Light Curves Research Articles

Comprehensive analysis of the eclipsing binaries V527 Dra and V2846 Cyg

Abstract This is the first comprehensive study of the eclipsing binaries V527 Dra and V2846 Cyg, based on radial velocities and ground- and space-based light curves. We perform detailed modeling of these data to derive the absolute parameters and the orbital properties of the two systems. V527 Dra is found to be a semi-detached, and V2846 Cyg a contact binary. Both show continual out-of-eclipse variations that can be explained by migrating dark spots of magnetic origin. We also perform the eclipse timing variation (ETV) analysis which reveals that V527 Dra has a tertiary companion whose mass (∼1M⊙) and orbital inclination (∼70○) are additionally constrained by radial velocities. The ETV diagram of V2846 Cyg displays a quadratic trend accompanied by a low-amplitude cyclic variation, likely due to a magnetic cycle, although further eclipse times are needed to provide a clearer explanation. Lastly, we demonstrate a correlation between the variations in spot parameters obtained via light curve modeling for individual orbital cycles and the residual ETVs, essentially confirming the assumption of magnetic activity in both systems.

X-ray flux and spectral variability of the blazar OJ 287 with Suzaku

Abstract We present analyses of Suzaku XIS light curves and spectra of the BL Lac object OJ 287 with observations positioned primarily around proposed recurrent optical outbursts. The first two observations were performed in 2007 April 10 – 13 (epoch 1) and 2007 November 7 – 9 (epoch 2) that respectively correspond to a low and a high optical state and which, within the binary supermassive black hole model for OJ 287, precede and follow the impact flare. The last three observations, made consecutively during 2015 May 3 – 9 (epoch 3), were during the post-impact state of the 2013 disc impact and are the longest continuous X-ray observation of OJ 287 taken before the optical outburst in 2015 December. Intraday variability is found in both the soft (0.5 – 2 keV) and hard (2 – 10 keV) bands. The discrete correction function analysis of the light curves in both bands peaks at zero lag during epochs 2 and 3, indicating that the emission in both bands was cospatial and emitted from the same population of leptons. Power spectral densities of all three light curves are red noise dominated, with a rather wide range of power spectrum slopes. These X-ray spectra are overall consistent with power-laws but with significantly different spectral indices. In the 2015 observations the X-ray spectrum softens during the flare, showing an obvious soft X-ray excess that was not evident in the 2007 observations. We discuss the implications of these observations on the jet, the possible accretion disc, and the binary supermassive black hole model proposed for the nearly periodic optical flaring of OJ 287.

Investigation of a W UMa-type contact binary GZ And in a physical triple system

GZ And is a variable star within the visually observed multiple-star system ADS 1693. Recent observations have yielded new light curves for GZ And, obtained using the Xinglong 85-cm telescope and the Transiting Exoplanet Survey Satellite (TESS) satellite. These light curves, along with radial velocity curves, were analyzed simultaneously to ascertain the fundamental physical parameters of GZ And’s components. The findings indicate that the primary star has a mass of M1 = 0.57 (4)M⊙, radius of R1 = 0.75 (2)R⊙, and luminosity of L1 = 0.42 (2)L⊙. The secondary star is characterized by a mass of M2 = 1.19 (9)M⊙, radius of R2 = 1.04 (3)R⊙, and luminosity of L2 = 0.63 (3)L⊙. Their orbital separation is determined to be a = 2.30 (6)R⊙. An analysis of the accumulated times of light minima reveals that GZ And is undergoing orbital period variations at a rate of dP/dt = −7.58 (7) × 10−8day ⋅ year−1, likely due to mass transfer from the more massive component to its lighter counterpart at a rate of dM2/dt = −9.06 (8) × 10−8M⊙⋅ year−1. Additionally, distance measurements for the component stars in ADS 1693, derived from Gaia DR3 astrometric data, suggest that ADS 1693A (GZ And) and ADS 1693B are gravitationally bound and likely originated from the same molecular cloud, sharing similar ages. This evidence supports the classification of GZ And as a W UMa-type contact binary within a physically associated triple system.

X-ray Sources Classification Using Machine Learning: A Study with EP-WXT Pathfinder LEIA

Abstract X-ray observations play a crucial role in time-domain astronomy. The Einstein Probe (EP), a recently launched X-ray astronomical satellite, emerges as a forefront player in the field of time-domain astronomy and high-energy astrophysics. With a focus on sys tematic surveys in the soft X-ray band, EP aims to discover high-energy transients and monitor variable sources in the universe. To achieve these objectives, a quick and reli able classification of observed sources is essential. In this study, we developed a machine learning classifier for autonomous source classification using data from the EP-WXT Pathfinder - Lobster Eye Imager for Astronomy (LEIA) and EP-WXT simulations. The proposed random forest classifier, built on selected features derived from light curves, en ergy spectra, and location information, achieves an accuracy of approximately 95% on EP simulation data and 98% on LEIA observational data. The classifier is integrated into the LEIA data processing pipeline, serving as a tool for manual validation and rapid classifi cation during observations. This paper presents an efficient method for the classification of X-ray sources based on single observations, along with implications of most effective features for the task. This work facilitates rapid source classification for the EP mission and also provides valuable insights into feature selection and classification techniques for enhancing the efficiency and accuracy of X-ray source classification that can be adapted to other X-ray telescope data.

A benchmark JWST near-infrared spectrum for the exoplanet WASP-39 b

AbstractObserving exoplanets through transmission spectroscopy supplies detailed information about their atmospheric composition, physics and chemistry. Before the James Webb Space Telescope (JWST), these observations were limited to a narrow wavelength range across the near-ultraviolet to near-infrared, alongside broadband photometry at longer wavelengths. To understand more complex properties of exoplanet atmospheres, improved wavelength coverage and resolution are necessary to robustly quantify the influence of a broader range of absorbing molecular species. Here we present a combined analysis of JWST transmission spectroscopy across four different instrumental modes spanning 0.5–5.2 μm using Early Release Science observations of the Saturn-mass exoplanet WASP-39 b. Our uniform analysis constrains the orbital and stellar parameters within subpercentage precision, including matching the precision obtained by the most precise asteroseismology measurements of stellar density to date, and it further confirms the presence of Na, K, H2O, CO, CO2 and SO2 as atmospheric absorbers. Through this process, we have improved the agreement between the transmission spectra of all modes, except for the NIRSpec PRISM, which is affected by partial saturation of the detector. This work provides strong evidence that uniform light curve analysis is an important aspect to ensuring reliability when comparing the high-precision transmission spectra provided by JWST.

Testing particle acceleration in blazar jets with continuous high-cadence optical polarization observations

Variability can be the pathway to understanding the physical processes in astrophysical jets. However, the high-cadence observations required to test particle acceleration models are still missing. Here we report on the first attempt to produce continuous, $>24$ hour polarization light curves of blazars using telescopes distributed across the globe, following the rotation of the Earth, to avoid the rising Sun. Our campaign involved 16 telescopes in Asia, Europe, and North America. We observed BL Lacertae and CGRaBS J0211+1051 for a combined 685 telescope hours. We find large variations in the polarization degree and angle for both sources on sub-hour timescales as well as a $ rotation of the polarization angle in CGRaBS J0211+1051 in less than two days. We compared our high-cadence observations to particle-in-cell magnetic reconnection and turbulent plasma simulations. We find that although the state-of-the-art simulation frameworks can produce a large fraction of the polarization properties, they do not account for the entirety of the observed polarization behavior in blazar jets.

Analysis of Gaia DR3 Data of Selected High Galactic Latitude Hα Emission Stars

Gaia DR3 data of 52 high galactic latitude Hα emission stars selected from the paper of Stephenson are analyzed. Ten new variable stars and eight new high velocity stars have been found. Details of six post-AGB stars and several other interesting stars are discussed. Many of the stars presented in this paper have Gaia DR3 light curves and spectra. A detailed study of these 52 stars is needed to derive their chemical composition and to further understand their binarity, circumstellar matter and evolutionary status. The astrophysical parameters from the Gaia DR3 data reveal several hot (OBA) and several F and G-type stars in this sample. Some of them are metal-poor stars.

Revealing the inner workings of the lensed quasar SDSS J1339+1310 : Insights from microlensing analysis

We aim to unveil the structure of the continuum and broad-emission line (BEL) emitting regions in the gravitationally lensed quasar SDSS J1339+1310 by examining the distinct signatures of microlensing present in this system. Our study involves a comprehensive analysis of ten years (2009--2019) of photometric monitoring data and seven spectroscopic observations acquired between 2007 and 2017. This work focuses on the pronounced deformations in the BEL profiles between images A and B, alongside the chromatic changes in their adjacent continua and the striking microlensing variability observed in the $r$-band light curves. We employed a statistical model to quantify the distribution and impact of microlensing magnifications and utilized a Bayesian approach to estimate the dimensions of various emission regions within the quasar. To establish a baseline relatively free of microlensing effects, we used the cores of the emission lines as a reference. The analysis of the $r$-band light curves reveals substantial microlensing variability in the rest-frame UV continuum, suggesting that image B is amplified relative to image A by a factor of up to six. This finding is corroborated by pronounced microlensing-induced distortions in all studied BEL profiles (Lyalpha , Si IV, C IV, C III

Analysis of Gaia DR3 Data of Selected High Galactic Latitude Hα Emission Stars

Gaia DR3 data of 52 high galactic latitude Hα emission stars selected from the paper of Stephenson are analyzed. Ten new variable stars and eight new high velocity stars have been found. Details of six post-AGB stars and several other interesting stars are discussed. Many of the stars presented in this paper have Gaia DR3 light curves and spectra. A detailed study of these 52 stars is needed to derive their chemical composition and to further understand their binarity, circumstellar matter and evolutionary status. The astrophysical parameters from the Gaia DR3 data reveal several hot (OBA) and several F and G-type stars in this sample. Some of them are metal-poor stars.

AstroSat Observations of the Dipping Low Mass X-ray Binary XB 1254−690

Abstract XB 1254−690 is a neutron star low-mass X-ray binary with an orbital period of 3.88 hrs, and it exhibits energy-dependent intensity dips, thermonuclear bursts, and flares. We present the results of an analysis of a long observation of this source using the AstroSat satellite. The X-ray light curve gradually changed from a high-intensity flaring state to a low-intensity one with a few dips. The hardness intensity diagram showed that the source is in a high-intensity banana state with a gradually changing flux. Based on this, we divide the observation into four flux levels for a flux-resolved spectral study. The X-ray spectra can be explained by a model consisting of absorption, thermal emission from the disc and non-thermal emission from the corona. From our studies, we detect a correlation between the temperature of the thermal component and the flux and we examine the implications of our results for the accretion disc geometry of this source.

Determining the viewing angle from TeV light curve of GRB 221009A

Abstract Gamma-ray bursts (GRBs) are among the most powerful explosive events in the universe. LHAASO recently observed the most luminous one: GRB 221009A, and unveiled its TeV light curve. The light curve exhibits a distinct jet break at around 670 seconds, enabling the derivation of the viewing angle based on the smoothness of the jet break. We constructed two models with or without considering the high-latitude radiation, where the viewing angle was treated as a free parameter, to fit the TeV light curve. We obtained the viewing angles being 9.4 × 10−4 radians and 5.9 × 10−3 radians, respectively. These values closely resemble an on-axis scenario, given the opening angle is 1.4 × 10−2 radians.

Occurrence Rates of Exosatellites Orbiting 3–30 M Jup Hosts from 44 Spitzer Light Curves

We conduct a comprehensive search for transiting exomoons and exosatellites within 44 archival Spitzer light curves of 32 substellar worlds with estimated masses ranging between 3 and 30 M Jup. This sample’s median host mass is 16 M Jup, inclusive of 14 planetary-mass objects, among which one is a wide-orbit exoplanet. We search the light curves for exosatellite signatures and implement a transit injection-recovery test, illustrating our survey’s capability to detect >0.7 R ⊕ exosatellites. Our findings reveal no substantial (>5σ) evidence for individual transit events. However, an unusual fraction of light curves favor the transit model at the 2–3σ significance level, with fitted transit depths consistent with terrestrial-sized (0.7–1.6 R ⊕) bodies. Comparatively, fewer than 2.2% of randomly generated normal distributions from an equivalent sample size exhibit a similar prevalence of outliers. Should one or two of these outliers represent a real exosatellite transit, it would imply an occurrence rate of η=0.61−0.34+0.49 short-period terrestrial exosatellites per system, consistent with the known occurrences rates for both solar system moons and mid-M dwarf exoplanets. We explore alternative astrophysical interpretations for these outliers, underscoring that transits are not the only plausible explanation. For orbital periods <0.8 days, the typical duration of the light curves, we constrain the occurrence rate of sub-Neptunes to η < 0.35 (95% confidence) and, if none of the detected outlier signals are real, the occurrence rate of terrestrial (∼Earth-sized) exosatellites to η < 0.51 (95% confidence). Forthcoming JWST observations of substellar light curves will enable the detection of sub-Io-sized exosatellites, allowing for much stronger constraints on this exosatellite population.

Image Deconvolution and Point-spread Function Reconstruction with STARRED: A Wavelet-based Two-channel Method Optimized for Light-curve Extraction

We present starred, a point-spread function (PSF) reconstruction, two-channel deconvolution, and light-curve extraction method designed for high-precision photometric measurements in imaging time series. An improved resolution of the data is targeted rather than an infinite one, thereby minimizing deconvolution artifacts. In addition, starred performs a joint deconvolution of all available data, accounting for epoch-to-epoch variations of the PSF and decomposing the resulting deconvolved image into a point source and an extended source channel. The output is a high-signal-to-noise-ratio, high-resolution frame combining all data and the photometry of all point sources in the field of view as a function of time. Of note, starred also provides exquisite PSF models for each data frame. We showcase three applications of starred in the context of the imminent LSST survey and of JWST imaging: (i) the extraction of supernovae light curves and the scene representation of their host galaxy; (ii) the extraction of lensed quasar light curves for time-delay cosmography; and (iii) the measurement of the spectral energy distribution of globular clusters in the “Sparkler,” a galaxy at redshift z = 1.378 strongly lensed by the galaxy cluster SMACS J0723.3-7327. starred is implemented in jax, leveraging automatic differentiation and graphics processing unit acceleration. This enables the rapid processing of large time-domain data sets, positioning the method as a powerful tool for extracting light curves from the multitude of lensed or unlensed variable and transient objects in the Rubin-LSST data, even when blended with intervening objects.

Two dynamically discovered compact object candidate binary systems from LAMOST low-resolution survey

ABSTRACT We report two binary systems, LAMOST J035540 + 381550 (hereafter J035540) and LAMOST J035916 + 400732 (hereafter J035916), identified through the Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST) low-resolution survey (LRS). Each of these two systems contains an M-type star orbiting with a invisible compact object candidate. Follow-up spectroscopic observations of Palomar 200-in. telescope (P200) enhance radial velocity measurements. We use radial velocities from LAMOST and P200, as well as light curves from Zwicky Transient Facility (ZTF) to constrain orbital parameters. The masses of the visible M-type stars are estimated by fitting the MIST isochrones and spectral energy distributions. The mass functions for the unseen companions are: $0.22\pm 0.01\,{\rm M}_{\odot }$ for J035540 and $0.16\pm 0.01\, {\rm M}_{\odot }$ for J035916. With the orbital and stellar parameters derived above and assuming the orbital inclination is 90° (edge-on), we find that the minimum masses of the invisible companions exceeds that of the visible stars. The single-lined feature and the dynamical evidence suggest the presence of compact objects. J035540’s ZTF light curve, modelled with phoebe, yields a compact object mass of $0.70^{+0.12}_{-0.05}\, {\rm M}_{\odot }$. For J035916, ellipsoidal modulation analysis constrains the light-curve amplitude, yielding a compact object mass range of $0.57-0.90\, {\rm M}_{\odot }$. The mass estimates indicate that both are likely white dwarfs. These findings underscore the efficiency of optical time-domain surveys and dynamical methods in identifying faint, massive white dwarfs, along with other compact objects in binaries.

The JWST weather report from the nearest brown dwarfs I: multiperiod JWST NIRSpec + MIRI monitoring of the benchmark binary brown dwarf WISE 1049AB

ABSTRACT We report results from 8 h of JWST/MIRI low resolution spectroscopic (LRS) monitoring directly followed by 7 h of JWST/NIRSpec prism spectroscopic monitoring of the benchmark binary brown dwarf WISE 1049AB, the closest, brightest brown dwarfs known. We find water, methane, and CO absorption features in both components, including the 3.3 μm methane absorption feature and a tentative detection of small grain ($\lt $ 1μm) silicate absorption at $\gt $8.5 μm in WISE 1049A. Both components vary significantly ($\gt 1~{{\rm per\ cent}}$), with WISE 1049B displaying larger variations than WISE 1049A. Using K-means clustering, we find three main transition points in wavelength for both components of the binary: (1) change in behaviour at $\sim$2.3 μm coincident with a CO absorption bandhead, (2) change in behaviour at 4.2 μm, close to the CO fundamental band at $\lambda \gt $ 4.4 µm, and (3) change in behaviour at 8.3–8.5 µm, potentially corresponding to silicate absorption. We interpret the light curves observed with both NIRSpec and MIRI as likely stemming from (1) a deep pressure level driving the double-peaked variability seen in WISE 1049B at wavelengths $\lt $2.3 and $\gt $8.5 µm, (2) an intermediate pressure level shaping the light-curve morphology between 2.3 and 4.2 µm, and (3) a higher altitude pressure level producing single-peaked and plateaued light-curve behaviour between 4.2 and 8.5 µm.

Exomoons and Exorings with the Habitable Worlds Observatory. I. On the Detection of Earth–Moon Analog Shadows and Eclipses

The highest priority recommendation of the Astro2020 Decadal Survey for space-based astronomy was the construction of an observatory capable of characterizing habitable worlds. In this paper series we explore the detectability of and interference from exomoons and exorings serendipitously observed with the proposed Habitable Worlds Observatory (HWO) as it seeks to characterize exoplanets, starting in this manuscript with Earth–Moon analog mutual events. Unlike transits, which only occur in systems viewed near edge-on, shadow (i.e., solar eclipse) and lunar eclipse mutual events occur in almost every star–planet–moon system. The cadence of these events can vary widely from ∼yearly to multiple events per day, as was the case in our younger Earth–Moon system. Leveraging previous space-based (EPOXI) light curves of a Moon transit and performance predictions from the LUVOIR-B concept, we derive the detectability of Moon analogs with HWO. We determine that Earth–Moon analogs are detectable with observation of ∼2–20 mutual events for systems within 10 pc, and larger moons should remain detectable out to 20 pc. We explore the extent to which exomoon mutual events can mimic planet features and weather. We find that HWO wavelength coverage in the near-infrared, specifically in the 1.4 μm water band where large moons can outshine their host planet, will aid in differentiating exomoon signals from exoplanet variability. Finally, we predict that exomoons formed through collision processes akin to our Moon are more likely to be detected in younger systems, where shorter orbital periods and favorable geometry enhance the probability and frequency of mutual events.

The story of SN 2021aatd: A peculiar 1987A-like supernova with an early-phase luminosity excess

There is a growing number of peculiar events that cannot be assigned to any of the main classes. SN 1987A and a handful of similar objects, thought to be explosive outcomes of blue supergiant stars, is one of them: while their spectra closely resemble those of H-rich (IIP) SNe, their light curve (LC) evolution is very different. Here we present the detailed photometric and spectroscopic analysis of SN 2021aatd, a peculiar Type II explosion. While its early-time evolution resembles that of the slowly evolving double-peaked SN 2020faa (although at a lower luminosity scale), after sim 40 days its LC shape becomes similar to that of SN 1987A-like explosions. In addition to comparing LCs, color curves, and spectra of SN 2021aatd to those of SNe 2020faa, 1987A, and other objects, we compared the observed spectra with our own SYN++ models and with the outputs of published radiative transfer models. We also carried out a detailed modeling of the pseudo-bolometric LCs of SNe 2021aatd and 1987A with a self-developed semi-analytical code, assuming a two-component ejecta (core + shell), and involving the rotational energy of a newborn magnetar in addition to radioactive decay. We find that the photometric and the spectroscopic evolution of SN 2021aatd can be well described with the explosion of a sim 15 $M_ blue supergiant star. Nevertheless, SN 2021aatd shows higher temperatures and weaker Na i D and Ba ii lines than SN 1987A, which is instead reminiscent of IIP-like atmospheres. With the applied two-component ejecta model (accounting for decay and magnetar energy), we can successfully describe the bolometric LC of SN 2021aatd, including the first sim 40-day phase showing an excess compared to 87A-like SNe, but being strikingly similar to that of the long-lived SN 2020faa. Nevertheless, finding a unified model that also explains the LCs of more luminous events (e.g., SN 2020faa) is still a matter of debate.

Progenitor mass and ejecta asymmetry of supernova 2023ixf from nebular spectroscopy

Supernova (SN) 2023ixf was discovered in the galaxy M101 in May 2023. Its proximity provided the scientific community an extremely valuable opportunity to study the characteristics of the SN and its progenitor. A point source detected on archival images and hydrodynamical modeling of the bolometric light curve have been used to constrain the former star's properties. There is a significant variation in the published results regarding the initial mass of the progenitor. Nebular spectroscopy can be used to enhance our understanding of the SN and its progenitor. We determined the SN progenitor mass by studying the first published nebular spectrum, taken 259 days after the explosion. We analyzed the nebular spectrum taken with GMOS at the Gemini North Telescope. We identified typical emission lines, such as O i Halpha , and Ca ii among others. Some species' line profiles show broad and narrow components, indicating two ejecta velocities and an asymmetric ejecta. We inferred the progenitor mass of SN 2023ixf by comparing its spectra with synthetic spectra and by measuring the forbidden oxygen doublet flux. Based on the flux ratio and the direct comparison with spectra models, the progenitor star of SN 2023ixf had a $M_ ZAMS $ between 12 and 15 $M_ We find that using the O i doublet flux provides a less tight constraint on the progenitor mass. Our results agree with those from hydrodynamical modeling of the early light curve and pre-explosion image estimates that point to a relatively low-mass progenitor.

A Study of Nine Extremely Low Mass Ratio-contact Binary Systems

Low-mass ratio systems (LMR) are a very interesting class of contact eclipsing binaries challenging the theoretical models of stability. These systems are also considered possible progenitors of the rare low-mass optical transients called red novae. In this study, we present the identification of 7 new totally eclipsing LMR systems from Catalina Sky Surveys (CSS) and 77 LMR candidates from the All Sky Automated Survey. Using the available CSS light curves and new multiband observations for CSS_J210228.3-031048 and CSS_J231513.3+345335 with the 2.3 m Aristarchos telescope at Helmos Observatory, we estimate their physical and absolute parameters and investigate their stability and their progenitors. The light curves are analyzed by performing a two-dimensional scan on the mass–ratio inclination plane with Phoebe-0.31 scripter, while the errors are estimated using Monte Carlo simulations and heuristic scanning of the parameter space. Our analysis revealed that all 9 CSS systems have extreme mass ratios from 0.09 to 0.16. Our statistical analysis of well-studied LMR contact binaries shows that LMR systems tend to have warmer and more massive primaries. The investigation of the progenitors of both low and higher-mass-ratio systems reveals a trend for the former to originate from higher-mass ancestors. Finally, we investigate the stability condition by calculating the ratio of spin angular momentum to orbital angular momentum and other stability indicators in the context of the reliability of the solutions.

Asteroseismology of the fast-rotating high-amplitude δ Scuti star V2367 Cygni

Abstract We present the comprehensive analysis of the high-amplitude δ Sct star V2367 Cygni. Firstly, we perform the frequency analysis for the whole available set of the Kepler and TESS photometry. Most of the frequency peaks are harmonics or combinations of the three known independent frequencies with the highest amplitudes, i.e.,ν1 = 5.66106 d−1, ν2 = 7.14898 d−1 and ν3 = 7.77557 d−1. The total number of independent frequencies is 26 and 25 from the Kepler and TESS light curve, respectively. Then, using the UBVRI time-series photometry, we unambiguously identify the dominant frequency ν1 as the radial mode, whereas in the case of frequencies ν2 and ν3 the most probable mode degrees are ℓ = 0 or ℓ = 2. However, only the frequency ν2 can be associated with a radial mode, and only if higher order effects of rotation are taken into account. Including the rotational mode coupling, we constructed complex seismic models of V2367 Cyg, which fit ν1 and ν2 as radial modes, and reproduce the amplitude of bolometric flux variations (the parameter f) for the dominant mode. The empirical values of f are derived from the UBVRI amplitudes and phases. We rely on the Bayesian analysis based on Monte Carlo simulations to derive constraints on evolutionary stage, mass, rotation, overshooting from the convective core and efficiency of convective transport in the envelope. Our seismic analysis clearly indicates that V2367 Cyg is in a post-MS phase of evolution. This is the first extensive seismic modelling that takes into account the effect of rotational coupling between pulsation modes.