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Aldo Serenelli

Publications and source records attributed to Aldo Serenelli.

At least 37 records · Page 2Linked to original sources

Prospects for Galactic and stellar astrophysics with asteroseismology of giant stars in the $\it{TESS}$ Continuous Viewing Zones and beyond

The NASA-$\it{TESS}$ mission presents a treasure trove for understanding the stars it observes and the Milky Way, in which they reside. We present a first look at the prospects for Galactic and stellar astrophysics by performing initial asteroseismic analyses of bright ($G < 11$) red giant stars in the $\it{TESS}$ Southern Continuous Viewing Zone (SCVZ). Using three independent pipelines, we detect $ν_{\mathrm{max}}$ and $Δν$ in 41% of the 15,405 star parent sample (6,388 stars), with consistency at a level of $\sim 2\%$ in $ν_{\mathrm{max}}$ and $\sim 5\%$ in $Δν$. Based on this, we predict that seismology will be attainable for $\sim 3\times10^{5}$ giants across the whole sky, subject to improvements in analysis and data reduction techniques. The best quality $\it{TESS}$-CVZ data, for 5,574 stars where pipelines returned consistent results, provide high quality power spectra across a number of stellar evolutionary states. This makes possible studies of, for example, the Asymptotic Giant Branch bump (AGBb). We demonstrate that mixed $\ell=1$ modes and rotational splitting are cleanly observed in the 1-year data set. By combining $\it{TESS}$-CVZ data with $\it{TESS}$-HERMES, $\it{SkyMapper}$, APOGEE and $\it{Gaia}$ we demonstrate the potential for Galactic archaeology studies using the data, which provides good age precision and accuracy that reproduces the age of high $\mathrm{[α/Fe]}$ stars and relationships between mass and kinematics from studies based on $\it{Kepler}$. Better quality astrometry and simpler target selection than the $\it{Kepler}$ sample makes this data ideal for studies of the local star formation history and evolution of the Galactic disc. These results provide a strong case for detailed spectroscopic follow-up in the CVZs to complement that which has been (or will be) collected by current surveys. [Abridged]

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The Gaia-ESO survey: 3D NLTE abundances in the open cluster NGC 2420 suggest atomic diffusion and turbulent mixing at the origin of chemical abundance variations

Atomic diffusion and mixing processes in stellar interiors influence the structure and the surface composition of stars. Some of these processes cannot yet be modelled from the first principles. This limits their applicability in stellar models used for studies of stellar populations and Galactic evolution. Our main goal is to put constrains on the stellar structure and evolution models using new refined measurements of chemical composition in stars of Galactic open cluster. We use medium-resolution, 19 200 <= R <= 21 500, optical spectra of the stars in the open cluster NGC 2420 obtained within the Gaia-ESO survey. The sample covers all evolutionary stages from the main-sequence to red giant branch. Stellar parameters are derived using a combined Bayesian analysis of spectra, 2MASS photometry, and astrometric data from Gaia DR2. The abundances of Mg, Ca, Fe, and Li are determined from non-local thermodynamic equilibrium (NLTE) synthetic spectra, computed using one-dimensional (1D) and averaged three-dimensional (3D) model atmospheres. We compare our results with a grid of Code d'Evolution Stellaire Adaptatif et Modulaire (CESTAM) stellar evolution models, which include atomic diffusion, turbulent and rotational mixing. We find prominent evolutionary trends in the abundances of Fe, Ca, Mg, and Li with the mass of the stars in the cluster. Fe, Mg, and Ca show a depletion at the cluster turn-off, but the abundances gradually increase and flatten near the base of the RGB. The abundance trend for Li displays a signature of rotational mixing on the main-sequence and abrupt depletion on the subgiant branch, which is caused by advection of Li-poor material to the surface. The analysis of abundances combined with the CESTAM model predictions allows us to place limits on the parameter space of the models and to constrain the zone in the stellar interior where turbulent mixing takes place.

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Testing the radius scaling relation with ${\it Gaia}$ DR2 in the ${\it Kepler}$ field

We compare radii based on ${\it Gaia}$ parallaxes to asteroseismic scaling relation-based radii of $\sim 300$ dwarfs $\&$ subgiants and $\sim 3600$ first-ascent giants from the ${\it Kepler}$ mission. Systematics due to temperature, bolometric correction, extinction, asteroseismic radius, and the spatially-correlated ${\it Gaia}$ parallax zero-point, contribute to a $2\%$ systematic uncertainty on the ${\it Gaia}$-asteroseismic radius agreement. We find that dwarf and giant scaling radii are on a parallactic scale at the $-2.1 \% \pm 0.5 \% {\rm \ (rand.)} \pm 2.0\% {\rm \ (syst.)}$ level (dwarfs) and $+1.7\% \pm 0.3\% {\rm \ (rand.)} \pm 2.0\% {\rm \ (syst.)}$ level (giants), supporting the accuracy and precision of scaling relations in this domain. In total, the $2\%$ agreement that we find holds for stars spanning radii between $0.8R_{\odot}$ and $30 R_{\odot}$. We do, however, see evidence for $\textit{relative}$ errors in scaling radii between dwarfs and giants at the $4\% \pm 0.6\%$ level, and find evidence of departures from simple scaling relations for radii above $30 R_{\odot}$. Asteroseismic masses for very metal-poor stars are still overestimated relative to astrophysical priors, but at a reduced level. We see no trend with metallicity in radius agreement for stars with $-0.5 <$ [Fe/H] $< +0.5$. We quantify the spatially-correlated parallax errors in the ${\it Kepler}$ field, which globally agree with the ${\it Gaia}$ team's published covariance model. We provide ${\it Gaia}$ radii, corrected for extinction and the ${\it Gaia}$ parallax zero-point for our full sample of $\sim 3900$ stars, including dwarfs, subgiants, and first-ascent giants.

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Insights from the APOKASC Determination of the Evolutionary State of Red-Giant Stars by consolidation of different methods

The internal working of low-mass stars is of great significance to both the study of stellar structure and the history of the Milky Way. Asteroseismology has the power to directly sense the internal structure of stars and allows for the determination of the evolutionary state -- i.e. has helium burning commenced or is the energy generated only by the fusion in the hydrogen-burning shell? We use observational data from red-giant stars in a combination (known as APOKASC) of asteroseismology (from the \textit{Kepler} mission) and spectroscopy (from SDSS/APOGEE). The new feature of the analysis is that the APOKASC evolutionary state determination is based on the comparison of diverse approaches to the investigation of the frequency-power spectrum. The high level of agreement between the methods is a strong validation of the approaches. Stars for which there is not a consensus view are readily identified. The comparison also facilitates the identification of unusual stars including those that show evidence for very strong coupling between p and g cavities. The comparison between the classification based on the spectroscopic data and asteroseismic data have led to a new value for the statistical uncertainty in APOGEE temperatures. These consensus evolutionary states will be used as an input for methods that derive masses and ages for these stars based on comparison of observables with stellar evolutionary models (`grid-based modeling') and as a training set for machine-learning and other data-driven methods of evolutionary state determination

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TESS Asteroseismology of the known red-giant host stars HD 212771 and HD 203949

The Transiting Exoplanet Survey Satellite (TESS) is performing a near all-sky survey for planets that transit bright stars. In addition, its excellent photometric precision enables asteroseismology of solar-type and red-giant stars, which exhibit convection-driven, solar-like oscillations. Simulations predict that TESS will detect solar-like oscillations in nearly 100 stars already known to host planets. In this paper, we present an asteroseismic analysis of the known red-giant host stars HD 212771 and HD 203949, both systems having a long-period planet detected through radial velocities. These are the first detections of oscillations in previously known exoplanet-host stars by TESS, further showcasing the mission's potential to conduct asteroseismology of red-giant stars. We estimate the fundamental properties of both stars through a grid-based modeling approach that uses global asteroseismic parameters as input. We discuss the evolutionary state of HD 203949 in depth and note the large discrepancy between its asteroseismic mass ($M_\ast = 1.23 \pm 0.15\,{\rm M}_\odot$ if on the red-giant branch or $M_\ast = 1.00 \pm 0.16\,{\rm M}_\odot$ if in the clump) and the mass quoted in the discovery paper ($M_\ast = 2.1 \pm 0.1\,{\rm M}_\odot$), implying a change $>30\,\%$ in the planet's mass. Assuming HD 203949 to be in the clump, we investigate the planet's past orbital evolution and discuss how it could have avoided engulfment at the tip of the red-giant branch. Finally, HD 212771 was observed by K2 during its Campaign 3, thus allowing for a preliminary comparison of the asteroseismic performances of TESS and K2. We estimate the ratio of the observed oscillation amplitudes for this star to be $A_{\rm max}^{\rm TESS}/A_{\rm max}^{\rm K2} = 0.75 \pm 0.14$, consistent with the expected ratio of $\sim0.85$ due to the redder bandpass of TESS.

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Stellar Astrophysics and Exoplanet Science with the Maunakea Spectroscopic Explorer (MSE)

The Maunakea Spectroscopic Explorer (MSE) is a planned 11.25-m aperture facility with a 1.5 square degree field of view that will be fully dedicated to multi-object spectroscopy. A rebirth of the 3.6m Canada-France-Hawaii Telescope on Maunakea, MSE will use 4332 fibers operating at three different resolving powers (R ~ 2500, 6000, 40000) across a wavelength range of 0.36-1.8mum, with dynamical fiber positioning that allows fibers to match the exposure times of individual objects. MSE will enable spectroscopic surveys with unprecedented scale and sensitivity by collecting millions of spectra per year down to limiting magnitudes of g ~ 20-24 mag, with a nominal velocity precision of ~100 m/s in high-resolution mode. This white paper describes science cases for stellar astrophysics and exoplanet science using MSE, including the discovery and atmospheric characterization of exoplanets and substellar objects, stellar physics with star clusters, asteroseismology of solar-like oscillators and opacity-driven pulsators, studies of stellar rotation, activity, and multiplicity, as well as the chemical characterization of AGB and extremely metal-poor stars.

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On the nature of the black-body stars

A selection of 17 stars in the Sloan Digital Sky Survey, previously identified as DC class white dwarfs (WDs), has been reported to show spectra very close to blackbody radiation in the wavelength range from ultraviolet to infrared. Due to the absence of lines and other details in their spectra, the surface gravity of these objects has not been previously well constrained and their effective temperatures have been determined by fits to the continuum spectrum using pure helium atmosphere models. We compute model atmospheres with pure helium and H/He mixtures and use Gaia DR2 parallaxes available for 16 out of the 17 selected stars to analyze their physical properties. We find that the atmospheres of the selected stars are very probably contaminated with a trace amount of hydrogen as $-6 \leq \log{N_H/N_{He}} \leq -5.4$. For the 16 stars with Gaia parallaxes, we calculate a mean stellar mass $0.606\pm 0.076\,M_\odot$, which represents typical mass values and surface gravities ($7.8<\log g<8.3$) for WDs.

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The Second APOKASC Catalog: The Empirical Approach

We present a catalog of stellar properties for a large sample of 6676 evolved stars with APOGEE spectroscopic parameters and \textit{Kepler} asteroseismic data analyzed using five independent techniques. Our data includes evolutionary state, surface gravity, mean density, mass, radius, age, and the spectroscopic and asteroseismic measurements used to derive them. We employ a new empirical approach for combining asteroseismic measurements from different methods, calibrating the inferred stellar parameters, and estimating uncertainties. With high statistical significance, we find that asteroseismic parameters inferred from the different pipelines have systematic offsets that are not removed by accounting for differences in their solar reference values. We include theoretically motivated corrections to the large frequency spacing ($Δν$) scaling relation, and we calibrate the zero point of the frequency of maximum power ($ν_{\rm max}$) relation to be consistent with masses and radii for members of star clusters. For most targets, the parameters returned by different pipelines are in much better agreement than would be expected from the pipeline-predicted random errors, but 22\% of them had at least one method not return a result and a much larger measurement dispersion. This supports the usage of multiple analysis techniques for asteroseismic stellar population studies. The measured dispersion in mass estimates for fundamental calibrators is consistent with our error model, which yields median random and systematic mass uncertainties for RGB stars of order 4\%. Median random and systematic mass uncertainties are at the 9\% and 8\% level respectively for RC stars.

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KELT-21b: A Hot Jupiter Transiting the Rapidly-Rotating Metal-Poor Late-A Primary of a Likely Hierarchical Triple System

We present the discovery of KELT-21b, a hot Jupiter transiting the $V=10.5$ A8V star HD 332124. The planet has an orbital period of $P=3.6127647\pm0.0000033$ days and a radius of $1.586_{-0.040}^{+0.039}$ $R_J$. We set an upper limit on the planetary mass of $M_P<3.91$ $M_J$ at $3σ$ confidence. We confirmed the planetary nature of the transiting companion using this mass limit and Doppler tomographic observations to verify that the companion transits HD 332124. These data also demonstrate that the planetary orbit is well-aligned with the stellar spin, with a sky-projected spin-orbit misalignment of $λ=-5.6_{-1.9}^{+1.7 \circ}$. The star has $T_{\mathrm{eff}}=7598_{-84}^{+81}$ K, $M_*=1.458_{-0.028}^{+0.029}$ $M_{\odot}$, $R_*=1.638\pm0.034$ $R_{\odot}$, and $v\sin I_*=146$ km s$^{-1}$, the highest projected rotation velocity of any star known to host a transiting hot Jupiter. The star also appears to be somewhat metal-poor and $α$-enhanced, with [Fe/H]$=-0.405_{-0.033}^{+0.032}$ and [$α$/Fe]$=0.145 \pm 0.053$; these abundances are unusual, but not extraordinary, for a young star with thin-disk kinematics like KELT-21. High-resolution imaging observations revealed the presence of a pair of stellar companions to KELT-21, located at a separation of 1.2" and with a combined contrast of $ΔK_S=6.39 \pm 0.06$ with respect to the primary. Although these companions are most likely physically associated with KELT-21, we cannot confirm this with our current data. If associated, the candidate companions KELT-21 B and C would each have masses of $\sim0.12$ $M_{\odot}$, a projected mutual separation of $\sim20$ AU, and a projected separation of $\sim500$ AU from KELT-21. KELT-21b may be one of only a handful of known transiting planets in hierarchical triple stellar systems.

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The First APOKASC Catalog of Kepler Dwarf and Subgiant Stars

(Abridged) We present the first APOKASC catalog of spectroscopic and asteroseismic data for 415 dwarfs and subgiants. Asteroseismic data have been obtained by Kepler in short cadence. The spectroscopic parameters are based on spectra taken as part of APOGEE and correspond to DR13 of SDSS. We analyze our data using two Teff scales, the spectroscopic values from DR13 and those derived from SDSS griz photometry. We use the differences in our results arising from these choices as a test of systematic Teff, and find that they can lead to significant differences in the derived stellar properties. Determinations of surface gravity ($\log{g}$), mean density ($ρ$), radius ($R$), mass ($M$), and age ($τ$) for the whole sample have been carried out with stellar grid-based modeling. We have assessed random and systematic error sources in the spectroscopic and seismic data, as well as in the grid-based modeling determination of the stellar quantities in the catalog. We provide stellar properties for both Teff scales. The median combined (random and systematic) uncertainties are 2% (0.01 dex; $\log{g}$), 3.4% ($ρ$), 2.6% ($R$), 5.1% ($M$), and 19% ($τ$) for the photometric Teff scale and 2% ($\log{g}$), 3.5% ($ρ$), 2.7% ($R$), 6.3% ($M$), and 23% ($τ$) for the spectroscopic scale. Comparisons with stellar quantities in the catalog by Chaplin et al.(2014) highlight the importance of metallicity measurements for determining stellar parameters accurately. We compare our results with those from other sources, including stellar radii determined from TGAS parallaxes and asteroseismic analyses based on individual frequencies. We find a very good agreement in all cases. Comparisons give strong support to the determination of stellar quantities based on global seismology, a relevant result for future missions such as TESS and PLATO. Table 5 corrected (wrongly listed SDSS Teff before).

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Helioseismic and Neutrino Data Driven Reconstruction of Solar Properties

In this work we use Bayesian inference to quantitatively reconstruct the solar properties most relevant to the solar composition problem using as inputs the information provided by helioseismic and solar neutrino data. In particular, we use a Gaussian process to model the functional shape of the opacity uncertainty to gain flexibility and become as free as possible from prejudice in this regard. With these tools we first readdress the statistical significance of the solar composition problem. Furthermore, starting from a composition unbiased set of standard solar models we are able to statistically select those with solar chemical composition and other solar inputs which better describe the helioseismic and neutrino observations. In particular, we are able to reconstruct the solar opacity profile in a data driven fashion, independently of any reference opacity tables, obtaining a 4% uncertainty at the base of the convective envelope and 0.8% at the solar core. When systematic uncertainties are included, results are 7.5% and 2% respectively. In addition we find that the values of most of the other inputs of the standard solar models required to better describe the helioseismic and neutrino data are in good agreement with those adopted as the standard priors, with the exception of the astrophysical factor $S_{11}$ and the microscopic diffusion rates, for which data suggests a 1% and 30% reduction respectively. As an output of the study we derive the corresponding data driven predictions for the solar neutrino fluxes.

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The brightness of the Red Giant Branch tip: Theoretical framework, a set of reference models, and predicted observables

The brightness of the tip of the Red Giant Branch is a useful reference quantity for several fields of astrophysics. An accurate theoretical prediction is needed for such purposes. Aims. We intend to provide a solid theoretical prediction for it, valid for a reference set of standard physical assumptions, and mostly independent of numerical details. We examine the dependence on physical assumptions and numerical details, for a wide range of metallicities and masses, and based on two different stellar evolution codes. We adjust differences between the codes to treat the physics as identical as possible. After we have succeeded in reproducing the tip brightness between the codes, we present a reference set of models based on the most up to date physical inputs, but neglecting microscopic diffusion, and convert theoretical luminosities to observed infrared colours suitable for observations of resolved populations of stars and include analytic fits to facilitate their use. We find that consistent use of updated nuclear reactions, including an appropriate treatment of the electron screening effects, and careful time-stepping on the upper red giant branch are the most important aspects to bring initially discrepant theoretical values into agreement. Small, but visible differences remain unexplained for very low metallicities and mass values at and above 1.2 Msun, corresponding to ages younger than 4 Gyr. The colour transformations introduce larger uncertainties than the differences between the two stellar evolution codes. We demonstrate that careful stellar modeling allows an accurate prediction for the luminosity of the Red Giant Branch tip. Differences to empirically determined brightnesses may result either from insufficient colour transformations or from deficits in the constitutional physics. We present the best-tested theoretical reference values to date.

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The more the merrier: grid based modelling of Kepler dwarfs with 5-dimensional stellar grids

We present preliminary results of our grid based modelling (GBM) of the dwarf/subgiant sample of stars observed with Kepler including global asteroseismic parameters. GBM analysis in this work is based on a large grid of stellar models that is characterized by five independent parameters: model mass and age, initial metallicity ($\zini$), initial helium ($\yini$), and mixing length parameter ($α_{mlt}$). Using this grid relaxes assumptions used in all previous GBM work where the initial composition is determined by a single parameter and that $α_{mlt}$ is fixed to a solar-calibrated value. The new grid allows us to study, for example, the impact of different galactic chemical enrichment models on the determination of stellar parameters such as mass radius and age. Also, it allows to include new results from stellar atmosphere models on $α_{mlt}$ in the GBM analysis in a simple manner. Alternatively, it can be tested if global asteroseismology is a useful tool to constraint our ignorance on quantities such as $\yini$ and $α_{mlt}$. Initial findings show that mass determination is robust with respect to freedom in the latter quantities, with a 4.4\% maximum deviation for extreme assumptions regarding prior information on $\yini-\zini$ relations and $α_{mlt}$. On the other hand, tests carried out so far seem to indicate that global seismology does not have much power to constrain $\yini-\zini$ relations of $α_{mlt}$ values without resourcing to additional information.

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Asteroseismology and Gaia: Testing Scaling Relations Using 2200 Kepler Stars with TGAS Parallaxes

We present a comparison of parallaxes and radii from asteroseismology and Gaia DR1 (TGAS) for 2200 Kepler stars spanning from the main sequence to the red giant branch. We show that previously identified offsets between TGAS parallaxes and distances derived from asteroseismology and eclipsing binaries have likely been overestimated for parallaxes <~ 5-10 mas (~ 90-98% of the TGAS sample). The observed differences in our sample can furthermore be partially compensated by adopting a hotter Teff scale (such as the infrared flux method) instead of spectroscopic temperatures for dwarfs and subgiants. Residual systematic differences are at the ~ 2% level in parallax across three orders of magnitude. We use TGAS parallaxes to empirically demonstrate that asteroseismic radii are accurate to ~ 5% or better for stars between ~ 0.8-8 Rsun. We find no significant offset for main-sequence (<~ 1.5 Rsun) and low-luminosity RGB stars (~ 3-8 Rsun), but seismic radii appear to be systematically underestimated by ~5% for subgiants (~ 1.5-3 Rsun). We find no systematic errors as a function of metallicity between [Fe/H] ~ -0.8 to +0.4 dex, and show tentative evidence that corrections to the scaling relation for the large frequency separation (Dnu) improve the agreement with TGAS for RGB stars. Finally, we demonstrate that beyond ~ 3 kpc asteroseismology will provide more precise distances than end-of-mission Gaia data, highlighting the synergy and complementary nature of Gaia and asteroseismology for studying galactic stellar populations.

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First evidence of multiple populations along the AGB from Strömgren photometry

Spectroscopic studies have demonstrated that nearly all Galactic globular clusters (GCs) harbour multiple stellar populations with different chemical compositions. Moreover, colour-magnitude diagrams based exclusively on Strömgrem photometry have allowed us to identify and characterise multiple populations along the RGB of a large number of clusters. In this paper we show for the first time that Strömgren photometry is also very effcient at identifying multiple populations along the AGB, and demonstrate that the AGB of M3, M92, NGC362, NGC1851, and NGC6752 are not consistent with a single stellar population. We also provide a catalogue of RGB and AGB stars photometrically identified in these clusters for further spectroscopic follow-up studies.We combined photometry and elemental abundances from the literature for RGB and AGB stars in NGC6752 where the presence of multiple populations along the AGB has been widely debated. We find that, while the MS, SGB, and RGB host three stellar populations with different helium and light element abundances, only two populations of AGB stars are present in the cluster. These results are consistent with standard evolutionary theory.

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The Correlation Between Mixing Length and Metallicity on the Giant Branch: Implications for Ages in the Gaia Era

In the updated APOGEE-Kepler catalog, we have asteroseismic and spectroscopic data for over 3000 first ascent red giants. Given the size and accuracy of this sample, these data offer an unprecedented test of the accuracy of stellar models on the post-main-sequence. When we compare these data to theoretical predictions, we find a metallicity dependent temperature offset with a slope of around 100 K per dex in metallicity. We find that this effect is present in all model grids tested and that theoretical uncertainties in the models, correlated spectroscopic errors, and shifts in the asteroseismic mass scale are insufficient to explain this effect. Stellar models can be brought into agreement with the data if a metallicity dependent convective mixing length is used, with $ Δα_{\rm ML, YREC} \sim 0.2$ per dex in metallicity, a trend inconsistent with the predictions of three dimensional stellar convection simulations. If this effect is not taken into account, isochrone ages for red giants from the Gaia data will be off by as much as a factor of 2 even at modest deviations from solar metallicity ([Fe/H]=$-$0.5).

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Effect of electromagnetic dipole dark matter on energy transport in the solar interior

In recent years, a revised set of solar abundances has led to a discrepancy in the sound-speed profile between helioseismology and theoretical solar models. Conventional solutions require additional mechanisms for energy transport within the Sun. Vincent et al. have recently suggested that dark matter with a momentum or velocity dependent cross section could provide a solution. In this work, we consider three models of dark matter with such cross sections and their effect on the stellar structure. In particular, the three models incorporate dark matter particles interacting through an electromagnetic dipole moment: an electric dipole, a magnetic dipole or an anapole. Each model is implemented in the \texttt{DarkStec} stellar evolution program, which incorporates the effects of dark matter capture and heat transport within the solar interior. We show that dark matter with an anapole moment of $\sim1\mathrm{GeV}^{-2}$ or magnetic dipole moment of $\sim10^{-3}μ_p$ can improve the sound-speed profile, small frequency separations and convective zone radius with respect to the Standard Solar Model. However, the required dipole moments are strongly excluded by direct detection experiments.

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Updated constraints on velocity and momentum-dependent asymmetric dark matter

We present updated constraints on dark matter models with momentum-dependent or velocity-dependent interactions with nuclei, based on direct detection and solar physics. We improve our previous treatment of energy transport in the solar interior by dark matter scattering, leading to significant changes in fits to many observables. Based on solar physics alone, DM with a spin-independent $q^{4}$ coupling provides the best fit to data, and a statistically satisfactory solution to the solar abundance problem. Once direct detection limits are accounted for however, the best solution is spin-dependent $v^2$ scattering with a reference cross-section of 10$^{-35}$ cm$^2$ (at a reference velocity of $v_0=220$ km s$^{-1}$), and a dark matter mass of about 5 GeV.

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