RR Lyrae Stars Belonging to the Candidate Globular Cluster Patchick 99

Patchick 99 is a candidate globular cluster located in the direction of the Galactic bulge, with a proper motion almost identical to the ﬁ eld and extreme ﬁ eld star contamination. A recent analysis suggests it is a low-luminosity globular cluster with a population of RR Lyrae stars. We present new spectra of stars in and around Patchick 99, targeting speci ﬁ cally the three RR Lyrae stars associated with the cluster as well as the other RR Lyrae stars in the ﬁ eld. A sample of 53 giant stars selected from proper motions and a position on the color – magnitude diagram are also observed. The three RR Lyrae stars associated with the cluster have similar radial velocities and distances, and two of the targeted giants also have radial velocities in this velocity regime and [ Fe / H ] metallicities that are slightly more metal-poor than the ﬁ eld. Therefore, if Patchick 99 is a bona ﬁ de globular cluster, it would have a radial velocity of − 92 ± 10 km s − 1 , a distance of 6.7 ± 0.4 kpc ( as determined from the RR Lyrae stars ) , and an orbit that con ﬁ nes it to the inner bulge.


INTRODUCTION
The globular clusters surrounding our Milky Way are nearly as old as the Universe itself.These roughly spherical collections of hundreds of thousands of tightly packed and gravitationally bound stars form in the early Universe in high-density peaks (Diemand et al. 2005;Boley et al. 2009).Their high density allows them to endure tidal disintegration, and they, therefore, witness most of the formation and evolution processes of galaxies, which they can be used to study (Brodie & Strader 2006).
In contrast to globular clusters in the halo, clusters in the inner Galaxy are more likely to in-spiral toward the galactic center due to the stronger tidal field in the inner Galaxy and dynamical friction.It is believed that clusters inside the central 2 kpc of the Milky Way have lost ∼80% of their initial population (Baumgardt & Hilker 2018).Therefore, low-luminosity/low-mass GCs should exist in the inner Galaxy and should likely be more ubiquitous in the inner Galaxy than the halo.However, to date, there is a factor of ∼5 times more low-luminosity GCs known in the halo of the Milky Way (Baumgardt et al. 2021).
One survey searching for potential low-luminosity candidate globular clusters in the inner Galaxy is the VISTA Variables in the Via-Lactea survey (VVV) survey, a large (∼1 billion star) photometric, infrared time domain survey of the disk and inner Galaxy (Minniti et al. 2010).Between 2011 and 2018, more than 100 new GC candidates in the bulge have been proposed, most of them (but not all) have low luminosities.After Gaia proper motions were released in 2018, it could be seen if "cluster" stars were moving together in proper motion space (e.g., Gran et al. 2019).However, stellar spectroscopy is still necessary to identify individual star cluster members from the field and to validate candidate star clusters as being separate from the field (some examples of this include Fernandez-Trincado et al. 2021;Gran et al. 2022).
This study focuses on the low-luminosity candidate GC Patchick 99 at (l,b)=(2.4884°,−6.1452°).Identified by Dana Patchick on 20 November 2004 using 2MASS imagery, the Deepskyhunters group (e.g., Kronberger et al. 2006) recognized it first as 'DSH J1815.7-2948'(D. Patchick, priv. communication).Since then, it has appeared in internal catalogs as Patchick 99.Bica et al. (2019) list it as a globular cluster in their compilation of star clusters, associations, and candidates in the Milky Way.It was the subject of a study by Garro et al. (2021), who postulate Patchick 99 is a bonafide globular cluster based on Gaia proper motions, color-magnitude diagrams (CMDs) from VVV photometry, and by identifying a population of RR Lyrae stars (RRLs) that were thought to be associated with Patchick 99.The extreme similarity in both the proper motion and the CMD between the field and the potential cluster stars makes identification of this cluster difficult, and no radial velocity measurements of this potential cluster exist to date.
The first spectroscopic observations are presented here in an attempt to probe the nature of Patchick 99, particularly by targeting its RR Lyrae star population.

Observations and Target Selection
The observations come from the AAOmega multifiber spectrograph on the Anglo-Australian Telescope (PROP-ID: O/2022A/3002) with the red 1700D grating centered at 8600 Å(so that the calcium II triplet lines were observed) giving a resolution of R∼11,000.Exposure times ranged from 4x30 min to 2x30 min, adjusting for weather and seeing conditions.The data reduction steps were carried out using the AAOmega 2dfdr software: Bias subtraction, quartz-flatfielding, cosmic ray cleaning, sky subtraction using 35 designated sky fibers, and wavelength calibration via arc-lamp exposures.The typical final spectrum had a wavelength range from 8350-8800 Å, with slight variations depending on the spectrum's exact position on the CCD.
In total, 53 giants, 41 red clump stars, and 271 RRLs within a 2 degree field of view of Patchick 99 were targeted.The selected giants had Gaia DR3 proper motions within (µ α , µ δ )=(−2.98 mas yr −1 ±2.5 mas yr −1 , −5.49 mas yr −1 ±2.5 mas yr −1 ) (the mean proper motion of Patchick 99 as presented in Garro et al. 2021;Gaia Collaboration et al. 2023) as well as a RUWE <1.2.This is a larger proper motion range than the proper motion uncertainty presented in Garro et al. (2021) to encompass all possible members.All 12 RRLs within 10 arcminutes of the cluster were observed, regardless of proper motion.Red clump stars from Johnson et al. (2022) with photometric [Fe/H] metallicities more metal-poor than −0.25 dex were included as the lowest priority targets in the configuration files.The giants were only observed once-each AAOmega plate configuration retained the same RRLs and red clump stars but cycled through different giant stars.
The focus here is the stars around the central 10 arcminutes of Patchick 99, for which the center of α=273.94583°andδ=−29.81278°presented in Garro et al. (2021) is used.Figure 1 (lower left panel) shows the proper motion distribution of the observed stars as compared to the underlying field observed in the Blanco DECam Bulge Survey (BDBS, Rich et al. 2020;Johnson et al. 2020).BDBS is a large optical survey of the southern Galactic bulge in the ugrizY filters spanning 200 square degrees from −11°<l <+11°and −13°<b <−2°(BDBS, Rich et al. 2020;Johnson et al. 2020).To avoid the foreground disk, all targeted stars had Gaia parallaxes ≤0.4 mas (Marchetti et al. 2022).
The BDBS CMD shows the isochrone using the cluster metallicity and age as put forward by Garro et al. ( 2021) ([Fe/H] = −0.2,age=10 Gyr).We also show the isochrone using the cluster metallicity determined here and an age more indicative of bulge GCs with RRLs ([Fe/H] = −0.7,age=12 Gyr).The optical CMD presented here is not used to constrain any cluster parameters but to verify consistency between the BDBS photometry and the cluster parameters derived here using RRLs.

Velocities
IRAF's xcsao routine was used to calculate radial velocities by cross-correlating science spectra against five calibration spectra.
These calibration templates were chosen from the Apache Point Observatory Galaxy Evolution Experiment (APOGEE DR17, Abdurro'uf et al. 2022) DR17 database and all observed during our 5-night run at the Anglo-Australian Telescope.
Twelve RRLs-ten RRab stars and two RRc stars-within 10 arcminutes of Patchick 99's center were observed three times during the observing run.The velocity curves for 10 of these RRLs are shown in Figure 2. The spectrum for the RRab star OGLE-BLG-RRLYR-35355 had a signal-to-noise per pixel of ≤2 and so was excluded from kinematic analysis.The RRc star OGLE-BLG-RRLYR-35447 was also excluded from analysis, as the extracted spectrum was a superposition of the two different stars landing in the AAOmega fiber, and we were unable to separate the two spectra to isolate that of the RRL.
The RRL velocity curves show the corresponding template from Prudil et al. (2024a), derived specifically for RRLs in the bulge.Each observation time was converted into pulsation phase, ϕ, using the OGLE pulsation ephemerides and pulsation periods so that maximum light falls at ϕ=0 for each RRL (OGLE, Udalski et al. 2015).These templates were used to calculate center-of-mass radial velocities for the stars, using the Fourier fits from the template spectra to fit the template model to the observations (Prudil et al. 2024a).The uncertainty adopted for each star is 10 km s −1 , which includes the uncertainties in the individual radial velocity measurements combined with the uncertainties in the template fitting.
Five of the ten stars were observed as part of the APOGEE DR17.To overplot these onto the radial velocity curves, the time of observation specified by the column JD in the APOGEE allVisit-dr17-synspec rev1.fits2file was used.There is good agreement between the APOGEE observations and our observations, except for the star OGLE-BLG-RRLYR-16094, where the APOGEE observations appear to be offset in phase by ∼0.35.This could be due to a varying period of this star, although this star is not flagged as a period-changing star or Blazhko variable in the OGLE catalog (Prudil & Skarka 2017).
We searched the Gaia DR3 database (Gaia Collaboration et al. 2023) for additional stars with proper motions, radial velocities, photometric metallicities, and photometric distances consistent with Patchick 99.Apart from the observed giants, we were not successful in finding any star in Gaia that we believed was consistent with Patchick 99 membership.

Velocities
Six RRLs are postulated to be Patchick 99 cluster members by Garro et al. (2021) based on their period-luminosity relation.However, only three of those have proper motions consistent with Patchick 99.The mean heliocentric radial velocity of these three stars is −92.3±6km s −1 .To take into account the random errors of ±10 km s −1 in the RRL systemic velocities, the intrinsic velocity dispersion, σ 2 0 = σ 2 vel -σ 2 err , is found.The obtained internal dispersion of σ 0 =3 km s −1 is typical for globular clusters, especially in the lower luminosity range.
The rotation curve of the Galactic bulge is well known (e.g., Kunder et al. 2012), and at the location of Patchick 99, the typical galactocentric velocity is ∼30 km s −1 .In contrast, the mean galactocentric velocity of the three Patchick 99 RRLs is ∼ −75 km s −1 , indicating their velocities are distinct from the underlying bulge field.
Four giants are found to be within the radial velocity range of the RRLs (i.e., between −107 and −75 km s −1 ).These are listed in Table 1.We show in §3.2 that two of those four giants, the two with radial velocities ∼ −100 km s −1 , have spectroscopic metallicities that are consistent with belonging to Patchick 99.The two giants with radial velocities of ∼ −80 km s −1 are not as metal-poor as the RRL and therefore more likely to belong to the bulge field.The two red clump stars have neither a consistent proper motion nor radial velocity and are shown in Figure 1 and Figure 3.
Table 1 lists the radial velocities of all the RR Lyrae stars, as well as the giants and red clump stars.A portion of the table is shown for clarity; all 53 observed giants are included in the electronic version of this paper.

Metallicity
The photometric metallicities for the observed RRab stars are calculated using the relations from Dekany et al. ( 2021) and are listed in Table 1 and  The SP ACE code (Boeche et al. 2021) was used to determine spectroscopic metallicities for both the giants and red clump stars in our sample.Kunder et al. (2024) use AAOmega spectra taken with the same wavelength range and resolution used here to show that SP ACE can reproduce [Fe/H] metallicities with an accuracy of 0.2 dex over a metallicity range of [Fe/H] ∼ −0.9 to ∼ +0.2 dex.
Two of the four giants with radial velocities similar to the RRL in Patchick 99 have [Fe/H] metallicities within one sigma of the Patchick 99 RRLs.These two stars are more metal-poor than the majority of the field stars and have an average [Fe/H] metallicity of −0.60.These are the most likely candidate Patchick 99 giants.

Distance and Orbit
Distances to the RRLs were determined using empirical period-absolute magnitude-metallicity (PMZ) relations from Prudil et al. (2024b), which are calibrated from local RRLs with Gaia parallaxes.These are intended to be used in conjunction with the Gaia catalog and the bulge photometric surveys of OGLE and VVV and are therefore particularly well suited for the RRLs presented here.Figure 3 (right panel) shows the distances of 9 of the 10 RRLs observed; OGLE-BLG-RRLYR-35364 is not shown, as it is at a distance of ∼26 kpc.This distance and radial velocity are consistent with OGLE-BLG-RRLYR-35364 belonging to the Sagittarius Dwarf Galaxy (Kunder & Chaboyer 2009).
The three candidate RRLs of Patchick 99 cluster in distance space, with distances within one sigma of each other.Their mean heliocentric distance is d ⊙ =6.7±0.4 kpc, which is similar to the distance of 6.6±0.6 kpc reported by Garro et al. (2021).The other RR Lyrae stars within 10' from Patchick 99 have distances offset from the candidate RRL cluster stars.
To simulate the orbital trajectory of Patchick 99 over the past Gyr, we used the Gala python package (Price-Whelan 2017; Price-Whelan et al. 2023).For this calculation, we adopt a Galactic potential with three components: a flattened 6x10 10 M ⊙ Miyamoto & Nagai (1975) stellar disk with a 3.5 kpc scale length and 0.280 kpc scale height; a tri-axial Long & Murali (1992) bar with M=10 10 M ⊙ and appropriate shape parameters (a=4 kpc, b=0.8 kpc, c=0.25 kpc, and α=25 degrees); and a 6x10 11 M ⊙ Navarro, Frenk & White (1996) dark matter halo with a 20 kpc scale radius.The cluster's present-day orbital parameters were defined with the values given earlier in this paper: namely, the cluster's position (RA = 273.94583•,Dec = −29.81278•),proper motion (µ α =−2.98±2.5 mas yr −1 , µ δ =−5.49±2.5 mas yr −1 ), radial velocity (−92±10 km s −1 ) and distance (6.7±0.4 kpc).By defining a timestep of −0.5 Myr and then integrating the orbit over 2000 steps, the last billion years of Patchick 99's orbit were calculated and shown in Figure 4.During this period, the cluster has been in a flattened orbit that does not extend beyond 1.75 kpc from the Galactic center or 0.75 kpc from the Galactic midplane.We have experimented with changing the distance, radial velocity, and proper motion within their uncertainties and also experimented with changing the Galactic potential.Although this does affect the specific shape of the orbit, the cluster always remains confined to the innermost 2 kpc of the Galactic center.

CONCLUSIONS AND FINAL REMARKS
Patchick 99 is a candidate low-luminosity GC located in the inner Galaxy.We present the first spectroscopic observations for stars within 10' of the center of Patchick 99 to determine the radial velocity of stars belonging to this structure.Our focus is on the RR Lyrae stars because giants are ubiquitous in the bulge field and heavily overlap with both the color-magnitude diagram and proper motion distribution of Patchick 99 (Garro et al. 2021).The use of RRLs as probes of globular clusters is advantageous as overdensities of horizontal branch stars can separate globular clusters from the crowded bulge field (e.g.Rich et al. 2020).
The three RRLs with proper motions consistent with the cluster have similar radial velocities of ⟨RV ⟩=−92.3±10km s −1 with a standard deviation of σ=3 km s −1 .They further clump in distance space, with a mean heliocentric distance of d ⊙ =6.7±0.4 kpc.Therefore, the RRL population of Patchick 99 suggests it is a bonafide low-luminosity GC on the near side of the bulge.

Z (kpc)
Figure 4.The integrated orbit of Patchick 99 using as initial conditions the distance and radial velocity presented here along with the position and proper motion values from Garro et al. (2021).The projection of the orbit on the Galactic plane (xy), the (x -z) plane, and the meridional plane (R -z) are all shown and suggest this candidate cluster is confined to the inner Galaxy.The cluster's present-day location is highlighted as a red dot.
A sample size of three is not ideal for determining the mean properties of a cluster; having a larger sample of stars would improve the mean velocity and dispersion for this potential cluster.The low luminosity of Patchick 99 means only a handful of giant and HB stars belonging to the cluster will exist, and identifying cluster members will be challenging.For example, Simpson et al. (2017) found only 11 cool giants and HB stars in the low-luminosity cluster ESO 452-SC11 (cluster mass of 6.8±3.4 x 10 3 M ⊙ ).In this study, very few giants targeted have properties indicating they could be probable cluster members.In particular, two of the 53 giants observed have velocities and [Fe/H] metallicities consistent with cluster membership.Probing the fainter main-sequence stars may be needed for future studies.The metallicities of these two giants combined with the photometric metallicities of the RRLs indicate a mean metallicity of −0.75±0.3dex.The metallicity and distance found here is consistent with isochrones fit to the BDBS CMD.
Given the low luminosity of Patchick 99, it is worth considering how likely it would be for this cluster to harbor a population of three RRLs.Synthetic HB procedures may be usefully adopted to predict relevant features of the frequency of RRLs as a function of cluster mass, but this is beyond the scope of our paper.Observationally, it is worth noting that ultra-faint dwarf galaxies with similar brightness as Patchick 99 have 1-12 RRLs (Martínez-Vázquez et al. 2019;Vivas et al. 2020).
The small mass of Patchick 99 combined with its position just a few kiloparsecs of the Galactic Center means it must have lost most of its initial mass and should be close to final dissolution (Baumgardt & Makino 2003).The spread in radial velocity and proper motion of the RRLs may indicate that Patchick 99 is a fragment of a larger tidally disrupted structure rather than a globular cluster.Additional observations focused on the region immediately surrounding Patchick 99 are necessary to better constrain the nature and characteristics of Patchick 99.
was used to account for extinction along the line-of-sight.Two possible MIST (MESA Isochrones and Stellar Tracks, Choi et al. 2016) isochrones that adopt the cluster's distance derived in this work (6.7±0.4 kpc)-one with [Fe/H]=−0.2and one with [Fe/H]=−0.7-areshown.The horizontal

Figure 1 .
Figure 1.Left, top: A BDBS z-band image of Patchick 99 is shown with dimensions of 9' x 4.5'; OGLE-BLG-RRLYR-35459, one of the three RRLs associated with this cluster, is highlighted.Left, bottom: This proper motion distribution shows spectroscopically targeted stars presented here (bolded) as compared to BDBS stars within 2.4 arcminutes of Patchick 99 (grey).The most probable members of Patchick 99 are the RRLs designated with circles (red) as well as the giants designated with upside-down triangles (magenta).Right: The BDBS color-magnitude diagram of stars within 2.4' of Patchick 99 (grey) as compared to the spectroscopically targeted stars presented here (bolded).

Figure 2 .
Figure 2. The line-of-sight velocity curves of ten RRLs within 10 arcmin of Patchick 99, where our observations are designated by solid circles (black).The Prudil et al. (2024a) templates shown are used to determine the systemic velocities for the RRLs.The three leftmost panels (red) indicate the RRLs with Gaia proper motions consistent with Patchick 99.The four center and rightmost RRL velocity curves do not have proper motions consistent with Patchick 99.Five stars have APOGEE observations, which are designated by diamonds (purple).

Figure 3 .
Figure 3. Left: The photometric and spectroscopic metallicities and heliocentric radial velocities of stars within 10 arcminutes of Patchick 99's center.The radial velocities of all RR Lyraes have an uncertainty of ∼10 km s −1 .Center: The heliocentric radial velocities of stars within 10 arcminutes of Patchick 99.Right: The heliocentric distances for the RR Lyrae stars within 10 arcminutes of Patchick 99's center.All: RR Lyrae stars with radial velocities and proper motions consistent with Patchick 99 are marked with red circles.Giants with radial velocities and proper motions consistent with Patchick 99 are marked with magenta upside-down triangles.

Table 1 .
This table is published in its entirety in the electronic version of this paper.A portion is shown here for clarity.The asterisk (*) symbol indicates stars with velocities and metallicities consistent with Patchick 99.