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Chris Flynn

Publications and source records attributed to Chris Flynn.

At least 19 recordsLinked to original sources
arXiv2026

A search for Fast Radio Bursts from globular clusters in M49 with FAST

The origins of fast radio bursts (FRBs) remain uncertain, although magnetars are a leading progenitor candidate. Because magnetars are thought to form primarily through core-collapse supernovae in young stellar populations, the discovery of FRB 20200120E in a globular cluster (GC) in the nearby galaxy M81 was unexpected given the ancient stellar populations of GCs. Expanding the sample of FRBs localised to nearby galaxies is therefore essential for testing FRB formation channels in old stellar environments. M49 (NGC 4472) is a nearby (~17 Mpc), radio-quiet giant elliptical galaxy in the Virgo cluster hosting about 7000 GCs, making it an ideal target for GC FRB searches. We conducted a 9-hour SnapShotCal observation of M49 using the Five-hundred-meter Aperture Spherical Telescope (FAST) 19-beam receiver, covering approximately 4230 GCs (2.1 hr per GC), and performed a comprehensive single-pulse search over a dispersion measure range of 0-5000 pc cm^-3. No unambiguous astrophysical FRBs were detected. The most significant trigger reached a post-processed signal-to-noise ratio of 8.6 sigma at a dispersion measure of 412.2 pc cm^-3, but is statistically consistent with thermal noise after accounting for the false-alarm rate. We derive a beam-averaged peak flux-density sensitivity of about 16.5 mJy (corresponding to a fluence limit of about 16.5 mJy ms for a 1 ms burst) and place an upper limit on the FRB occurrence rate of 4.7 x 10^-4 FRB GC^-1 hr^-1. Our non-detection constrains only bright bursts above this fluence threshold during the observing window.

astro-ph.HE↗
arXiv2026

Revisiting GW170817 at milliarcsecond scale: high-precision constraints on jet geometry and $H_0$

The historic detection of gravitational waves from the electromagnetically bright binary neutron star merger GW170817 enabled the first standard siren measurement of Hubble's constant ($H_0$). The accuracy and precision of this measurement depends crucially on how well the merger inclination angle is constrained, given its strong covariance with luminosity distance ($D_L$). Modeling the light-curve of the jet's afterglow provides constraints on inclination, but is highly dependent on the similarly uncertain jet opening angle. Past studies have improved on this by invoking high-resolution radio observations, obtained through very long baseline interferometry (VLBI). We present a Bayesian visibility-plane model-fitting framework that provides a more informed and robust measurement of the viewing geometry of GW170817 and of $H_0$, by including all relevant VLBI data, robustly handling systematic uncertainties and rigorously sampling model parameter space. By fitting new hydrodynamical afterglow models with a continuum of jet geometries, we obtain a viewing angle of $18.^{\circ}3-20.^{\circ}3$ (for a fixed cosmology with $D_L=40.7$ Mpc, as used in most previous analyses). We extend our framework to fit for $D_L$ and $H_0$ directly, and marginalize over an ensemble of plausible peculiar velocity corrections to obtain viewing angle $16.^{\circ}8-19.^{\circ}2$, $D_L=44.0\pm1.6$ Mpc and $H_0=65.5\pm4.4$ km s$^{-1}$ Mpc$^{-1}$. Notably, the peak of our $H_0$ posterior is within $0.5\sigma$ of the early-Universe Planck $H_0$ value, but $1.7\sigma$ from the late-Universe SH0ES measurement. We discuss potential caveats and the implications of this result in the context of the current discrepancy between early and late-Universe measurements of the Hubble constant.

astro-ph.HE↗
arXiv2026

Galactic Stellar Halo Luminosity Function

We measure the luminosity function (LF) of the Milky Way's stellar halo, using a magnitude complete, distance limited sample of stars from $Gaia$ DR3. Stars with high transverse velocities are selected, to isolate a high purity sample of the local halo. We adopt a cutoff transverse velocity of 250$\,$km$\,$s$^{-1}$, yielding 24,471 stars, and compute the halo LF, taking into account the effects of sample selection criteria. The LF displays similar features as are found in the well-probed LF of nearby, metal-rich disk stars, showing a strong peak at an absolute magnitude of around $M_G=10$, and a flattening near $M_G\sim7$ (Wielen dip). The $Gaia$ sample yields the first measurement of the LF continuously from the dimmest main sequence halo stars (subdwarfs) at an absolute $M_G$ magnitude near 13 mag to bright giants at $M_G\sim-3$. We obtain a local stellar halo number density of $1.7\times10^{-4}$ stars$\,$pc$^{-3}$ and disk-to-halo ratio by stellar number density of 480:1. We convert the $Gaia$ $G$ band measurements for our sample stars to Johnson-Kron-Cousins $V$ band, compute the $V$-band halo LF, and compare it to previous studies published over many decades that cover a wide range of techniques used. We discuss applications of the LF to the measurement of the luminosity and stellar mass of the Milky Way halo.

astro-ph.GA↗
arXiv2025

Detection of over 37,000 giant pulses per hour from PSR J1823$-$3021A with UHF baseband observations from MeerKAT

Giant pulses (GPs) occur in high magnetic-field millisecond pulsars (MSPs) and young Crab-like pulsars. Motivated by the fast radio bursts (FRBs) discovered in a globular cluster (GC) in the M81, we undertook baseband observations of PSR J1823$-$3021A, the most active GP emitter in a GC with the MeerKAT UHF band receiver (544-1088 MHz). The steep spectral index of the pulsar yields a GP rate of over 37,000 GPs/hr with $S/N>7$, significantly higher than the 3000 GPs/hr rate detected by Abbate et al. 2020 with the L-band (856-1712 MHz) receiver. Similarly to Abbate et al 2020, we find that the GPs are (1) strongly clustered in 2 particular phases of its rotation, (2) well described by a power-law in terms of energies, (3) typically broadband, and have steep spectral indices of $\approx-3$. Although the integrated pulse profile is not significantly polarised ($<1\%$ linear and $<3\%$ circular), one of the brightest GPs displays notable polarisation of $7\%$ (linear) and $8\%$ (circular). The high-time resolution data reveals the GPs have a range of single-peak and multi-peak morphologies, including GPs with three distinct peaks. For the first time, we measured the temporal scattering of the pulsar using 49 bright, narrow, single-pulse GPs, obtaining a mean value of $5.5\pm0.6$ $\mu$s at 1 GHz. The distinct periodicity and low polarisation of GPs differentiate them from typical FRBs, although potential quasi-periodicity substructures in some GPs may suggest a connection to magnetars/FRBs.

astro-ph.HE↗
arXiv2024

Efficient Summation of Arbitrary Masks -- ESAM

Searches for impulsive, astrophysical transients are often highly computationally demanding. A notable example is the dedispersion process required for performing blind searches for Fast Radio Bursts (FRBs) in radio telescope data. We introduce a novel approach - Efficient Summation of Arbitrary Masks (ESAM) - which efficiently computes 1-D convolution of many arbitrary 2-D masks, and can be used to carry out dedispersion over thousands of dispersion trials efficiently. Our method matches the accuracy of the traditional brute force technique in recovering the desired Signal-to-Noise ratio (S/N) while reducing computational cost by around a factor of 10. We compare its performance with existing dedispersion algorithms, such as the Fast Dispersion Measure Transform (FDMT) algorithm, and demonstrate how ESAM provides freedom to choose arbitrary masks and further optimise computational cost versus accuracy. We explore the potential applications of ESAM beyond FRB searches.

astro-ph.IM↗
arXiv2024

The neutron star mass, distance, and inclination from precision timing of the brilliant millisecond pulsar J0437$-$4715

The observation of neutron stars enables the otherwise impossible study of fundamental physical processes. The timing of binary radio pulsars is particularly powerful, as it enables precise characterization of their (three-dimensional) positions and orbits. PSR~J0437$-$4715 is an important millisecond pulsar for timing array experiments and is also a primary target for the Neutron Star Interior Composition Explorer (NICER). The main aim of the NICER mission is to constrain the neutron star equation of state by inferring the compactness ($M_p/R$) of the star. Direct measurements of the mass $M_p$ from pulsar timing therefore substantially improve constraints on the radius $R$ and the equation of state. Here we use observations spanning 26 years from Murriyang, the 64-m Parkes radio telescope, to improve the timing model for this pulsar. Among the new precise measurements are the pulsar mass $M_p=1.418\pm 0.044$ $M_{\odot}$, distance $D=156.96 \pm 0.11$ pc, and orbital inclination angle $i=137.506 \pm 0.016^\circ$, which can be used to inform the X-ray pulse profile models inferred from NICER observations. We demonstrate that these results are consistent between multiple data sets from the Parkes Pulsar Timing Array (PPTA), each modeled with different noise assumptions. Using the longest available PPTA data set, we measure an apparent second derivative of the pulsar spin frequency and discuss how this can be explained either by kinematic effects due to the proper motion and radial velocity of the pulsar or excess low-frequency noise such as a gravitational-wave background.

astro-ph.HE↗
arXiv2024

Probing the strength of radial migration via churning by using metal-rich red giant stars from APOGEE

Making use of the APOGEE DR17 catalogue with high quality data for 143,509 red giant branch stars we explore the strength of different mechanisms that causes a star to radially migrate in the Milky Way stellar disk. At any position in the disk we find stars that are more metal-rich than the local interstellar medium. This is surprising and normally attributed to the migration of these stars after their formation inside their current Galactocentric-radius. Such stars are prime candidates for studying the strength of different migratory processes. We specifically select two types of metal-rich stars: i) super metal-rich stars ([Fe/H] > 0.2) and ii) stars that are more metal-rich than their local environment. For both, we explore the distribution of orbital parameters and ages as evidence of their migration history. We find that most super metal-rich stars have experienced some amount of churning as they have orbits with Rg >= 5 kpc. Furthermore, about half of the super metal-rich stars are on non-circular orbits (ecc > 0.15) and therefore also have experienced blurring. The metallicity of young stars in our sample is generally the same as the metallicity of the interstellar medium, suggesting they have not radially migrated yet. Stars with lower metallicity than the local environment have intermediate to old ages. We further find that super metal-rich stars have approximately the same age distribution at all Galactocentric-radii, which suggests that radial migration is a key mechanism responsible for the chemical compositions of stellar populations in the Milky Way.

astro-ph.GA↗
arXiv2024

North-South asymmetries in the Galactic thin disk associated with the vertical phase spiral as seen using LAMOST-Gaia stars

We select 1,052,469 (754,635) thin disk stars from {\it Gaia} eDR3 and LAMOST DR7 in the range of Galactocentric radius $R$ (guiding center radius $R_\mathrm{g}$) from 8 to 11\,kpc to investigate the asymmetries between the North and South of the disk midplane. More specifically we analyze the vertical velocity dispersion profiles ($\sigma_{v_{z}}(z$)) in different bins of $R$ ($R_\mathrm{g}$) and $[\mathrm{Fe/H}]$. We find troughs in the profiles of $\sigma_{v_{z}}(z)$ located in both the North ($z \sim 0.7$\,kpc) and South ($z \sim -0.5$\,kpc) of the disk at all radial and chemical bins studied. The difference between the Northern and Southern vertical velocity dispersion profiles ($\Delta\sigma_{v_{z}}(|z|)$) shows a shift between curves of different $R$ and $R_\mathrm{g}$. A similar shift exists in these NS asymmetry profiles further divided into different $[\mathrm{Fe/H}]$ ranges. The sample binned with $R_\mathrm{g}$ more clearly displays the features in the velocity dispersion profiles. The shift in the peaks of the $\Delta\sigma_{v_{z}}$ profiles and the variation in the phase spiral shape binned by metallicity indicate the variation of the vertical potential profiles and the radial metallicity gradient. The wave-like signal in NS asymmetry of $\sigma_{v_{z}}(z)$ largely originates from phase spiral; while the NS asymmetry profiles of [Fe/H] only display a weak wave-like feature near solar radius. We perform a test particle simulation to qualitatively reproduce the observed results. A quantitative explanation of the NS asymmetry in the metallicity profile needs careful consideration of the spiral shape and the perturbation model, and we leave this for future work.

astro-ph.GA↗
arXiv2023

Search for gravitational wave signals from known pulsars in LIGO-Virgo O3 data using the 5n-vector ensemble method

The 5n-vector ensemble method is a multiple test for the targeted search of continuous gravitational waves from an ensemble of known pulsars. This method can improve the detection probability combining the results from individually undetectable pulsars if few signals are near the detection threshold. In this paper, we apply the 5n-vector ensemble method to the O3 data set from the LIGO and Virgo detectors considering an ensemble of 201 known pulsars. We find no evidence for a signal from the ensemble and set a 95% credible upper limit on the mean ellipticity assuming a common exponential distribution for the pulsars' ellipticities. Using two independent hierarchical Bayesian procedures, we find upper limits of $1.2 \times 10^{-9}$ and $2.5 \times 10^{-9}$ on the mean ellipticity for the 201 analyzed pulsars.

gr-qc↗
arXiv2023

The Third Fermi Large Area Telescope Catalog of Gamma-ray Pulsars

We present 294 pulsars found in GeV data from the Large Area Telescope (LAT) on the Fermi Gamma-ray Space Telescope. Another 33 millisecond pulsars (MSPs) discovered in deep radio searches of LAT sources will likely reveal pulsations once phase-connected rotation ephemerides are achieved. A further dozen optical and/or X-ray binary systems co-located with LAT sources also likely harbor gamma-ray MSPs. This catalog thus reports roughly 340 gamma-ray pulsars and candidates, 10% of all known pulsars, compared to $\leq 11$ known before Fermi. Half of the gamma-ray pulsars are young. Of these, the half that are undetected in radio have a broader Galactic latitude distribution than the young radio-loud pulsars. The others are MSPs, with 6 undetected in radio. Overall, >235 are bright enough above 50 MeV to fit the pulse profile, the energy spectrum, or both. For the common two-peaked profiles, the gamma-ray peak closest to the magnetic pole crossing generally has a softer spectrum. The spectral energy distributions tend to narrow as the spindown power $\dot E$ decreases to its observed minimum near $10^{33}$ erg s$^{-1}$, approaching the shape for synchrotron radiation from monoenergetic electrons. We calculate gamma-ray luminosities when distances are available. Our all-sky gamma-ray sensitivity map is useful for population syntheses. The electronic catalog version provides gamma-ray pulsar ephemerides, properties and fit results to guide and be compared with modeling results.

astro-ph.HE↗
arXiv2023

Spectropolarimetric variability in the repeating fast radio burst source FRB 20180301A

As the sample size of repeating fast radio bursts (FRBs) has grown, an increasing diversity of phenomenology has emerged. Through long-term multi-epoch studies of repeating FRBs, it is possible to assess which phenomena are common to the population and which are unique to individual sources. We present a multi-epoch monitoring campaign of the repeating FRB source 20180301A using the ultra-wideband low (UWL) receiver observations with Murriyang, the Parkes 64-m radio telescope. The observations covered a wide frequency band spanning approximately 0.7--4 GHz, and yielded the detection of 46 bursts. None of the repeat bursts displayed radio emission in the range of 1.8--4 GHz, while the burst emission peaked at 1.1 GHz. We discover evidence for secular trends in the burst dispersion measure, indicating a decline at a rate of $-2.7\pm0.2\,{\rm pc\,cm^{-3}\,yr^{-1}}$. We also found significant variation in the Faraday rotation measure of the bursts across the follow-up period, including evidence of a sign reversal. While a majority of bursts did not exhibit any polarization, those that did show a decrease in the linear polarization fraction as a function of frequency, consistent with spectral depolarization due to scattering, as observed in other repeating FRB sources. Surprisingly, no significant variation in the polarization position angles was found, which is in contrast with earlier measurements reported for the FRB source. We measure the burst rate and sub-pulse drift rate variation and compare them with the previous results. These novel observations, along with the extreme polarization properties observed in other repeating FRBs, suggest that a sub-sample of FRB progenitors possess highly dynamic magneto-ionic environments.

astro-ph.HE↗
arXiv2023

Survey for Distant Solar Twins (SDST) -- III. Identification of new solar twin and solar analogue stars

The Survey for Distant Solar Twins (SDST) aims to find stars very similar to the Sun at distances 1-4 kpc, several times more distant than any currently known solar twins and analogues. The goal is to identify the best stars with which to test whether the fine-structure constant, alpha, varies with dark matter density in our Galaxy. Here we use EPIC, our line-by-line differential technique, to measure the stellar parameters - effective temperature Teff, surface gravity log g, metallicity [Fe/H] - from moderate resolution (R < 32,000) spectra of 877 solar twin and analogue candidates (547 at 1-4 kpc) observed with the HERMES spectrograph on the Anglo-Australian Telescope. These are consistent with expectations for Teff and log g from photometry, and for [Fe/H] from the Besancon stellar population model. EPIC provides small enough uncertainties (~90 K, 0.08 dex, 0.05 dex, respectively), even at the low signal-to-noise ratios available (S/N >~ 25 per pixel), to identify 299 new solar analogues (> 90% confidence), and 20 solar twins (>50% confidence), 206 and 12 of which are at 1-4 kpc. By extending EPIC to measure line broadening and lithium abundance from HERMES spectra, and with ages derived from isochrone fitting with our stellar parameters, we identify 174 solar analogues at 1-4 kpc which are relatively inactive, slowly rotating, and with no evidence of spectroscopic binarity. These are the preferred targets for follow-up spectroscopy to measure alpha.

astro-ph.SR↗
arXiv2022

A limit on variations in the fine-structure constant from spectra of nearby Sun-like stars

The fine structure constant, $α$, sets the strength of the electromagnetic force. The Standard Model of particle physics provides no explanation for its value, which could potentially vary. The wavelengths of stellar absorption lines depend on $α$, but are subject to systematic effects owing to astrophysical processes in stellar atmospheres. We measured precise line wavelengths using 17 stars, selected to have almost identical atmospheric properties to those of the Sun (solar twins), which reduces those systematic effects. We found that $α$ varies by $\lesssim$50 parts-per-billion (ppb) within 50 parsecs from Earth. Combining the results from all 17 stars provides an empirical, local reference for stellar measurements of $α$ with an ensemble precision of 12 ppb.

astro-ph.SR↗
arXiv2022

Survey for Distant Solar Twins (SDST) -- II. Design, observations and data

Studies of solar twins have key impacts on the astronomical community, but only $\sim$100--200 nearby solar twins ($<$ 1 kpc) have been reliably identified over the last few decades. The aim of our survey (SDST) is to identify $\sim$150--200 distant solar twins and analogues (up to $\lesssim$ 4 kpc) closer to the Galactic Centre. We took advantage of the precise Gaia and Skymapper surveys to select Sun-like candidates in a 2-degree field, which were observed with the HERMES spectrograph on the Anglo-Australian Telescope. We successfully built up the required signal-to-noise ratio (25-per-pixel in the HERMES red band) for most targets as faint as Gaia G of 17.4 mag. The stellar photometric/astrometric parameters (e.g., \teff, \logg, mass) of our candidates are derived in this paper, while the spectroscopic parameters will be presented in the third paper in this SDST series. The selection success rate - the fraction of targets which belong to solar twins or analogues - was estimated from simulated survey data and the Besançon stellar population model, and compared with the actual success rate of the survey. We find that expected and actual success rates agree well, indicating that the numbers of solar twins and analogues we discover in SDST are consistent with expectations, affirming the survey approach. These distant solar analogues are prime targets for testing for any variation in the strength of electromagnetism in regions of higher dark matter density, and can make additional contributions to our understanding of, e.g., Galactic chemical evolution in the inner Milky Way.

astro-ph.SR↗
arXiv2022

Probing Galactic variations in the fine-structure constant using solar twin stars: systematic errors

Sun-like stars are a new probe of variations in the fine-structure constant, $α$, via the solar twins approach: velocity separations of close pairs of absorption lines are compared between stars with very similar stellar parameters, i.e. effective temperature, metallicity and surface gravity within 100K, 0.1 dex and 0.2 dex of the Sun's values. Here we assess possible systematic errors in this approach by analysing $\gtrsim$10,000 archival exposures from the High-Accuracy Radial velocity Planetary Searcher (HARPS) of 130 stars covering a much broader range of stellar parameters. We find that each transition pair's separation shows broad, low-order variations with stellar parameters which can be accurately modelled, leaving only a small residual, intrinsic star-to-star scatter of 0-33 m/s (average $\approx$7 m/s, $\approx$10$^{-4}$Å at 5000Å). This limits the precision available from a single pair in one star. We consider potential systematic errors from a range of instrumental and astrophysical sources (e.g. wavelength calibration, charge transfer inefficiency, stellar magnetic activity, line blending) and conclude that variations in elemental abundances, isotope ratios and stellar rotational velocities may explain this star-to-star scatter. Finally, we find that the solar twins approach can be extended to solar analogues - within 300K, 0.3 dex and 0.4 dex of the Sun's parameters - without significant additional systematic errors, allowing a much larger number of stars to be used as probes of variation in $α$, including at much larger distances.

astro-ph.SR↗
arXiv2022

Probing Galactic variations in the fine-structure constant using solar twin stars: methodology and results

The rich absorption spectra of Sun-like stars are enticing probes for variations in the fine-structure constant, $α$, which gauges the strength of electromagnetism. While individual line wavelengths are sensitive to $α$, they are also sensitive to physical processes in the stellar atmospheres, which has precluded their use so far. Here we demonstrate a new, differential approach using solar twins: velocity separations between close pairs of transitions are compared across stars with very similar physical properties, strongly suppressing astrophysical and instrumental systematic errors. We utilise 423 archival exposures of 18 solar twins from the High-Accuracy Radial velocity Planetary Searcher (HARPS), in which calibration errors can be reduced to $\lesssim$3 m/s. For stars with $\approx$10 high signal-to-noise ratio spectra ($\ge$200 per pixel), velocity separations between pairs are measured with $\approx$10 m/s statistical precision. A companion paper assesses a range of systematic error sources using 130 stars, with a greater range of stellar parameters, providing accurate corrections for astrophysical effects and a residual, intrinsic star-to-star scatter of 0-13 m/s. Within these uncertainties, we find no evidence for velocity separation differences in 17 transition pairs between solar twins. In a second companion paper, this is found to limit local ($\lesssim$50 pc) variations in $α$ to $\approx$50 parts per billion, $\sim$2 orders of magnitude less than other Galactic constraints.

astro-ph.SR↗
arXiv2022

The ultra narrow FRB20191107B, and the origins of FRB scattering

We report the detection of FRB20191107B with the UTMOST radio telescope at a dispersion measure (DM) of 714.9 ${\rm pc~cm^{-3}}$. The burst consists of three components, the brightest of which has an intrinsic width of only 11.3 $μ$s and a scattering tail with an exponentially decaying time-scale of 21.4 $μ$s measured at 835 MHz. We model the sensitivity of UTMOST and other major FRB surveys to such narrow events. We find that $>60\%$ of FRBs like FRB20191107B are being missed, and that a significant population of very narrow FRBs probably exists and remains underrepresented in these surveys. The high DM and small scattering timescale of FRB20191107B allows us to place an upper limit on the strength of turbulence in the Intergalactic Medium (IGM), quantified as scattering measure (SM), of ${\rm SM_{IGM} < 8.4 \times 10^{-7} ~kpc~m^{-20/3}}$. Almost all UTMOST FRBs have full phase information due to real-time voltage capture which provides us with the largest sample of coherently dedispersed single burst FRBs. Our 10.24 $μ$s time resolution data yields accurately measured FRB scattering timescales. We combine the UTMOST FRBs with 10 FRBs from the literature and find no obvious evidence for a DM-scattering relation, suggesting that IGM is not the dominant source of scattering in FRBs. We support the results of previous studies and identify the local environment of the source in the host galaxy as the most likely region which dominates the observed scattering of our FRBs.

astro-ph.HE↗
arXiv2022

Milky Way Mass with K Giants and BHB Stars Using LAMOST, SDSS/SEGUE, and Gaia: 3D Spherical Jeans Equation and Tracer Mass Estimator

We measure the enclosed Milky Way mass profile to Galactocentric distances of $\sim70$ and $\sim50$ kpc using the smooth, diffuse stellar halo samples of Bird et al. The samples are LAMOST and SDSS/SEGUE K giants (KG) and SDSS/SEGUE blue horizontal branch (BHB) stars with accurate metallicities. The 3D kinematics are available through LAMOST and SDSS/SEGUE distances and radial velocities and {\it Gaia} DR2 proper motions. Two methods are used to estimate the enclosed mass: 3D spherical Jeans equation and Evans et al. tracer mass estimator (TME). We remove substructure via the Xue et al. method based on integrals of motion. We evaluate the uncertainties on our estimates due to random sampling noise, systematic distance errors, the adopted density profile, and non-virialization and non-spherical effects of the halo. The tracer density profile remains a limiting systematic in our mass estimates, although within these limits we find reasonable agreement across the different samples and the methods applied. Out to $\sim70$ and $\sim50$ kpc, the Jeans method yields total enclosed masses of $4.3\pm0.95$ (random) $\pm0.6$ (systematic) $\times10^{11}$ M$_\odot$ and $4.1\pm1.2$ (random) $\pm0.6$ (systematic) $\times10^{11}$ M$_\odot$ for the KG and BHB stars, respectively. For the KG and BHB samples we find a dark matter virial mass of $M_{200}=0.55^{+0.15}_{-0.11}$ (random) $\pm0.083$ (systematic) $\times10^{12}$ M$_\odot$ and $M_{200}=1.00^{+0.67}_{-0.33}$ (random) $\pm0.15$ (systematic) $\times10^{12}$ M$_\odot$, respectively.

astro-ph.GA↗