Existence of Tidal Tails for the Globular Cluster NGC 5824

Context. Several dynamically cold streams have been associated with certain globular clusters (GCs) based on orbital energies and angular momenta. Some of these streams are surprisingly far apart from their progenitors and one such pair is Triangulum and NGC 5824. Triangulum can be considered as a piece of NGC 5824 leading tail since the cluster's future orbit matches with the stream's track well. The existence of the leading tail for NGC 5824 is the motivation behind the search for its trailing tail. Aims. Our goal is to confirm the connection between Triangulum and NGC 5824 and seek the trailing tail of the cluster. Methods. The selection of member stars of Triangulum is made through various cuts in metallicity, proper motions (PMs), radial velocity and color-magnitude diagram (CMD). The selected members are compared in phase space to a mock stream which models the disruption of NGC 5824. We then try to detect the trailing tail of the cluster based on a modified matched-filter technique. Stars are assigned weights using their color differences from the cluster's locus in CMD. These weights are further scaled based on stars' departures from expected PMs of the model stream. Results. A total of 26 member stars for Triangulum are obtained and 16 of them are newly identified. These members are consistent with the mock stream in the phase space and their metalicity and position on the CMD are in good agreements with NGC 5824. By applying the matched-filter, a tenuous trailing tail of the cluster is detected, spanning $\sim$ 50$^\circ$ long on sky. The signature matches with the mock stream's trajectory well. Conclusions. Our results support that Triangulum stream acts as a part of the leading tail for NGC 5824. On the trailing side, we have detected a 50$^\circ$ tail extended from the cluster. The existence of both leading and trailing tails for the GC NGC 5824 is verified.

The connections between ω Centauri and Fimbulthul (Ibata et al. 2019), NGC 3201 and Gjöll (Palau & Miralda-Escudé 2021), and NGC 4590 and Fjörm (Palau & Miralda-Escudé 2019) have been reported, which suggest that the associations between a stream and a GC, where the GC does not connect directly to the stream, are present in the Milky Way.By exploring the orbits, Bonaca et al. (2021) further attributed five more streams to extant GCs (Table 1 therein), and one pair is Triangulum and NGC 5824.The Triangulum stream was first detected by Bonaca et al. (2012) using a matched-filter technique (Rockosi et al. 2002).Thereafter, Martin et al. (2013) kinematically discovered a part of the stream and provided 11 possible member stars.The stream is in the direction of M 31 and M 33 galaxies, and far apart from NGC 5824.However, the cluster's future orbit passes through the stream's trajectory, implying a connection between them (Fig. 4 in Bonaca et al. 2021).Li et al. (2022) further confirmed this connection by comparing a model stream of NGC 5824 in phase space to the Triangulum member stars from Martin et al. (2013).Therefore, the Triangulum stream could be treated as a piece of the NGC 5824 leading tail.
Based on the picture that tidal tails are developed symmetrically around GCs (Küpper et al. 2010), the existence of a leading tail for NGC 5824 motivates us to search for its trailing tail.In this work, we provide a confirmation of the connection between Triangulum and NGC 5824, which is similar to that of Li et al. (2022) but with member stars that span a wider extent of sky (∼16 • ).We further applied a modified matched-filter method (Grillmair 2019) to look for the trailing tail of NGC 5824.The paper is organized as follows.In Sect.2, we introduce the data.In Sect.3, we show the selection of Triangulum member stars and compare them to a model stream of NGC 5824.The detection of the cluster's trailing tail is given in Sect. 4. We present a discussion in Sect. 5 and draw our conclusion in Sect.6.

Data
To obtain the individual members of Triangulum, we made use of high-quality astrometric and photometric data provided by the Gaia EDR3 (Gaia Collaboration 2021; Lindegren et al. 2021;Riello et al. 2021), along with the spectroscopic data from the Sloan Extension for Galactic Understanding and Exploration (SEGUE; Yanny et al. 2009) and the Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST; Cui et al. 2012;Zhao et al. 2006Zhao et al. , 2012;;Liu et al. 2015) surveys.We retrieved stars from the Gaia EDR3 gaia_source catalog overlapping with the stream region on the celestial sphere.The stream region was determined by limiting 22 • < δ < 41 • and moving δ = −4.4α+ 128.5 by ±1 • along the α direction (green area in Fig. 1), where the equation was defined in Bonaca et al. (2012) to describe the stream coordinates.It should be noted that Bonaca et al. (2012) traced Triangulum to δ 23 • − 35 • , and Martin et al. (2014) extended the stream further north to δ 40 • .Our choice of δ extent was based on both of them.The zero-point correction in the parallax was implemented using the code provided by Lindegren et al. (2021), which required astrometric_params_solved >3.The corrections of G-band magnitude and the BP/RP excess factor were applied as instructed in Riello et al. (2021).In order to ensure good astrometric and photometric solutions, only stars with a renormalized unit weight error (RUWE) < 1.4 and an absolute corrected BP/RP excess factor smaller than three times the associated uncertainty (see Sect. 9.4 in Riello et al. 2021) were retained.Given that both of estimated distances of the stream in Bonaca et al. (2012) and Martin et al. (2013) are farther than 20 kpc, we removed foreground stars that satisfy the criterion − 3σ > 0.05 mas.The remaining stars were crossmatched with Sloan Digital Sky Survey (SDSS)/SEGUE DR16 (Ahn et al. 2012) and LAMOST DR8, by which the metallicity and heliocentric radial velocity were obtained.For stars that are common in both data sets, we adopted measurements from SEGUE because signal-to-noise ratios of spectra in SEGUE are mostly higher than those in LAMOST.
The data for detecting trailing tail of NGC 5824 were also obtained from Gaia EDR3.Stars within the sky box of 210 • < α < 250 • and −40 • < δ < 30 • were retrieved (orange area in Fig. 1) and reduced with the same procedures as above (including the foreground stars removing1 ).Since the spectroscopic surveys are unavailable in this sky region, only Gaia data were used.
In Fig. 1, we show projections of the data (green and orange areas), along with a mock stream (red dots), which is described in Sect.3.2.The black line represents the Galactic plane, and the blue (inverted) triangle represents the direction of the Galactic (anti) center.It should be noted that the NGC 5824 field was designed exactly based on the mock stream.

Triangulum member stars
Cross-matching between Gaia sources and spectroscopic data yielded 1968 stars.Bonaca et al. (2012) presented an estimate of Triangulum's [Fe/H] to be ∼−1.0dex, while Martin et al. (2013) contended a poorer metallicity −2.2 dex for the stream.In order to obtain as many member stars as possible, we adopted [Fe/H] < −1.0 dex as the selection criterion and were left with 451 candidates.After this cut, an overdensity can be seen clearly in proper motion (PM) space (top panel of Fig. 2, only the local region around the overdensity is shown).We overplotted the member candidates provided by Martin et al. (2013, cross-matched with Gaia EDR3) and verified that this overdensity exactly corresponds to the Triangulum stream.To pick out stream stars, we defined a dispersion ellipse whose center and semiaxes were determined based on the known candidates from Martin et al. (2013).The center (1.014, 0.012) mas yr −1 is the mean PM of the members in α and δ, and the semiaxes (0.777, 1.116) mas yr −1 are three times the PM dispersions in respective directions.47 stars enclosed within the ellipse were selected.
These stars were then plotted in δ−V r plane (middle panel of Fig. 2) and a dominant monotonic sequence was clearly discernable.Generally, the radial velocities of a halo stream are supposed to change monotonically along coordinates, as long as there is no turning point contained (such as an apogalacticon), such as Pal 5 (Ishigaki et al. 2016), GD-1 (Bovy et al. 2016), NGC 5466 (Yang et al. 2022), and the Hríd and Gjöll streams (Ibata et al. 2021).Hence, we considered that this dominant sequence should correspond to Triangulum stream.We fitted a straight line to the sequence where weights were given by the uncertainties of V r .The relation can be described with the equation V r = −4.6δ+ 86.5.31 stars with V r consistent to the fit in 3σ range were retained.
Finally, we rejected four more outliers on the basis of the color-magnitude diagram (CMD) and 27 member stars followed a typical GC isochrone (bottom panel of Fig. 2).All sources here were extinction-corrected using the Schlegel et al. (1998) maps as recalibrated by Schlafly & Finkbeiner (2011), with RV = 3.1, assuming A G /A V = 0.83627, A BP /A V = 1.08337, and A RP /A V = 0.63439 2 .The detailed information of the 27 member stars is summarized in Table 1.

NGC 5824 model stream
Li et al. ( 2022) have modeled the disruption of NGC 5824 in a static Milky Way potential plus a moving Large Magellanic Cloud (LMC).As the authors pointed out, the model stream matched well with observations of Triangulum.Motivated by this, we also generated our own mock stream to make a similar comparison between the model and the data, using the identified member stars above, which span a wider extent of sky.The model body is nearly identical to that of Li et al. (2022), but specific configurations are different, such as the Milky Way potential, the adopted mass and radius of LMC, the velocity dispersion and integration time (see details below).
We used the Python package GALA (Price-Whelan 2017), which is designed for performing common tasks needed in Galactic Dynamics, to model the disruption of NGC 5824.The procedure closely followed that of Yang et al. (2022) as applied to NGC 5466.The adopted Milky Way potential consisted of 2 These extinction ratios are listed on the Padova model site http: //stev.oapd.inaf.it/cgi-bin/cmd.No. NFW halo (Navarro et al. 1996), Φ halo : where r is the Galactocentric radius, R is the cylindrical radius and z is the vertical height.For the bulge and disks, we adopted the parameters from Pouliasis et al. (2017 Model I).The virial mass M virial and concentration c used to initialize the NFW halo were from McMillan (2017).Those chosen parameters are summarized in Table 2. Following El-Falou & Webb (2022), we took a Hernquist Potential (Hernquist 1990) as the internal potential of the LMC: where r is the distance to the LMC center, and M LMC and a LMC are set to 10 11 M and 10.2 kpc as well.The position and velocity of the LMC were taken from Gaia Collaboration (2018).
As for the internal gravity of the GC NGC 5824, we chose a Plummer potential: with a M GC of 7.6 × 10 5 M and a b GC of 6.51 pc (half-mass radius; Baumgardt & Hilker 2018).Here r denotes the distance to the cluster's center.The position and velocity of NGC 5824 came from Vasiliev & Baumgardt (2021) and Harris (1996Harris ( , 2010 edition) edition).
The solar distance to the Galactic center, the circular velocity at the Sun, and the solar velocities relative to the Local Standard of Rest were set to 8 kpc, 220 km s −1 (Bovy et al. 2012) and (11.1, 12.24, 7.25) km s −1 (Schönrich et al. 2010), respectively.
In the static Milky Way potential accompanied with a moving LMC, the cluster was initialized 2 Gyr ago3 and integrated forward from then on, releasing two particles (in leading and trailing directions respectively) at Lagrange points (Gibbons et al. 2014) every 0.05 Myr with a total of 40 000 steps.The velocity dispersion was set to 11.9 km s −1 (Baumgardt & Hilker 2018) and the cluster mass was fixed during this process.By doing so, a mock stream for NGC 5824 was obtained, as illustrated by the red dots in Fig. 1.We note that the observed Triangulum (green area) deviates a little from the locus of the mock stream, which also happened in Bonaca et al. (2021, Fig. 4 therein) and Li et al. (2022, Fig. 8 therein).We consider that this deviation between the observation and simulation might be common.

Phase space
We compared the Triangulum member stars to the model stream of NGC 5824 in phase space.In Fig. 3, right ascension α, It can be seen that even though the selection process of member stars in Sect.3.1 was completely independent of the model, the stream particles show good consistency with the observations in phase space.We note an outlier that falls too far from the others in µ δ plane.This star was selected by Martin et al. (2013) based on sky position, radial velocity, metallicity, and CMD, when PM measurements were unavailable.We mark it with "×" in Table 1 and remove it in subsequent analysis.Furthermore, we do not show the distance plane here because there is some confusion, and we present a discussion about it in Sect. 5.

Metallicity and CMD
To further examine whether Triangulum is stripped from GC NGC 5824, we compared them on the basis of metallicity and a CMD.
The metallicity distribution of Triangulum members is presented in Fig. 4 To compare Triangulum with GC NGC 5824 in CMD, we need to know the stream's distance.Xue et al. (2011) estimated distances of ∼5000 BHB stars by matching them in (u − g, g − r) space to theoretical colors for BHB stars with a series of absolute magnitudes.The individual distances of four BHB stars in our sample could be obtained from this catalog: 28.8, 26.9, 30.6, and 26.0 kpc for stars with No. 4, 8, 24, and 26 in Table 1, respectively.This yielded a median distance of 27.85 kpc, close to 26 kpc proposed by Bonaca et al. (2012).In addition, we also estimated distances to all 26 stars (see Sect. 5) using the method from Carlin et al. (2015), which is a Bayesian approach with the likelihood estimated via a comparison of spectroscopically derived atmospheric parameters to a grid of stellar isochrones, and which returns a posterior probability density function for a star's absolute magnitude.This yielded a median value at 33 kpc, similar to the 35 kpc estimated by Martin et al. (2013).We adopted the distance to the Triangulum stream as ∼30 kpc, which is a median value between the BHB distance and our estimate.
In the CMD, we moved the member stars from 30 to 32.1 kpc, where GC NGC 5824 is located (Harris 1996(Harris , 2010 edition) edition), and found that they matched well, as shown in Fig. 5.The cluster stars here marked in the orange dots were obtained through sky and PM selections, as instructed by Kundu et al. (2021).Specifically, we retrieved stars within the tidal radius r t = 5.73 of NGC 5824 (Harris 1996(Harris , 2010 edition) edition) and cleaned the data following the procedures described in Sect. 2. A twodimensional Gaussian mixture model consisting of two Gaussians was then fitted in PM space to distinguish the cluster and A37, page 5 of 10 The black line denotes the RGB locus obtained by fitting the RGB stars directly with a third-order polynomial, which is used in Sect.4.1 to assign weights in CMD.
The connection between the stream and the cluster, based on the three aspects above, confirms that Triangulum was disrupted from GC NGC 5824.In other words, the stream can be treated as a part of the cluster's leading tail.

Detecting the trailing tail
Motivated by the existence of leading tail for NGC 5824, in this section we aim to search for its trailing tail.

A modified matched-filter method
Combining PMs and a CMD together to search for extratidal structures of GCs has proved to be an effective technique (e.g., Kundu et al. 2019aKundu et al. ,b, 2021)).We adopted the method from Grillmair (2019), who applied a modified matched-filter technique and successfully detected a 50 • long tidal tail for GC M5.
Stars fetched in Sect. 2 were assigned weights based on their locations in the CMD and PM space.In the CMD, individual stars in the NGC 5824 field were assigned weights according to their color differences from the cluster locus, assuming a Gaussian error distribution: Here color and σ color denote G BP −G RP and corresponding errors.
Color errors were simply calculated through where σ G BP and σ G RP were obtained with a propagation of flux errors (see CDS website4 ).color 0 was determined by the cluster RGB locus (the black line in Fig. 5) at a given G magnitude of a star.When assigning weights, we did not include σ G since uncertainties in the G band are much smaller than those in G BP and G RP (on the order of ∼0.1) for Gaia photometry.Stars from G = 15 mag (tip of the cluster's RGB) to the Gaia limit G 21 mag were investigated.
The PMs of the model stream generated in Sect.3.2 were further employed to weight stars.Figure 6 shows the stream particles within the NGC 5824 field in phase space, which serve as an estimate to the real stream.In PM space, weights were computed as: where µ * α , µ δ , σ µ * α and σ µ δ are measured PMs and corresponding errors, and µ * α,0 and µ δ,0 are the components of PMs predicted at each star's δ based on the model stream's locus (blue lines of PM panels in Fig. 6).The locus was obtained by dividing the particles into δ bins (bin width = 1 • ) and calculating medians of PMs in each bin.It is worth noting that PM errors are multiplied by n and we chose a moderate n = 2 here, which was designed to allow some deviations between the model and the observations.This can be illustrated using a one-dimensional example (see Fig. 7).Assuming that there is a stream star (if it exists) with µ δ = x and σ µ δ = 0.4 mas yr −1 and the µ δ,0 predicted by the model stream at the star's δ is 2 mas yr −1 , the star's weight is then determined by a Gaussian with mean = 2 and sigma = 0.4 (n = 1, red line) or 0.8 (n = 2, green line).If the model predicts the stream very well, that is x is very close to 2 mas yr −1 , the red line (n = 1) gives a higher weight to the star apparently.However, the model stream is just an approximation of the real one and it is likely that there are small deviations between them, which might lead x to fall out of the blue dashed lines.When this happens, the green line (n = 2) gives a higher weight.We compared results using different n values and verified that n = 2 is the most favorable.
Finally, stars weights were obtained by multiplying w CMD and w PMs , and then summed in 0.2 • × 0.2 • sky pixels to expose structures.

Results
A weighted sky map was obtained after applying the above method to data in the cluster field, which is shown in the left panel of Fig. 8.To make the stream look more prominent, pixels with summed weights >80 and <2 were masked such that excessively strong noises and the weak background are not shown.The map was then smoothed with a Gaussian kernel of σ = 0.5 • .The stretch is logarithmic, with brighter areas corresponding to higher weight regions.The blue circle at the bottom marks the location of NGC 5824.The white area in the bottom right corner is due to the proximity to the Galactic disk, which is further masked in the middle and right panels.
Due to the photometric depth of Gaia, the cluster's main sequence stars are not observable and only RGB stars, of which there are much fewer, can be used to trace the underlying trailing tail.However, some stream-like signals are still detected.In the left panel, it is clear that there are several structures (marked with arrows) with higher weights between δ −21 and −4 • that could be connected smoothly and likely extended from NGC 5824.In  7).The red and green lines represent Gaussians centered at 2 with sigma = 0.4 and 0.8 mas yr −1 , respectively.
the middle panel, we overplot the trajectory of the model stream (small red dots) and find that it passes well through the structures.An additional segment of δ 6−16 • is a further extension of the stream.There is a gap in the middle at δ −4−6 • , corresponding to the most distant range of the model stream (see the distance panel in Fig. 6), where many RGB stars might have been darker than 21 mag.The detected signature traces the cluster's trailing tail to ∼50 • whose path can be roughly fitted using α = 4.07 × 10 −5 δ 3 + 6.68 × 10 −3 δ 2 + 0.37δ + 232.45, (8) where −33 • < δ < 16 • .In the right panel of Fig. 8, stars enclosed by the red lines were selected to calculate the statistical significance of the stream.The δ range is −22 • −−3 • .The central dashed line represents a more precise description of the stream of this region, which is given by with offset = 0 • .The left and right boundaries correspond to offset = −4 and 4 • , respectively.A bin width = 0.2 • was used, and at offset = −4, −3.8, −3.6. . ., weights of stars around Eq. ( 9) ±0.1 • were integrated to create a lateral profile of the stream, as displayed in Fig. 9.The central peak at offset = 0 • represents the stream feature.The larger random counts on the positive side are caused by higher stellar density near the disk.The significance is defined as S = (w stream − w background )/σ background , where w stream is the stream signal, and w background and σ background are the mean and standard deviation of weights for off-stream regions 0.5 • < |offset| < 4 • .We get S = 7.5 and 3.6 for negative and positive sides, respectively, and S is 4.3 if both are considered.It can be inferred from Fig. 9 that the stream's width is expected to be 0.2  Bonaca et al. (2021) pointed out that GC NGC 5824 and Cetus (Newberg et al. 2009), which is a stellar stream with a dwarf galaxy origin, have very close orbital energies and angular momenta.Similar orbital trajectories between them were also demonstrated in Chang et al. (2020).This raises the question of whether the features on the trailing side of the cluster belong to Cetus stream.
Combining the results here with previous researches on Cetus, we present four reasons why the detected features are indeed related to the trailing tail of NGC 5824: (i) the width of features in Fig. 8 is only 0.2 • , which is thin compared to a stream produced by a dwarf galaxy; (ii) Cetus stars should have a relatively spread distribution in the CMD.However, the stream features indicated with arrows in Fig. 8 disappear if the RGB locus used to weight stars in CMD is shifted either blueward or redward by 0.1 mag, which means that they are exactly corresponding to NGC 5824; (iii) Chang et al. (2020) pointed out that GC NGC 5824 should not be the core of Cetus, implying that there is no direct connection between the cluster and Cetus stream.Furthermore, Yuan et al. (2022) concentrated on searching for Cetus's members using data covering the cluster but they did not detect any densely populated structure around NGC 5824, and as a result, the features should not be a part of Cetus; and (iv) Triangulum as a piece of the leading tail also provides weak evidence of existence of the trailing tail.

Discussion
When comparing the distance between Triangulum and the model stream, we found some incompatibilities and we showed these in Fig. 10.Bonaca et al. (2012) estimated Triangulum's distance to be 26 ± 4 kpc (the lower black error bar) while Martin et al. (2013) proposed 35 ± 3 kpc (the upper black error bar) for the stream.As mentioned above, we adopted a distance of 30 kpc (the solid green line) and we found that the member stars matched well with GC NGC 5824 in the CMD.However, under a static Milky Way potential plus a moving LMC, the resulting model stream predicts that Triangulum's distance should be about 20-25 kpc (gray dots), which is true both in this work and in the work of Li et al. (2022, the second panel of Fig. 8 therein).This brings about some confusion as to why there is such a difference.Sheffield et al. (2014) presented an analysis on TriAnd1 (d ∼ 20 kpc) and TriAnd2 (d ∼ 28 kpc; Martin et al. 2007), two other stellar substructures in the direction of M 31 and M 33.They showed that, even though the two structures are separated by more than 5 kpc in distance, they are indistinguishable in radial velocity and PMs.We note that this kinematic feature is very similar to that of Triangulum when compared to the model stream.The real and mock streams are separated by more than 5 kpc as well, but their trends in phase space are still in concordance.Considering that the stream and those structures are in exactly the same region, it is very likely that Triangulum has been affected by the mechanism that affects TriAnd1 and TriAnd2.Specifically, either related to a dwarf galaxy (Sheffield et al. 2014) or the Galactic disk (Xu et al. 2015), some process that created TriAnd1 and TriAnd2 might push Triangulum farther away (30 kpc) from where it should be (20-25 kpc).We anticipate that this prediction could be proved by later simulations on the formation of TriAnd overdensities.It is also worth noting that there is another stream segment named Turbio (Shipp et al. 2018) between Triangulum and GC NGC 5824 that was considered to be disrupted from the cluster based on their similar dynamics in Bonaca et al. (2021) and Li et al. (2022).We did not inspect this stream due to a lack of spectroscopic data.It is expected that upcoming observations will provide more details on connections between Turbio and the cluster, and even more opportunities for searching for other stream segments on the leading side.If these can be confirmed,   Xue et al. (2011).The red dots and error bars represent distances and corresponding errors for all member stars estimated using the method of Carlin et al. (2015).The dashed red line corresponds to their median value, 33 kpc.The solid green line marks the adopted distance, 30 kpc.Two black error bars represent 26 ± 4 kpc (Bonaca et al. 2012) and 35 ± 3 kpc (Martin et al. 2013).
NGC 5824 tidal tails would be the longest cold stream ever discovered in the Milky Way.A37, page 9 of 10

Conclusions
We first validate the connection between the Triangulum stream and NGC 5824.A total of 26 stream member stars are selected and 16 of them are newly identified.We model the cluster's disruption under a static Milky Way potential accompanied with a moving LMC.The real stream is compared to the mock one in phase space and consistent trends can be found.In metallicity and a CMD, the member stars and the cluster are also in good agreement.These results support the previous statement that Triangulum originates from GC NGC 5824 (Bonaca et al. 2021;Li et al. 2022).
Given that Triangulum can be considered as a segment of the cluster's leading tail, we examine the existence of its trailing tail.Using a matched-filter method that combines a CMD and PMs to weight stars, we find a ∼50 • trailing tail for GC NGC 5824.The features match well with the model stream.Although the signals are tenuous and discrete, a peak of >3σ over background noises can still be discerned in the lateral stream profile, from which we estimate that its width is 0.2 • .We expect that followup observations will provide more details about the NGC 5824 stream.

Fig. 1 .
Fig. 1.Sky projections of the data (green and orange areas) and a mock stream (red dots).The black line represents the Galactic plane and the blue (inverted) triangle represents the direction of Galactic (anti) center.The black circle denotes the GC NGC 5824.

Fig. 2 .
Fig. 2. Selections of Triangulum member stars.The gray dots represent rejected stars and the red dots represent the selected stars during each step.The member candidates identified by Martin et al. (2013) are marked by the green points.Top panel: local region of the overdensity in PM space, where the ellipse is defined to select member candidates in this step.Middle panel: stars in δ−V r plane, where the error bars represent three times the uncertainties of V r , and the red line is a linear fit to the stream sequence.Bottom panel: those candidates in a CMD.

Table 2 .
Adopted parameters for the Galactic potential.α and µ δ , and radial velocity V r as a function of declination δ are presented from top to bottom.The gray dots represent the stream particles within the same sky area as Triangulum.The member stars are shown by the red and green points.
. There are four blue horizontal branch (BHB) stars and 22 red giant branch (RGB) stars.For the whole sample, the mean value [Fe/H] = −2.10 and standard deviation σ [Fe/H] = 0.26 dex are consistent with those of Martin et al. (2013; [Fe/H] = −2.2,σ [Fe/H] = 0.3 dex).The purpose of picking out RGB stars separately is to enable a comparison to some chemical researches on NGC 5824.Mucciarelli et al. (2018) analyzed 87 RGB stars of the cluster and obtained a metallicity distribution peaked at [Fe/H] = −2.11dex, which is very similar to the [Fe/H] = −2.14dex that we found.The observed scatter σ [Fe/H] = 0.22 dex is probably caused by observational uncertainties in low-resolution spectra (R ∼ 1800).

Fig. 3 .
Fig. 3. Right ascension α, PMs µ * α and µ δ , and radial velocity V r as a function of declination δ are presented from top to bottom.The gray dots represent the stream particles within the same sky area as Triangulum.The green and red points represent the stream member stars.
Fig. 4. Metallicity distribution of Triangulum member stars.The red bars represent the whole sample and the green bars correspond to only RGB stars.

Fig. 5 .
Fig. 5. Orange dots represent GC NGC 5824 stars.The red and green dots represent Triangulum members.The black line denotes the RGB locus obtained by directly fitting the RGB stars with a third-order polynomial.

Fig. 6 .
Fig. 6.Planes of α, heliocentric distance, proper motion in α and δ, and radial velocity as a function of δ, are shown from top to bottom.The pink dots represent the model stream particles within the NGC 5824 field.The red circle represents GC NGC 5824.The blue lines denote medians of y-axis values in each δ bin with a bin width of 1 • .

Fig. 8 .
Fig. 8. Log stretch of a matched filter map in the NGC 5824 field.The sky pixel width is 0.2 • and the map is smoothed with a Gaussian kernel of σ = 0.5 • .Three panels present the same map.The white arrows in the left panel point to the stream features.The locus of the model stream is overplotted using the small red dots in middle panel.The right panel illustrates the way of creating the stream's lateral profile (see text).The bottom right region close to the Galactic disk is masked in the middle and right panels.

Fig. 9 .
Fig. 9. Stream one-dimensional profile.The offset coordinate is defined as deviation from the stream along the α direction (see Eq. (9)).

Fig. 10 .
Fig. 10.Heliocentric distance as a function of δ.The gray dots represent the stream particles.The blue points represent the four BHB stars in our samples, whose distances come from Xue et al. (2011).The red dots and error bars represent distances and corresponding errors for all member stars estimated using the method ofCarlin et al. (2015).The dashed red line corresponds to their median value, 33 kpc.The solid green line marks the adopted distance, 30 kpc.Two black error bars represent 26 ± 4 kpc(Bonaca et al. 2012) and 35 ± 3 kpc(Martin et al. 2013).
• , because signals drop back to the level of background when |offset| > 0.1 • , which means that there are few stream signals beyond this range.If we adopt d = 39 kpc for this segment based on the model, the physical width is 136 pc.4.3.Understanding if the detected features are a part of Cetus