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At least 145 records · Page 8

Nonvirialized axion search sensitive to Doppler effects in the Milky Way halo

The Axion Dark Matter eXperiment (ADMX) has previously excluded Dine-Fischler-Srednicki- Zhitnisky (DFSZ) axions between 680-790 MHz under the assumption that the dark matter is described by the isothermal halo model. However, the precise nature of the velocity distribution of dark matter is still unknown, and alternative models have been proposed. Here, we report the results of a non-virialized axion search over the mass range 2.81–3.31 µeV, corresponding to the frequency range 680–800 MHz. This analysis marks the most sensitive search for non-virialized axions sensitive to Doppler effects in the Milky Way Halo to date. Accounting for frequency shifts due to the detector’s motion through the Galaxy, we exclude cold flow relic axions with a velocity dispersion of $\mathscr{O}$(10 -7 )c with 95% confidence.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Constraining neutrino-DM interactions with Milky Way dwarf spheroidals and supernova neutrinos

We constrain the neutrino-dark matter cross section using properties of the dark matter density profiles of Milky Way dwarf spheroidal galaxies. The constraint arises from core-collapse supernova neutrinos scattering on dark matter as a form of energy injection, allowing the transformation of the dark matter density profile from a cusped profile to a flatter profile. We assume a standard cosmology of dark energy and cold, collisionless, and non-self-interacting dark matter. By requiring that the dark matter cores do not lose too much mass or overshoot constraints from stellar kinematics, we place an upper limit on the cross section of σ ν − DM ( E ν = 15 MeV , m χ ≲ 130 GeV ) ≈ 3.4 × 10 − 23 cm 2 and σ ν − DM ( E ν = 15 MeV , m χ ≳ 130 GeV ) ≈ 3.2 × 10 − 27 ( m χ 1 GeV ) 2 cm 2 , which is stronger than previous bounds for these energies. Consideration of baryonic feedback or host galaxy effects on the dark matter profile can strengthen this constraint. Published by the American Physical Society 2024

Astronomy & Astrophysics↗

Mixed warm dark matter constraints using Milky Way satellite galaxy counts

Warm dark matter has been strongly constrained in recent years as the sole component of dark matter. However, a less-explored alternative is that dark matter consists of a mixture of warm and cold dark matter (MWDM). In this work, we use observations of Milky Way satellite galaxies to constrain MWDM scenarios where the formation of small-scale structure is suppressed either by generic thermal relic warm dark matter or a sterile neutrino produced through the Shi-Fuller mechanism. To achieve this, we model satellite galaxies by combining numerical simulations with semianalytical models for the subhalo population, and use a galaxy-halo connection model to match galaxies onto dark matter subhalos. By comparing the number of satellites predicted by MWDM models to the observed satellite population from the Dark Energy Survey and Pan-STARRS1, we constrain the fraction of warm dark matter, f WDM , as a function of its mass, m WDM . We exclude dark matter being composed entirely of thermal relic warm dark matter with m WDM ≤ 6.6 keV at a posterior ratio of 10 ∶ 1 , consistent with previous works. However, we find that warm dark matter with smaller mass is allowed when mixed with cold dark matter, and that the f WDM constraints strengthen with decreasing m WDM until they plateau at f WDM ≲ 0.45 for m WDM ≲ 1.5 keV . Likewise, in the case of a sterile neutrino with mass of 7 keV produced through the Shi-Fuller mechanism, we exclude a fraction of f ν s ≲ 0.45 , independent of mixing angle. Our results extend constraints on MWDM to a region of parameter space that has been relatively unconstrained with previous analysis.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Milky way bulge extra-tidal star survey: MWBest

The Milky Way Bulge Extra-Tidal Star Survey (MWBest) is a spectroscopic initiative aimed at identifying stars that have been tidally stripped from globular clusters in the inner regions of the Galaxy. As part of the Visiting Faculty Program at Fermilab, we have developed theoretical tools and simulations to compare against observed signatures of extra-tidal stars surrounding both bulge globular clusters (GCs) and low-luminosity clusters. By combining the spatial distributions of simulated stripped stars with new MWBest observations, we are gaining insight into the gravitational potential of the inner Galaxy and the role that bulge GCs may play in enriching the surrounding field star population. We further explore the hypothesis that some low-luminosity bulge GCs may in fact be dense clumps of debris, stripped from more massive GCs as they migrate inward due to dynamical friction.

Kunder, Andrea [Unlisted, US, WA]↗

Two Ultra-faint Milky Way Stellar Systems Discovered in Early Data from the DECam Local Volume Exploration Survey

We report the discovery of two ultra-faint stellar systems found in early data from the DECam Local Volume Exploration survey (DELVE). The first system, Centaurus I (DELVE J1238-4054), is identified as a resolved overdensity of old and metal-poor stars with a heliocentric distance of ${\rm D}_{\odot} = 116.3_{-0.6}^{+0.6}$ kpc, a half-light radius of $r_h = 2.3_{-0.3}^{+0.4}$ arcmin, an age of $\tau > 12.85$ Gyr, a metallicity of $Z = 0.0002_{-0.0002}^{+0.0001}$, and an absolute magnitude of $M_V = -5.55_{-0.11}^{+0.11}$ mag. This characterization is consistent with the population of ultra-faint satellites, and confirmation of this system would make Centaurus I one of the brightest recently discovered ultra-faint dwarf galaxies. Centaurus I is detected in Gaia DR2 with a clear and distinct proper motion signal, confirming that it is a real association of stars distinct from the Milky Way foreground; this is further supported by the clustering of blue horizontal branch stars near the centroid of the system. The second system, DELVE 1 (DELVE J1630-0058), is identified as a resolved overdensity of stars with a heliocentric distance of ${\rm D}_{\odot} = 19.0_{-0.6}^{+0.5} kpc$, a half-light radius of $r_h = 0.97_{-0.17}^{+0.24}$ arcmin, an age of $\tau = 12.5_{-0.7}^{+1.0}$ Gyr, a metallicity of $Z = 0.0005_{-0.0001}^{+0.0002}$, and an absolute magnitude of $M_V = -0.2_{-0.6}^{+0.8}$ mag, consistent with the known population of faint halo star clusters. Here, given the low number of probable member stars at magnitudes accessible with Gaia DR2, a proper motion signal for DELVE 1 is only marginally detected. We compare the spatial position and proper motion of both Centaurus I and DELVE 1 with simulations of the accreted satellite population of the Large Magellanic Cloud (LMC) and find that neither is likely to be associated with the LMC.

79 ASTRONOMY AND ASTROPHYSICS↗

Milky Way Satellite Census -- II. Galaxy-Halo Connection Constraints Including the Impact of the Large Magellanic Cloud

The population of Milky Way (MW) satellites contains the faintest known galaxies, and thus provides essential insight into galaxy formation and dark matter microphysics. Here, we combine a model of the galaxy--halo connection with newly derived observational selection functions based on searches for satellites in photometric surveys over nearly the entire high-Galactic-latitude sky. In particular, we use cosmological zoom-in simulations of MW-like halos that include realistic Large Magellanic Cloud (LMC) analogs to fit the position-dependent MW satellite luminosity function. We report decisive evidence for the statistical impact of the LMC on the MW satellite population due to an estimated $6.5\pm 1.5$ observed LMC-associated satellites, consistent with the number of LMC satellites inferred from $\textit{Gaia}$ proper motion measurements, confirming the predictions of cold dark matter models for the existence of satellites within satellite halos. Moreover, we infer that the LMC fell into the MW within the last $2\ \rm{Gyr}$ at high confidence. Based on our detailed full-sky modeling, we find that the faintest observed satellites inhabit halos with peak virial masses below $2.2\times 10^{8}\ M_{\rm{\odot}}$ at $95\%$ confidence, and we place the first robust constraints on the fraction of halos that host galaxies in this regime. We predict that the faintest detectable satellites occupy halos with peak virial masses above $10^{6}\ M_{\rm{\odot}}$, highlighting the potential for powerful galaxy formation and dark matter constraints from future dwarf galaxy searches.

79 ASTRONOMY AND ASTROPHYSICS↗

The SAGA Survey. II. Building a Statistical Sample of Satellite Systems around Milky Way–like Galaxies

In this work, we present the Stage II results from the ongoing Satellites Around Galactic Analogs (SAGA) Survey. Upon completion, the SAGA Survey will spectroscopically identify satellite galaxies brighter than M r,o = -12.3 around 100 Milky Way (MW) analogs at z ~ 0.01. In Stage II, we have more than quadrupled the sample size of Stage I, delivering results from 127 satellites around 36 MW analogs with an improved target selection strategy and deep photometric imaging catalogs from the Dark Energy Survey and the Legacy Surveys. We have obtained 25,372 galaxy redshifts, peaking around z = 0.2. These data significantly increase spectroscopic coverage for very low redshift objects in 17 < r o < 20.75 around SAGA hosts, creating a unique data set that places the Local Group in a wider context. The number of confirmed satellites per system ranges from zero to nine and correlates with host galaxy and brightest satellite luminosities. We find that the number and luminosities of MW satellites are consistent with being drawn from the same underlying distribution as SAGA systems. The majority of confirmed SAGA satellites are star-forming, and the quenched fraction increases as satellite stellar mass and projected radius from the host galaxy decrease. Overall, the satellite quenched fraction among SAGA systems is lower than that in the Local Group. We compare the luminosity functions and radial distributions of SAGA satellites with theoretical predictions based on cold dark matter simulations and an empirical galaxy–halo connection model and find that the results are broadly in agreement.

79 ASTRONOMY AND ASTROPHYSICS↗

R-process-rich Stellar Streams in the Milky Way*

We present high-resolution Magellan/MIKE spectra of 22 bright (9 < V < 13.5) metal-poor stars (-3.18 < [Fe/H] < -1.37) in three different stellar streams, the Helmi debris stream, the Helmi trail stream, and the ω Centauri progenitor stream. We augment our Helmi debris sample with results for 10 stars by Roederer et al. for a total of 32 stars. Detailed chemical abundances of light elements as well as heavy neutron-capture elements have been determined for our 22 stars. All three streams contain carbon-enhanced stars. For 13 stars, neutron-capture element lines were detectable, and they all show signatures in agreement with the scaled solar r -process pattern, albeit with a large spread of -0.5 < [Eu/Fe] < +1.3. Eight of these stars show an additional small s -process contribution superposed onto their r -process pattern. This could be discerned because of the relatively high signal-to-noise ratio of the spectra given that the stars are close by in the halo. Our results suggest that the progenitors of these streams experienced one or more r -process events early on, such as a neutron star merger or another prolific r -process source. This widely enriched these host systems before their accretion by the Milky Way. The small s -process contribution suggests the presence of asymptotic giant branch stars and associated local (inhomogeneous) enrichment as part of the ongoing chemical evolution by low-mass stars. Stars in stellar streams may thus be a promising avenue for studying the detailed history of large dwarf galaxies and their role in halo assembly with easily accessible targets for high-quality spectra of many stars.

Astronomy & Astrophysics↗

Simultaneous Estimation of Large-scale Structure and Milky Way Dust Extinction from Galaxy Surveys

The high cosmological precision offered by the next generation of galaxy surveys hinges on improved corrections for Galactic dust extinction. We explore the possibility of estimating both the dust extinction and large-scale structure from a single photometric galaxy survey, making use of the predictable manner in which Milky Way dust affects the measured brightness and colors of galaxies in a given sky location in several redshift bins. To test our method, we use a synthetic catalog from a cosmological simulation designed to model the Vera C. Rubin Observatory Legacy Survey of Space and Time. At high Galactic latitude (|b| ≳ 20°) and a resolution of 1° (7'), we predict the uncertainty in the measurement of dust extinction, E(B - V), to be 0.005 mag (0.015 mag). This is similar to the uncertainty of existing dust maps, illustrating the feasibility of our method. Simultaneous estimation of large-scale structure is predicted to recover the galaxy overdensity δ with a precision of ~0.01 (~0.05) at 1° (7') resolution. Finally, we also introduce a Bayesian formalism that combines prior information from existing dust maps with the likelihood of Galactic dust extinction determined from the excursion of observed galaxy properties.

79 ASTRONOMY AND ASTROPHYSICS↗

The Missing Satellite Problem outside of the Local Group. II. Statistical Properties of Satellites of Milky Way–like Galaxies

We present a new observation of satellite galaxies around seven Milky Way (MW)–like galaxies located outside of the Local Group (LG) using Subaru/Hyper Suprime-Cam imaging data to statistically address the missing satellite problem. We select satellite galaxy candidates using magnitude, surface brightness, Sérsic index, axial ratio, FWHM, and surface brightness fluctuation cuts, followed by visual screening of false positives such as optical ghosts of bright stars. We identify 51 secure dwarf satellite galaxies within the virial radius of nine host galaxies, two of which are drawn from the pilot observation presented in Paper I. We find that the average luminosity function of the satellite galaxies is consistent with that of the MW satellites, although the luminosity function of each host galaxy varies significantly. We observe an indication that more massive hosts tend to have a larger number of satellites. Physical properties of the satellites such as the size–luminosity relation are also consistent with the MW satellites. However, the spatial distribution is different; we find that the satellite galaxies outside of the LG show no sign of concentration or alignment, while that of the MW satellites is more concentrated around the host and exhibits a significant alignment. As we focus on relatively massive satellites with M V < –10, we do not expect that the observational incompleteness can be responsible here. This trend might represent a peculiarity of the MW satellites, and further work is needed to understand its origin.

79 ASTRONOMY AND ASTROPHYSICS↗

The Chocolate Chip Cookie Model: Dust Geometry of Milky Way–like Disk Galaxies

We present a new two-component dust geometry model, the Chocolate Chip Cookie model, where the clumpy nebular regions are embedded in a diffuse stellar/interstellar medium disk, like chocolate chips in a cookie. By approximating the binomial distribution of the clumpy nebular regions with a continuous Gaussian distribution and omitting the dust scattering effect, our model solves the dust attenuation process for both the emission lines and stellar continua via analytical approaches. Our Chocolate Chip Cookie model successfully fits the inclination dependence of both the effective dust reddening of the stellar components derived from stellar population synthesis and that of the emission lines characterized by the Balmer decrement for a large sample of Milky Way–like (MW-like) disk galaxies selected from the main galaxy sample of the Sloan Digital Sky Survey. Our model shows that the clumpy nebular disk is about 0.55 times thinner and 1.6 times larger than the stellar disk for MW-like galaxies, whereas each clumpy region has a typical optical depth of τ cl,V ~ 0.5 in the V band. After considering the aperture effect, our model prediction on the inclination dependence of dust attenuation is also consistent with observations. Not only that, in our model, the dust attenuation curve of the stellar population naturally depends on the inclination, and its median case is consistent with the classical Calzetti law. As the modeling constraints are from the optical wavelengths, our model is unaffected by the optically thick dust component, which however could bias the model's prediction of the infrared emissions.

79 ASTRONOMY AND ASTROPHYSICS↗

Proper Motions, Orbits, and Tidal Influences of Milky Way Dwarf Spheroidal Galaxies

We combine Gaia early data release 3 astrometry with accurate photometry and utilize a probabilistic mixture model to measure the systemic proper motion of 52 dwarf spheroidal (dSph) satellite galaxies of the Milky Way (MW). For the 46 dSphs with literature line-of-sight velocities we compute orbits in both a MW and a combined MW + Large Magellanic Cloud (LMC) potential and identify Car II, Car III, Hor I, Hyi I, Phx II, and Ret II as likely LMC satellites. 40% of our dSph sample has a >25% change in pericenter and/or apocenter with the MW + LMC potential. For these orbits, we use a Monte Carlo sample for the observational uncertainties for each dSph and the uncertainties in the MW and LMC potentials. We predict that Ant II, Boo III, Cra II, Gru II, and Tuc III should be tidally disrupting by comparing each dSph's average density relative to the MW density at its pericenter. dSphs with large ellipticity (CVn I, Her, Tuc V, UMa I, UMa II, UMi, Wil 1) show a preference for their orbital direction to align with their major axis even for dSphs with large pericenters. We compare the dSph radial orbital phase to subhalos in MW-like N-body simulations and infer that there is not an excess of satellites near their pericenter. With projections of future Gaia data releases, we find that dSph's orbital precision will be limited by uncertainties in the distance and/or MW potential rather than in proper motion precision. Finally, we provide our membership catalogs to enable community follow-up.

79 ASTRONOMY AND ASTROPHYSICS↗

The Circular Velocity Curve of the Milky Way from 5–25 kpc Using Luminous Red Giant Branch Stars

We present a sample of 254,882 luminous red giant branch (LRGB) stars selected from the APOGEE and LAMOST surveys. By combining photometric and astrometric information from the Two Micron All Sky Survey and Gaia survey, the precise distances of the sample stars are determined by a supervised machine-learning algorithm: the gradient-boosted decision trees. To test the accuracy of the derived distances, member stars of globular clusters (GCs) and open clusters are used. The tests by cluster member stars show a precision of about 10% with negligible zero-point offsets, for the derived distances of our sample stars. The final sample covers a large volume of the Galactic disk(s) and halo of 0 < R < 30 kpc and |Z| ≤ 15 kpc. The rotation curve (RC) of the Milky Way across the radius of 5 ≲ R ≲ 25 kpc has been accurately measured with ~54,000 stars of the thin disk population selected from the LRGB sample. The derived RC shows a weak decline along R with a gradient of -1.83 ± 0.02 (stat.) ± 0.07 (sys.) km s -1 kpc -1 , in excellent agreement with the results measured by previous studies. The circular velocity at the solar position, yielded by our RC is 234.04 ± 0.08 (stat.) ± 1.36 (sys.) km s -1 , again in great consistency with other independent determinations. From the newly constructed RC, as well as constraints from other data, we have constructed a mass model for our Galaxy, yielding a mass of the dark matter halo of M 200 = (8.05 ± 1.15) × 10 11 M ⊙ with a corresponding radius of R 200 = 192.37 ± 9.24 kpc and a local dark matter density of 0.39 ± 0.03 GeV cm -3 .

79 ASTRONOMY AND ASTROPHYSICS↗

Chemodynamical Analysis of Metal-rich High-eccentricity Stars in the Milky Way's Disk

We present a chemodynamical analysis of 11,562 metal-rich, high-eccentricity halo-like main-sequence stars, which have been referred to as the Splash or Splashed Disk, selected from the Sloan Digital Sky Survey and Large Sky Area Multi-Object Fiber Spectroscopic Telescope. When divided into two groups, a low-[α/Fe] population (LAP) and a high-[α/Fe] population (HAP), based on kinematics and chemistry, we find that they exhibit very distinct properties, indicative of different origins. From a detailed analysis of their orbital inclinations, we suggest that the HAP arises from a large fraction (~90%) of heated disk stars and a small fraction (~10%) of in situ stars from a starburst population, likely induced by interaction of the Milky Way with the Gaia-Sausage/Enceladus (GSE) or another early merger. The LAP comprises about half accreted stars from the GSE and half formed by the GSE-induced starburst. Our findings further imply that the Splash stars in our sample originated from at least three different mechanisms: accretion, disk heating, and a merger-induced starburst.

79 ASTRONOMY AND ASTROPHYSICS↗

Strong Dark Matter Self-interactions Diversify Halo Populations within and surrounding the Milky Way

Abstract We perform a high-resolution cosmological zoom-in simulation of a Milky Way (MW)–like system, which includes a realistic Large Magellanic Cloud analog, using a large differential elastic dark matter self-interaction cross section that reaches ≈100 cm 2 g −1 at relative velocities of ≈10 km s −1 , motivated by the diverse and orbitally dependent central densities of dwarf galaxies within and surrounding the MW. We explore the effects of dark matter self-interactions on satellite, splashback, and isolated halos through their abundance, central densities, maximum circular velocities, orbital parameters, and correlations between these variables. We use an effective constant cross section model to analytically predict the stages of our simulated halos’ gravothermal evolution, demonstrating that deviations from the collisionless R max – V max relation can be used to select deeply core-collapsed halos, where V max is a halo’s maximum circular velocity, and R max is the radius at which it occurs. We predict that a sizable fraction (≈20%) of subhalos with masses down to ≈10 8 M ⊙ is deeply core collapsed in our SIDM model. Core-collapsed systems form ≈10% of the isolated halo population down to the same mass; these isolated, core-collapsed halos would host faint dwarf field galaxies with extremely steep central density profiles. Finally, most halos with masses above ≈10 9 M ⊙ are core-forming in our simulation. Our study thus demonstrates how self-interactions diversify halo populations in an environmentally dependent fashion within and surrounding MW-mass hosts, providing a compelling avenue to address the diverse dark matter distributions of observed dwarf galaxies.

79 ASTRONOMY AND ASTROPHYSICS↗

Six More Ultra-faint Milky Way Companions Discovered in the DECam Local Volume Exploration Survey

We report the discovery of six ultra-faint Milky Way satellites identified through matched-filter searches conducted using Dark Energy Camera (DECam) data processed as part of the second data release of the DECam Local Volume Exploration (DELVE) survey. Leveraging deep Gemini/GMOS-N imaging (for four candidates) as well as follow-up DECam imaging (for two candidates), we characterize the morphologies and stellar populations of these systems. We find that these candidates all share faint absolute magnitudes (M$_{V}$ ≥ −3.2 mag) and old, metal-poor stellar populations (τ > 10 Gyr, [Fe/H] < −1.4 dex). Three of these systems are more extended (r$_{1/2}$ > 15 pc), while the other three are compact (r$_{1/2}$ < 10 pc). From these properties, we infer that the former three systems (Boötes V, Leo Minor I, and Virgo II) are consistent with ultra-faint dwarf galaxy classifications, whereas the latter three (DELVE 3, DELVE 4, and DELVE 5) are likely ultra-faint star clusters. Using data from the Gaia satellite, we confidently measure the proper motion of Boötes V, Leo Minor I, and DELVE 4, and tentatively detect a proper-motion signal from DELVE 3 and DELVE 5; no signal is detected for Virgo II. We use these measurements to explore possible associations between the newly discovered systems and the Sagittarius dwarf spheroidal, the Magellanic Clouds, and the Vast Polar Structure, finding several plausible associations. Our results offer a preview of the numerous ultra-faint stellar systems that will soon be discovered by the Vera C. Rubin Observatory and highlight the challenges of classifying the faintest stellar systems.

79 ASTRONOMY AND ASTROPHYSICS↗

ESCARGOT: Mapping Vertical Phase Spiral Characteristics Throughout the Real and Simulated Milky Way

Abstract The recent discovery of a spiral pattern in the vertical kinematic structure in the solar neighborhood provides a prime opportunity to study nonequilibrium dynamics in the Milky Way from local stellar kinematics. Furthermore, results from simulations indicate that even in a limited volume, differences in stellar orbital histories allow us to trace variations in the initial perturbation across large regions of the disk. We present ESCARGOT , a novel algorithm for studying these variations in both simulated and observed data sets. ESCARGOT automatically extracts key quantities from the structure of a given phase spiral, including the time since perturbation and the perturbation mode. We test ESCARGOT on simulated data and show that it is capable of accurately recovering information about the time since the perturbation occurred as well as subtle differences in phase spiral morphology due to stellar locations in the disk at the time of perturbation. We apply ESCARGOT to kinematic data from data release 3 of the Gaia mission in bins of guiding radius. We show that similar structural differences in morphology occur in the Gaia phase spirals as a function of stellar orbital history. These results indicate that the phase spirals are the product of a complex dynamical response in the disk with large-scale coupling between different regions of phase space.

Darragh-Ford, Elise (ORCID:0000000288005652)↗

A Search for Faint Resolved Galaxies Beyond the Milky Way in DES Year 6: A New Faint, Diffuse Dwarf Satellite of NGC 55

We report results from a systematic wide-area search for faint dwarf galaxies at heliocentric distances from 0.3 to 2 Mpc using the full 6 yr of data from the Dark Energy Survey (DES). Unlike previous searches over the DES data, this search specifically targeted a field population of faint galaxies located beyond the Milky Way virial radius. We derive our detection efficiency for faint, resolved dwarf galaxies in the Local Volume with a set of synthetic galaxies and expect our search to be complete to M$_{V}$ ∼ (−7, −10) mag for galaxies at D = (0.3, 2.0) Mpc. We find no new field dwarfs in the DES footprint, but we report the discovery of one high-significance candidate dwarf galaxy at a distance of , a potential satellite of the Local Volume galaxy NGC 55, separated by 47′ (physical separation as small as 30 kpc). We estimate this dwarf galaxy to have an absolute V-band magnitude of and an azimuthally averaged physical half-light radius of , making this one of the lowest surface brightness galaxies ever found with . This is the largest, most diffuse galaxy known at this luminosity, suggesting possible tidal interactions with its host.

79 ASTRONOMY AND ASTROPHYSICS↗