Split Multiplets Research Articles

Rotation of ZZ Ceti stars as seen by TESS

Context. Knowing the rotation rates and masses of white dwarf stars is an important step towards characterising the angular momentum transport mechanism in their progenitors, and coupling the cores of red giants to their envelopes. However, deriving these rotation rates is not an easy task. One can use the rotational broadening of spectral lines, but there is another way to gather reliable information on the stellar rotation periods of pulsators: through studying the splitting effect of rotation on oscillation frequencies. Aims. We aim to derive stellar rotation periods in the TESS sample for as many white dwarf pulsators as possible. Methods. We rely on light-curve analysis of the TESS observations, and search for closely spaced frequency multiplets that could be rotationally split pulsation modes. We work with triplet frequencies, even if one or two triplet components are only marginally detectable. We also utilise ground-based observations available from the literature in an attempt to confirm the presence of several triplets. Results. We successfully identified rotationally split multiplets and derived rotation rates for 14 stars. The fastest rotators we identified have rotation periods of 6.6–10.0 h. The majority of the pulsators rotate with periods of 11.9–47.5 h, while we derived 85.5 and 93.2 h periods for the slowest rotators. In addition to providing stellar mass estimations, our results confirm previous findings that larger-mass WDs rotate faster than their lower-mass counterparts. We determine the rotation periods of four stars for the first time.

KIC 6951642: A confirmed Kepler γ Doradus – δ Scuti star with intermediate to fast rotation in a possible single-lined binary system

Context. KIC 6951642 has been reported as a candidate hybrid pulsator of type-γ Doradus – δ Scuti from observations of the first quarters of the Kepler mission. The regular patterns seen in the Fourier spectra of the Kepler and Transiting Exoplanet Survey Satellite TESS light curves and the sinusoidal modulation of its surface brightness suggest the additional presence of rotational modulation and stellar activity, respectively. Aims. We aim to investigate the pulsating nature of KIC 6951642 and to search for the signature of rotation and/or activity in the light curves. Methods. We performed an iterative frequency search of both Fourier spectra, and searched for regular patterns in them. We applied spectrum synthesis to determine the atmospheric stellar parameters. Since KIC 6951642 was reported to belong to a spectroscopic binary system, we fitted the time delays derived from the light curves with the radial velocities obtained from published as well as new spectra in an attempt to improve the quality of the first orbit. Results. Follow-up spectroscopy showed that KIC 6951642 is a fast-rotating F0-type star in a possible single-lined binary with a period of ∼4.8 yr. In the low-frequency regime, we identified the frequencies of 0.721 d−1 as well as of 0.0087 d−1. We attribute the first frequency to stellar rotation, and the second one to stellar activity with a cycle of length of 3.2 yr. We also detected g modes, with the strongest mode located at 2.238 d−1, as well as three asymmetric multiplets (with a mean spacing of 0.675 ± 0.044 d−1). In the high-frequency regime, we detected frequencies of type-δ Scuti, with the strongest mode located at 13.96 d−1, as well as seven asymmetric multiplets (with a mean spacing of 0.665 ± 0.084 d−1). We subsequently identified a few more frequencies that appear to be combinations of a g or p mode and one of the higher cited frequencies not due to pulsations. Conclusions. We propose that KIC 6951642 accomadates for a fast-rotating γ Dor – δ Sct hybrid star with various rotationally split multiplets of g and p modes and that it also displays a cycle lasting years of (possible) stellar activity.

Five young δ Scuti stars in the Pleiades seen with Kepler/K2

ABSTRACT We perform mode identification for five δ Scuti stars in the Pleiades star cluster, using custom light curves from K2 photometry. By creating échelle diagrams, we identify radial and dipole mode ridges, comprising a total of 28 radial and 16 dipole modes across the five stars. We also suggest possible identities for those modes that lie offset from the radial and dipole ridges. We calculate non-rotating stellar pulsation models to verify our mode identifications, finding good agreement within the age and metallicity constraints of the cluster. We also find that for all stars, the least dense models are preferred, reflecting the lower density of these oblate, rotating stars. Three of the five stars show rotationally split multiplets. We conclude that the sample shows promise for asteroseismic rotation rates, masses, and ages with rotating models in the future. Our preliminary modelling also indicates some sensitivity to the helium abundance.

TESS cycle 1 observations of roAp stars with 2-min cadence data

ABSTRACT We present the results of a systematic search for new rapidly oscillating Ap (roAp) stars using the 2-min cadence data collected by the Transiting Exoplanet Survey Satellite (TESS) during its Cycle 1 observations. We identify 12 new roAp stars. Amongst these stars we discover the roAp star with the longest pulsation period, another with the shortest rotation period, and six with multiperiodic variability. In addition to these new roAp stars, we present an analysis of 44 known roAp stars observed by TESS during Cycle 1, providing the first high-precision and homogeneous sample of a significant fraction of the known roAp stars. The TESS observations have shown that almost 60 per cent (33) of our sample of stars are multiperiodic, providing excellent cases to test models of roAp pulsations, and from which the most rewarding asteroseismic results can be gleaned. We report four cases of the occurrence of rotationally split frequency multiplets that imply different mode geometries for the same degree modes in the same star. This provides a conundrum in applying the oblique pulsator model to the roAp stars. Finally, we report the discovery of non-linear mode interactions in α Cir (TIC 402546736, HD 128898) around the harmonic of the principal mode – this is only the second case of such a phenomenon.

Asteroseismology of tidally distorted sdB stars

ABSTRACT Most subdwarf B stars are located in post-common envelope binaries. Many are in short-period systems subject to tidal influence, and many show pulsations useful for asteroseismic inference. In combination, one must quantify when and how tidal distortion affects the normal modes. We present a method for computing tidal distortion and associated frequency shifts. Validation is by application to polytropes and comparison with previous work. For typical sdB stars, a tidal distortion to the radius of between $0.2\,$ and $2\,$ per cent is generated for orbital periods of 0.1 d. Application to numerical helium core-burning stars identifies the period and mass-ratio domain where tidal frequency shifts become significant and quantifies those shifts in terms of binary properties and pulsation modes. Tidal shifts disrupt the symmetric form of rotationally split multiplets by introducing an asymmetric offset to modes. Tides do not affect the total spread of a rotationally split mode unless the stars are rotating sufficiently slowly that the rotational splitting is smaller than the tidal splitting.

Flavor physics without flavor symmetries

We quantitatively analyze a quark-lepton flavour model derived from a six-dimensional supersymmetric theory with $SO(10)\times U(1)$ gauge symmetry, compactified on an orbifold with magnetic flux. Two bulk $\mathbf{16}$-plets charged under the $U(1)$ provide the three quark-lepton generations whereas two uncharged $\mathbf{10}$-plets yield two Higgs doublets. At the orbifold fixed points mass matrices are generated with rank one or two. Moreover, the zero modes mix with heavy vectorlike split multiplets. The model possesses no flavour symmetries. Nevertheless, there exist a number of relations between Yukawa couplings, remnants of the underlying GUT symmetry and the wave function profiles of the zero modes, which lead to a prediction of the light neutrino mass scale, $m_{\nu_1} \sim 10^{-3}$ eV and heavy Majorana neutrino masses in the range from $10^{12}$ GeV to $10^{14}$ GeV. The model successfully includes thermal leptogenesis.

Superparticle phenomenology from the natural mini-landscape

The methodology of the heterotic mini-landscape attempts to zero in on phenomenologically viable corners of the string landscape where the effective low energy theory is the Minimal Supersymmetric Standard Model with localized grand unification. The gaugino mass pattern is that of mirage-mediation. The magnitudes of various SM Yukawa couplings point to a picture where scalar soft SUSY breaking terms are related to the geography of fields in the compactified dimensions. Higgs fields and third generation scalars extend to the bulk and occur in split multiplets with TeV scale soft masses. First and second generation scalars, localized at orbifold fixed points or tori with enhanced symmetry, occur in complete GUT multiplets and have much larger masses. This picture can be matched onto the parameter space of generalized mirage mediation. Naturalness considerations, the requirement of the observed electroweak symmetry breaking pattern, and LHC bounds on mg together limit the gravitino mass to the m3/2 ∼ 5-60 TeV range. The mirage unification scale is bounded from below with the limit depending on the ratio of squark to gravitino masses. We show that while natural SUSY in this realization may escape detection even at the high luminosity LHC, the high energy LHC with sqrt{s}=33 TeV could unequivocally confirm or exclude this scenario. It should be possible to detect the expected light higgsinos at the ILC if these are kinematically accessible, and possibly also discriminate the expected compression of gaugino masses in the natural mini-landscape picture from the mass pattern expected in models with gaugino mass unification. The thermal WIMP signal should be accessible via direct detection searches at the multi-ton noble liquid detectors such as XENONnT or LZ.

Flavor mixings in flux compactifications

A multiplicity of quark-lepton families can naturally arise as zero-modes in flux compactifications. The flavour structure of quark and lepton mass matrices is then determined by the wave function profiles of the zero-modes. We consider a supersymmetric $SO(10)\times U(1)$ model in six dimensions compactified on the orbifold $T^2/{\mathbb Z_2}$ with Abelian magnetic flux. A bulk $\mathbf{16}$-plet charged under the $U(1)$ provides the quark-lepton generations whereas two uncharged $\mathbf{10}$-plets yield two Higgs doublets. Bulk anomaly cancellation requires the presence of additional $\mathbf{16}$- and $\mathbf{10}$-plets. The corresponding zero-modes form vectorlike split multiplets that are needed to obtain a successful flavour phenomenology. We analyze the pattern of flavour mixings for the two heaviest families of the Standard Model and discuss possible generalizations to three and more generations.

Magnetic Excitations in Polyoxotungstate-Supported Lanthanoid Single-Molecule Magnets: An Inelastic Neutron Scattering and ab Initio Study.

Inelastic neutron scattering (INS) has been used to investigate the crystal field (CF) magnetic excitations of the analogs of the most representative lanthanoid-polyoxometalate single-molecule magnet family: Na9[Ln(W5O18)2] (Ln = Nd, Tb, Ho, Er). Ab initio complete active space self-consistent field/restricted active space state interaction calculations, extended also to the Dy analog, show good agreement with the experimentally determined low-lying CF levels, with accuracy better in most cases than that reported for approaches based only on simultaneous fitting to CF models of magnetic or spectroscopic data for isostructural Ln families. In this work we demonstrate the power of a combined spectroscopic and computational approach. Inelastic neutron scattering has provided direct access to CF levels, which together with the magnetometry data, were employed to benchmark the ab initio results. The ab initio determined wave functions corresponding to the CF levels were in turn employed to assign the INS transitions allowed by selection rules and interpret the observed relative intensities of the INS peaks. Ultimately, we have been able to establish the relationship between the wave function composition of the CF split LnIII ground multiplets and the experimentally measured magnetic and spectroscopic properties for the various analogs of the Na9[Ln(W5O18)2] family.

Parametrizing the time variation of the ‘surface term’ of stellar p-mode frequencies: application to helioseismic data

The solar-cyle variation of acoustic mode frequencies has a frequency dependence related to the inverse mode inertia. The discrepancy between model predictions and measured oscillation frequencies for solar and solar-type stellar acoustic modes includes a significant frequency-dependent term known as the surface term that is also related to the inverse mode inertia. We parametrize both the surface term and the frequency variations for low-degree solar data from Birmingham Solar-Oscillations Network (BiSON) and medium-degree data from the Global Oscillations Network Group (GONG) using the mode inertia together with cubic and inverse frequency terms. We find that for the central frequency of rotationally split multiplets the cubic term dominates both the average surface term and the temporal variation, but for the medium-degree case the inverse term improves the fit to the temporal variation. We also examine the variation of the even-order splitting coefficients for the medium-degree data and find that, as for the central frequency, the latitude-dependent frequency variation, which reflects the changing latitudinal distribution of magnetic activity over the solar cycle, can be described by the combination of a cubic and an inverse function of frequency scaled by inverse mode inertia. The results suggest that this simple parametrization could be used to assess the activity-related frequency variation in solar-like asteroseismic targets.

UNEXPECTED SERIES OF REGULAR FREQUENCY SPACING OF δ SCUTI STARS IN THE NON-ASYMPTOTIC REGIME. II. SAMPLE–ECHELLE DIAGRAMS AND ROTATION

ABSTRACT A sequence search method was developed for searching for regular frequency spacing in δ Scuti stars by visual inspection (VI) and algorithmic search. The sample contains 90 δ Scuti stars observed by CoRoT. An example is given to represent the VI. The algorithm (SSA) is described in detail. The data treatment of the CoRoT light curves, the criteria for frequency filtering, and the spacings derived by two methods (i.e., three approaches: VI, SSA, and FT) are given for each target. Echelle diagrams are presented for 77 targets for which at least one sequence of regular spacing was identified. Comparing the spacing and the shifts between pairs of echelle ridges revealed that at least one pair of echelle ridges is shifted to midway between the spacing for 22 stars. The estimated rotational frequencies compared to the shifts revealed rotationally split doublets, triplets, and multiplets not only for single frequencies, but for the complete echelle ridges in 31 δ Scuti stars. Using several possible assumptions for the origin of the spacings, we derived the large separation ( ) that are distributed along the mean density versus large separations relation derived from stellar models.

A subsynchronously rotating pulsating subdwarf B star in a short-period binary with a white dwarf companion

We present our analysis of KIC 7664467, an sdB pulsator that we have found to be residing in a 1.56-day binary system with a whitedwarf companion. This system was observed photometrically with the Kepler spacecraft and spectroscopically with ground-based telescopes. We analyzed the amplitude spectra detecting 61 periods, rotationally split multiplets, and an equally spaced sequence in period. These two features helped with the mode identification. We derived both the binary and rotation periods showing that this is another binary system with a subsynchronous sdB star. From our spectroscopy of the sdB star, we determined Teff = 27440 ± 120 K, log g = 5.38 ± 0.02 dex. The abundance pattern follows the general trend observed in sdB stars, where light metals are subsolar, while the Fe abundance is very close to the solar value. We found the N enrichment and low abundances of C and O that resemble the equilibrium abundances of the CNO cycle. We could also measure the Mg and Si abundances. Using the radial velocity amplitude K1 = 57(3) km s −1 and the Doppler boosting-dominated photometric signal at the orbital period, we constrained the companion to be a compact object, almost certainly a white dwarf.

Insights into internal effects of common-envelope evolution using the extended Kepler mission

We present an analysis of the binary and physical parameters of a unique pulsating white dwarf with a main-sequence companion, SDSS J1136+0409, observed for more than 77 d during the first pointing of the extended Kepler mission: K2 Campaign 1. Using new ground-based spectroscopy, we show that this post-common-envelope binary has an orbital period of 6.89760103(60) h, which is also seen in the photometry as a result of Doppler beaming and ellipsoidal variations of the secondary. We spectroscopically refine the temperature of the white dwarf to 12 330 ± 260 K and its mass to 0.601 ± 0.036 M⊙. We detect seven independent pulsation modes in the K2 light curve. A preliminary asteroseismic solution is in reasonable agreement with the spectroscopic atmospheric parameters. Three of the pulsation modes are clearly rotationally split multiplets, which we use to demonstrate that the white dwarf is not synchronously rotating with the orbital period but has a rotation period of 2.49 ± 0.53 h. This is faster than any known isolated white dwarf, but slower than almost all white dwarfs measured in non-magnetic cataclysmic variables, the likely future state of this binary.

Detecting non-uniform period spacings in theKeplerphotometry ofγDoradus stars: methodology and case studies

Context. The analysis of stellar oscillations is one of the most reliable ways to probe stellar interiors. Recent space missions such as Kepler have provided us with an opportunity to study these oscillations with unprecedented detail. For many multi-periodic pulsators such as {\gamma} Doradus stars, this led to the detection of dozens to hundreds of oscillation frequencies that could not be found from ground-based observations. Aims. We aim to detect non-uniform period spacings in the Fourier spectra of a sample of {\gamma} Doradus stars observed by Kepler. Such detection is complicated by both the large number of significant frequencies in the space photometry and by overlapping non-equidistant rotationally split multiplets. Methods. Guided by theoretical properties of gravity-mode oscillation of {\gamma} Doradus stars, we developed a period-spacing detection method and applied it to Kepler observations of a few stars, after having tested the performance from simulations. Results. The application of the technique resulted in the clear detection of non-uniform period spacing series for three out of the five treated Kepler targets. Disadvantages of the technique are also discussed, and include the disability to distinguish between different values of the spherical degree and azimuthal order of the oscillation modes without additional theoretical modelling. Conclusions. Despite the shortcomings, the method is shown to allow solid detections of period spacings for {\gamma} Doradus stars, which will allow future asteroseismic analyses of these stars.

Échelle diagrams and period spacings of g modes inγDoradus stars from four years ofKeplerobservations

We use photometry from the Kepler Mission to study oscillations in gamma Doradus stars. Some stars show remarkably clear sequences of g modes and we use period echelle diagrams to measure period spacings and identify rotationally split multiplets with l=1 and l=2. We find small deviations from regular period spacings that arise from the gradient in the chemical composition just outside the convective core. We also find stars for which the period spacing shows a strong linear trend as a function of period, consistent with relatively rapid rotation. Overall, the results indicate it will be possible to apply asteroseismology to a range of gamma Dor stars.

KIC 10526294: a slowly rotating B star with rotationally split, quasi-equally spaced gravity modes

Massive stars are important for the chemical enrichment of the universe. Since internal mixing processes influence their lives, it is very important to place constraints on the corresponding physical parameters, such as core overshooting and the internal rotation profile, so as to calibrate their stellar structure and evolution models. Although asteroseismology has been shown to be able to deliver the most precise constraints so far, the number of detailed seismic studies delivering quantitative results is limited. Our goal is to extend this limited sample with an in-depth case study and provide a well-constrained set of asteroseismic parameters, contributing to the ongoing mapping efforts of the instability strips of the beta Cep and SPB stars. We derived fundamental parameters from high-resolution spectra using spectral synthesis techniques. We used custom masks to obtain optimal light curves from the original pixel level data from the Kepler satellite. We used standard time-series analysis tools to construct a set of significant pulsation modes that provide the basis for the seismic analysis carried out afterwards. We find that KIC 10526294 is a cool SPB star, one of the slowest rotators ever found. Despite this, the length of Kepler observations is sufficient to resolve narrow rotationally split multiplets for each of its 19 quasi-equally spaced dipole modes. The number of detected consecutive (in radial order) dipole modes in this series is higher than ever before. The observed amount of splitting shows an increasing trend towards longer periods, which - largely independent of the seismically calibrated stellar models - points towards a non-rigid internal rotation profile. From the average splitting we deduce a rotation period of ~188 d. From seismic modelling, we find that the star is young with a central hydrogen mass fraction X_c>0.64; it has a core overshooting alpha_ov<=0.15.

Asteroseismology revealing trapped modes in KIC 10553698A

The subdwarf-B pulsator, KIC 10553698A, is one of 16 such objects observed with one-minute sampling for most of the duration of the Kepler Mission. Like most of these stars, it displays a rich g-mode pulsation spectrum with several clear multiplets that maintain regular frequency splitting. We identify these pulsation modes as components of rotationally split multiplets in a star rotating with a period of about 41 d. From 162 clearly significant periodicities, we are able to identify 156 as likely components of l=1 or l=2 multiplets. For the first time we are able to detect l=1 modes that interpose in the asymptotic period sequences and that provide a clear indication of mode trapping in a stratified envelope, as predicted by theoretical models. A clear signal is also present in the Kepler photometry at 3.387 d. Spectroscopic observations reveal a radial-velocity amplitude of 64.8 km/s. We find that the radial-velocity variations and the photometric signal have phase and amplitude that are perfectly consistent with a Doppler-beaming effect and conclude that the unseen companion, KIC 10553698B, must be a white dwarf most likely with a mass close to 0.6 solar masses.

Core-coupled states and split proton-neutron quasiparticle multiplets in122−126Ag

Neutron-rich silver isotopes were populated in the fragmentation of a 136Xe beam and the relativistic fission of 238U. The fragments were mass analyzed with the GSI Fragment separator and subsequently implanted into a passive stopper. Isomeric transitions were detected by 105 HPGe detectors. Eight isomeric states were observed in 122-126Ag nuclei. The level schemes of 122,123,125Ag were revised and extended with isomeric transitions being observed for the first time. The excited states in the odd-mass silver isotopes are interpreted as core-coupled states. The isomeric states in the even-mass silver isotopes are discussed in the framework of the proton-neutron split multiplets. The results of shell-model calculations, performed for the most neutron-rich silver nuclei are compared to the experimental data.

Proton stability in supersymmetricSU(5)

Within supersymmetric $SU(5)$ grand unified theory (GUT) we suggest mechanisms for suppression of baryon number violating dimension five and six operators. The mechanism is based on the idea of split multiplets (i.e. quarks and leptons are not coming from a single GUT state) which is realized by an extension with additional vectorlike matter. The construction naturally avoids wrong asymptotic relation ${\stackrel{^}{M}}_{D}={\stackrel{^}{M}}_{E}$. Thus, the long-standing problems of the minimal supersymmetric $SU(5)$ GUT can be resolved. In a particular example of flavor structure and with additional $\mathcal{U}(1)\ifmmode\times\else\texttimes\fi{}{\mathcal{Z}}_{3N}$ symmetry we demonstrate how the split multiplet mechanism works out. Namely, the considered model is compatible with successful gauge coupling unification and realistic fermion mass pattern. The nucleon decay rates are relatively suppressed and can be well compatible with current experimental bounds.

Rupture length and duration of the 2004 Aceh‐Sumatra earthquake from the phases of the Earth's gravest free oscillations

The Aceh‐Sumatra 2004 earthquake strongly excited the Earth's free oscillations. Well separated split multiplets provide useful information on the earthquake source. Particularly, the phases of split singlets constrain the duration, rupture length and mean rupture velocity. We analyze the initial phases of some of the Earth's gravest free oscillations (0S2, 0S3, 0S0 and 1S0) in order to constrain the space‐time finiteness of the source. We use recordings of vertical broadband seismometers and superconducting gravimeters from several worldwide geophysical networks. We estimate a rupture length of about 1220 km, a source time duration of about 500 s, and a mean rupture velocity of 2.4 km/s.