The Milky Way Bulge Extra-tidal Star Survey: BH 261 (AL 3)

The Milky Way Bulge extra-tidal star survey is a spectroscopic survey with the goal of identifying stripped globular cluster stars from inner Galaxy clusters. In this way, an indication of the fraction of metal-poor bulge stars that originated from globular clusters can be determined. We observed and analyzed stars in and around BH 261, an understudied globular cluster in the bulge. From seven giants within the tidal radius of the cluster, we measured an average heliocentric radial velocity of 〈RV〉 = −61 ± 2.6 km s−1 with a radial velocity dispersion of 〈σ〉 = 6.1 ± 1.9 km s−1. The large velocity dispersion may have arisen from tidal heating in the cluster’s orbit about the Galactic center, or because BH 261 has a high dynamical mass as well as a high mass-to-light ratio. From spectra of five giants, we measure an average metallicity of 〈[Fe/H]〉 = −1.1 ± 0.2 dex. We also spectroscopically confirm an RR Lyrae star in BH 261, which yields a distance to the cluster of 7.1 ± 0.4 kpc. Stars with 3D velocities and metallicities consistent with BH 261 reaching to ∼0.°5 from the cluster are identified. A handful of these stars are also consistent with the spatial distribution of potential debris from models focusing on the most recent disruption of the cluster.


INTRODUCTION
The connection between Globular Clusters (GCs) in the inner Galaxy and the hierarchical growth of the Milky Way is still largely unknown.One reason bulge globular clusters (GCs) are difficult to place into proper context within our Galaxy's formation is that they often have features not seen in the GC halo or disk population.For example, Terzan 5 and Liller 1 are bulge GC fossil fragments that host an old (∼12 Gyr) and young (∼1-3 Gyr) stellar population (e.g., Ferraro et al. 2021).NGC 6441 and NGC 6388 are bulge GCs with abnormal horizontal branches -too blue and extended for their [Fe/H] metallicities and with abnormal frequencies and pulsation properties in their RR Lyrae populations (Pritzl et al. 2000(Pritzl et al. , 2001)).The Galactic bulge is home to the most metal-rich GCs in our Galaxy, and studies of the elemental abundances (e.g., O and Na) in bulge GC stars indicate that the evolution of many bulge GCs are not similar to that of the halo (e.g., Muñoz et al. 2017).
Especially the metal-poor stars in the field of the bulge appear to be connected to inner Galaxy GCs.Field stars with [N/Fe] over-abundances are thought to be former members of a population of GCs that was previously dissolved and/or evaporated (e.g., Schiavon et al. 2017;Fernández-Trincado et al. 2021).This is the same mechanism that has been shown to donate stars to the halo (e.g., Martell et al. 2011;Koch et al. 2019).Stripped GC stars are also contenders for the origin of the double RC feature in the bulge, as it has been shown that the chemical abundances of the stars in the X-shaped bulge are consistent with having been formed from GC fossil remnants (Lim et al. 2021).Although it is expected that Galactic GCs lose mass through processes like evaporation and tidal stripping (e.g., Leon et al. 2000;Baumgardt & Junichiro 2003;Moreno et al. 2014;Baumgardt et al. 2021), the extent of stripped GC stars in the bulge is unclear.Yet in the bulge, where dynamical friction is much higher than in the halo, this process is likely a significant mechanism of the make-up of the bulge field, especially for the metal-poor bulge population.
One hindrance in being able to draw connections between inner Galaxy GCs and place this population into context with Milky Way formation, is that these are dense systems in a crowded, extinguished part of the Milky Way, so observational analysis of inner Galaxy GCs is difficult.Many of the inner Galaxy GCs are understudied, with basic parameters such as radial velocities and metallicities being undetermined, prompting new spectroscopic survey's to target inner Galaxy GCs (e.g., Saviane et al 2012;Dias et al. 2016;Kunder et al. 2021;Geisler et al. 2021).The Milky Way Bulge extra-tidal star survey, MWBest, has the goal of spectroscopically identifying stripped globular cluster stars from inner Galaxy clusters.Globular cluster stars can and will escape close to the tidal boundary of the cluster as it moves through the inner Galaxy, influenced by the tidal force of the Milky Way, but the detection of stripped globular cluster stars in the inner Galaxy is limited in number (e.g., Gnedin & Ostiker 1997;Meylan & Combes 2000;Kunder et al. 2014Kunder et al. , 2018;;Minniti et al. 2018;Kundu et al. 2019).The tidal force inflates the cluster (tidal heating), and tidal stripping removes mass in its outer region.Due to the severe crowding of the bulge, we concentrate on potential extra-tidal stars that lie a few tidal-radii (∼ 1 − 5× r t ) away from the cluster center.
This paper focuses on the bulge globular cluster BH 261.Andrews & Lindsay (1967) list it as AL 3, van den Bergh, S. & Hagen (1975) list it as BH 261, and Lauberts (1982) list it as ESO456-SC78.The first colormagnitude diagrams (CMDs) of this region by Carraro et al. (2005) show very little evidence that it is a true cluster.It was the photometry presented in Ortolani et al. (2006) that allowed this cluster to be confirmed as a GC, and provided a photometric distance, reddening and metallicity from isochrone fitting.A deep CMD of BH 261 is presented by Cohen et al. (2018), who confirm a sparse, blue horizontal branch morphology using the Hubble Space T elescope (HST).Since then, new photometry from Gaia (Gaia Collaboration 2016, 2021) and VVV (Minniti et al. 2010) has been presented by Gran et al. (2022), finding a photometric distance that places the cluster 50% further away, on the far-side of the bulge, and finding a photometric metallicity that is a factor of 10 more metal-poor.
Spectroscopic studies of stars in BH 261 include those by Baumgardt et al. (2019), Barbuy et al. (2021) and Geisler et al. (2023), who report an average radial velocity of −29.4 km s −1 , −57.9±4.3 km s −1 , and −44.9±3.8 km s −1 , respectively.One reason for these differing results may be the small sample sizes (∼3 stars in each study), or it could be that BH 261 has a larger velocity dispersion then is able to be reported with the small sample sizes.The spectroscopic [Fe/H] of BH 261 is measured to be between ∼−1.0 and ∼−1.3 (Barbuy et al. 2021;Geisler et al. 2023), also based on three member stars.
The spectroscopic observations presented here allow a more detailed dynamical study to be carried out, since our observations extend out to ∼2 • from the cluster center, or ∼20 tidal-radii.In §2 the new data collected is described, and the radial velocities and metallicities are presented in §3.In 3.4 the extra-tidal stars identified are compared to theoretical predictions of tidal debris from the initial conditions of BH 261, and a comparison between BH 261 and other bulge GCs is carried out.The conclusions are in §4.

OBSERVATIONS AND DATA REDUCTIONS
2.1.Target selection BH 261 is heavily contaminated by both Galactic disk stars as well as bulge field stars, which makes efficient target selection difficult.The Gaia catalog (Gaia Collaboration 2022) was used to apply proper motion and parallax criteria to select stars consistent with the cluster and to cull both foreground and field stars, as shown in Figure 1.In particular, stars with proper motions within µ α ±1.5 mas yr −1 and µ δ ±1.5 mas yr −1 of the mean proper motion of the cluster were selected, where the mean proper motion of BH 261 is µ α cosδ = 3.589±0.022mas yr −1 , µ δ =−3.570±0.020mas yr −1 (Vasiliev & Baumgardt 2021).Stars with parallax values larger than 0.4 mas were discarded, as it was shown that these stars in general are part of the foreground disk (Marchetti et al. 2022).Proper motion and parallax information is not precise enough for cluster membership of BH 261; our derived radial velocities are ultimately used to select the most likely cluster members.
The Blanco DECam Bulge Survey (BDBS) catalog (Rich et al. 2020;Johnson et al. 2020) was also used to select targets for the cluster, selecting stars with u and i photometry that would, in principle, encompass the cluster's red giant branch (RGB) and blue horizontal branch (BHB).BDBS is a photometric survey covering more than 200 square degrees of the Southern Galactic bulge using the ugrizY filters on the Dark Energy Cam-  The stars assigned the highest priority were those within the tidal radius of BH 261 that were consistent with being blue horizontal branch (BHB) stars.Because the BHB is more offset from the bulge field population (see Figure 2), this should maximize the number of bonafide BH 261 stars.However, BHB stars have a hotter temperatures than giants and red giants, so the proximity to and systematic blueward offset of the calcium infrared triplet to the hydrogen Paschen lines complicates stellar parameter determination.
We also targeted red clump stars with photometric metallicities more metal-poor than [Fe/H] = −0.3dex.Johnson et al. (2020Johnson et al. ( , 2022) ) show that u-i colors can be used to obtain color-[Fe/H] relations for red clump stars good to ∼0.2 dex.This precision is comparable to that of most spectroscopic metallicities of bulge stars (see also Lim et al. 2021).The targeted stars have BDBS u-band photometry with formal uncertainties of u err <0.024 mag, with the observed stars with u ∼18 mag or brighter having u err <0.01 mag.

Observations and Reduction
New spectra were collected using the AAOmega multifibre spectrograph at the 3.9 m Anglo-Australian Telescope (Siding Spring Observatory, Coonabarabran, NSW, Australia).The five night run occurred 20 July -24 July, 2022 (PROP-ID: O/2022A/3002).Plate configurations for the Two Degree Field (2dF) fibre positioner contained a combination of RR Lyrae stars, red clump stars and giants centered on the cluster and filling the 2 degree field of view, as shown in Figure 3.All of the stars targeted have proper motions consistent with BH 261.The field was observed twice with two different configurations -different giant stars were observed in both configurations to maximize number of potential cluster stars and extra-tidal stars, but the same red clump stars were observed as they are fainter, incase the spectra needed to be stacked.Also, the same RR Lyrae stars were observed in each configuration to maximize phase coverage for these pulsating variables.
A dual setup was used to employ the red 1700D grating, centered at 8600 Å and the blue 2500V grating, centered at 5000 Å.In this manner, the easily seen calcium triplet (CaT) lines in the red were observed, and for the brightest stars, the Mg line at 5180 Å in the blue was prominent.This paper uses only the red part of the spectra, and any analyses of metallicities and [Mg/Fe] will be presented at a later stage.The exposure times ranged from 4x30 min to 2x30 min, adjusting for weather and observing conditions.The typical signal-to-noise was ∼5 per pixel for the fainter horizontal branch stars and ∼45 per pixel for the brighter giants.
The bias subtraction, cosmic ray cleaning, quartzflatfielding, wavelength calibration via arc-lamp exposures, sky subtraction using dedicated sky fibers, and optimal extraction of the science spectra were carried out using AAO's 2dfdr pipeline (AAO Software Team 2015).The final wavelength range is 8350-8800 Å, with slight variations depending on the exact position of the spectra on the CCD.
The three spectra we used as cross-correlation templates were stars observed during the same run, selected from the Apache Point Observatory Galaxy Evolution Experiment (APOGEE, Eisenstein et al. 2011) database.In particular, APOGEE 2M18134674-2926056 (RV=27.88±0.03),APOGEE 2M17514997-2906055 (RV=−187.33±0.02)and APOGEE 2M17521244-2919510 (RV=65.13±0.05)were adopted as radial velocity templates.This led to a median velocity error of ∼3 km s −1 for the giants and 9 km s −1 for the fainter and hotter HB stars.
Two epochs of observations were collected for the RR Lyrae star OGLE-BLG-RRLYR-35078, and these are shown in Figure 4 (right panel).Each epoch of observation is phased using the OGLE pulsation ephemerides and pulsation period.To calculate the mean radial velocity, the RRc template presented in Prudil et al. ( 2023) is adopted.The photometric scaling relation adopted between the photometric amplitude, Amp V , and lineof-sight velocity amplitude, Amp los , is Amp los = 54(1) × Amp V .This was derived specifically for RRc pulsators from five well-sampled local RR Lyrae stars observed by APOGEE (Prudil et al. 2023).For Amp V , Fig. 3.-Left: The stars in and around BH 261 targeted spectroscopically with AAOmega@AAT.The field is centered on the GC BH 261.Right: Example spectra from AAOmega illustrating the difference in quality between a bright giant (i=14.678mag), a faint HB star (i=16.814mag), the hot RRc star (i=15.538mag) and a typical red clump star (i=16.515mag).The spectra have been normalized and are offset for clarity.
the OGLE I-Amplitude is transformed to Amp V using Amp V =1.72 × Amp I (Kunder et al. 2013;Prudil et al. 2023).The determined systemic velocity and its uncertainty is −39.8±12.4km s −1 .The 12.4 km s −1 uncertainty in the systemic velocity comes from adding in quadrature the 9.8 km s −1 individual radial velocity uncertainty to the 7.6 km s −1 uncertainty from the model fitted to find the systemic velocity.The source of uncertainty comes from the faint magnitude of this star combined with its hotter temperature.The shaded grey in Figure 4 about the scaled RRc template designates a 9.8 km s −1 uncertainty.
The APOGEE DR17 catalog contains a number of RR Lyrae star observations, including two epochs of observations of OGLE-BLG-RRLYR-35078.The allVisit-r12-l33.fits file was used to extract the exact time each observation was taken as listed in the column JD.The Julian Date from this file refers to the middle of an exposure sequence, which is determined from exposure-time weighted mean of the mid-exposure times.Again using the OGLE time of maximum brightness and OGLE period, the phase of each APOGEE RRL observation was calculated.The APOGEE radial velocity observations give a systemic velocity of −67.2±2.3 km s −1 .The APOGEE mean velocity as well as that derived here are both consistent with the range of velocities seen for stars in BH 261.Therefore, the radial velocity also confirms OGLE-BLG-RRLYR-35078 is a cluster member, in agreement with its proper motion and spatial proximity to the cluster.
The radial velocity of OGLE-BLG-RRLYR-35078 presented here, −39.8±12.4km s −1 , is used throughout the paper, as the Calcium Triplet lines are stronger than the spectral lines in the APOGEE H-band wavelength regime, especially at the hotter temperatures of firstovertone RR Lyrae stars.Further, APOGEE's reduction pipeline (Nidever et al. 2015) stacks all spectra of a given object to increase SNR and a radial velocity on the stacked spectra is determined.This radial velocity is a first estimate, or a base for prior, for further radial velocity determination for that given star.This procedure may be sub-optimal for stars that change their radial velocities with amplitudes of ∼15-50 km s −1 in short periods, like RR Lyrae stars.The small formal uncertainties in the APOGEE spectra of 2.2 kms −1 and 1.5 kms −1 are almost certainly underestimated given the signal-tonoise of 4.1 and 7.6, respectively.As far as we know, this is the first publication using the APOGEE DR17 measurements of RR Lyrae stars, and we look forward to further discussion of APOGEE radial velocities for RR Lyrae stars in potential forthcoming papers.
The SP ACE code (Boeche & Grebel 2016;Boeche et al. 2021) was utilized for the determination of [Fe/H] metallicities for the giants.For the red clump stars observed, photometric metallicities were calculated from the calibration between DECam passbands and [Fe/H] as presented in Johnson et al. (2020Johnson et al. ( , 2022)).Spectroscopic metallicities from SP ACE are used to verify the authenticity of the red clump [Fe/H] metallicities.The spectroscopic metallicities are discussed in more detail in 3.4.

Distance
The distance to BH 261 has been determined from CMD fitting and ranges from d ⊙ = 6.0±0.6 kpc from optical CMD fitting (Ortolani et al. 2006;Barbuy et al. 2021) to d ⊙ = 9.12 kpc from infrared CMD fitting (Gran et al. 2022).There is unfortunately no DR3 parallax or kinematic distance for BH 261 (Baumgardt et al. 2021).The reason for the large discrepancy in distance from CMD fitting is that there is a degeneracy between metallicity and distance: adopting a [Fe/H] ∼ −1.0 leads to a distance of ∼d ⊙ = 6.0 kpc whereas adopting a more metal poor [Fe/H] ∼ −2.5 leads to a distance of d ⊙ ∼ 9.5 kpc.The advantage of adopting a more metal-poor value for BH 261 is that a larger distance to the cluster makes it easier to explain its large velocity dispersion despite its low luminosity, as this gives a mass-to-light ratio more in line with what is seen for typical GCs.The recent spectroscopic [Fe/H] metallicities for BH 261 in Geisler et al. (2023) agree with the metallicity put forward by Barbuy et al. (2021) and Ortolani et al. (2006), making it unlikely that the further distance is appropriate.
We report a RR Lyrae star -OGLE-BLG-RRLYR-35078 -that both lies 0.4' from the center of the cluster, and has a proper motion consistent with BH 261.Our derived radial velocity further indicates it is a cluster member.As such, this star can provide an independent indicator to estimate the distance to BH 261.
Empirical period absolute magnitude metallicity (PMZ) relations for RR Lyrae stars have greatly improved, especially since the trigonometric parallaxes measured by Gaia have been released.For the determination of the distance to this RRc star, the newly calibrated PMZ relations in Prudil et al. (2023)

Color-magnitude diagram
The BDBS photometry combined with Gaia astrometry allow a modern optical CMD of BH 261 to be constructed and so we focus first on the cluster itself in an effort to validate the cluster parameters determined independently without the use of BDBS photom-etry (e.g., distance and metallicity).Figure 2 shows the de-reddened proper-motion cleaned u 0 versus (u−g) 0 and r 0 versus (r − z) 0 CMD of a region within 3.2' of BH 261.A 3.2' radius is chosen because it is large enough to encompass both enough cluster and field BDBS stars to see a differentiation between the two when separated by proper motion, and it is also small enough where most of the radial velocity confirmed cluster stars are present (see Figure 4).All stars have been dereddened using the extinctions from the Simion et al. (2017) reddening map, which has a resolution of 1' x 1'.The reddening vectors were computed using Green et al. (2018) for the grizy bands and Schlafly & Finkbeiner (2011) for the u band, as outlined in Johnson et al. (2020).The Green et al. (2018) extinction vector is preferred as it is based on a combination of broad band stellar colors and APOGEE spectra, where most of the APOGEE reference stars used belong to the disk and bulge.Kader et al. (2023) derive high-resolution extinction maps for 14 GCs in BDBS and show that these reddening maps are in agreement with the VVV map used here.Still, we note the u-band extinction vector is notoriously difficult to calibrate, and large uncertainties in the u-band extinction can arise from small variations in the reddening law between different lines-of-sight.The range of extinction values within the central 3.2' of BH 261 varies from E(B − V ) ∼ = 0.25 -0.36, with a mean of E(B − V ) =0.29 mag.
The isochrones used are from the publicly available Modules for Experiments in Astrophysics (MESA) Isochrones and Stellar Tracks (MIST) database (Choi et al. 2016).The isochrones were transformed from theoretical coordinates to the appropriate bandpasses using a combination of the SDSS and PanSTARRS color transformation schemes.The α-element enhancement is accounted for following the procedure described in Joyce et al. (2023).The shorter wavelength passbands (e.g., u-band) allow for the largest discrimination between isochrones with e.g., different metallicities and ages, but shorter wavelength passbands are also more sensitive to reddening and extinction variations, as discussed above.
The isochrones with metallicities of [Fe/H] ∼ −0.9 to [Fe/H] ∼ −1.1 dex with an old age (∼13-13.5 Gyr) are in agreement with the u − g CMD.A 13.4 Gyr isochrone age was used to be similar to the 13.4±1 Gyr estimated by Barbuy et al. (2021).Most bulge GCs with [Fe/H] ∼ −1.0 and BHB have ages in this range (e.g., Kerber et al. 2018), and it has been shown that one avenue to produce such metal-rich GCs with a BHB is by them having a very old age (e.g., Lee et al. 1994).We note that very low metallicities are not needed for stellar relics in the bulgethe chemical enrichment of the bulge is faster than many other places in the MW (e.g., Zoccali et al. 2006;Bensby et al. 2013), and a flat age-metallicity relation for inner Galaxy GCs has been established (Marín-Franch et al. 2009;Massari et al. 2019).
The radial velocity members falling along the BHB of the cluster (see Figure 2) confirm that BH 261 does have an extended BHB, despite it being relatively metal-rich.It has been suggested that BH 261's broad HB could be due to a number of blue straggler (BS) stars.Although this may be the case, we find that the contamination in this region of the CMD from field stars in not trivial.From our sample of 5 spectroscopically targeted possible BHB stars (all with proper motions consistent with BH 261), 2/5 have radial velocities excluding them from being cluster members.This ratio is similar to the giant stars we targeted and highlights the difficulty obtaining clean cluster samples from proper motions and position on the CMD alone.
The ugrizY BDBS photometry of all stars within 3.2' of BH 261 is presented in Table 1.

Velocities
The derived radial velocities as a function of distance from the cluster center are shown in Figure 4 (left panel).There is a grouping of stars within 4' of the cluster with radial velocities between −35 km s −1 and −80 km s −1 which we consider the most probable member stars currently within BH 261.To search for systematic offsets between different samples of BH 261 stars, our stars are cross-matched with the sample presented in Geisler et al. (2023) and Barbuy et al. (2021).There are two stars in our sample that overlap with those in Geisler et al. ( 2023) -Gaia-4050600806719928576 and Gaia-4050624308743727744.The radial velocities presented here agree within one-sigma of the radial velocities reported in Table 2 of Geisler et al. (2023), both when the total velocity error of 7.5 km s −1 is adopted for the Geisler et al. (2023) measurements, (which arises from the error in centering the image in the spectrograph combined with the standard deviation of the different crosscorrelations) as well as when the smaller, statistical errors in velocity of ∼2 km s −1 are adopted.
The most probable cluster members of BH 261 are listed in Table 2, along with (1) the Gaia DR3 ID of each star, (2) the right ascension of the star from Gaia, (3) the declination of the star from Gaia in degrees, (4) the proper motion in right ascension direction as provided, by Gaia (µ α * = µ α cosδ), (5) the proper motion in declination as provided by Gaia, (6) the heliocentric radial velocity, (7) the [Fe/H] metallicity from SP ACE, and (8) the distance the star is from the cluster center.
The [Fe/H] metallicities of these stars, as discussed in 3.4 below, are also consistent with being more metalpoor than the field population.Therefore, the stars most likely currently within the cluster BH 261 (1) are within the cluster tidal radius, (2) have an RV that falls within the error plus intrinsic dispersion (generously adopted as ±15 km s −1 ) from the cluster mean, (3) have an [Fe/H] value within ±0.3 dex of the mean metallicity of the cluster, and (4) have a proper motion that lies within two standard deviations from the cluster mean.These criteria have been used by a number of similar studies discriminating between bulge cluster members and surrounding field stars (e.g., Parisi et al. 2022;Dias et al. 2022;Geisler et al. 2023).
The mean velocity of these 12 stars is < RV > = −56±3 km s −1 with a radial velocity dispersion of < σ > = 7.0±1.9km s −1 .This velocity dispersion is higher than reported in previous studies, but is also based on a sample size that is a factor of 4 larger.Although most foreground stars should be distinguishable with parallax, background stars can not.Removing the star with the most negative radial velocity, a star 1.9 arcminutes from the cluster center, a mean velocity of < RV > = −54±2 km s −1 with a radial velocity dispersion of < σ > = 5.0±1.7 km s −1 is found.This brings down the veloc- ity dispersion.Note that this star has a [Fe/H] metallicity consistent with the metallicity of BH 261, and is more metal-poor than the field, which is why it is still included as a potential cluster member.Removing the horizontal branch stars, which have larger radial velocity uncertainties, as well as one giant with a radial velocity uncertainty of 10 km s −1 , the mean velocity is < RV > = −61±2.6km s −1 with a radial velocity dispersion of < σ > = 6.1±1.9 km s −1 .
Including the other four independent radial velocity measurements -3 stars from Barbuy et al. (2021) and 1 star from Geisler et al. ( 2023) -gives a sample of 16 stars.We then remove the stars with both the highest and lowest velocities to obtain a mean velocity of −53.6±2.0 km s −1 with a dispersion of 5.9±1.9km s −1 .
There may be other stars belonging to BH 261, as stars with radial velocities in this range exist out to as far as our observations go.Before evaluating the likelihood of extra-tidal stars around BH 261, [Fe/H] metallicities are calculated.
Figure 5 shows the Milky Way GCs analyzed in Baumgardt & Hilker (2018) with measured absolute magnitudes and intrinsic velocity dispersion values.The σ 2 0 parameter comes from the following equation σ 2 0 = σ 2 velσ 2 errors , where σ vel is the standard deviation of the radial velocity distribution of the cluster members and σ errors is the mean error of the velocity measurements.Using the radial velocity measurements from the 11 red clump and giant stars19 , a log σ 2 0 = 1.7 km s −1 is found.Removing the two stars in the sample with the highest and lowest radial velocities gives a log σ 2 0 = 1.3 km s −1 .
A velocity dispersion value based on the spread in the proper motions only can also be calculated.Because the proper motions are derived independently than the radial velocities presented here, this could be a further check as to the validity or our radial velocities.In this case, the Gaia proper motions are converted into tangential velocities (v t ) in km s −1 using the d=7100 pc distance found here and the relation v t = 4.74µd, where µ is the total proper motion in arcsec yr −1 and 4.74 is the conversion of distance (pc to km), angle (from arcsec to radians), and time (from years to seconds).We similarly recover a log σ 2 0 = 1.5 km s −1 .If the radial velocity membership criteria adopted here is too generous, the radial velocity outliers do not significantly affect the log σ 2 0 value of the cluster, as supported by the independent σ 0 value determined from proper motion measurements.
Figure 5 indicates that inner Galaxy GCs typically have larger internal velocity dispersions at the same luminosity as compared to GCs in the halo and disk.BH 261 is anomalous in that it has an internal velocity dispersion that generally is in line for clusters with brighter intrinsic magnitudes.The paucity of bulge GCs with M V > −6 is likely due to the difficulty of detecting and studying low luminosity GCs in the crowded and heavily-extincted bulge.The analysis presented here improves the properties of BH 261, especially important in the low-luminosity GC regime.

[Fe/H] Metallicities
The near-infrared region around the CaT is ideal for the determinations of radial velocities due to the strong CaT lines.There is also spectral information in this regime that can be used to constrain temperature, gravity and chemical abundances (e.g., Ruchti et al. 2010;Koch et al. 2017).The SP ACE code (Boeche et al. 2021;Boeche & Grebel 2016) was designed to derive stellar parameters and chemical abundances over the spectral resolution interval R = 2000-40,000 and over the wavelength interval 4800-6860 Å and over 8400-8924 Å.It was originally developed for elemental abundance determination for the Radial Velocity Experiment (RAVE) (Kunder et al. 2017;Steinmetz et al. 2020), which covers the same wavelength range as the spectra collected here.Although SP ACE can be used to measure individual abundances for different chemical species (Mg, Al, Si, Ca, Ti, Fe, and Ni), only [Fe/H] abundances are presented here.The lower signal-to-noise of the spectra give the most reliable results for the Fe I and Fe II lines, which are the most numerous in our wavelength regime.SP ACE was fitted to the 8450-8493 Å, 8503-8535 Å, 8550-8660 Å and 8670-8800 Å wavelength regimes in order to avoid the strong CaT lines which often cause difficulties in precise abundances and stellar parameter determination.
The wide coverage of APOGEE stars in the inner Galaxy allowed us to allocate a few fibers in our science fields to the re-observation of APOGEE bulge giants.The higher resolution of the APOGEE spectra (R∼22,000 vs our R∼10,000 spectra) as well as the high SNR for APOGEE stars (∼100-200), made it advantageous to use these as calibration standards.In total, 9 bulge giants in the APOGEE survey were observed during our run with our particular setup; they all have measured stellar parameters released in DR17 and span a wide range of [Fe/H] metallicities (see Figure 6).We also incorporated 6 APOGEE stars that were observed in previous AAT runs by our group with the same AAOmega setup to use as calibration standards.
Figure 6 (right panel) shows the SP ACE [Fe/H] metallicities as compared to those published by APOGEE.The temperature and gravity regime of SP ACE is within T eff =[3600,7400] K and log g=[0.2,5.0].For the two APOGEE stars with temperatures that are a few hundred Kelvin cooler than 3600 K, SP ACE did not converge, and therefore not all APOGEE stars observed were able to serve as metallicity standards.The uncertainty in [Fe/H] from SP ACE as compared to the APOGEE metalliciites is ∼0.2 dex.There is an indication that SP ACE under-predicts the [Fe/H] for high-metallicity stars, and over-predicts the [Fe/H] in the low-metallicity regime, but SP ACE is able to reproduce the [Fe/H] of our observed spectra between the range of ∼ −0.9 to ∼ +0.2 dex.
None of the 3 observed BHB stars have SP ACE metallicities that could be measured, since BHB have temperatures hotter than ∼8000 K. Also, hot BHB stars can have atmospheric effects like levitation and diffusion that mask their true abundances.SP ACE did converge to provide a [Fe/H] estimate for 5 of the 8 noncalibrating giants observed.The other three giants have a low SNR which was the likely why SP ACE failed to provide metallicities for these stars.A weighted-mean metallicity of < [Fe/H] >= −1.07 ± 0.22 is found.No evidence of a spread in the metallicity in BH 261 is seen, but our sample size is small and our formal [Fe/H] uncertainty is 0.2 dex.

Extra-tidal stars
In order to find signatures of BH 261 dissolving by the strong tidal field of the Milky Way, the tidal radius of the cluster needs to be known.Unfortunately the tidal radius of BH 261 is uncertain.There are difficulties in defining the tidal radius, both theoretically and observationally, and although there are correlations between the calculated theoretical and observational radii, it is not uncommon to find discrepancies between tidal radii estimates when using theoretical and observational approaches (e.g., Moreno et al. 2014).Ortolani et al. (2006) find the density profile merges with the background at 3.4±0.4arcminutes, and the 2010 edition of the Harris (1996) catalog list a tidal radius of 4' for BH 261.The tidal radius listed in Baumgardt et al. (2021) is 20.63 pc, which at the distance listed in their catalog (6100 pc), corresponds to 11.6'.
We use ASteCA (Automated Stellar Cluster Analysis) with the BDBS photometry combined with Gaia astrometry in an attempt to obtain an estimate of the tidal radius of BH 261.ASteCA is a python code (Perren et al. 2015) designed to perform a thorough analysis of star clusters (open or globular), modeling spatial, structural, and photometric parameters.ASteCA can determine cluster membership probabilities by utilizing a decontamination algorithm.It allows estimation of the center and radius of the cluster, along with density profiles, luminosity functions, and color-magnitude diagrams to study the stellar population within the cluster.
ASteCA was fed 7215 stars from BDBS with useful metallicity of our targeted stars as determined from SP ACE is shown in blue.Five giant stars within the cluster tidal radius with radial velocities consistent with the cluster are high-lighted in red.There are five giants with both [Fe/H] metallicities and radial velocities outside of the tidal radius; these are extra-tidal giant star candidates.The tidal radius determined here (3.5) is indicated by the solid line at a distance of 5.4' from the cluster center.Right Top: The observed sample spectra (black) of bh261 1 197.fits of the BH 261 giants within the tidal radius of the cluster is shown.The best-fit spectra from SP ACE is overlaid in red, where only the portion of the spectra sampled by SP ACE is shown.Note that the Campos wavelength axis used here extends to a longer wavelength range than used in Koch et al. (2017).Right Bottom: A comparison between seven APOGEE bulge giants and the [Fe/H] derived from SP aCE using the Campos wavelength range.
photometry and Gaia astrometry and that are within 30 arcminutes from the center of BH 261.The sample of stars was constrained to have 0.0 mas yr −1 < µ α <+5.0 mas yr −1 and 0.0 mas yr −1 > µ δ > −5.0 mas yr −1 , as well as parallax <0.4 mas, in an attempt to minimize field star contamination.In total, ASteCA was run ∼30 times, utilizing different BDBS and Gaia color-combination CMDs, with tightening proper motion limits.The solutions for the physical parameters derived from the King models (King 1962(King , 1966) ) remained stable once we tightened the proper motion limits.We used the extinction corrections from Simion et al. (2017).
ASteCA is not the ideal tool for discerning extratidal structures, as the decontamination procedure uses the field stars outside the cluster radius to determine the cluster membership.However, the code's unbiassed method of determining cluster parameters is useful to defining the radial density profile of the cluster and its members, thereby giving an indication of the tidal radius of the cluster.
We search for extra-tidal stars by targetting red clump stars as well as giants with proper motions consistent with BH 261. Figure 8 (left panel) shows the velocities of all giants and red clump stars targeted spectroscopically.These all have proper motions consistent with BH 261 (see Figure 1) and reach to 65 arc minutes from the center of the cluster.This corresponds to approximately 6 -10 times the cluster's tidal radius, depending on the exact calculation used for the tidal radius.
Our observations detect BH 261 stars with distances out to ∼4 arcminutes from the cluster center, but beyond this distance, there is no clear over-density of stars with radial velocities consistent with BH 261.There are a few giants and red clump stars with velocities similar to BH 261 between 5' and 10' from the cluster center, but these have metallicities that are more in-line with the bulge field as opposed to a GC.Beyond a distance of 10' from the cluster center, a handful of stars are identified that have both radial velocities and [Fe/H] metallicities consistent with BH 261.The most likely extra-tidal star candidates have both radial velocities and SP ACE metallicities consistent with BH 261; these are listed in Table 3.
It is estimated that contamination rates in the BDBS red clump star catalog is ∼30% (30% of the stars actually are not red clump stars, instead belonging to i.e., the bulge red giant branch, inner disc or halo, Johnson et al. 2022).Photometric metallicities may not be correct unless the star is on the red clump.In an attempt to remove any non-red clump members contaminating our sample as well as to confirm the [Fe/H] metallicities of The Gala python package (Price-Whelan 2017, 2022) is used to generate a model of the dynamics of BH 261's potential extra-tidal members.Gala provides several routines that allow the creation of mock stellar streams, by initializing new star particles at the cluster's Lagrange points with a specified frequency and with randomized velocity offsets consistent with a specified velocity dispersion.The orbits of each set of new star particles are then evolved forward in time within the combined gravitational potential of the cluster plus the potential of the Galaxy to reveal the spatial and kinematic structure that would be expected at the present day.Using the cluster's position (RA = 273.527• , Dec −28.635 • ), distance (7.1 kpc), proper motion (µ α = 3.566 mas yr −1 , µ δ = −3.590mas −1 ), radial velocity (−61 km s −1 ) and mass (2.4x10 4 M ⊙ ), Gala calculates the cluster's orbit in a Galactic potential.Here the adopted potential for the Milky Way is a three-component potential model consisting of the bar (an implementation of the model used in Long & Murali 1992), a Miyamoto-Nagai potential for the galactic disk (Miyamoto & Nagai 1975), and a spherical Navarro-Frenk-White (NFW, Navarro et al. 1997) potential for the dark matter distribution.The bar is tilted with respect to the x-axis by 25 degrees, has a mass 1/6 of the mass of the disk component and the long-axis scale length of the bar is set to 4 kpc (Bland-Hawthorn & Gerhard 2016).
We simulate the ejection of star particles using the Fardal Stream Generator (Fardal et al. 2015).The Fardal Stream Generator simulates the formation of extra-tidal structures via external tidal stripping, rather than more violent internal relaxation processes.The locations of the Lagrange points from which stars are ejected, as well as the velocity offsets the stars receive when they are ejected, are set to be consistent with the cluster's mass and density profile, and the velocity dispersion expected for a fully thermalized population.The frequency with which star particles are ejected, however, is non-physical: we simulate ejection events every 0.5 Myrs over the past 100 Myrs, to ensure that we densely sample all positions and velocities for which tidally stripped stars would be present.
A comparison of the location of the candidate extratidal stars we have identified with the synthetic extratidal stars in the Gala simulations is shown in Figure 9 (left panel).Because the most recent stellar debris will be both physically closest to the cluster, and the most kinematically coherent, we focus on the debris produced within the last 100 Myrs, which is most amenable to detection in our spectroscopic observations.Also, the simulated debris produced within the last 100 Myrs is the least affected by the adopted potential of the Milky Way.
The Gala simulation does suggest that ejected stars from BH 261 could show a stream of stars, with arms on the leading and trailing end of the orbital path of the cluster.Our observations are limited to the brightest stars, which given the low-luminosity of BH 261, would likely not to have the spatial density to show a clear stream.Still, we may be able to detect tidal disruption, which could follow a coherent structure.No stellar tidal streams have been seem emanating from bulge GCs to date, although a low-luminosty (M V = −3.0 ± 0.5, similar to that found for the lowest-mass GCs) stream, the Ophiuchus stream, has been detected near the MW bulge region, above the center of the Galaxy (Bernard et al. 2014).Its old (∼12 Gyr) and relatively homo- geneously metal-poor population and α-enhanced stars suggest that the progenitor would most likely be a globular cluster(e.g., Sesar et al. 2015).However, because of its short length and short orbital period of the stream, it should have been disrupted fairly recently, but no progenitor is visible.In an attempt to explain the Ophiuchus stream, models and mechanisms to enhance the density of some stellar streams in the inner halo/bulge have been put forward, but to date no model can explain the short Ophiuchus stream with such a short orbital period (e.g., Hattori et al. 2016;Price-Whelan et al. 2016;Lane et al. 2020).Observational analysis to detect additional substructures in the inner Galaxy is needed for a more complete understanding of the Milky Way's gravitational potential and therefore a better dynamical study of clusters as they pass through the inner Galaxy, which are complicated by also the influenced by the Galactic bar, it's rotations and how the bar has changed with time(e.g., Hattori et al. 2016).
Only a handful of the stars with radial velocities consistent with BH 261 are spatially coincident with the predicted 100 Myr tidal debris.Extra-tidal stars that do not fall along the cluster's current orbit could have arisen due to effects not included in Gala, such as stars ejected due to shocks caused by the tidal field of the Galaxy and/or stars ejected from tidal interactions with the galactic plane (e.g., Moreno et al. 2014), or a much larger dispersion of ejection velocities and angles due to intra-cluster interactions, such as those simulated by the core particle spray algorithm (Grondin et al. 2023).Although less significant, stars can also be ejected due to interactions with the giant molecular clouds (e.g., Amorisco et al. 2016), a process Gala is unable to incorporate.
Given the large velocity dispersion of BH 261 and hence a potentially larger dynamical mass, we also used Gala with a cluster mass more in-line with the dynamical mass of the cluster, 1x10 6 M ⊙ .Figure 9 (middle panel) shows that in this case, the comparison of the observed extratidal stars with simulations is improved.
High-resolution spectroscopy to chemically fingerprint the extra-tidal star candidates would allow a deeper characterization into the origin of these stars.There are a handful of extra-tidal star candidates that fall along the predicted tidal debris, but it is likely that most of the candidate extra-tidal stars listed in Table 3 are not recently stripped from the cluster.That few stars are currently being stripped from BH 261 would be in agreement with the cluster's low luminosity -the cluster does not have as many stars left for it to lose today as it had in the past.This would be consistent with BH 261 being an old, low-mass cluster so that any extra-tidal stars are likely to be white dwarfs, rather than more massive main sequence stars and giants.In this case, it was be difficult to detect extra-tidal stars from our observations.If the extra-tidal candidates are confirmed to be bona fide extra-tidal stars, that might indicate the velocity dispersion of BH 261 is driven by tidal heating rather than a high mass-to-light ratio.

CONCLUSIONS
In order to better understand the bulge field population as well as to observe the processes inner Galaxy GCs undergo in their passage through the inner Galaxy, the MWBest spectroscopic survey is identifying stripped Fig. 9.-The simulated tidal tails for BH 261 (grey), calculated with the cluster's best fit parameters, are compared to the most promising BH 261 extra-tidal candidates presented here.The inset in the upper left corner designates the length of time the cluster orbit is integrated forwards as well as the mass of BH 261 used in the simulation.The width of the stripped stars is tight when using a small GC mass (i.e., the mass inferred from its luminosity), and the simulated tidal tails occupy a greater area around the center of the cluster as a larger GC mass is used (i.e., the mass inferred from its velocity dispersion).
stars from inner Galaxy GCs.On average, mass lost from low-mass/low-luminosity globular clusters such in the inner parts of the Milky Way, such as BH 261, will be considerably larger than for clusters with presentday masses larger than 10 5 M ⊙ (Baumgardt et al. 2021).These low-mass/low-luminosity clusters started off with masses greater than ∼ 10 6 M ⊙ and have lost mass as they move through the Galaxy.By integrating the orbits of the Milky Way GC backward in time and applying suitable recipes to account for the effects of dynamical friction and mass-loss of stars to the clusters, Baumgardt et al. (2021) show that especially clusters inside the central 2 kpc of the MW have lost a large portion (∼80 %) of their initial populations.BH 261 has the smallest mass of the Milky Way GCs listed in Baumgardt et al. (2021), weighing in at ∼2.4±0.6 x 10 4 M ⊙ .It is also one of the few low luminosity bulge GCs, with an absolute magnitude of M V =−4.43 mag.In fact, there are only two well-studied bulge GCs (those with more than 10 stars with radial velocity measurements) listed in the Baumgardt et al. ( 2021) catalogue with M V > −6, the other one being ESO 452-SC11 (see Koch et al. 2017;Simpson et al. 2017).
In order to carry out a search for extra-tidal stars around the BH 261, a better characterization of this GC is needed.Using BDBS photometry combined with Gaia astrometry, the radial density profile of the cluster region is decomtaminted and fit with a King profile using ASteCA.In this way we derive a core radius of BH 261 of r c = 0.35', a cluster radius of r cl = 2.6', and a tidal radius of r t = 5.4'.
We carried out the largest spectroscopic analysis of stars within the tidal radius of BH 261.From the 7 giant stars with the best radial velocities within ∼4' of the center of BH 261, a mean velocity of < RV > = −61±2.6km s −1 with a radial velocity dispersion of < σ > = 6.1±1.9 km s −1 is found.When all 12 BH 261 stars within ∼4' of the center are considered a mean velocity of < RV > = −56±1.7 km s −1 with a radial velocity dispersion of < σ > = 7.0±1.9km s −1 is found.This average velocity is consistent with that of Barbuy et al. (2021), who find < RV > = −57.9±4.3 km s −1 .It differs from that of Baumgardt et al. (2019) who find < RV > = −29.4km s −1 , and it differs from that of Geisler et al. (2023) who find < RV > = −44.9±3.8 s −1 .However, the stars observed here encompass the velocity values reported in previous studies.For example, the three observed stars in Barbuy et al. (2021) span a large velocity range with velocities of −67.65±3.65 km s −1 , −57.93±4.28km s −1 and −29.57±5.85km s −1 .Similarly, the three observed stars in Geisler et al. (2023) have velocities of −52.5±1.9 km s −1 , −42.33±1.2km s −1 and −39.9±2.3 km s −1 .What is consistent in all spectroscopic studies of BH 261 to date is that the velocity spread is not insignificant.The larger sample of stars presented here allows for a more robust value for a mean velocity.
The SP ACE code was utilized for the determination of [Fe/H] metallicities, and from spectra of 5 giants, an average [Fe/H] ∼ −1.1 ± 0.11 dex is found.By identifying a RR Lyrae star in BH 261, the distance to the cluster is found to be 7.1±0.4kpc.This, as well as direct spectroscopic measurements of [Fe/H] from 5 giant stars in BH 261, confirms BH 261 is on the near-side of the bulge.As discussed also in Gran et al. (2022), this shorter distance indicates BH 261 has an abnormally low-luminosity as compared to its stellar velocity dispersion.New BDBS photometry in the ugrizY passbands is presented of the central region of BH 261 and is used to check for consistency between the cluster parameters and the optical CMD of BH 261.The MIST isochrones with the cluster's distance and metallicity derived in this work (7.1 kpc and −1.1 dex) show good agreement with the BDBS CMDs and with an old cluster age, of ∼13 Gyr.Such an age is similar to other bulge GCs with blue HBs (Kerber et al. 2018).
A search for candidate extra-tidal stars spanning the radial velocity and proper motion range of BH 261 was carried out.A few of our most promising extra-tidal candidates -those with radial velocities, proper motions and [Fe/H] metallicities consistent with BH 261 -are consistent with Gala simulations of the dynamical evolution of the cluster using the present day mass of the cluster.But most are only consistent with recent tidal debris from BH 261 if a larger cluster mass is used.BH 261 is an old, low-mass cluster, and it may be that most stripped stars today are white dwarfs, rather than more massive giants we are able to target spectroscopically.

Fig. 1 .
Fig.1.-TheGaia proper motion distribution of the BDBS stars centered in a 3.2 arc minute radius from BH 261.Blue points show stars with proper motions within 1.5 mas yr −1 in both µα and µ δ of the mean proper motion of the cluster, as well as those with stars with parallax values smaller than 0.4 mas.The black points indicate stars that were spectroscopically targeted, and those with red highlights are those that were found to be radial velocity members.The star symbol (green) indicates the RR Lyrae star OGLE-BLG-RRLYR-35078.

Fig. 2 .
Fig. 2.-The BDBS color-magnitude diagram showing the horizontal branch stars (triangles), giants (circles) and RR Lyrae star (star) for which radial velocities have been determined from AAOmega@AAT.The filled red symbols indicate those stars that have radial velocities consistent with BH 261 (see Table 2), whereas the open triangle and circles are those stars that do not have velocities consistent with the cluster.The underlying BDBS stellar distribution in this field is shown with small grey points and those with proper motions consistent with the cluster are shown in blue.The black lines show the MIST (MESA Isochrones and Stellar Tracks, Choi et al. 2016) isochrone from which the cluster's distance is derived in this work (7.1 kpc).
era.Photometry of approximately 250 million unique sources is available in BDBS, spanning the Galactic longitude range from l=−10 • to +10 • and the Galactic latitude range from b=−3 • to −10 • .

Fig. 4 .
Fig. 4.-Left: The heliocentric velocities of our targeted stars within 5 arc-minutes of BH 261.The clump of twelve stars with radial velocities of ∼−60 km s −1 within the 3.5 arcmin of the cluster are consistent with being BH 261 stars.Right: The radial velocity curve of the first-overtone RR Lyrae, OGLE-BLG-RRLYR-35078, which has both a proper motion and a radial velocity consistent with BH 261.The RRc template from Prudil et al. (2023) is used to obtain a center-of-mass radial velocity.The APOGEE DR17 observations are also shown, but not used in the radial velocity determination.
are employed.Briefly, thePrudil et al. (2023) calibrating dataset consists of 100 RR Lyrae stars with mean intensity magnitudes, reddenings, pulsation properties, iron abundances, and parallaxes from Gaia DR3.Both RRab and RRc pulsators are included in the calibrating set and it was shown that their derived PMZ relations accurately estimate the distance moduli to NGC 6121, NGC 5139, the LMC and SMC, as well as the the prototype of RR Lyrae class, RR Lyr.Because the motivation behind thePrudil et al. (2023) PMZ relations is to use them for RR Lyrae stars toward the Galactic bulge, special care is given to calibrate the relations to the OGLE and VVV photometric system directly.Further, a homogeneous metallicity scale is used for the calibrating sample that allows the direct use of photometric metallicity derived from the OGLE I-band photometry.The Prudil et al. (2023) PMZ relations are used to investigate the distance to BH 261.Assuming A k = 0.04 ± 0.02 mag, and a photometric metallicity of [Fe/H] = −1.25 (Dekany et al. 2021), a distance of d=7132 ±312 pc is derived from the OGLE I-band and the VVV K s band.Using only the VVV J and K s bands, A k = 0.08 ± 0.09 mag is found, and a distance of d=7006 ±427 pc is derived.Throughout the paper, we adopt a distance of 7.1 ± 0.3 kpc as the distance to BH 261.The [Fe/H] = −1.25 Dekany et al. (2021) metallicity for the BH 261 RR Lyrae star is based on the For et al. (2011); Chadid et al. (2017); Sneden et al. (2017); Crestani et al. (2021) metallicity scale, abbreviated CFCS.This is different than the SP ACE and APOGEE metallicity scale.To quantify the difference between these two metallicity scales, the average Dekany et al. (2021) metallicity of RR Lyrae stars in the bulge GCs with at least 6 RR Lyrae stars is determined.Two of those GCs have published [Fe/H] abundances from APOGEE's ASPCAP.NGC 6642 has an APOGEE derived [Fe/H] = −1.11(Geisler et al. 2021) and 19 OGLE RR Lyrae stars with an average CFCS photometric [Fe/H] = −1.42.FSR1758 has an APOGEE derived [Fe/H] = −1.43(Romero-Colmenares et al. 2021) and 9 OGLE RR Lyrae stars with an average CFCS photometric [Fe/H] = −1.84.Therefore, the RR Lyrae star photometric metallicities are ∼ −0.3 dex more metal-poor than the APOGEE ASPCAP [Fe/H] metallicity.The BH 261 RR Lyrae metallicity of [Fe/H] = −1.25 corresponds to [Fe/H] = −0.95dex on the APOGEE/ASPCAP scale, in agreement with the SP ACE derived metallicity of BH 261 giants in 3.4.

Fig. 5 .
Fig. 5.-Absolute integrated magnitude (M V ) and velocity dispersion (log σ 2 0 ) for clusters analyzed by Baumgardt & Hilker (2018).The open black points indicate globular clusters that are further than 3.35 kpc from the Galactic center, where as the filled blue points indicate inner Galaxy globular clusters -those with galactocentric distances less than 3.35 kpc.The red triangle designates BH 261.

Fig. 7 .
Fig. 7.-The combined BDBS photometry with Gaia proper motion radial density profile of the BH 261 cluster region.The dots are the stars per arcmin 2 taking the cluster center as the origin.The horizontal dashed black line indicates the field density.The King profile fit is indicated with the green dashed curve and the cluster core radius is indicated by the dotted vertical green line.The red vertical line indicates the assigned radius of BH 261 with the uncertainty region marked as a gray shaded area.The tidal radius is indicated by the solid vertical line at radius of 5.38 arcminutes.A rescale of the main plot is shown in the top inset.the red clump stars, SP ACE is run on the red clump stellar spectra with both photometric metallicities and radial velocities consistent with BH 261, i.e., those star with radial velocities between −35 > RV > −80 km s −1 and a photometric [Fe/H] < −0.5.These are the most probable extra-tidal stars.Figure 8 (right panel) shows a comparison between the photometric and spectroscopic [Fe/H] metallicities for the 16 red clump stars for which SP ACE converged and that have parameters indicating they could be extra-tidal stars.Two of those have SP ACE metallicities that are too metal-rich to be part of the cluster, and these are excluded from the sample of potential extra-tidal star candidates.The Gala python package (Price-Whelan 2017, 2022) is used to generate a model of the dynamics of BH 261's potential extra-tidal members.Gala provides several routines that allow the creation of mock stellar streams, by initializing new star particles at the cluster's Lagrange points with a specified frequency and with randomized velocity offsets consistent with a specified velocity dispersion.The orbits of each set of new star particles are then evolved forward in time within the combined gravitational potential of the cluster plus the potential of the Galaxy to reveal the spatial and kinematic structure that would be expected at the present day.Using the cluster's position (RA = 273.527• , Dec −28.635 • ), distance (7.1 kpc), proper motion (µ α = 3.566 mas yr −1 , µ δ = −3.590mas −1 ), radial velocity (−61 km s −1 ) and mass (2.4x10 4 M ⊙ ), Gala calculates the cluster's orbit in a Galactic potential.Here the adopted potential for the Milky Way is a three-component potential model consisting of the bar (an implementation of the model used in Long & Murali 1992), a Miyamoto-Nagai potential for the galactic disk (Miyamoto & Nagai 1975), and a spherical Navarro-Frenk-White (NFW, Navarro et al. 1997) potential for the dark matter distribution.The bar is tilted with respect to the x-axis by 25 degrees, has a mass 1/6 of the mass of the disk component and the long-axis scale length of the bar is set to 4 kpc (Bland-Hawthorn & Gerhard 2016).

Fig. 8 .
Fig. 8.-Left: The heliocentric velocities of our targeted stars within 65 arc-minutes of BH 261, with the tidal radius at rt=5.4' indicated by the solid grey line.The uncertainties in radial velocity is ∼4 km s −1 , except for the horizontal branch stars, where the RV uncertainty is ∼9 km s −1 .Large (green) stars represent the targeted RR Lyrae stars.The stars with both SP ACE metallicities, photometric metallicities and radial velocities consistent with BH 261 are circled, and are potential extra-tidal stars belonging to BH 261.Right: A comparison between the photometric [Fe/H] and spectroscopic [Fe/H] is shown for the stars with both photometric metallicities and radial velocities consistent with BH 261.The two red clump stars with spectroscopic [Fe/H] metallicities that are discrepant from the photometric metallicities also have T ef f and log g values suggesting they are not red clump giants.

TABLE 1 Blanco
DECam Bulge Survey (BDBS) photometry of stars within 3.2' from BH 261 Gaia proper motions, radial velocities and [Fe/H] metallicities of the probable member stars of BH 261 Gaia proper motions, radial velocities and spectroscopic [Fe/H] metallicities of the candidate extra-tidal stars stripped from BH 261 AMK acknowledges support from grant AST-2009836 from the National Science Foundation.The grant support provided, in part, by the M.J. Murdock Charitable Trust (NS-2017321) is acknowledged.This work was made possible through the Preparing for Astrophysics with LSST Program, supported by the Heising-Simons Foundation and managed by Las Cumbres Observatory.M.J. gratefully acknowledges funding of MATISSE: Measuring Ages Through Isochrones, Seismology, and Stellar Evolution, awarded through the European Commission's Widening Fellowship.This project has received funding from the European Union's Horizon 2020 research and innovation programme.This project used data obtained with the Dark Energy Camera (DECam), which was constructed by the Dark Energy Survey (DES) collaboration.Funding for the DES Projects has been provided by the US Department of Energy, the US National Science Foundation, the Ministry of Science and Education of Spain, the Science and Technology Facilities Council of the United Kingdom, the Higher Education Funding Council for England, the National Center for Supercomputing Applications at the University of Illinois at Urbana-Champaign, the Kavli Institute for Cosmological Physics at the University of Chicago, Center for Cosmology and Astro-Particle Physics at the Ohio State University, the Mitchell Institute for Fundamental Physics and Astronomy at Texas A&M University, Financiadora de Estudos e Projetos, Fundação Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro, Conselho Nacional de Desenvolvimento Científico e Tecnológico and the Ministério da Ciência, Tecnologia e Inovação, the Deutsche Forschungsgemeinschaft and the Collaborating Institutions in the Dark Energy Survey.