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The method of multivariable Mendelian randomization uses genetic variants to instrument multiple exposures, to estimate the effect that a given exposure has on an outcome conditional on all other exposures included in a linear model. Unfortunately, the inclusion of every additional exposure makes a weak instruments problem more likely, because we require conditionally strong genetic predictors of each exposure. This issue is well appreciated in practice, with different versions of F-statistics routinely reported as measures of instument strength. Less transparently, however, these F-statistics are sometimes used to guide instrument selection, and even to decide whether to report empirical results. Rather than discarding findings with low F-statistics, weak instrument-robust methods can provide valid inference under weak instruments. For multivariable Mendelian randomization with two-sample summary data, we encourage use of the inference strategy of Andrews (2018) that reports both robust and non-robust confidence sets, along with a statistic that measures how reliable the non-robust confidence set is in terms of coverage. We also propose a novel adjusted-Kleibergen statistic that corrects for overdispersion heterogeneity in genetic associations with the outcome.

We study accretion remnants around Milky Way analogs in the IllustrisTNG simulations to determine how well commonly used distribution functions (DFs) describe their phase-space distributions. We identify 30 Milky Way analogs and 116 remnants from mergers with stellar mass ratios greater than 1:20. Two-power density profiles, as well as rotating constant-anisotropy and Osipkov-Merritt DFs are fit to the remnants. We determine that the remnants are suitable for equilibrium modelling by assessing them in the context of the Jeans equation. Each of the models we consider are reasonably able to fit the stellar remnant energy and angular momentum distribution, as well as the magnitude and shape of velocity dispersion profiles. Case studies matched to two well-known merger remnants in the stellar halo-Gaia-Sausage/Enceladus (GS/E) and Sequoia-are explored in more depth. We find good evidence that remnants with high anisotropy $\beta$, such as GS/E, are better modelled with a superposition of two Osipkov-Merritt DFs than either a constant-anisotropy model or a single Osipkov-Merritt DF. We estimate an Osipkov-Merritt profile with scale radius between 2-4 kpc would be a good first-order representation of GS/E, and comment on existing observational evidence for this as well as studies which could demonstrate it. Overall, we find that DF-based models work well for describing the kinematics of large merger remnants. Our results will be an important reference for future studies which seek to constrain both the spatial and kinematic properties of merger remnants in the Milky Way stellar halo., Comment: 17 pages, 11 figures. Submitted to MNRAS. Comments welcome

This work presents the Globular cluster Extra-tidal Mock Star (GEMS) catalogue of extra-tidal stars and binaries created via three-body dynamical encounters in globular cluster cores. Using the particle-spray code Corespray, we sample N=50,000 extra-tidal stars and escaped recoil binaries for 159 Galactic globular clusters. Sky positions, kinematics, stellar properties and escape information are provided for all simulated stars. Stellar orbits are integrated in seven different static and time-varying Milky Way gravitational potential models where the structure of the disc, perturbations from the Large Magellanic Cloud and the mass and sphericity of the Milky Way's dark matter halo are all investigated. We find that the action coordinates of the mock extra-tidal stars are largely Galactic model independent, where minor offsets and broadening of the distributions between models are likely due to interactions with substructure. Importantly, we also report the first evidence for stellar stream contamination by globular cluster core stars and binaries for clusters with pericentre radii larger than five kiloparsecs. Finally, we provide a quantitative tool that uses action coordinates to match field stars to host clusters with probabilities. Ultimately, combining data from the GEMS catalogue with information of observed stars will allow for association of extra-tidal field stars with any Galactic globular cluster; a requisite tool for understanding population-level dynamics and evolution of clusters in the Milky Way., Comment: 23 pages, 12 figures, 1 table. Accepted for publication in Monthly Notices of the Royal Astronomical Society. For the associated GEMS catalogue, please visit https://zenodo.org/records/8436703

The \textit{Gaia}-Sausage/Enceladus (GS/E) structure is an accretion remnant which comprises a large fraction of the Milky Way's stellar halo. We study GS/E using high-purity samples of kinematically selected stars from APOGEE DR16 and \textit{Gaia}. Employing a novel framework to account for kinematic selection biases using distribution functions, we fit density profiles to these GS/E samples and measure their masses. We find that GS/E has a shallow density profile in the inner Galaxy, with a break between 15--25~kpc beyond which the profile steepens. We also find that GS/E is triaxial, with axis ratios 1:0.55:0.45 (nearly prolate), and the major axis is oriented about 80~degrees from the Sun--Galactic centre line and 16 degrees above the plane. We measure a stellar mass for GS/E of $1.45\,^{+0.92}_{-0.51}\,\mathrm{(stat.)}\,^{+0.13}_{-0.37} \mathrm{(sys.)}\ \times10^{8}$~\Msun. Our mass estimate is lower than others in the literature, a finding we attribute to the excellent purity of the samples we work with. We also fit a density profile to the entire Milky Way stellar halo, finding a mass in the range of $6.7-8.4 \times 10^{8}$~\Msun, and implying that GS/E could make up as little as 15-25~per~cent of the mass of the Milky Way stellar halo. Our lower stellar mass combined with standard stellar-mass-to-halo mass relations implies that GS/E constituted a minor 1:8 mass-ratio merger at the time of its accretion., Comment: Accepted in MNRAS

We present the four-year survey results of monthly submillimeter monitoring of eight nearby ($< 500 $pc) star-forming regions by the JCMT Transient Survey. We apply the Lomb-Scargle Periodogram technique to search for and characterize variability on 295 submillimeter peaks brighter than 0.14 Jy beam$^{-1}$, including 22 disk sources (Class II), 83 protostars (Class 0/I), and 190 starless sources. We uncover 18 secular variables, all of them protostars. No single-epoch burst or drop events and no inherently stochastic sources are observed. We classify the secular variables by their timescales into three groups: Periodic, Curved, and Linear. For the Curved and Periodic cases, the detectable fractional amplitude, with respect to mean peak brightness, is $\sim4$ % for sources brighter than $\sim$ 0.5 Jy beam$^{-1}$. Limiting our sample to only these bright sources, the observed variable fraction is 37 % (16 out of 43). Considering source evolution, we find a similar fraction of bright variables for both Class 0 and Class I. Using an empirically motivated conversion from submillimeter variability to variation in mass accretion rate, six sources (7 % of our full sample) are predicted to have years-long accretion events during which the excess mass accreted reaches more than 40 % above the total quiescently accreted mass: two previously known eruptive Class I sources, V1647 Ori and EC 53 (V371 Ser), and four Class 0 sources, HOPS 356, HOPS 373, HOPS 383, and West 40. Considering the full protostellar ensemble, the importance of episodic accretion on few years timescale is negligible, only a few percent of the assembled mass. However, given that this accretion is dominated by events of order the observing time-window, it remains uncertain as to whether the importance of episodic events will continue to rise with decades-long monitoring., Comment: Accepted for publication in the Astrophysical Journal

In the $Gaia$ era stellar kinematics are extensively used to study Galactic halo stellar populations, to search for halo structures, and to characterize the interface between the halo and hot disc populations. We use distribution function-based models of modern datasets with 6D phase space data to qualitatively describe a variety of kinematic spaces commonly used in the study of the Galactic halo. Furthermore, we quantitatively assess how well each kinematic space can separate radially anisotropic from isotropic halo populations. We find that scaled action space (the ``action diamond'') is superior to other commonly used kinematic spaces at this task. We present a new, easy to implement selection criterion for members of the radially-anisotropic $Gaia$-Enceladus merger remnant. Assuming a 1:1 ratio of $Gaia$-Enceladus stars to more isotropic halo, we find our selection achieves a sample purity of 82 per cent in our models with respect to contamination from the more isotropic halo. We compare this criterion to literature criteria, finding that it produces the highest purity in the resulting samples, at the expense of a modest reduction in completeness. We also show that selection biases that underlie nearly all contemporary spectroscopic datasets can noticeably impact the $E-L_{z}$ distribution of samples in a manner that may be confused for real substructure. We conclude by providing recommendations for how authors should use stellar kinematics in the future to study the Galactic stellar halo., Comment: MNRAS in press

The low-metallicity, kinematically interesting dwarf stars studied by Stephens \& Boesgaard (2002, SB02) are re-examined using Gaia DR2 astrometry, and updated model atmospheres and atomic line data. New stellar parameters are determined based on the Gaia DR2 parallactic distances and Dartmouth Stellar Evolution Database isochrones. These are in excellent agreement with spectroscopically determined stellar parameters for stars with [Fe/H]$>-2$; however, large disagreements are found for stars with [Fe/H]$\le-2$, with offsets as large as $\Delta$T$_{\rm eff}\sim+500$ K and $\Delta$log\,$g\sim+1.0$. A subset of six stars (test cases) are analysed ab initio using high resolution spectra with Keck HIRES and Gemini GRACES. This sub-sample is found to include two $\alpha$-challenged dwarf stars, suggestive of origins in a low mass, accreted dwarf galaxy. The orbital parameters for the entire SB02 sample are re-determined using \textit{Gaia} DR2 data. We find 11 stars that are dynamically coincident with the \textit{Gaia}-Sausage accretion event and another 17 with the \textit{Gaia}-Sequoia event in action space. Both associations include low-mass, metal-poor stars with isochrone ages older than 10 Gyr. Two dynamical subsets are identified within \textit{Gaia}-Sequoia. When these subsets are examined separately, a common knee in [$\alpha$/Fe] is found for the \textit{Gaia}-Sausage and low orbital energy \textit{Gaia}-Sequoia stars. A lower metallicity knee is tentatively identified in the \textit{Gaia}-Sequoia high orbital energy stars. If the metal-poor dwarf stars in these samples are true members of the \textit{Gaia}-Sausage and \textit{Gaia}-Sequoia events, then they present a unique opportunity to probe the earlier, more pristine, star formation histories of these systems., Comment: 20-21 pages, 20 figures, accepted for publication in MNRAS Slight mismatch between published version and arXiv version, rectified now

The Ophiuchus stream is a short arc-like stellar feature of uncertain origin located $\sim 5$ kpc North of the Galactic centre. New proper motions from the second $Gaia$ data release reconcile the direction of motion of stream members with the stream arc, resolving a puzzling mismatch reported in earlier work. We use N-body simulations to show that the stream is likely only on its second pericentric passage, and thus was formed recently. The simulations suggest that the entire disrupted progenitor is visible in the observed stream today, and that little further tidal debris lies beyond the ends of the stream. The luminosity, length, width, and velocity dispersion of the stream suggest a globular cluster (GC) progenitor substantially fainter and of lower surface brightness than estimated in previous work, and unlike any other known globulars in the Galaxy. This result suggests the existence of clusters that would extend the known GC population to fainter and more weakly bound systems than hitherto known. How such a weakly-bound cluster of old stars survived until it was disrupted so recently, however, remains a mystery. Integrating backwards in time, we find that the orbits of Sagittarius and Ophiuchus passed within $\sim 5$ kpc of each other about $\sim 100$ Myrs ago, an interaction that might help resolve this puzzle., Comment: 11 pages, 7 figures, submitted to MNRAS

We analyze results from the first eighteen months of monthly sub-mm monitoring of eight star-forming regions in the JCMT Transient Survey. In our search for stochastic variability in 1643 bright peaks, only the previously identified source, EC53, shows behavior well above the expected measurement uncertainty. Another four sources, two disks and two protostars, show moderately-enhanced standard deviations in brightness, as expected for stochastic variables. For the two protostars, this apparent variability is the result of single epochs that are much brighter than the mean. In our search for secular brightness variations that are linear in time, we measure the fractional brightness change per year for 150 bright peaks, fifty of which are protostellar. The ensemble distribution of slopes is well fit by a normal distribution with sigma ~ 0.023. Most sources are not rapidly brightening or fading in the sub-mm. Comparison against time-randomized realizations shows that the width of the distribution is dominated by the uncertainty in the individual brightness measurements of the sources. A toy model for secular variability reveals that an underlying Gaussian distribution of linear fractional brightness change sigma = 0.005 would be unobservable in the present sample, whereas an underlying distribution with sigma = 0.02 is ruled out. Five protostellar sources, 10% of the protostellar sample, are found to have robust secular measures deviating from a constant flux. The sensitivity to secular brightness variations will improve significantly with a larger time sample, with a factor of two improvement expected by the conclusion of our 36-month survey., Comment: Accepted for publication in ApJ. 27 pages, 15 figures, 7 tables

Investigating variability at the earliest stages of low-mass star formation is fundamental in understanding how a protostar assembles mass. While many simulations of protostellar disks predict non-steady accretion onto protostars, deeper investigation requires robust observational constraints on the frequency and amplitude of variability events characterised across the observable SED. In this study, we develop methods to robustly analyse repeated observations of an area of the sky for submillimetre variability in order to determine constraints on the magnitude and frequency of deeply embedded protostars. We compare \mbox{850 $\mu$m} JCMT Transient Survey data with archival JCMT Gould Belt Survey data to investigate variability over 2-4 year timescales. Out of 175 bright, independent emission sources identified in the overlapping fields, we find 7 variable candidates, 5 of which we classify as \textit{Strong} and the remaining 2 as \textit{Extended} to indicate the latter are associated with larger-scale structure. For the \textit{Strong} variable candidates, we find an average fractional peak brightness change per year of |4.0|\% yr$^{-1}$ with a standard deviation of $2.7\%\mathrm{\:yr}^{-1}$. In total, 7\% of the protostars associated with \mbox{850 $\mu$m} emission in our sample show signs of variability. Four of the five \textit{Strong} sources are associated with a known protostar. The remaining source is a good follow-up target for an object that is anticipated to contain an enshrouded, deeply embedded protostar. In addition, we estimate the \mbox{850 $\mu$m} periodicity of the submillimetre variable source, EC 53, to be \mbox{567 $\pm$ 32 days} based on the archival Gould Belt Survey data., Comment: 33 Pages, 19 figures, Accepted in ApJ

Most protostars have luminosities that are fainter than expected from steady accretion over the protostellar lifetime. The solution to this problem may lie in episodic mass accretion -- prolonged periods of very low accretion punctuated by short bursts of rapid accretion. However, the timescale and amplitude for variability at the protostellar phase is almost entirely unconstrained. In "A JCMT/SCUBA-2 Transient Survey of Protostars in Nearby Star Forming Regions", we are monitoring monthly with SCUBA-2 the sub-mm emission in eight fields within nearby (<500 pc) star forming regions to measure the accretion variability of protostars. The total survey area of ~1.6 sq.deg. includes ~105 peaks with peaks brighter than 0.5 Jy/beam (43 associated with embedded protostars or disks) and 237 peaks of 0.125-0.5 Jy/beam (50 with embedded protostars or disks). Each field has enough bright peaks for flux calibration relative to other peaks in the same field, which improves upon the nominal flux calibration uncertainties of sub-mm observations to reach a precision of ~2-3% rms, and also provides quantified confidence in any measured variability. The timescales and amplitudes of any sub-mm variation will then be converted into variations in accretion rate and subsequently used to infer the physical causes of the variability. This survey is the first dedicated survey for sub-mm variability and complements other transient surveys at optical and near-IR wavelengths, which are not sensitive to accretion variability of deeply embedded protostars., Comment: ApJ, accepted

Though there has been a significant amount of work investigating the early stages of low-mass star formation in recent years, the evolution of the mass assembly rate onto the central protostar remains largely unconstrained. Examining in depth the variation in this rate is critical to understanding the physics of star formation. Instabilities in the outer and inner circumstellar disk can lead to episodic outbursts. Observing these brightness variations at infrared or submillimetre wavelengths sets constraints on the current accretion models. The JCMT Transient Survey is a three-year project dedicated to studying the continuum variability of deeply embedded protostars in eight nearby star-forming regions at a one month cadence. We use the SCUBA-2 instrument to simultaneously observe these regions at wavelengths of 450 $\mu$m and 850 $\mu$m. In this paper, we present the data reduction techniques, image alignment procedures, and relative flux calibration methods for 850 $\mu$m data. We compare the properties and locations of bright, compact emission sources fitted with Gaussians over time. Doing so, we achieve a spatial alignment of better than 1" between the repeated observations and an uncertainty of 2-3\% in the relative peak brightness of significant, localised emission. This combination of imaging performance is unprecedented in ground-based, single dish submillimetre observations. Finally, we identify a few sources that show possible and confirmed brightness variations. These sources will be closely monitored and presented in further detail in additional studies throughout the duration of the survey., Comment: 24 pages, 15 figures, 2 Tables, Accepted in ApJ

The purpose of this research was to: 1) identify the competencies considered essential for entry-level administrators of financial aid at four-year universities, and 2) determine what method of training leads to these competencies according to financial aid directors. A Computer-based Delphi process was implemented because of its flexibility and adaptability. [For complete proceedings, see ED491481.]