFR}\propto {R_e^{-0.28}}$ at fixed $M_\ast$, consistent with the global Kennicutt–Schmidt (KS) law. This finding suggests that galaxy sizes contribute to the scatter of the SFMS. However, at $M_\ast \gt M_c$ the relationship between SFR and $R_e$ diminishes. Low-mass galaxies above the mean of the SFMS have smaller radii, exhibit compact and centrally concentrated profiles resembling green valley (GV) and quiescent galaxies at the same mass, and have higher $M_{\text{H}_2}{/}M_\rm{H\,{\small I}}$. Conversely, those below the SFMS exhibit larger radii, lower densities, have no GV or quiescent counterparts at their mass and have lower $M_{\text{H}_2}/M_\rm{H\,{\small I}}$. The above data suggest two pathways for quenching low-mass galaxies, $M_\ast \le {}M_c$: a fast one that changes the morphology on the SFMS and a slow one that does not. Above $M_c$, galaxies below the SFMS resemble GV and quiescent galaxies structurally, implying that they undergo a structural transformation already within the SFMS. For these massive galaxies, CG are strongly bimodal, with SFMS galaxies exhibiting negative colour gradients, suggesting most star formation occurs in their outskirts, maintaining them within the SFMS.