Models Of Stars Research Articles

Analysing radio pulsar timing noise with a Kalman filter: a demonstration involving PSR J1359−6038

ABSTRACT In the standard two-component crust-superfluid model of a neutron star, timing noise can arise when the two components are perturbed by stochastic torques. Here it is demonstrated how to analyse fluctuations in radio pulse times of arrival with a Kalman filter to measure physical properties of the two-component model, including the crust-superfluid coupling time-scale and the variances of the crust and superfluid torques. The analysis technique, validated previously on synthetic data, is applied to observations with the Molonglo Observatory Synthesis Telescope of the representative pulsar PSR J1359−6038. It is shown that the two-component model is preferred to a one-component model, with log Bayes factor 6.81 ± 0.02. The coupling time-scale and the torque variances on the crust and superfluid are measured with 90 per cent confidence to be $10^{7.1^{+0.8}_{-0.5}}$$\rm {s}$ and $10^{-24.0^{+0.4}_{-5.6}}$$\rm {rad^2~s^{-3}}$ and $10^{-21.7^{+3.5}_{-0.9}}$$\rm {rad^2~s^{-3}}$, respectively.

Charged anisotropic composite stellar object with strange, polytropic and gaseous matter

In this study, we build a charged star model with three layers with distinct equations of state. The core, intermediate layer, and envelope layer obey linear, polytropic, and Chaplygin equations of state, respectively. The model satisfies the physical requirements for the matter variables, gravitational potentials, and stability conditions. We have generated within-acceptable range masses and radii for stars. We also recover the masses and radii for the stars PSRJ1903+0327, PSRJ1614-2230, SAXJ1808.4-3658, Vela X-1, and EXO1785-248 from earlier investigations which shows astrophysical significance of our model.

Non-radial oscillations in newly born compact star considering effects of phase transition

Abstract The massive stars end their lives by supernova explosions leaving central compact objects that may evolve into neutron stars. Initially, after birth, the star remains hot and gradually cools down. We explore the matter and star properties during this initial stage of the compact stars considering the possibility of the appearance of deconfined quark matter in the core of the star. At the initial stage after the supernova explosion, the occurrence of non-radial oscillation in the newly born compact object is highly possible. Non-radial oscillations are an important source of GWs. There is a high chance for GWs from these oscillations, especially the nodeless fundamental (f-) mode to be detected by next-generation GW detectors. We study the evolution in frequencies of non-radial oscillation after birth considering phase transition and predicting the possible signature for different possibilities of theoretical compact star models.

The Fourier approach and testing for cointegration in LSTAR model

This paper proposes a new logistic smooth transition autoregressive (LSTAR) cointegration test by combining the Fourier function to catch the structural changes that occur over time and the LSTAR model to consider the nonlinearity. Logistic and exponential functions are the main transition functions defining the nonlinearity in STAR models since the exponential smooth transition autoregressive (ESTAR) and LSTAR models can explain the different structures of economic variables. The Fourier approach is a simple and effective way to model the structural changes in time series as an alternative to dummy variables. The most significant advantage of the method is that it does not require prior knowledge about the date, number of breaks, or forms. Monte Carlo simulation results show that the proposed test has good size and power properties for different sample sizes and parameters. The results also revealed that the power performance of the proposed test and the Fourier ESTAR test offered by Güriş and Sedefoğlu (2022) are close to each other. The steps of the Fourier-based tests are illustrated by providing an empirical example of testing the validity of the purchasing power parity (PPP) hypothesis in Türkiye.

Cost-effective prognostic evaluation of breast cancer: using a STAR nomogram model based on routine blood tests.

Breast cancer (BC) is the most common and prominent deadly disease among women. Predicting BC survival mainly relies on TNM staging, molecular profiling and imaging, hampered by subjectivity and expenses. This study aimed to establish an economical and reliable model using the most common preoperative routine blood tests (RT) data for survival and surveillance strategy management. We examined 2863 BC patients, dividing them into training and validation cohorts (7:3). We collected demographic features, pathomics characteristics and preoperative 24-item RT data. BC risk factors were identified through Cox regression, and a predictive nomogram was established. Its performance was assessed using C-index, area under curves (AUC), calibration curve and decision curve analysis. Kaplan-Meier curves stratified patients into different risk groups. We further compared the STAR model (utilizing HE and RT methodologies) with alternative nomograms grounded in molecular profiling (employing second-generation short-read sequencing methodologies) and imaging (utilizing PET-CT methodologies). The STAR nomogram, incorporating subtype, TNM stage, age and preoperative RT data (LYM, LYM%, EOSO%, RDW-SD, P-LCR), achieved a C-index of 0.828 in the training cohort and impressive AUCs (0.847, 0.823 and 0.780) for 3-, 5- and 7-year OS rates, outperforming other nomograms. The validation cohort showed similar impressive results. The nomogram calculates a patient's total score by assigning values to each risk factor, higher scores indicating a poor prognosis. STAR promises potential cost savings by enabling less intensive surveillance in around 90% of BC patients. Compared to nomograms based on molecular profiling and imaging, STAR presents a more cost-effective, with potential savings of approximately $700-800 per breast cancer patient. Combining appropriate RT parameters, STAR nomogram could help in the detection of patient anemia, coagulation function, inflammation and immune status. Practical implementation of the STAR nomogram in a clinical setting is feasible, and its potential clinical impact lies in its ability to provide an early, economical and reliable tool for survival prediction and surveillance strategy management. However, our model still has limitations and requires external data validation. In subsequent studies, we plan to mitigate the potential impact on model robustness by further updating and adjusting the data and model.

Color-flavor locked quark stars in Rastall–Rainbow gravity

We investigate the hydrostatic equilibrium configurations of strange stars within the framework of Rastall–Rainbow theory of gravity. These stars are primarily composed of strange quark matter, with its distribution governed by the color-flavor-locked phase of quark matter equation of state (EoS). Using this EoS, we numerically solve the modified Tolman–Oppenheimer–Volkoff equation to obtain different quark star models. We find that the parameters from this modified gravity have specific contributions to the structure of quark stars and introduce new descriptions for massive celestial bodies. Also, the mass–radius relation strongly depends on the parameters from the considered EoS. Furthermore, we analyze the impact of these parameters on the gravitational redshift and compactness of quark stars.

Effect of nuclear reactions rates and core boundary mixing on the seismology of red clump stars

Context. Modeling of the stars in the red clump (RC), that is, core helium-burning stars that have gone through a He flash, is challenging because of the uncertainties associated with the physical processes in their core and during the helium flash. By probing the internal stellar structure, asteroseismology allows us to constrain the core properties of RC stars and eventually, to improve our understanding of this evolutionary phase. Aims. We aim to quantify the impact on the seismic properties of the RC stars of the two main core modeling uncertainties: core boundary mixing, and helium-burning nuclear reaction rates. Methods. Using the MESA stellar evolution code, we computed models with different core boundary mixing as well as different 3α and 12C(α, γ)16O nuclear reaction rates. We investigated the impact of these parameters on the period spacing ΔΠ, which is a probe of the region around the core. Results. We find that different core boundary mixing schemes yield significantly different period spacings, with differences of 30 s between the maximum ΔΠ value computed with semiconvection and maximal overshoot. We show that an increased rate of 12C(α, γ)16O lengthens the core helium-burning phase, which extends the range of ΔΠ covered by the models during their evolution. This results in a difference of 10 s between the models computed with a nominal rate and a rate multiplied by 2, which exceeds the observational uncertainties. The effect of changing the 3α reaction rate is comparatively small. Conclusions. The core boundary mixing is the main source of uncertainty in the seismic modeling of RC stars. Moreover, the effect of the 12C(α, γ)16O is non-negligible, even though it is difficult to distinguish from the effect of the mixing. This degeneracy could be seen more frequently in the future in the new seismic data from the PLATO mission and through theoretical constraints from numerical simulations.

Production of s-process elements in asymptotic giant branch stars as revealed by Gaia/GSP-Spec abundances

Context. The recent parameterisation by the GSP-Spec module of Gaia/Radial Velocity Spectrometer stellar spectra has produced an homogeneous catalogue of about 174 000 asymptotic giant branch (AGB) stars. Among the 13 chemical elements presented in this Gaia third data release, the abundance of two of them (cerium and neodymium) have been estimated in most of these AGB stars. These two species are formed by slow neutron captures (s-process) in the interior of low- and intermediate-mass stars. They belong to the family of second-peak s-process elements. Aims. We study the content and production rate of Ce and Nd in AGB stars, using the atmospheric parameters and chemical abundances derived by the GSP-Spec module. Methods. We defined a working sample of 19 544 AGB stars with high-quality Ce and/or Nd abundances, selected by applying a specific combination of the GSP-Spec quality flags. We compared these abundances with the yield production predicted by AGB evolutionary models. Results. We first confirmed that the majority of the working sample is composed of AGB stars by estimating their absolute magnitude in the K-band and their properties in a Gaia-2MASS diagram. We also checked that these stars are oxygen-rich AGB stars, as assumed during the GSP-Spec parameterisation. We found a good correlation between the Ce and Nd abundances, confirming the high quality of the derived abundances and that these species indeed belong to the same s-process family. We also found higher Ce and Nd abundances for more evolved AGB stars of similar metallicity, illustrating the successive mixing episodes enriching the AGB star surface in s-process elements formed deeper in their stellar interior. We then compared the observed Ce and Nd abundances with the FRUITY and Monash AGB yields and found that the higher Ce and Nd abundances cannot be explained by AGB stars of masses higher than 5 M⊙. In contrast, the yields predicted by both models for AGB stars with an initial mass between ∼1.5 and ∼2.5 M⊙ and metallicities between ∼−0.5 and ∼0.0 dex are fully compatible with the observed GSP-Spec abundances. Conclusions. This work based on the largest catalogue of high-quality second-peak s-element abundances in oxygen-rich AGB stars allows evolutionary models to be constrained and confirms the fundamental role played by low- and intermediate-mass stars in the enrichment of the Universe in these chemical species.

Streaming instability in neutron star magnetospheres: No indication of soliton-like waves

Context. Coherent radiation of pulsars, magnetars, and fast radio bursts could, in theory, be interpreted as radiation from solitons and soliton-like waves. Solitons are meant to contain a large number of electric charges confined on long timescales and can radiate strongly via coherent curvature emission. However, solitons are also known to undergo a wave collapse, which casts doubts on the correctness of the soliton radio emission models of neutron stars. Aims. We investigated the evolution of the caviton type of solitons self-consistently formed by the relativistic streaming instability and compared their apparent stability in 1D calculations with more generic 2D cases, in which the solitons are seen to collapse. Three representative cases of beam Lorentz factors and plasma temperatures were studied to obtain soliton dispersion properties. Methods. We utilized 1D electrostatic and 2D electromagnetic relativistic particle-in-cell simulations at kinetic microscales. Results. We find that no solitons are generated by the streaming instability in the 2D simulations. Only superluminal L-mode (relativistic Langmuir) waves are produced during the saturation of the instability, but these waves have smaller amplitudes than the waves in the 1D simulations. The amplitudes tend to decrease after the instability has saturated, and only waves close to the light line, ω = ck, remain. Solitons in the 1D approach are stable for γb ≳ 60, but they disappear for low beam Lorentz factors, γb < 6. Conclusions. Our examples show that the superluminal soliton branch that is formed in 1D simulations will not be generated by the relativistic streaming instability when more dimensional degrees of freedom are present. The soliton model cannot, therefore, be used to explain the coherent radiation of pulsars, magnetars, and fast radio bursts – unless one can show that there are alternative plasma mechanisms for the soliton generation.

Tests of Disk-locking in T Tauri Stars of the Orion Nebula Cluster

We look for specific correlations predicted by magnetospheric accretion models for young stars that assume disk-locking using stellar and accretion parameters derived from low-resolution HST-STIS spectra of 33 T Tauri stars in the Orion Nebula Cluster. Our results provide strong support for the correlation predicted by a model that does not constrain the stellar magnetic field to a specific geometry, while little support is found for the correlation that assumes a dipolar stellar field geometry. These results support the conclusions from similar studies of older T Tauri stars in Taurus and NGC 2264 and underscore the role that trapped flux plays in regulating a young star’s angular momentum as detailed by Ostriker & Shu. While our targets were all selected to be accreting young stars based on photometric indices, approximately half of the observed stars show no significant signs of accretion in our spectra, illustrating the difficulty in using photometric indices to find accreting stars and the possible role that variability has in the appearance of spectra in young stars. Although values of accretion luminosity derived from our models agree well with those derived from Hβ luminosity for strongly accreting stars, we find that accretion luminosity derived from Hβ luminosity is not a reliable parameter for discriminating between weakly accreting and nonaccreting T Tauri stars due to chromospheric emission that is likely present in all T Tauri stars.

A two-dimensional perspective of the rotational evolution of rapidly rotating intermediate-mass stars

Context. Recently, the first successful attempt at computing stellar structure and evolution models in two dimensions was presented with models that include centrifugal deformation and self-consistently compute the velocity field. Aims. The aim of the present study is to explore the rotational evolution of two-dimensional models of stars rotating at a significant fraction of their critical angular velocity. From the predictions of these models, we aim to improve our understanding of the formation of single Be stars. Methods. Using the ESTER code, which solves the stellar structure of a rotating star in two dimensions with time evolution, we computed evolution tracks of stars of between 4 and 10 M⊙ for initial rotation rates ranging between 60 and 90% of the critical rotation rate. Furthermore, we compute models for both a Galactic metallicity and an SMC metallicity. Results. A minimum initial rotation rate at the start of the main sequence is needed to spin up the star to critical rotation within its main sequence lifetime. This threshold depends on the stellar mass, and increases with increasing mass. The models do not predict any stars above 8 M⊙ to reach (near-)critical rotation during the main sequence. Furthermore, we find the minimum threshold of initial angular velocity is lower for SMC metallicity than for Galactic metallicity, which is in agreement with the increased fraction of observed Be stars in lower metallicity environments. The strong difference in the rotational evolution between different masses is not predicted by any one-dimensional stellar evolution models. Conclusions. Our self-consistent two-dimensional stellar evolution models provide further insight into the rotational evolution of intermediate-mass stars, and our predictions are consistent with observations of velocity distributions and the fraction of Be stars amongst B-type stars. We find that stars with a mass above 8 M⊙ do not increase their fraction of critical rotation during the main sequence. As a fraction of stars above 8 M⊙ have been observed to display the Be phenomenon, other processes or formation channels must be at play, or, alternatively, critical rotation is not required for the Be phenomenon above this mass.

Physical Correlations and Predictions Emerging from Modern Core-collapse Supernova Theory

In this paper, we derive correlations between core-collapse supernova observables and progenitor core structures that emerge from our suite of 20 state-of-the-art 3D core-collapse supernova simulations carried to late times. This is the largest such collection of 3D supernova models ever generated and allows one to witness and derive testable patterns that might otherwise be obscured when studying one or a few models in isolation. From this panoramic perspective, we have discovered correlations between explosion energy, neutron star gravitational birth masses, 56Ni and α-rich freezeout yields, and pulsar kicks and theoretically important correlations with the compactness parameter of progenitor structure. We find a correlation between explosion energy and progenitor mantle binding energy, suggesting that such explosions are self-regulating. We also find a testable correlation between explosion energy and measures of explosion asymmetry, such as the ejecta energy and mass dipoles. While the correlations between two observables are roughly independent of the progenitor zero-age main-sequence (ZAMS) mass, the many correlations we derive with compactness cannot unambiguously be tied to a particular progenitor ZAMS mass. This relationship depends on the compactness/ZAMS mass mapping associated with the massive star progenitor models employed. Therefore, our derived correlations between compactness and observables may be more robust than with ZAMS mass but can nevertheless be used in the future once massive star modeling has converged.

Angular momentum and chemical transport by azimuthal magnetorotational instability in radiative stellar interiors

Context. The transport of angular momentum and chemical elements within evolving stars remains poorly understood. Asteroseismic and spectroscopic observations of low-mass main sequence stars and red giants reveal that their radiative cores rotate orders of magnitude slower than classical predictions from stellar evolution models and that the abundances of their surface light elements are too small. Magnetohydrodynamic (MHD) turbulence is considered a primary mechanism to enhance the transport in radiative stellar interiors but its efficiency is still largely uncertain. Aims. We explore the transport of angular momentum and chemical elements due to azimuthal magnetorotational instability, one of the dominant instabilities expected in differentially rotating radiative stellar interiors. Methods. We employed 3D MHD direct numerical simulations in a spherical shell of unstratified and stably stratified flows under the Boussinesq approximation. The background differential rotation was maintained by a volumetric body force. We examined the transport of chemical elements using a passive scalar. Results. We provide evidence of magnetorotational instability for purely azimuthal magnetic fields in the parameter regime expected from local and global linear stability analyses. Without stratification and when the Reynolds number Re and the background azimuthal field strength are large enough, we observed dynamo action driven by the instability at values of the magnetic Prandtl number Pm in the range 0.6 − 1, which is the smallest ever reported in a global setup. When considering stable stratification at Pm = 1, the turbulence is transitional and becomes less homogeneous and isotropic upon increasing buoyancy effects. The transport of angular momentum occurs radially outward and is dominated by the Maxwell stresses when stratification is large enough. We find that the turbulent viscosity decreases when buoyancy effects strengthen and scales with the square root of the ratio of the reference rotation rate Ωa to the Brunt–Väisälä frequency N. The chemical turbulent diffusion coefficient scales with stratification similarly to the turbulent viscosity, but is lower in amplitude so that the transport of chemicals is slower than the one of angular momentum, in agreement with recent stellar evolution models of low-mass stars. Conclusions. We show that the transport induced by azimuthal magnetorotational instability scales somewhat slowly with stratification and may enforce rigid rotations of red giant cores on a timescale of a few thousand years. In agreement with recent stellar evolution models of low-mass stars, the instability transports chemical elements less efficiently than angular momentum.

Investigating stable quark stars in Rastall-Rainbow gravity and their compatibility with gravitational wave observations

We present a stable model for quark stars in Rastall-Rainbow (R-R) gravity. The structure of this configuration is obtained by utilizing an interacting quark matter equation of state. The R-R gravity theory is developed as a combination of two distinct theories, namely, the Rastall theory and the gravity's rainbow formalism. Depending on the model parameters (λ¯,η,Σ,Beff), the mass-radius relations are numerically computed for modified Tolman-Oppenheimer-Volkoff (TOV) equations with proper boundary conditions. The stability of equilibrium configuration has been checked through the static stability criterion, adiabatic index and the sound velocity. Our calculations predict larger maximum masses for quark stars, and the obtained results are compatible with accepted masses and radii values, including constraints from GW190814 and GW170817 events in all the studied cases.

Singularity‐Free Charged Compact Star Model Under F(Q)$F(Q)$‐Gravity Regime

AbstractIn this paper, the possibility of existing a novel class of compact charged spheres based on a charged perfect fluid within the realm of gravity theory is explored. The authors started by proposing physically meaningful explicit formulas for the potential, denoted , and the electric field to find a close‐form solution. More precisely, the change of the dependent variable approach by exploiting the transformation is applied. Successively, the field equations analytically are solved and generate the most general solution, which leads us to examine various significant aspects of the stellar system. These aspects comprise the regularity of gravitational potentials, energy density and pressure, electric charge, the mass‐radius relationship, subluminal sound velocities in the radial direction, and the adiabatic index for charged compact stars. For a more in‐depth system study, mass measurements using contour diagrams are carried out. This mainly involves varying the variable parameters and to distinguish their effect on the mass distribution within the stellar structure. What is more, the electric charge controls the stability of the stellar system is shown, which yields that a stable system can possess a maximum charge of order . The results strongly argue that charged stars could conceivably exist in nature and that such a deviation from traditional theories may be seen in future astrophysical observations.

Study on physical properties and maximum mass limit of Finch–Skea anisotropic model under Karmarkar condition in [formula omitted]-gravity

The primary objective of this work is to study the dynamical characteristics of an anisotropic compact star model with spherical symmetry. This investigation is conducted in the framework of modified f(Q) gravity. To simplify the calculations, we employ the Karmarkar condition and derive a differential equation that establishes a relationship between two crucial components of the spacetime namely eν and eλ. Additionally, we incorporate the well-known Finch–Skea structure as the component representing grr and subsequently find the resulting form of the component gtt from the relation of metric functions to formulate the precise solutions for the stellar structure. To assess the behavior of the anisotropic fluid and stability of the compact star, we use the observed values of mass and radius for the compact star model PSRJ0437−4715. The graphical analysis depicts that the stellar structure possesses physical viability and exhibits intriguing properties. Furthermore, we predicted the mass–radius relation along with the maximum mass limit of several objects for different parameter values by assuming two different surface densities. It is discovered that the compactness rises when density increases.

Impact of [formula omitted] gravity on anisotropic compact star model and stability analysis

The aim of this study is to explore the relativistic anisotropic configuration of a hybrid star in the proximity of strange quark matter and normal baryonic matter within the context of f(Q) theory of gravity. To associate pressure and density due to strange quark matter, the MIT bag model equation of state has been exploited. Here, for establishing the dynamical equations, the Krori–Barua ansatz and a linear form of f(Q) have been considered. We further utilize the Schwarzschild metric as an exterior geometry to find the unknown parameters. Furthermore, several physical properties such as energy density, pressure components, anisotropy, sound speeds, energy conditions, compactness factor, etc., have been analyzed through the graphical representation. Additionally, the variation of bag constant Bg and the measurement of the mass have been examined through contour plots. We further study the mass–radius (M−R) relation to determine the maximum permitted mass. According to our analysis, the maximum mass of a hybrid star rises to more than 2 M⊙ when ‘m’ is decreased. For instance, with m=0.2, the mass of the hybrid star is about 2.6M⊙, which is in the lower mass gap and corresponds to the mass of the lighter component of the GW190814 event. Finally, our investigation validates the stability of the suggested model. We came to the conclusion that f(Q) gravity theory can produce super massive hybrid stars and provide a plausible explanation of the M−R relation that satisfies the observable constraints.

Collapsing Shear‐Free Anisotropic Embedding Star Model in f(R)$f(R)$ Gravity

AbstractThe current paper studied the dynamics of shear‐free and spherically symmetric collapsing stars by incorporating the features of anisotropic dissipative fluid in the realm of gravity. A complete radiative star model that describes the early static configuration obeying the embedding class 1 approach is generated. To acquittance the exact solutions of the geometric variables, a specific form of pressure anisotropy along with a time‐dependent Karmarkar condition is employed, leading to a spacetime solution that seems to be potentially reliable and regular throughout the collapse process. The matching conditions have been thoroughly investigated between the interior geometry and the Vaidya outgoing solution over the junction interface. The physical attributes of our solutions to the Einstein field equations under two viable and cosmologically well‐consistent models of are manifested. The presented features are in a stable equilibrium state and sustainable to model a dynamic structure of gravitational collapse without forming the black hole.

Hydrodynamic models of pulsation period evolution in R Hydrae

ABSTRACT Pulsation period evolution during the helium–shell flash in the Mira variable R Hya is investigated using consistent stellar evolution and non-linear stellar pulsation computations. The initial and time-dependent inner boundary conditions for the equations of radiation hydrodynamics describing non-linear stellar oscillations were determined using a grid of TP–AGB model sequences with initial masses on the main sequence 1.5M⊙ ≤ MZAMS ≤ 5.0M⊙ and the initial metallicity Z = 0.014. The setup of initial conditions for hydrodynamic models corresponds to ≈100 yr prior to the maximum of the helium–shell luminosity and ensures that the stellar envelope of the evolution model is under both hydrostatic and thermal equilibrium. Solution of the equations of hydrodynamics allowed us to determine the temporal variation of the pulsation period Π(t) during ≈500 yr. Within this time interval R Hya is a fundamental mode pulsator. The period temporal dependencies Π(t) calculated for the AGB star models at the beginning of the third dredge-up phase and with masses $4.4M_{\odot }\lessapprox M\lessapprox 4.5M_{\odot }$ are in agreement with observational estimates of the period of R Hya obtained during last two centuries. The mean radius of R Hya pulsation models at the end of the XX century ($470 R_{\odot }\lessapprox \bar{R}\lessapprox 490 R_{\odot }$) agrees with observational estimates obtained using the interferometric angular diameter measurements.

Classical Cepheid pulsation properties in the Rubin-LSST filters

ABSTRACT Homogeneous multiwavelength observations of classical Cepheids from the forthcoming Rubin-LSST have the potential to significantly contribute to our understanding of the evolutionary and pulsation properties of these pulsating stars. Updated pulsation models for classical Cepheid stars have been computed under various assumptions about chemical compositions, including relatively low metallicity (Z = 0.004 with Y = 0.25 and Z = 0.008 with Y = 0.25), solar metallicity (Z = 0.02 with Y = 0.28), and supersolar metallicity environments (Z = 0.03 with Y = 0.28). From the predicted periods, intensity-weighted mean magnitudes, and colours, we have derived the first theoretical pulsation relations in the Rubin-LSST filters (ugrizy), including period–luminosity–colour, period–Wesenheit, and period–age–colour relations. We find that the coefficients of these relations are almost insensitive to the efficiency of superadiabatic convection but are significantly affected by the assumption of the mass–luminosity relation and the adopted chemical composition. Metal-dependent versions of these relations are also derived, representing valuable tools for individual distance determinations and correction for metallicity effects on the cosmic distance scale.