<table><caption>**Table 3**
(Continued)</caption><thead><tr><th>s<sub>ID</sub><br>(1)</th><th>Name<br>(2)</th><th>Sample<br>(3)</th><th>α<sub>0</sub><br>(4)</th><th>α<sub>pole</sub><br>(5)</th><th>δ<sub>pole</sub><br>(6)</th><th>n<br>(7)</th><th>n<sub>v</sub><br>(8)</th><th>M<sub>*</sub><br>(M<sub>c</sub>)<br>(9)</th><th>⟨[Fe/H]⟩<br>(10)</th><th>References<br>(11)</th><th>Remarks<br>(12)</th></tr></thead><tbody><tr><td>63</td><td>Kshir</td><td>1</td><td>230.196</td><td>229.22</td><td>-21.937</td><td>141</td><td>7</td><td>2200</td><td>-1.83</td><td>(7)</td><td>...</td></tr><tr><td>64</td><td>Svol</td><td>1</td><td>231.711</td><td>28.918</td><td>60.957</td><td>234</td><td>16</td><td>2000</td><td>-1.98</td><td>(1)</td><td>...</td></tr><tr><td>65</td><td>Gaia-9</td><td>1</td><td>236.238</td><td>169.091</td><td>-13.272</td><td>233</td><td>25</td><td>950</td><td>-2.21</td><td>(1)</td><td>...</td></tr><tr><td>66</td><td>Ophiuchus</td><td>0</td><td>242.576</td><td>18.564</td><td>-79.685</td><td>391</td><td>72</td><td>4800</td><td>-1.98</td><td>(3, 14)</td><td>...</td></tr><tr><td>67</td><td>NGC6101</td><td>0</td><td>246.451</td><td>227.979</td><td>16.954</td><td>94</td><td>3</td><td>4800</td><td>-1.98</td><td>(3)</td><td>...</td></tr><tr><td>68</td><td>M92</td><td>0</td><td>259.281</td><td>232.737</td><td>-43.4</td><td>202</td><td>23</td><td>2100</td><td>-2.31</td><td>(3)</td><td>...</td></tr><tr><td>69</td><td>NGC6397</td><td>0</td><td>265.175</td><td>268.821</td><td>35.811</td><td>1207</td><td>17</td><td>2500</td><td>-2.02</td><td>(3)</td><td>...</td></tr><tr><td>70</td><td>Gaia-11</td><td>0</td><td>267.612</td><td>195.778</td><td>-15.134</td><td>84</td><td>3</td><td>1100</td><td>-1.19</td><td>(2)</td><td>Strange CMD, velocities unclear</td></tr><tr><td>71</td><td>Hrid</td><td>0</td><td>280.228</td><td>187.604</td><td>2.034</td><td>666</td><td>29</td><td>2000</td><td>-1.13</td><td>(7)</td><td>...</td></tr><tr><td>72</td><td>C-7</td><td>1</td><td>283.419</td><td>76.064</td><td>-35.517</td><td>239</td><td>16</td><td>1500</td><td>-1.52</td><td>(10)</td><td>Two superposed streams</td></tr><tr><td>73</td><td>New-20</td><td>0</td><td>314.963</td><td>50.439</td><td>18.37</td><td>12</td><td>4</td><td>8</td><td>-1.76</td><td>(15)</td><td>...</td></tr><tr><td>74</td><td>New-21</td><td>0</td><td>316.569</td><td>243.966</td><td>-56.299</td><td>762</td><td>3</td><td>7000</td><td>-0.87</td><td>(2)</td><td>High velocity</td></tr><tr><td>75</td><td>Phlegethon</td><td>1</td><td>322.720</td><td>55.023</td><td>-8.319</td><td>632</td><td>41</td><td>1700</td><td>-2.19</td><td>(8)</td><td>...</td></tr><tr><td>76</td><td>NGC7089</td><td>0</td><td>323.363</td><td>235.973</td><td>72.865</td><td>15</td><td>2</td><td>300</td><td>-1.65</td><td>(3)</td><td>...</td></tr><tr><td>77</td><td>NGC7099</td><td>0</td><td>325.092</td><td>79.501</td><td>-44.028</td><td>54</td><td>3</td><td>680</td><td>-2.27</td><td>(3)</td><td>...</td></tr><tr><td>78</td><td>New-22</td><td>0</td><td>325.847</td><td>211.35</td><td>-34.781</td><td>55</td><td>10</td><td>580</td><td>-0.98</td><td>(2)</td><td>Velocities unclear</td></tr><tr><td>79</td><td>New-23</td><td>0</td><td>329.825</td><td>188.254</td><td>66.646</td><td>44</td><td>6</td><td>120</td><td>-2.25</td><td>(8)</td><td>...</td></tr><tr><td>80</td><td>New-24</td><td>0</td><td>334.183</td><td>59.385</td><td>20.639</td><td>56</td><td>7</td><td>170</td><td>-0.64</td><td>(16)</td><td>Compact, velocities unclear</td></tr><tr><td>81</td><td>New-25</td><td>0</td><td>335.959</td><td>50.194</td><td>23.447</td><td>121</td><td>12</td><td>18,000</td><td>-1.68</td><td>(2)</td><td>Velocities unclear, superposed streams?</td></tr><tr><td>82</td><td>New-26</td><td>0</td><td>341.875</td><td>23.599</td><td>-51.695</td><td>43</td><td>4</td><td>300</td><td>-0.17</td><td>(2)</td><td>Velocities unclear</td></tr><tr><td>83</td><td>New-27</td><td>0</td><td>342.224</td><td>80.278</td><td>-5.92</td><td>37</td><td>8</td><td>410</td><td>-2.08</td><td>(2)</td><td>Velocities unclear</td></tr><tr><td>84</td><td>NGC7492</td><td>0</td><td>347.111</td><td>89.005</td><td>-34.892</td><td>26</td><td>1</td><td>3300</td><td>-1.78</td><td>(3)</td><td>...</td></tr><tr><td>85</td><td>C-19</td><td>1</td><td>354.356</td><td>81.45</td><td>-6.346</td><td>46</td><td>12</td><td>3200</td><td>-3.58</td><td>(1)</td><td>...</td></tr><tr><td>86</td><td>Jhelum</td><td>1</td><td>355.231</td><td>5.299</td><td>37.216</td><td>986</td><td>160</td><td>17,000</td><td>-2.12</td><td>(9)</td><td>...</td></tr><tr><td>87</td><td>Tuc-3</td><td>0</td><td>359.150</td><td>176.704</td><td>-30.396</td><td>102</td><td>34</td><td>12,000</td><td>-2.49</td><td>(17)</td><td>...</td></tr></tbody></table>

**Note.** Columns (1) and (2) list the identification number *s*<sub>ID</sub> and name of the stream; a value of “1” in column (3) marks whether the stream is part of the chosen sample of 29 streams that were used to constrain the Galactic potential. Columns (4)–(6) list, respectively, the zero-point in R.A. and position of the pole of the coordinate system used to derive the *φ*<sub>1</sub> and *φ*<sub>2</sub> stream coordinates. Columns (7) and (8) report the number of stars found in the structure, and the number with measured radial velocity, respectively. Column (9) reports the stellar mass estimate, computed assuming that each stream sample is complete to *G*<sub>0</sub> = 20 mag, and that its stellar population follows a PARSEC model isochrone of age 12.5 Gyr with the metallicity value given in column (10). Column (11) lists the source of the metallicity information. Some brief comments on the nature of the structure are given in column (12). We note that stream #6 (“Kwando,” Grillmair 2017) appears to be the same structure as the “Cetus/Palca” stream (Yuan et al. 2022a). Note also that one star (Gaia ID 3267948604442696448) in stream #8 (“New-2”) is a member of group #4 of Dodd et al. (2023), but closer inspection shows that these two structures are different, with stream #8 showing narrow spatial and kinematic coherence.

**References.** (1) Martin et al. (2022); (2) Martin et al. (2023); (3) Harris (2010); (4) Li et al. (2021); (5) Wan et al. (2020); (6) Grillmair (2017); (7) SDSS; (8) LAMOST; (9) Ji et al. (2020); (10) This work; (11) Roederer & Gnedin (2019); (12) Koposov et al. (2023); (13) Yuan et al. (2020); (14) Caldwell et al. (2020); (15) Gaia BP/RP; (16) Andrae et al. (2023); (17) Li et al. (2019).

were harder to discover simply because they are more diffuse than those found earlier. For instance, streams 8, 17, and 22 are examples of very metal-poor structures ([Fe/H] = -2.07, -2.71, and -2.18, respectively) that subtend a long angle over the sky (62°, 69°, and 80°, respectively) are nearby (≈1.2, ≈1.5, and ≈1.25 kpc distant, respectively) and display a well-defined velocity gradient.

We will discuss the new findings in detail in a future contribution, but here, we nevertheless briefly mention some interesting highlights, either because the new stream is particularly interesting, or because the new data or analysis conveys some new insight into the previously known structure. We will discuss these highlighted streams in order of their *s*<sub>ID</sub> index.

### 9.1. Stream #17 (New-3)

This newly discovered structure has 120 candidate members, including 10 radial velocity measurements and 22 with excellent parallaxes (ω/δω > 10), which are all

within 2 kpc of the Sun. A chemical abundance analysis with the MyGIsFOS code (Sbordone et al. 2014) of the stars observed at high resolution with the UVES instrument will be presented elsewhere. However, we note here that the two well-measured stars (with Gaia IDs: 3089847099636770560, 3074553030332697344) have [Fe/H] metallicities of -2.75 and -2.67, respectively, which places this system close to the most metal-poor known.

Another surprising property of this stream is its orbit. We use the machinery described in Section 5 to fit the phase-space data, using again only the velocity-confirmed members. The resulting progenitor path is displayed in Figure 18 in relation to the Sun (yellow circle), the Galactic Center, and the positions of the RR Lyrae members of the Sagittarius dwarf galaxy in Gaia DR3, which we have selected using the parameter filter described in Ibata et al. (2020a). It therefore seems highly probable that stream #17 formed in the early universe as a globular cluster satellite of the Sagittarius dwarf, and was brought into the Galaxy with it.
<figure><img src="image_21.png" /><figcaption>**Figure 18.** Orbit of stream #17 compared to the present-day structure of the Sagittarius dwarf galaxy, as seen from Gaia DR3 RR Lyrae extracted using the astrometric filter of Ibata et al. (2020a). The orbit is shown integrated backward in time for 1 Gyr, and can be seen to correspond very closely in position to this sample of RR Lyrae stars. The position of the Sun is marked with a yellow dot.</figcaption></figure>

## 9.2. Fitting Stream #48 (Orphan) with the LMC

The notable missing structure in the sample of 29 long thin streams, which we set aside from our MCMC exploration above, is stream #48 (Orphan-Chenab, Belokurov et al. 2007), which is known to be strongly affected by the LMC (Erkal et al. 2019). We will now attempt to fit this structure using our test-particle algorithm, which was built to handle precisely this sort of situation with the host galaxy and one or several massive perturbers moving under each other’s gravitational influence.

Our new contribution to the problem is that we can now impose what we expect is currently the most accurate Milky Way mass model, at least for the spatial region contained by the 29 fitted streams in Figures 16 and 17. Onto our now moving Milky Way model, we add a moving NFW potential to model the LMC.<fnref n="22" /> We take the value of the center and the proper motions of the LMC from Gaia Collaboration et al. (2018), we adopt the distance from Pietrzyński et al. (2019), and the radial velocity from van der Marel et al. (2002). We further estimate from Ludlow et al. (2014) that a plausible concentration for the NFW model of the LMC to be $c_{LMC} = 12.5$. Following Koposov et al. (2023), we model the progenitor with a mass of $2.67 \times 10^7 M_{\odot}$ and a Plummer scale radius of 1 kpc.

In Figure 19, we show the result of our stream modeling using just the preferred Milky Way model with $\beta_h = 3$ found in Section 8 (green dots), while the maximum-likelihood fit upon adding the LMC has a model mass (defined as $M_{200}$) of $M_{LMC} = 1.5 \times 10^{11} M_{\odot}$ (black dots). However, these models clearly fail to reproduce the large-scale behavior of the stream faithfully, and are much less convincing than the fits of Koposov et al. (2023). Imposing a mass of $M_{LMC} = 2.85 \times 10^{11} M_{\odot}$ as inferred by Koposov et al. (2023), results in a lower likelihood fit

in our Galactic potential model that shows poor agreement with the proper motion measurements. Further work is needed to ascertain whether axisymmetric double-power-law halo models are capable of encapsulating the properties of the Milky Way sufficiently well all the way from the inner to the outer regions of the Galaxy.

## 9.3. Stream #49 (Gaia-1)

Many of the streams possess stars with high velocity along the line of sight (see Figures 7–9) and many possess high proper motion. It is interesting to consider those stars for which the Gaia parallaxes $\omega$ are sufficiently good to also identify stars with high total velocity. To this end, we show in Figure 20 the actions ($J_r, J_{\phi}, J_z$) and orbital energy $E_{\text{tot}}$ of the objects in our STREAMFINDER sample that have $\omega/\delta\omega > 7$ and measured radial velocity. (In this work, we have chosen negative $J_{\phi}$ to correspond to prograde rotation.) The outlier in this plane is stream #49 (Gaia-1, Paper I), which thanks to one well-measured Gaia star (ID 3578950965917470208, with $\omega/\delta\omega = 9.5$) can be seen to have very high radial action $J_r$ and to have energy that puts it close to being unbound in the (relatively heavy) McMillan (2017) potential. Indeed, this star is actually unbound in the lighter MW2014 potential model (Bovy 2015). At its present radial location of $r = 8.95 \pm 0.36$ kpc, the 1% lower limit to the mass of the Keplerian potential that would bind this star is $0.41 \times 10^{12} M_{\odot}$. We note that the magnitude of the velocity of this star is $816 \pm 82$ km s$^{-1}$, where the uncertainty is almost completely due to parallax uncertainty. The direction of motion of this stream is such that it is just now arriving into the inner Galaxy from the outer halo. So unless this system is an intergalactic traveler, the requirement that it is bound to the Milky Way places a strong lower limit on the total mass of our Galaxy. Furthermore, its metallicity is [Fe/H] = -1.8, which is not extremely metal-poor for a stream, so the possibility that this is

<footnote n="22">²² To isolate the effect of the Milky Way and the LMC, all other Local Group galaxies are set to zero mass.</footnote>
<figure><img src="image_21.png" /><figcaption>**Figure 18.** Orbit of stream #17 compared to the present-day structure of the Sagittarius dwarf galaxy, as seen from Gaia DR3 RR Lyrae extracted using the astrometric filter of Ibata et al. (2020a). The orbit is shown integrated backward in time for 1 Gyr, and can be seen to correspond very closely in position to this sample of RR Lyrae stars. The position of the Sun is marked with a yellow dot.</figcaption></figure>

## 9.2. Fitting Stream #48 (Orphan) with the LMC

The notable missing structure in the sample of 29 long thin streams, which we set aside from our MCMC exploration above, is stream #48 (Orphan-Chenab, Belokurov et al. 2007), which is known to be strongly affected by the LMC (Erkal et al. 2019). We will now attempt to fit this structure using our test-particle algorithm, which was built to handle precisely this sort of situation with the host galaxy and one or several massive perturbers moving under each other’s gravitational influence.

Our new contribution to the problem is that we can now impose what we expect is currently the most accurate Milky Way mass model, at least for the spatial region contained by the 29 fitted streams in Figures 16 and 17. Onto our now moving Milky Way model, we add a moving NFW potential to model the LMC.<fnref n="22" /> We take the value of the center and the proper motions of the LMC from Gaia Collaboration et al. (2018), we adopt the distance from Pietrzyński et al. (2019), and the radial velocity from van der Marel et al. (2002). We further estimate from Ludlow et al. (2014) that a plausible concentration for the NFW model of the LMC to be $c_{LMC} = 12.5$. Following Koposov et al. (2023), we model the progenitor with a mass of $2.67 \times 10^7 M_\odot$ and a Plummer scale radius of 1 kpc.

In Figure 19, we show the result of our stream modeling using just the preferred Milky Way model with $\beta_h = 3$ found in Section 8 (green dots), while the maximum-likelihood fit upon adding the LMC has a model mass (defined as $M_{200}$) of $M_{LMC} = 1.5 \times 10^{11} M_\odot$ (black dots). However, these models clearly fail to reproduce the large-scale behavior of the stream faithfully, and are much less convincing than the fits of Koposov et al. (2023). Imposing a mass of $M_{LMC} = 2.85 \times 10^{11} M_\odot$ as inferred by Koposov et al. (2023), results in a lower likelihood fit

in our Galactic potential model that shows poor agreement with the proper motion measurements. Further work is needed to ascertain whether axisymmetric double-power-law halo models are capable of encapsulating the properties of the Milky Way sufficiently well all the way from the inner to the outer regions of the Galaxy.

## 9.3. Stream #49 (Gaia-1)

Many of the streams possess stars with high velocity along the line of sight (see Figures 7–9) and many possess high proper motion. It is interesting to consider those stars for which the Gaia parallaxes $\omega$ are sufficiently good to also identify stars with high total velocity. To this end, we show in Figure 20 the actions ($J_r, J_\phi, J_z$) and orbital energy $E_{tot}$ of the objects in our STREAMFINDER sample that have $\omega/\delta\omega > 7$ and measured radial velocity. (In this work, we have chosen negative $J_\phi$ to correspond to prograde rotation.) The outlier in this plane is stream #49 (Gaia-1, Paper I), which thanks to one well-measured Gaia star (ID 3578950965917470208, with $\omega/\delta\omega = 9.5$) can be seen to have very high radial action $J_r$ and to have energy that puts it close to being unbound in the (relatively heavy) McMillan (2017) potential. Indeed, this star is actually unbound in the lighter MW2014 potential model (Bovy 2015). At its present radial location of $r = 8.95 \pm 0.36$ kpc, the 1% lower limit to the mass of the Keplerian potential that would bind this star is $0.41 \times 10^{12} M_\odot$. We note that the magnitude of the velocity of this star is $816 \pm 82$ km s$^{-1}$, where the uncertainty is almost completely due to parallax uncertainty. The direction of motion of this stream is such that it is just now arriving into the inner Galaxy from the outer halo. So unless this system is an intergalactic traveler, the requirement that it is bound to the Milky Way places a strong lower limit on the total mass of our Galaxy. Furthermore, its metallicity is [Fe/H] = -1.8, which is not extremely metal-poor for a stream, so the possibility that this is

<footnote n="22">²² To isolate the effect of the Milky Way and the LMC, all other Local Group galaxies are set to zero mass.</footnote>
<figure><img src="image_22.png" /></figure>

**Figure 19.** Fit to stream #48 (Orphan-Chenab). Here, the potential includes a moving model for the Milky Way as well as a massive moving LMC, while the stream progenitor loses mass over a period of 5 Gyr. Black dots show the best-fit stream model with both the Milky Way and the LMC, where the latter has a mass of $M_{LMC} = 1.5 \times 10^{11} M_{\odot}$. In contrast, the green dots show the result of setting $M_{LMC} = 0$. The Milky Way host is represented by the model derived previously from orbit fitting (corresponding to the mass model with $\beta_h = 3$ fit in Figure 13).

a pristine system being accreted for the first time seems very implausible.

As stream #49 is in the selected sample of long thin streams, this object is already taken into account in our MCMC search. However, the constraint that the stars should be bound to the Milky Way was not used. This would be an easy upgrade to add to the algorithm in future work.

In any case, it is interesting that a single star, whose astrometry will be even more accurately measured in future Gaia data releases, can be used to set a lower bound on the Galaxy's mass. The fact that this star is a member of a stream allows us to obtain a clearer view of its origin and possible history of previous interactions.

## 9.4. Stream #53 (GD-1)

We will briefly revisit the kinematics of stream #53 (GD-1, Grillmair & Dionatos 2006) given the improved data on the system. Our very limited aim here is to motivate the likelihood

<figure><img src="image_23.png" /></figure>

**Figure 20.** Actions and energy of the 190 stars with measured radial velocities and excellent (>7σ) astrometric parallaxes, calculated in the McMillan (2017) potential model (for easier comparison to earlier work). Color encodes the stream $s_{ID}$ identification as in Figure 6.

model that was used as a template in the fitting software detailed above in Sections 5–6.

The mean line-of-sight velocity profile of GD-1 as a function of $\phi_1$ was fit previously by Ibata et al. (2020b). The distribution of residuals from that function is shown both as a function of angle $\phi_1$ along the stream in Figure 21(a) and as a histogram in Figure 21(b) (where we sum over the full angular range $\phi_1 = [-12^\circ, 8, 102^\circ]$ of the velocity members), and appears to show significant wings. To quantify this possibility, we again used an MCMC procedure to fit the data set with a single Gaussian model, and reran the fit with a two-component Gaussian model, including, of course, the individual velocity measurement uncertainties when computing the likelihoods. The p-value for the measured difference in log-likelihood between the maximum-likelihood fits of the two models is $\approx 1.2 \times 10^{-7}$, indicating that the more complex model with two Gaussians provides a significantly better fit to the data compared to the simpler single Gaussian model.

The two-component fit has means $\mu_1 = 3.2 \pm 0.7$ km s$^{-1}$, $\mu_2 = 0.8 \pm 3.9$ km s$^{-1}$, dispersions $\sigma_1 = 7.4 \pm 1.1$ km s$^{-1}$, $\sigma_2 = 29.1 \pm 6.1$ km s$^{-1}$ and a fraction $0.73 \pm 0.09$ in component 1. Thus, there is strong evidence that GD-1 has a cocoon-like envelope around it, as suggested by the simulations of
<figure><img src="image_22.png" /></figure>

**Figure 19.** Fit to stream #48 (Orphan-Chenab). Here, the potential includes a moving model for the Milky Way as well as a massive moving LMC, while the stream progenitor loses mass over a period of 5 Gyr. Black dots show the best-fit stream model with both the Milky Way and the LMC, where the latter has a mass of $M_{LMC} = 1.5 \times 10^{11} M_{\odot}$. In contrast, the green dots show the result of setting $M_{LMC} = 0$. The Milky Way host is represented by the model derived previously from orbit fitting (corresponding to the mass model with $\beta_h = 3$ fit in Figure 13).

a pristine system being accreted for the first time seems very implausible.

As stream #49 is in the selected sample of long thin streams, this object is already taken into account in our MCMC search. However, the constraint that the stars should be bound to the Milky Way was not used. This would be an easy upgrade to add to the algorithm in future work.

In any case, it is interesting that a single star, whose astrometry will be even more accurately measured in future Gaia data releases, can be used to set a lower bound on the Galaxy's mass. The fact that this star is a member of a stream allows us to obtain a clearer view of its origin and possible history of previous interactions.

### 9.4. Stream #53 (GD-1)

We will briefly revisit the kinematics of stream #53 (GD-1, Grillmair & Dionatos 2006) given the improved data on the system. Our very limited aim here is to motivate the likelihood

<figure><img src="image_23.png" /></figure>

**Figure 20.** Actions and energy of the 190 stars with measured radial velocities and excellent (>7σ) astrometric parallaxes, calculated in the McMillan (2017) potential model (for easier comparison to earlier work). Color encodes the stream $s_{ID}$ identification as in Figure 6.

model that was used as a template in the fitting software detailed above in Sections 5–6.

The mean line-of-sight velocity profile of GD-1 as a function of $\phi_1$ was fit previously by Ibata et al. (2020b). The distribution of residuals from that function is shown both as a function of angle $\phi_1$ along the stream in Figure 21(a) and as a histogram in Figure 21(b) (where we sum over the full angular range $\phi_1 = [-12^\circ 8, 102^\circ 5]$ of the velocity members), and appears to show significant wings. To quantify this possibility, we again used an MCMC procedure to fit the data set with a single Gaussian model, and reran the fit with a two-component Gaussian model, including, of course, the individual velocity measurement uncertainties when computing the likelihoods. The p-value for the measured difference in log-likelihood between the maximum-likelihood fits of the two models is $\approx 1.2 \times 10^{-7}$, indicating that the more complex model with two Gaussians provides a significantly better fit to the data compared to the simpler single Gaussian model.

The two-component fit has means $\mu_1 = 3.2 \pm 0.7$ km s$^{-1}$, $\mu_2 = 0.8 \pm 3.9$ km s$^{-1}$, dispersions $\sigma_1 = 7.4 \pm 1.1$ km s$^{-1}$, $\sigma_2 = 29.1 \pm 6.1$ km s$^{-1}$ and a fraction $0.73 \pm 0.09$ in component 1. Thus, there is strong evidence that GD-1 has a cocoon-like envelope around it, as suggested by the simulations of
<figure><img src="image_24.png" /><figcaption>**Figure 21.** Line-of-sight velocity structure in the GD-1 stream. The velocity residuals from the profile previously fit by Ibata et al. (2020b) are shown (a) as a function of $\phi_1$ position angle along the stream, and can be seen to have a wide dispersion. Fitting Gaussians to this distribution (b) strongly suggests the presence of at least two Gaussian components.</figcaption></figure>

Carlberg (2020) and Carlberg & Agler (2023), which posit that stream progenitors were accreted inside dark matter subhalos.

Finally, given the new DR3 data set, and given the center for GD-1 calculated from the midpoint of the mass-weighted stellar population along the stream presented in Section 8, we believe it is useful to consider the counts along the stream as a function of physical path length, as shown in Figure 22. To achieve this coordinate conversion, we use the distance profile derived in Ibata et al. (2020b). The epicyclic spikes with periodicity 2.64 kpc identified in that contribution are very clear in this new representation. While dark matter subhaloes are expected to cause gaps in streams (Carlberg 2012), they are highly unlikely to produce such regular behavior.

<figure><img src="image_25.png" /><figcaption>**Figure 22.** Density as a function of physical path length along the GD-1 stream. The path length zero-point is set to $\phi_1 = 0$. The probable current location of the progenitor is marked, and vertical dashed lines show the periodicity derived by Ibata et al. (2020b). Our data masking at the position of the old open cluster M67 is responsible for the reduced counts at the marked location, which unfortunately coincides with a predicted peak.</figcaption></figure>

## 9.5. Streams #54 (ω Cen/Fimbulthul) and #55

One of the early successes of our STREAMFINDER program was the discovery of a tidal tail of ω Cen (Ibata et al. 2019a), the most massive globular cluster in the Milky Way, and long thought to be the central remnant of an accreted dwarf galaxy (Majewski et al. 2000; Bekki & Freeman 2003). A total of 22 stars of this stream (#54) currently have good parallaxes ($\bar{\omega}/\delta\bar{\omega} > 7$) and velocities, and consequently appeared in the action and energy diagram displayed in Figure 20 (which we discussed previously in relation to stream #49). Interestingly, a further 18 stars (with the same quality cut) belong to another structure identified by STREAMFINDER (stream #55) that is almost coincident in the action-energy diagram. The mean values and rms scatter of these integrals of motion are ($J_r, J_\phi, J_z$) = (207 ± 60, 663 ± 110, 198 ± 120) km s⁻¹ kpc and $E_{tot} = -1.78 \pm 0.06 \times 10^5$ km² s⁻² for stream #54 and ($J_r, J_\phi, J_z$) = (217 ± 160, 797 ± 190, 200 ± 60) = km s⁻¹ kpc and $E_{tot} = -1.73 \pm 0.11 \times 10^5$ km² s⁻² for stream #55. This coincidence strongly suggests a common origin between the two groups.

The association between the two streams is explored further in Figure 23. Panel (a) shows the end result of the N-body simulation of ω Cen presented by Ibata et al. (2019a). A peculiarity of that model is that it incorporated an initial rotation of the cluster model in order to reproduce the observed present-day rotation of ω Cen (Bianchini et al. 2013), which was also found to be necessary to reproduce the peculiar knee-shaped structure of the stream as seen in projection on the sky. In panel (a), particles at a heliocentric distance of $d < 6$ kpc that were still bound to the cluster 1 Gyr ago are displayed in color, with the particles that were no longer bound to the progenitor 0.5 Gyr ago shown in green. The corresponding distribution on the sky is displayed in Galactic coordinates in (b), along with
<figure><img src="image_24.png" /></figure>

<figure><img src="image_25.png" /><figcaption>**Figure 21.** Line-of-sight velocity structure in the GD-1 stream. The velocity residuals from the profile previously fit by Ibata et al. (2020b) are shown (a) as a function of $\phi_1$ position angle along the stream, and can be seen to have a wide dispersion. Fitting Gaussians to this distribution (b) strongly suggests the presence of at least two Gaussian components.</figcaption></figure>

Carlberg (2020) and Carlberg & Agler (2023), which posit that stream progenitors were accreted inside dark matter subhalos.

Finally, given the new DR3 data set, and given the center for GD-1 calculated from the midpoint of the mass-weighted stellar population along the stream presented in Section 8, we believe it is useful to consider the counts along the stream as a function of physical path length, as shown in Figure 22. To achieve this coordinate conversion, we use the distance profile derived in Ibata et al. (2020b). The epicyclic spikes with periodicity 2.64 kpc identified in that contribution are very clear in this new representation. While dark matter subhaloes are expected to cause gaps in streams (Carlberg 2012), they are highly unlikely to produce such regular behavior.

<figure><img src="image_26.png" /><figcaption>**Figure 22.** Density as a function of physical path length along the GD-1 stream. The path length zero-point is set to $\phi_1 = 0$. The probable current location of the progenitor is marked, and vertical dashed lines show the periodicity derived by Ibata et al. (2020b). Our data masking at the position of the old open cluster M67 is responsible for the reduced counts at the marked location, which unfortunately coincides with a predicted peak.</figcaption></figure>

## 9.5. Streams #54 (ω Cen/Fimbulthul) and #55

One of the early successes of our STREAMFINDER program was the discovery of a tidal tail of ω Cen (Ibata et al. 2019a), the most massive globular cluster in the Milky Way, and long thought to be the central remnant of an accreted dwarf galaxy (Majewski et al. 2000; Bekki & Freeman 2003). A total of 22 stars of this stream (#54) currently have good parallaxes ($\bar{\omega}/\delta\bar{\omega} > 7$) and velocities, and consequently appeared in the action and energy diagram displayed in Figure 20 (which we discussed previously in relation to stream #49). Interestingly, a further 18 stars (with the same quality cut) belong to another structure identified by STREAMFINDER (stream #55) that is almost coincident in the action-energy diagram. The mean values and rms scatter of these integrals of motion are ($J_r, J_\phi, J_z$) = (207 ± 60, 663 ± 110, 198 ± 120) km s⁻¹ kpc and $E_{tot} = -1.78 \pm 0.06 \times 10^5$ km² s⁻² for stream #54 and ($J_r, J_\phi, J_z$) = (217 ± 160, 797 ± 190, 200 ± 60) = km s⁻¹ kpc and $E_{tot} = -1.73 \pm 0.11 \times 10^5$ km² s⁻² for stream #55. This coincidence strongly suggests a common origin between the two groups.

The association between the two streams is explored further in Figure 23. Panel (a) shows the end result of the N-body simulation of ω Cen presented by Ibata et al. (2019a). A peculiarity of that model is that it incorporated an initial rotation of the cluster model in order to reproduce the observed present-day rotation of ω Cen (Bianchini et al. 2013), which was also found to be necessary to reproduce the peculiar knee-shaped structure of the stream as seen in projection on the sky. In panel (a), particles at a heliocentric distance of $d < 6$ kpc that were still bound to the cluster 1 Gyr ago are displayed in color, with the particles that were no longer bound to the progenitor 0.5 Gyr ago shown in green. The corresponding distribution on the sky is displayed in Galactic coordinates in (b), along with
<figure><img src="image_26.png" /><figcaption>**Figure 23.** Observations and model of streams #54 and #55. The present-day snapshot of the Ibata et al. (2019a) ω Cen model is shown in the x-y plane (a), oriented such that the location of the Sun lies at (−R⊙, 0). Particles that were still bound in the simulation 0.5 Gyr ago and currently lie at a heliocentric distance *d* < 6 kpc are colored blue, while those also at *d* < 6 kpc that were bound 1 Gyr ago are colored green. The same colored particles are shown again in panel (b), along with the velocity-confirmed members of stream #54 (brown) and #55 (gray, using the color scheme of Figure 20). The filled green area within 15° of the Galactic plane highlights the region where high source density and extinction render it very challenging to detect streams. The model particles of the older (green) part of the stream that lies below *b* = −15° are reproduced in panels (c) and (d), which show, respectively, the line-of-sight velocity and parallax behavior of both the data and simulations.</figcaption></figure>

the locations of streams #54 and #55. Although the modeled
stream produces a young spatially thin (blue) component, the
progenitor is sufficiently massive (with a present-day model
mass of 4.2 × 10⁶ M⊙) to scatter particles into an older, broader
(green) feature as well. The older part of the stream is also
visible in panel (b) in the form of a population of particles
below b = −15°, approximately coincident on the sky with the
location of stream #55. Panels (c) and (d) reproduce again the
older (green) model stream selection from panel (b), but further

trimmed to show only those particles with *b* < −15°. The line-of-sight velocity (c) and parallax (d) trends of this subsample of the model approximate the corresponding observed properties of stream #55. A similar phase-space structure is present in the simulations of Ferrone et al. (2023).

Hence, this structure, like stream #54 (Fimbulthul), is also
trailing tidal arm debris from the disruption of ω Cen. The bulk
of the sample is located ≈3 kpc away from the Sun and covers
much of the southern bulge region.
<figure><img src="image_27.png" /><figcaption>**Figure 23.** Observations and model of streams #54 and #55. The present-day snapshot of the Ibata et al. (2019a) ω Cen model is shown in the x-y plane (a), oriented such that the location of the Sun lies at (−R⊙, 0). Particles that were still bound in the simulation 0.5 Gyr ago and currently lie at a heliocentric distance *d* < 6 kpc are colored blue, while those also at *d* < 6 kpc that were bound 1 Gyr ago are colored green. The same colored particles are shown again in panel (b), along with the velocity-confirmed members of stream #54 (brown) and #55 (gray, using the color scheme of Figure 20). The filled green area within 15° of the Galactic plane highlights the region where high source density and extinction render it very challenging to detect streams. The model particles of the older (green) part of the stream that lies below *b* = −15° are reproduced in panels (c) and (d), which show, respectively, the line-of-sight velocity and parallax behavior of both the data and simulations.</figcaption></figure>

the locations of streams #54 and #55. Although the modeled
stream produces a young spatially thin (blue) component, the
progenitor is sufficiently massive (with a present-day model
mass of 4.2 × 10⁶ M⊙) to scatter particles into an older, broader
(green) feature as well. The older part of the stream is also
visible in panel (b) in the form of a population of particles
below b = −15°, approximately coincident on the sky with the
location of stream #55. Panels (c) and (d) reproduce again the
older (green) model stream selection from panel (b), but further

trimmed to show only those particles with *b* < −15°. The line-of-sight velocity (c) and parallax (d) trends of this subsample of the model approximate the corresponding observed properties of stream #55. A similar phase-space structure is present in the simulations of Ferrone et al. (2023).

Hence, this structure, like stream #54 (Fimbulthul), is also
trailing tidal arm debris from the disruption of ω Cen. The bulk
of the sample is located ≈3 kpc away from the Sun and covers
much of the southern bulge region.
<figure><img src="image_27.png" /><figcaption>**Figure 24.** Radial distribution of the stream stars with measured line-of-sight velocity. The radial component (a) and azimuthal component (b) of the velocity vector in a Galactocentric frame are displayed on the ordinate axes. The velocity components are chosen such that positive $v_r$ indicates motion away from the globular cluster, while $v_\phi > 0$ corresponds to retrograde motion with respect to the Galactic disk. Color again encodes the stream $s_{ID}$ identification number, as in Figure 6. The $(1\sigma)$ error bars are estimated by generating 1000 random realizations of each observed star consistent with the observational uncertainties and projecting into these Galactocentric coordinates.</figcaption></figure>

# 10. Discussion and Conclusions

## 10.1. Overview

In this contribution we have presented a large catalog of stellar streams, extracted in a homogeneous manner from the Gaia DR3 data set. We hunted for these structures using an improved version of the STREAMFINDER algorithm (Malhan & Ibata 2018), employing a stream template with a spatial dispersion of 50 pc so as to find structures resulting from the expected dissolution of globular clusters or very small dwarf satellite galaxies. This work is a continuation of our search

<figure><img src="image_28.png" /><figcaption>**Figure 25.** Comparison of the metallicity distribution of the stellar streams detected in Gaia DR3 with STREAMFINDER with the full sample of Galactic globular clusters (Harris 2010).</figcaption></figure>

efforts with the Gaia DR2 (Paper I; Ibata et al. 2019b) and EDR3 (Ibata et al. 2021b; Malhan et al. 2022) catalogs. Despite the radial velocity information being very sparse, the new velocity constraints, along with other enhancements in the algorithm detailed in Section 2, have allowed us to improve stream statistics and detect more subtle, diffuse structures.

We also embarked on a large follow-up campaign of the stream sources with the VLT/UVES high-resolution spectrograph (together with earlier observations in 2018–2020 with CFHT/ESPaDOnS in the Northern Hemisphere). Some low-resolution spectroscopic observations with INT/IDS were also obtained. Combining these data with public spectroscopic surveys has resulted in a catalog containing ≈24,500 thin stream stars, including 2178 line-of-sight velocities (extracted from a total sample of $0.79 \times 10^9$ Gaia stars passing the magnitude, extinction, and spatial cuts, of which $24 \times 10^6$ also have radial velocity measurements). This represents a significant expansion and refinement over previous catalogs. We expect the data set to be of considerable astrophysical interest for charting the Galactic mass distribution, probing dark substructures, and investigating alternative ideas for the workings of gravity.

The detected streams sample a large volume of the Galaxy, as can be seen in Figure 24, where we display the Galactocentric radius of the stars with measured line-of-sight velocity along with their velocity projections along the radial ($v_r$) and azimuthal ($v_\phi$) directions in a nonrotating Galactocentric frame. A slight majority (48) of the streams in Figure 24(b) have prograde orbits, while 37 display retrograde motion. However, the ratio of the two directions should not be overinterpreted, as significant additional analysis needs to be undertaken to quantify the detection biases introduced by the STREAMFINDER approach. In particular, we expect retrograde streams to be much easier to detect as they will display far greater contrast than prograde streams in proper motion space.
<figure><img src="image_28.png" /><figcaption>**Figure 24.** Radial distribution of the stream stars with measured line-of-sight velocity. The radial component (a) and azimuthal component (b) of the velocity vector in a Galactocentric frame are displayed on the ordinate axes. The velocity components are chosen such that positive $v_r$ indicates motion away from the globular cluster, while $v_\phi > 0$ corresponds to retrograde motion with respect to the Galactic disk. Color again encodes the stream $s_{ID}$ identification number, as in Figure 6. The $(1\sigma)$ error bars are estimated by generating 1000 random realizations of each observed star consistent with the observational uncertainties and projecting into these Galactocentric coordinates.</figcaption></figure>

# 10. Discussion and Conclusions

## 10.1. Overview

In this contribution we have presented a large catalog of stellar streams, extracted in a homogeneous manner from the Gaia DR3 data set. We hunted for these structures using an improved version of the STREAMFINDER algorithm (Malhan & Ibata 2018), employing a stream template with a spatial dispersion of 50 pc so as to find structures resulting from the expected dissolution of globular clusters or very small dwarf satellite galaxies. This work is a continuation of our search

<figure><img src="image_29.png" /><figcaption>**Figure 25.** Comparison of the metallicity distribution of the stellar streams detected in Gaia DR3 with STREAMFINDER with the full sample of Galactic globular clusters (Harris 2010).</figcaption></figure>

efforts with the Gaia DR2 (Paper I; Ibata et al. 2019b) and EDR3 (Ibata et al. 2021b; Malhan et al. 2022) catalogs. Despite the radial velocity information being very sparse, the new velocity constraints, along with other enhancements in the algorithm detailed in Section 2, have allowed us to improve stream statistics and detect more subtle, diffuse structures.

We also embarked on a large follow-up campaign of the stream sources with the VLT/UVES high-resolution spectrograph (together with earlier observations in 2018–2020 with CFHT/ESPaDOnS in the Northern Hemisphere). Some low-resolution spectroscopic observations with INT/IDS were also obtained. Combining these data with public spectroscopic surveys has resulted in a catalog containing ≈24,500 thin stream stars, including 2178 line-of-sight velocities (extracted from a total sample of $0.79 \times 10^9$ Gaia stars passing the magnitude, extinction, and spatial cuts, of which $24 \times 10^6$ also have radial velocity measurements). This represents a significant expansion and refinement over previous catalogs. We expect the data set to be of considerable astrophysical interest for charting the Galactic mass distribution, probing dark substructures, and investigating alternative ideas for the workings of gravity.

The detected streams sample a large volume of the Galaxy, as can be seen in Figure 24, where we display the Galactocentric radius of the stars with measured line-of-sight velocity along with their velocity projections along the radial ($v_r$) and azimuthal ($v_\phi$) directions in a nonrotating Galactocentric frame. A slight majority (48) of the streams in Figure 24(b) have prograde orbits, while 37 display retrograde motion. However, the ratio of the two directions should not be overinterpreted, as significant additional analysis needs to be undertaken to quantify the detection biases introduced by the STREAMFINDER approach. In particular, we expect retrograde streams to be much easier to detect as they will display far greater contrast than prograde streams in proper motion space.
## 10.2. Metallicity Distribution of Stellar Streams

We collated the metallicities of the detected streams from the literature, from individual metallicity measurements of member stars extracted from public spectroscopic and photometric surveys, and from our own follow-up spectroscopic observations. The resulting values are listed in Table 3, along with the source of the measurements. The Gaia-12 and Hydrus streams appear to be particularly interesting due to their low metallicity in the Martin et al. (2023) metallicity catalog based on Gaia DR3 BP/RP spectro-photometry. Spectroscopic follow-up observations will be useful to confirm the pristine nature of these structures.

Updating the sample previously analyzed in Martin et al. (2022), in Figure 25, we compare the metallicity distribution function (MDF; using the values listed in Table 3) with that of the globular clusters listed in the compilation by Harris (2010). Because of the adopted stream template of Gaussian dispersion 50 pc, we expect the streams presented in this contribution to be mainly the remnants of globular clusters, although we note that the class of small and extremely low-luminosity systems that have recently been discovered (Mau et al. 2020; Cerny et al. 2023; Smith et al. 2024), and which may be very low-mass dwarf galaxies, are also possible progenitor candidates. The peak of the MDF of the streams can be seen to be ≈0.75 dex more metal-poor than that of the surviving clusters.

Cosmological simulations show that, on average, accreted (metal-poor) globular clusters experienced weaker tidal fields compared to in situ (metal-rich) clusters over cosmic time (Renaud et al. 2017). However, that study did not explicitly investigate differences in tidal fields as a function of metallicity for the accreted cluster population itself. If this dependence of tidal history on metallicity in the accreted population is small, the observed difference in the MDF between streams and surviving globular clusters would suggest that metal-poor globular clusters are more susceptible to disruption compared to their metal-rich counterparts. This could be the consequence of metal-poor globular clusters originally being formed with lower masses or densities. Among the surviving globular clusters in the Galactic halo, there appears to be a correlation such that the most metal-rich are also the least massive (Parmentier & Gilmore 2001), which argues against mass being the primary driver, and suggests that density may be more important. Supporting this perspective, Bianchini et al. (2017) propose that metal-rich globular clusters may have formed in a denser initial state, characterized by shorter relaxation times. Their analysis seeks to explain the observed trend in dynamical mass-to-light (M/L) ratios with metallicity: metal-rich globular clusters, at least in M31, exhibit lower M/L ratios compared to their metal-poor counterparts (Strader et al. 2011, although we note that the formation history of M31 is likely to be strikingly different from our own). A denser formation with rapid relaxation times could accelerate the evolution of metal-rich globular clusters toward lower M/L ratios, due to the preferential ejection of low-mass stars and stellar remnants.

Alternatively, the MDF difference may be a manifestation of the fact that the most metal-rich globular clusters in the Galaxy tend to have a higher fraction of disk orbits or orbits confined to the innermost regions of the Galaxy, and are more likely to have been formed in situ. Both types of orbits produce streams that would be harder to detect with STREAMFINDER, as the algorithm performs less well for very diffuse streams, streams in very high-density regions, as in the bulge, or streams

confined to the disk. Ferrone et al. (2023) have shown that orbits with low apocenters produce streams on the sky that are very different from classical streams such as Palomar 5, and thus, they would be harder to detect by hunting along orbits. The differences between the stream and the globular clusters MDF may thus be a selection effect. Quantifying this requires computationally expensive completeness tests, and will be explored in a future contribution.

Clearly, there are multiple factors that could contribute to the observed difference in the metallicity distribution between streams and surviving clusters, including the initial conditions at formation, the strength of the tidal field experienced over time, and the bias of the methodology used to detect the streams. A comprehensive analysis will be needed to disentangle these various factors.

## 10.3. MCMC Exploration of Streams and Milky Way

Given this unprecedented data set, we decided to also invest substantial effort to build analysis tools that would allow us to build an updated global model of the Milky Way. The computational task is daunting; however, as reasonably realistic axisymmetric Galactic mass models have in excess of 10 parameters, while six parameters are needed to define the orbit of each stream progenitor, and at least a mass and a scale radius is required to define the simplest (Plummer) mass model for each of the latter. The approach we took was to devise two algorithms. The first algorithm is a simpler orbit-fitting analysis, which uses, we believe for the first time, a correction function for each of the observable parameters so as to better approximate stream tracks. The Galactic mass model parameters and the stream kinematics are optimized through an MCMC search. The second algorithm integrates test particles around dissolving progenitors within a dynamic Local Group environment, where the massive host and perturbing galaxies are allowed to move each under the influence of the gravity of the other massive bodies, but with the massless test particles having no effect on other bodies. While the second algorithm is capable of a full MCMC exploration, in the current contribution, we used it primarily to derive the orbit-to-stream corrections needed for the first approach. In future work, we intend to use this algorithm to explore stream and satellite dynamics throughout the Local Group.

## 10.4. Halo Constraints

The analysis presented in Section 8 started from a simple fit to extant circular velocity and terminal velocity data (together with some additional kinematic constraints) and progressively added in the information from GD-1, which is the best-measured stream, then from streams with known globular clusters, and finally from the selected full sample of 29 long and thin streams. Our hope had been that a model of the complexity of that presented here could be fully constrained by the present data set, with no strong priors needed. However, it transpires that in allowing the halo outer power-law parameter $\beta_h$ to vary, we obtain solutions to the virial mass that reach up to our imposed limit of $M_{200} < 2 \times 10^{12} M_\odot$ (which corresponds to half of the 95% upper limit to the mass of the Local Group, as determined by Peñarrubia et al. 2014). With this constraint, the most likely value of the outer slope parameter is $\beta_h \approx 2.5$. Cosmological simulations of galaxy formation predict that dark matter halos have profiles that have on average an
## 10.2. Metallicity Distribution of Stellar Streams

We collated the metallicities of the detected streams from the literature, from individual metallicity measurements of member stars extracted from public spectroscopic and photometric surveys, and from our own follow-up spectroscopic observations. The resulting values are listed in Table 3, along with the source of the measurements. The Gaia-12 and Hydrus streams appear to be particularly interesting due to their low metallicity in the Martin et al. (2023) metallicity catalog based on Gaia DR3 BP/RP spectro-photometry. Spectroscopic follow-up observations will be useful to confirm the pristine nature of these structures.

Updating the sample previously analyzed in Martin et al. (2022), in Figure 25, we compare the metallicity distribution function (MDF; using the values listed in Table 3) with that of the globular clusters listed in the compilation by Harris (2010). Because of the adopted stream template of Gaussian dispersion 50 pc, we expect the streams presented in this contribution to be mainly the remnants of globular clusters, although we note that the class of small and extremely low-luminosity systems that have recently been discovered (Mau et al. 2020; Cerny et al. 2023; Smith et al. 2024), and which may be very low-mass dwarf galaxies, are also possible progenitor candidates. The peak of the MDF of the streams can be seen to be ≈0.75 dex more metal-poor than that of the surviving clusters.

Cosmological simulations show that, on average, accreted (metal-poor) globular clusters experienced weaker tidal fields compared to in situ (metal-rich) clusters over cosmic time (Renaud et al. 2017). However, that study did not explicitly investigate differences in tidal fields as a function of metallicity for the accreted cluster population itself. If this dependence of tidal history on metallicity in the accreted population is small, the observed difference in the MDF between streams and surviving globular clusters would suggest that metal-poor globular clusters are more susceptible to disruption compared to their metal-rich counterparts. This could be the consequence of metal-poor globular clusters originally being formed with lower masses or densities. Among the surviving globular clusters in the Galactic halo, there appears to be a correlation such that the most metal-rich are also the least massive (Parmentier & Gilmore 2001), which argues against mass being the primary driver, and suggests that density may be more important. Supporting this perspective, Bianchini et al. (2017) propose that metal-rich globular clusters may have formed in a denser initial state, characterized by shorter relaxation times. Their analysis seeks to explain the observed trend in dynamical mass-to-light (M/L) ratios with metallicity: metal-rich globular clusters, at least in M31, exhibit lower M/L ratios compared to their metal-poor counterparts (Strader et al. 2011, although we note that the formation history of M31 is likely to be strikingly different from our own). A denser formation with rapid relaxation times could accelerate the evolution of metal-rich globular clusters toward lower M/L ratios, due to the preferential ejection of low-mass stars and stellar remnants.

Alternatively, the MDF difference may be a manifestation of the fact that the most metal-rich globular clusters in the Galaxy tend to have a higher fraction of disk orbits or orbits confined to the innermost regions of the Galaxy, and are more likely to have been formed in situ. Both types of orbits produce streams that would be harder to detect with STREAMFINDER, as the algorithm performs less well for very diffuse streams, streams in very high-density regions, as in the bulge, or streams

confined to the disk. Ferrone et al. (2023) have shown that orbits with low apocenters produce streams on the sky that are very different from classical streams such as Palomar 5, and thus, they would be harder to detect by hunting along orbits. The differences between the stream and the globular clusters MDF may thus be a selection effect. Quantifying this requires computationally expensive completeness tests, and will be explored in a future contribution.

Clearly, there are multiple factors that could contribute to the observed difference in the metallicity distribution between streams and surviving clusters, including the initial conditions at formation, the strength of the tidal field experienced over time, and the bias of the methodology used to detect the streams. A comprehensive analysis will be needed to disentangle these various factors.

## 10.3. MCMC Exploration of Streams and Milky Way

Given this unprecedented data set, we decided to also invest substantial effort to build analysis tools that would allow us to build an updated global model of the Milky Way. The computational task is daunting; however, as reasonably realistic axisymmetric Galactic mass models have in excess of 10 parameters, while six parameters are needed to define the orbit of each stream progenitor, and at least a mass and a scale radius is required to define the simplest (Plummer) mass model for each of the latter. The approach we took was to devise two algorithms. The first algorithm is a simpler orbit-fitting analysis, which uses, we believe for the first time, a correction function for each of the observable parameters so as to better approximate stream tracks. The Galactic mass model parameters and the stream kinematics are optimized through an MCMC search. The second algorithm integrates test particles around dissolving progenitors within a dynamic Local Group environment, where the massive host and perturbing galaxies are allowed to move each under the influence of the gravity of the other massive bodies, but with the massless test particles having no effect on other bodies. While the second algorithm is capable of a full MCMC exploration, in the current contribution, we used it primarily to derive the orbit-to-stream corrections needed for the first approach. In future work, we intend to use this algorithm to explore stream and satellite dynamics throughout the Local Group.

## 10.4. Halo Constraints

The analysis presented in Section 8 started from a simple fit to extant circular velocity and terminal velocity data (together with some additional kinematic constraints) and progressively added in the information from GD-1, which is the best-measured stream, then from streams with known globular clusters, and finally from the selected full sample of 29 long and thin streams. Our hope had been that a model of the complexity of that presented here could be fully constrained by the present data set, with no strong priors needed. However, it transpires that in allowing the halo outer power-law parameter $\beta_h$ to vary, we obtain solutions to the virial mass that reach up to our imposed limit of $M_{200} < 2 \times 10^{12} M_\odot$ (which corresponds to half of the 95% upper limit to the mass of the Local Group, as determined by Peñarrubia et al. 2014). With this constraint, the most likely value of the outer slope parameter is $\beta_h \approx 2.5$. Cosmological simulations of galaxy formation predict that dark matter halos have profiles that have on average an
asymptotic $r^{-3}$ slope in their outer regions (Navarro et al. 1997). Yet there is also an environmental dependence (Avila-Reese et al. 1999), with steeper slopes in galaxy clusters, and shallower slopes ($\beta \approx 2.3-2.7$) in groups and galaxy systems. Thus, the PDF of $\beta_h$ found in Figure 14 is therefore not unexpected for the case of the Milky Way. Nevertheless, because the MCMC exploration does reach the $M_{200}$ limit when $\beta_h$ is free, we select the fits with the outer halo power-law parameter fixed to $\beta_h = 3$ as our preferred model.<fnref n="23" />

The fitted value of the halo inner power-law parameter $\gamma_h = 0.97_{-0.21}^{+0.17}$ is fully consistent with the NFW profile, and the scale radius $r_{0,h} = 14.7_{-1.0}^{+4.7}$ kpc is also consistent at $\approx 1\sigma$ with expectations for the Milky Way from $\Lambda$CDM based models (Klypin et al. 2002), as is the inferred virial mass of $M_{200} = 1.09_{-0.14}^{+0.19} \times 10^{12} M_{\odot}$. Wilkinson & Evans (1999) introduced the mass interior to 50 kpc as a useful measure of the Galaxy, finding $M_{R<50} = 0.54_{-0.36}^{+0.02} \times 10^{12} M_{\odot}$. Our fitted value of $M_{R<50} = 0.46 \pm 0.03 \times 10^{12} M_{\odot}$ is fully consistent with this, and with the posterior distribution shown by McMillan (2017; their Figure 6). This mass is essentially identical to the value of $M_{R<50} = 0.468_{-0.034}^{+0.032} \times 10^{12} M_{\odot}$ derived by Shen et al. (2022) from an analysis of the kinematics of 168 halo stars in the H3 survey. However, our fits appear to be in tension with the recent detection of a Keplerian decline in the Galactic rotation curve (Jiao et al. 2023), which implies a total Milky Way mass of $0.206_{-0.013}^{+0.024} \times 10^{12} M_{\odot}$; in future work, it will be interesting to explore how the two analyses can be tallied.

We note, however, that our results should not be taken as inconsistent with those of Portail et al. (2017) and Cole & Binney (2017), who found a cored halo with an inner slope shallower than 0.6 in the central 2 kpc, since the present study is not well suited to constrain the mass profile in that region, given the 29 streams considered here. A detailed study of the dark matter distribution in this central region would need a realistic model of the bar (e.g., Portail et al. 2017; Monari et al. 2019).

The local dark matter density, assuming that it is given solely by the density of the halo component, is tightly constrained at $\rho_{h,\odot} = 0.0114 \pm 0.0007 M_{\odot} \text{pc}^{-3}$. This is consistent at the $2\sigma$ level with the best-fit value of $\rho_{h,\odot} = 0.0101 M_{\odot} \text{pc}^{-3}$ found by McMillan (2017).

The mass flattening of the double-power-law model of the dark matter halo is found to be tightly constrained to $q_{m,h} = 0.749_{-0.030}^{+0.026}$. While this constraint pertains to the global structure of the halo model, the bulk of the stars in the sample that possess line-of-sight velocity measurements resides in the vicinity of the Sun, with half of the sample lying within 13.5 kpc of the Galactic Center, and 90% within 21.6 kpc. Thus, most of the information that constrains our measurement of the density flattening comes from approximately the scale radius of the halo. At similar distances, Koposov et al. (2010) find a potential flattening of $q_{\Phi} = 0.87_{-0.03}^{+0.07}$ from an analysis of the GD-1 stream, while Küpper et al. (2015) derived $q_{\Phi} = 0.95_{-0.12}^{+0.16}$ from the Palomar 5 stream, which together gives a weighted mean of $q_{\Phi} = 0.88 \pm 0.05$. For axisymmetric potentials that are close to spherical, the relation between potential and density flattening is $1 - q_{\Phi} \approx \frac{1}{3}(1 - q_m)$

(Binney & Tremaine 2008), implying $q_m \approx 0.64 \pm 0.15$, which is consistent with our finding at the $1\sigma$ level (of course both GD-1 and Palomar 5 are in our sample, and as such our measurement is not fully independent of theirs). At nearer distances close to the Sun, Dodd et al. (2022) have recently suggested that the dark halo has a density flattening of $q_{m,h} = 1.2$, which they deduce from the azimuthal to vertical resonance of stars in the nearby Helmi streams. At larger distances of up to 100 kpc, the stream of the Sagittarius dwarf galaxy provides one of the few constraints on the dark matter halo shape. There was considerable debate whether the data on this stream implied the presence of a spherical (Ibata et al. 2001), an oblate (Johnston et al. 2005), a prolate (Helmi 2004), or a triaxial (Law & Majewski 2010) dark halo. More recently, Vasiliev et al. (2021) studied the evolution of the Sagittarius stream, taking the LMC and the reflex motion of the Milky Way into account, and they suggest a complicated configuration in which the Galactic dark matter is triaxial and changes shape and orientation as a function of radius. This may explain why the earlier studies, which examined different tracers at different distances, drew different conclusions. In future work, it will be interesting to explore whether their halo model improves the fits to the sample of stellar streams considered here.

## 10.5. Disk Constraints

Our fits put strong constraints on the large-scale mass and structure of the disk components of the Milky Way. The thin disk is found to have a scale length of $h_{R,d} = 2.17_{-0.08}^{+0.18}$ kpc and scale height of $h_{z,d} = 0.347_{-0.010}^{+0.007}$ kpc, while the same properties of the thick disk are, respectively, $h_{R,t} = 1.62_{-0.13}^{+0.72}$ kpc and $h_{z,t} = 0.86_{-0.02}^{+0.03}$ kpc. The combined mass of the two stellar disks is $M_{d+t} = 4.20_{-0.53}^{+0.44} \times 10^{10} M_{\odot}$, of which $9.5_{-1.4}^{+14.3}\%$ resides in the thick disk. In terms of the surface density at the Solar radius, we find that the local thick disk constitutes $12.4\% \pm 0.7\%$ of the combined disk surface density, while the local thick disk density fraction is $5.4\% \pm 0.4\%$. The disk structural parameters we measure are contained within the range reported in the literature review and meta-analysis by Bland-Hawthorn & Gerhard (2016). To help visualize the behavior of our best-fit model, we show its rotation curve in Figure 26.

As a sanity check of (primarily) the stellar disk components of our model, we compare in Figure 27 the profile of the $K_{z,1.1}$ vertical acceleration at a position of $z = 1.1$ kpc above the Galactic plane to the values of this parameter derived from the analysis of Bovy & Rix (2013). We did not use their data set in our model fitting because the uncertainties on their data points are correlated, yet one can see that the model follows the $K_{z,1.1}$ trend reasonably well. Like the McMillan (2017) model, ours slightly underpredicts the Bovy & Rix (2013) $K_{z,1.1}$ data at small radii, but our model follows the profile closely at $R \gtrsim 6.5$ kpc.

Our model is fitted primarily to dynamical constraints, and so the properties of the disk models we find should reflect a decomposition of their mass distribution given the imposed double-exponential analytic form. In contrast, when the thick disk is defined using chemical abundances, the resulting thin and thick disk masses have been found to be very similar (Snaith et al. 2014). This difference may be the result of using mass models that are too simple for these components in the

<footnote n="23">²³ Obviously, we could have incorporated the results of the Peñarrubia et al. (2014) analysis into our MCMC search as a Bayesian prior, but we deem that the present approach presents a clearer view of the constraints provided by the STREAMFINDER data set.</footnote>
asymptotic $r^{-3}$ slope in their outer regions (Navarro et al. 1997). Yet there is also an environmental dependence (Avila-Reese et al. 1999), with steeper slopes in galaxy clusters, and shallower slopes ($\beta \approx 2.3-2.7$) in groups and galaxy systems. Thus, the PDF of $\beta_h$ found in Figure 14 is therefore not unexpected for the case of the Milky Way. Nevertheless, because the MCMC exploration does reach the $M_{200}$ limit when $\beta_h$ is free, we select the fits with the outer halo power-law parameter fixed to $\beta_h = 3$ as our preferred model.<fnref n="23" />

The fitted value of the halo inner power-law parameter $\gamma_h = 0.97_{-0.21}^{+0.17}$ is fully consistent with the NFW profile, and the scale radius $r_{0,h} = 14.7_{-1.0}^{+4.7}$ kpc is also consistent at $\approx 1\sigma$ with expectations for the Milky Way from $\Lambda$CDM based models (Klypin et al. 2002), as is the inferred virial mass of $M_{200} = 1.09_{-0.14}^{+0.19} \times 10^{12} M_{\odot}$. Wilkinson & Evans (1999) introduced the mass interior to 50 kpc as a useful measure of the Galaxy, finding $M_{R<50} = 0.54_{-0.36}^{+0.02} \times 10^{12} M_{\odot}$. Our fitted value of $M_{R<50} = 0.46 \pm 0.03 \times 10^{12} M_{\odot}$ is fully consistent with this, and with the posterior distribution shown by McMillan (2017; their Figure 6). This mass is essentially identical to the value of $M_{R<50} = 0.468_{-0.034}^{+0.032} \times 10^{12} M_{\odot}$ derived by Shen et al. (2022) from an analysis of the kinematics of 168 halo stars in the H3 survey. However, our fits appear to be in tension with the recent detection of a Keplerian decline in the Galactic rotation curve (Jiao et al. 2023), which implies a total Milky Way mass of $0.206_{-0.013}^{+0.024} \times 10^{12} M_{\odot}$; in future work, it will be interesting to explore how the two analyses can be tallied.

We note, however, that our results should not be taken as inconsistent with those of Portail et al. (2017) and Cole & Binney (2017), who found a cored halo with an inner slope shallower than 0.6 in the central 2 kpc, since the present study is not well suited to constrain the mass profile in that region, given the 29 streams considered here. A detailed study of the dark matter distribution in this central region would need a realistic model of the bar (e.g., Portail et al. 2017; Monari et al. 2019).

The local dark matter density, assuming that it is given solely by the density of the halo component, is tightly constrained at $\rho_{h,\odot} = 0.0114 \pm 0.0007 M_{\odot} \text{pc}^{-3}$. This is consistent at the $2\sigma$ level with the best-fit value of $\rho_{h,\odot} = 0.0101 M_{\odot} \text{pc}^{-3}$ found by McMillan (2017).

The mass flattening of the double-power-law model of the dark matter halo is found to be tightly constrained to $q_{m,h} = 0.749_{-0.030}^{+0.026}$. While this constraint pertains to the global structure of the halo model, the bulk of the stars in the sample that possess line-of-sight velocity measurements resides in the vicinity of the Sun, with half of the sample lying within 13.5 kpc of the Galactic Center, and 90% within 21.6 kpc. Thus, most of the information that constrains our measurement of the density flattening comes from approximately the scale radius of the halo. At similar distances, Koposov et al. (2010) find a potential flattening of $q_{\Phi} = 0.87_{-0.03}^{+0.07}$ from an analysis of the GD-1 stream, while Küpper et al. (2015) derived $q_{\Phi} = 0.95_{-0.12}^{+0.16}$ from the Palomar 5 stream, which together gives a weighted mean of $q_{\Phi} = 0.88 \pm 0.05$. For axisymmetric potentials that are close to spherical, the relation between potential and density flattening is $1 - q_{\Phi} \approx \frac{1}{3}(1 - q_m)$

(Binney & Tremaine 2008), implying $q_m \approx 0.64 \pm 0.15$, which is consistent with our finding at the $1\sigma$ level (of course both GD-1 and Palomar 5 are in our sample, and as such our measurement is not fully independent of theirs). At nearer distances close to the Sun, Dodd et al. (2022) have recently suggested that the dark halo has a density flattening of $q_{m,h} = 1.2$, which they deduce from the azimuthal to vertical resonance of stars in the nearby Helmi streams. At larger distances of up to 100 kpc, the stream of the Sagittarius dwarf galaxy provides one of the few constraints on the dark matter halo shape. There was considerable debate whether the data on this stream implied the presence of a spherical (Ibata et al. 2001), an oblate (Johnston et al. 2005), a prolate (Helmi 2004), or a triaxial (Law & Majewski 2010) dark halo. More recently, Vasiliev et al. (2021) studied the evolution of the Sagittarius stream, taking the LMC and the reflex motion of the Milky Way into account, and they suggest a complicated configuration in which the Galactic dark matter is triaxial and changes shape and orientation as a function of radius. This may explain why the earlier studies, which examined different tracers at different distances, drew different conclusions. In future work, it will be interesting to explore whether their halo model improves the fits to the sample of stellar streams considered here.

## 10.5. Disk Constraints

Our fits put strong constraints on the large-scale mass and structure of the disk components of the Milky Way. The thin disk is found to have a scale length of $h_{R,d} = 2.17_{-0.08}^{+0.18}$ kpc and scale height of $h_{z,d} = 0.347_{-0.010}^{+0.007}$ kpc, while the same properties of the thick disk are, respectively, $h_{R,t} = 1.62_{-0.13}^{+0.72}$ kpc and $h_{z,t} = 0.86_{-0.02}^{+0.03}$ kpc. The combined mass of the two stellar disks is $M_{d+t} = 4.20_{-0.53}^{+0.44} \times 10^{10} M_{\odot}$, of which $9.5_{-1.4}^{+14.3}\%$ resides in the thick disk. In terms of the surface density at the Solar radius, we find that the local thick disk constitutes $12.4\% \pm 0.7\%$ of the combined disk surface density, while the local thick disk density fraction is $5.4\% \pm 0.4\%$. The disk structural parameters we measure are contained within the range reported in the literature review and meta-analysis by Bland-Hawthorn & Gerhard (2016). To help visualize the behavior of our best-fit model, we show its rotation curve in Figure 26.

As a sanity check of (primarily) the stellar disk components of our model, we compare in Figure 27 the profile of the $K_{z,1.1}$ vertical acceleration at a position of $z = 1.1$ kpc above the Galactic plane to the values of this parameter derived from the analysis of Bovy & Rix (2013). We did not use their data set in our model fitting because the uncertainties on their data points are correlated, yet one can see that the model follows the $K_{z,1.1}$ trend reasonably well. Like the McMillan (2017) model, ours slightly underpredicts the Bovy & Rix (2013) $K_{z,1.1}$ data at small radii, but our model follows the profile closely at $R \gtrsim 6.5$ kpc.

Our model is fitted primarily to dynamical constraints, and so the properties of the disk models we find should reflect a decomposition of their mass distribution given the imposed double-exponential analytic form. In contrast, when the thick disk is defined using chemical abundances, the resulting thin and thick disk masses have been found to be very similar (Snaith et al. 2014). This difference may be the result of using mass models that are too simple for these components in the

<footnote n="23">²³ Obviously, we could have incorporated the results of the Peñarrubia et al. (2014) analysis into our MCMC search as a Bayesian prior, but we deem that the present approach presents a clearer view of the constraints provided by the STREAMFINDER data set.</footnote>
<figure><img src="image_29.png" /><figcaption>**Figure 26.** Circular velocity of the most likely Galaxy model with $\beta_h = 3$ (purple line). The shaded (yellow) region shows the 1$\sigma$ spread derived from the models explored in the MCMC chain. We show for comparison the Eilers et al. (2019) data set; the selected subset at $R < 15$ kpc where the effects of the Galactic warp and flaring are less likely to be problematic is highlighted in green.</figcaption></figure>

<figure><img src="image_30.png" /><figcaption>**Figure 27.** Profile of the $K_{z,1.1}$ vertical acceleration $z = 1.1$ kpc above the Galactic plane. The best Milky Way model (purple) together with its (1$\sigma$) uncertainties derived from the MCMC chain are compared to the analysis of Bovy & Rix (2013). Note that these data were not used to derive the mass model.</figcaption></figure>

dynamical analysis; broken exponentials may be more appropriate (Lian et al. 2022).

## 10.6. M/L Ratio

It is interesting to consider the M/L ratio of the luminous components of the Galaxy, given that our model is fit to

dynamical constraints and relative star counts. The extinction-corrected K-band absolute magnitude was measured from COBE data (Drimmel & Spergel 2001) to be $M_K = -24.02$, and Hammer et al. (2007) estimate a 0.1 mag uncertainty on this value from a comparison to earlier measurements. Adopting $M_{K\odot} = 3.3$ (Bell et al. 2003), we find a K-band M/L ratio of the stellar components of the Milky Way of $M_{*,MW}/L = 0.61 \pm 0.08 M_{\odot}/L_{\odot}$, which is substantially lower than the K-band M/L = $0.95 \pm 0.03 M_{\odot}/L_{\odot}$ derived by Bell et al. (2003) from a stellar populations analysis of Two Micron All Sky Survey (2MASS) and SDSS galaxies. However, those authors use a universal initial mass function (IMF) tailored to produce maximum-disk solutions, and they comment that values $\approx 30\%$ lower are obtained with a Kroupa et al. (1993) IMF. Hence, with plausible assumptions about the IMF, our Milky Way stellar mass estimate based on stream dynamics is fully consistent with the stellar mass based on stellar evolution models and the integrated luminosity of the Milky Way.

## 10.7. Toward a Nonparametric Model of the Galaxy

The very tight constraints we have derived on the local dark matter and on the structure of the Galactic components are clearly, in part, an artifact of the rigidity of the analytic functions (Equations (8) and (9)) used to describe them. In future work, we hope to overcome this limitation; indeed, our motivation in developing the orbit-to-stream correction functions $\Delta_{\Theta}(\phi_1)$ was to be able to reuse them to derive a nonparametric Galactic model using the machinery developed in Ibata et al. (2021a). That method uses an unsupervised machine learning procedure to derive the transformation from positions and velocities along orbits to canonical actions and angles, and thereby effectively builds a data-driven Hamiltonian of the Galaxy.

## 10.8. Highlighted Streams

While a detailed exposition of the properties of the new streams is beyond the scope of the present paper, and will be presented in a future contribution, in Section 9, we nevertheless briefly discussed some highlights and insights from the new catalog.

1. Stream #17 is a very metal-poor stream, with a metallicity of $[Fe/H] = -2.7$ that is below the expected floor for cluster formation (Beasley et al. 2019). It is currently passing through the solar neighborhood, yet it appears to have been a satellite of the Sagittarius dwarf galaxy. It will be fascinating to model the dynamics of this system further to ascertain when and under what conditions its backward path can be made to coincide precisely with that of the Sagittarius dwarf. We suspect that this will require the perturbing effect of the LMC to also be taken into account, for which the stream-fitting machinery presented in Section 6, with its capability of implementing the forces due to several perturbers at once, should be ideal. The extreme proximity of this extra-galactic system may also be useful for stellar population and chemical analyses.

2. For stream #48 (Orphan-Chenab), we briefly investigate with our dynamical stream-fitting software whether our newly fitted Milky Way mass model affects the conclusion that a massive LMC is needed to reproduce the observed phase-space structure of this stream. While
<figure><img src="image_30.png" /><figcaption>**Figure 26.** Circular velocity of the most likely Galaxy model with $\beta_h = 3$ (purple line). The shaded (yellow) region shows the 1$\sigma$ spread derived from the models explored in the MCMC chain. We show for comparison the Eilers et al. (2019) data set; the selected subset at $R < 15$ kpc where the effects of the Galactic warp and flaring are less likely to be problematic is highlighted in green.</figcaption></figure>

<figure><img src="image_31.png" /><figcaption>**Figure 27.** Profile of the $K_{z,1.1}$ vertical acceleration $z = 1.1$ kpc above the Galactic plane. The best Milky Way model (purple) together with its (1$\sigma$) uncertainties derived from the MCMC chain are compared to the analysis of Bovy & Rix (2013). Note that these data were not used to derive the mass model.</figcaption></figure>

dynamical analysis; broken exponentials may be more appropriate (Lian et al. 2022).

## 10.6. M/L Ratio

It is interesting to consider the M/L ratio of the luminous components of the Galaxy, given that our model is fit to

dynamical constraints and relative star counts. The extinction-corrected K-band absolute magnitude was measured from COBE data (Drimmel & Spergel 2001) to be $M_K = -24.02$, and Hammer et al. (2007) estimate a 0.1 mag uncertainty on this value from a comparison to earlier measurements. Adopting $M_{K\odot} = 3.3$ (Bell et al. 2003), we find a K-band M/L ratio of the stellar components of the Milky Way of $M_{*,MW}/L = 0.61 \pm 0.08 M_{\odot}/L_{\odot}$, which is substantially lower than the K-band M/L = $0.95 \pm 0.03 M_{\odot}/L_{\odot}$ derived by Bell et al. (2003) from a stellar populations analysis of Two Micron All Sky Survey (2MASS) and SDSS galaxies. However, those authors use a universal initial mass function (IMF) tailored to produce maximum-disk solutions, and they comment that values $\approx 30\%$ lower are obtained with a Kroupa et al. (1993) IMF. Hence, with plausible assumptions about the IMF, our Milky Way stellar mass estimate based on stream dynamics is fully consistent with the stellar mass based on stellar evolution models and the integrated luminosity of the Milky Way.

## 10.7. Toward a Nonparametric Model of the Galaxy

The very tight constraints we have derived on the local dark matter and on the structure of the Galactic components are clearly, in part, an artifact of the rigidity of the analytic functions (Equations (8) and (9)) used to describe them. In future work, we hope to overcome this limitation; indeed, our motivation in developing the orbit-to-stream correction functions $\Delta_{\Theta}(\phi_1)$ was to be able to reuse them to derive a nonparametric Galactic model using the machinery developed in Ibata et al. (2021a). That method uses an unsupervised machine learning procedure to derive the transformation from positions and velocities along orbits to canonical actions and angles, and thereby effectively builds a data-driven Hamiltonian of the Galaxy.

## 10.8. Highlighted Streams

While a detailed exposition of the properties of the new streams is beyond the scope of the present paper, and will be presented in a future contribution, in Section 9, we nevertheless briefly discussed some highlights and insights from the new catalog.

1. Stream #17 is a very metal-poor stream, with a metallicity of $[Fe/H] = -2.7$ that is below the expected floor for cluster formation (Beasley et al. 2019). It is currently passing through the solar neighborhood, yet it appears to have been a satellite of the Sagittarius dwarf galaxy. It will be fascinating to model the dynamics of this system further to ascertain when and under what conditions its backward path can be made to coincide precisely with that of the Sagittarius dwarf. We suspect that this will require the perturbing effect of the LMC to also be taken into account, for which the stream-fitting machinery presented in Section 6, with its capability of implementing the forces due to several perturbers at once, should be ideal. The extreme proximity of this extra-galactic system may also be useful for stellar population and chemical analyses.

2. For stream #48 (Orphan-Chenab), we briefly investigate with our dynamical stream-fitting software whether our newly fitted Milky Way mass model affects the conclusion that a massive LMC is needed to reproduce the observed phase-space structure of this stream. While
the best-fit solution has $M_{LMC} = 1.5 \times 10^{11} M_{\odot}$ (consistent with Erkal et al. 2019), we find that our models do not yet give a satisfactory representation of the stream's large-scale morphology, which we suspect is due to an insufficient flexibility of the adopted Milky Way halo density model.

3. Stream #49 is remarkable due to its very large radial action: it is presently arriving from the outer halo and so its high-velocity members place useful constraints on the total mass of the Galaxy. Indeed, the astrometry of one of its bright member stars was very well measured by Gaia (ID 3578950965917470208), and the derived total energy of this star is in tension with the popular MW2014 Galactic potential model (Bovy 2015), unless the system is not bound to the Milky Way, which seems highly unlikely.

4. We revisit stream #53 (GD-1), and show that the line-of-sight velocity distribution is best modeled as a combination of two components, a kinematically cold part with dispersion $7.4 \pm 1.1 \text{ km s}^{-1}$ and a hot component with dispersion $29.1 \pm 6.1 \text{ km s}^{-1}$. Such kinematic structure is consistent with simulations where globular clusters form at random locations within dark matter subhalos and are subsequently accreted onto large galaxies (Carlberg 2020; Carlberg & Agler 2023). We also used the updated catalog to clearly demonstrate the periodicity of the spikes in the number counts along this stream when viewed as a function of physical distance along the structure: such periodicity is highly unlikely to be due to random encounters with dark matter subhalos.

5. Finally, we argue that stream #55 is a tidal feature of ω Cen, the most massive of the Milky Way's globular clusters, and is a broader and significantly closer counterpart to the previously discovered stream #54 (Fimbulthul). This trailing arm structure skirts the southern bulge at a heliocentric distance of ≈3 kpc. It appears to be constituted of stars that were lost to ω Cen between 0.5 and 1 Gyr ago, whereas the stream #54 stars were lost more recently than 0.5 Gyr ago. We suspect that the observed relative densities of streams #54 and #55 could be used in future work to refine the disruption model and so better understand the dynamical history of this unique and important cluster.

## 10.9. Limitations

While we have tried to render the analysis as realistic as possible, there are several limitations to our approach. First of all, our Milky Way model is axisymmetric, which is clearly unrealistic, especially in the inner Galaxy where dynamics are dominated by the bar. Indeed, some of the streams we removed from the sample were rejected precisely because we feared that their small pericenters made them highly susceptible to the bar, and hence, that they would be poorly reproduced with our axisymmetric model. The recent work of Thomas et al. (2023) shows that it is now possible to overcome such limitations, and following their lead, we hope to be able to include non-axisymmetric components in our MCMC exploration in the near future. Similarly, it may be useful to include spiral arms in the modeling, though we suspect their influence will be relatively minor for the halo streams we have considered.

Using a double-power-law mass model with a single shape parameter may also be too limiting, as hinted by the analysis in Section 9.2. It may be necessary to consider a basis function approach (e.g., Petersen et al. 2022) to model the mass distribution in a more realistic manner.

In our future work, we intend to use the algorithms developed here to explore the combined effect of the LMC, the Sagittarius dwarf, and other potential perturbers on the full population of stellar streams.

## 10.10. Concluding Remarks

The upcoming huge WEAVE and 4MOST spectroscopic campaigns that will soon be launched promise an exciting future for this field of study. The present work was based on a relatively small number of velocity-confirmed stream members, and our statistics could easily be improved by an order of magnitude with observations from those spectroscopic surveys. Furthermore, the next Gaia DR4 release will substantially improve the proper motion and parallax accuracy, most probably allowing yet more systems to be detected with our algorithm and tightening the constraints on the known structures.

However, the most exciting use of this data now is to use it to try to shed light on the dark matter, and ascertain whether the observed stream morphology, structure, substructure, and dynamics allow us to prefer one dark matter model over others.

## Acknowledgments

R.I., N.M., D.A., B.F., G.M., R.E., and A.S. acknowledge funding from the Agence Nationale de la Recherche (ANR project ANR-18-CE31-0006, ANR-18-CE31-0017, and ANR-19-CE31-0017), from CNRS/INSU through the Program National Galaxies et Cosmologie, and from the European Research Council (ERC) under the European Unions Horizon 2020 research and innovation program (grant agreement No. 834148). F.R. acknowledges support provided by the University of Strasbourg Institute for Advanced Study (USIAS), within the French national program Investment for the Future (Excellence Initiative) IdEx-Unistra. M.B. acknowledges the financial support to this research by INAF, through the Mini Grant assigned to the project “Chemo-dynamics of the Accreted Halo of the Milky Way (CHAM)” (PI: M. Bellazzini), and by the Italian Ministero dell'Università della Ricerca through the PRIN 2022 Grant 2022LLP8TK_001 “LEGO—Reconstructing the building blocks of the Galaxy by chemical tagging” (PI: A. Mucciarelli). G.T. acknowledges support from Agencia Estatal de Investigación del Ministerio de Ciencia en Innovación (AEI-MICIN) under grant No. PID2020-118778GB-I00/10.13039/501100011033, the MICIN under grant No. FJC2018-037323-I, and the AEI under grant No. CEX2019-000920-S. A.A.A. acknowledges support from the Herchel Smith Fellowship at the University of Cambridge and a Fitzwilliam College research fellowship supported by the Isaac Newton Trust. E.S. acknowledges funding through the VIDI grant “Pushing Galactic Archeology to its limits” (with project number VI.Vidi.193.093), which is funded by the Dutch Research Council (NWO). This research has been partially funded by a Spinoza award by NWO (SPI 78-411). This research was supported by the International Space Science Institute (ISSI) in Bern, through ISSI International Team project 540 (The Early Milky Way).
the best-fit solution has $M_{LMC} = 1.5 \times 10^{11} M_{\odot}$ (consistent with Erkal et al. 2019), we find that our models do not yet give a satisfactory representation of the stream's large-scale morphology, which we suspect is due to an insufficient flexibility of the adopted Milky Way halo density model.

3. Stream #49 is remarkable due to its very large radial action: it is presently arriving from the outer halo and so its high-velocity members place useful constraints on the total mass of the Galaxy. Indeed, the astrometry of one of its bright member stars was very well measured by Gaia (ID 3578950965917470208), and the derived total energy of this star is in tension with the popular MW2014 Galactic potential model (Bovy 2015), unless the system is not bound to the Milky Way, which seems highly unlikely.

4. We revisit stream #53 (GD-1), and show that the line-of-sight velocity distribution is best modeled as a combination of two components, a kinematically cold part with dispersion $7.4 \pm 1.1 \text{ km s}^{-1}$ and a hot component with dispersion $29.1 \pm 6.1 \text{ km s}^{-1}$. Such kinematic structure is consistent with simulations where globular clusters form at random locations within dark matter subhalos and are subsequently accreted onto large galaxies (Carlberg 2020; Carlberg & Agler 2023). We also used the updated catalog to clearly demonstrate the periodicity of the spikes in the number counts along this stream when viewed as a function of physical distance along the structure: such periodicity is highly unlikely to be due to random encounters with dark matter subhalos.

5. Finally, we argue that stream #55 is a tidal feature of ω Cen, the most massive of the Milky Way's globular clusters, and is a broader and significantly closer counterpart to the previously discovered stream #54 (Fimbulthul). This trailing arm structure skirts the southern bulge at a heliocentric distance of ≈3 kpc. It appears to be constituted of stars that were lost to ω Cen between 0.5 and 1 Gyr ago, whereas the stream #54 stars were lost more recently than 0.5 Gyr ago. We suspect that the observed relative densities of streams #54 and #55 could be used in future work to refine the disruption model and so better understand the dynamical history of this unique and important cluster.

## 10.9. Limitations

While we have tried to render the analysis as realistic as possible, there are several limitations to our approach. First of all, our Milky Way model is axisymmetric, which is clearly unrealistic, especially in the inner Galaxy where dynamics are dominated by the bar. Indeed, some of the streams we removed from the sample were rejected precisely because we feared that their small pericenters made them highly susceptible to the bar, and hence, that they would be poorly reproduced with our axisymmetric model. The recent work of Thomas et al. (2023) shows that it is now possible to overcome such limitations, and following their lead, we hope to be able to include non-axisymmetric components in our MCMC exploration in the near future. Similarly, it may be useful to include spiral arms in the modeling, though we suspect their influence will be relatively minor for the halo streams we have considered.

Using a double-power-law mass model with a single shape parameter may also be too limiting, as hinted by the analysis in Section 9.2. It may be necessary to consider a basis function approach (e.g., Petersen et al. 2022) to model the mass distribution in a more realistic manner.

In our future work, we intend to use the algorithms developed here to explore the combined effect of the LMC, the Sagittarius dwarf, and other potential perturbers on the full population of stellar streams.

## 10.10. Concluding Remarks

The upcoming huge WEAVE and 4MOST spectroscopic campaigns that will soon be launched promise an exciting future for this field of study. The present work was based on a relatively small number of velocity-confirmed stream members, and our statistics could easily be improved by an order of magnitude with observations from those spectroscopic surveys. Furthermore, the next Gaia DR4 release will substantially improve the proper motion and parallax accuracy, most probably allowing yet more systems to be detected with our algorithm and tightening the constraints on the known structures.

However, the most exciting use of this data now is to use it to try to shed light on the dark matter, and ascertain whether the observed stream morphology, structure, substructure, and dynamics allow us to prefer one dark matter model over others.

## Acknowledgments

R.I., N.M., D.A., B.F., G.M., R.E., and A.S. acknowledge funding from the Agence Nationale de la Recherche (ANR project ANR-18-CE31-0006, ANR-18-CE31-0017, and ANR-19-CE31-0017), from CNRS/INSU through the Program National Galaxies et Cosmologie, and from the European Research Council (ERC) under the European Unions Horizon 2020 research and innovation program (grant agreement No. 834148). F.R. acknowledges support provided by the University of Strasbourg Institute for Advanced Study (USIAS), within the French national program Investment for the Future (Excellence Initiative) IdEx-Unistra. M.B. acknowledges the financial support to this research by INAF, through the Mini Grant assigned to the project “Chemo-dynamics of the Accreted Halo of the Milky Way (CHAM)” (PI: M. Bellazzini), and by the Italian Ministero dell'Università della Ricerca through the PRIN 2022 Grant 2022LLP8TK_001 “LEGO—Reconstructing the building blocks of the Galaxy by chemical tagging” (PI: A. Mucciarelli). G.T. acknowledges support from Agencia Estatal de Investigación del Ministerio de Ciencia en Innovación (AEI-MICIN) under grant No. PID2020-118778GB-I00/10.13039/501100011033, the MICIN under grant No. FJC2018-037323-I, and the AEI under grant No. CEX2019-000920-S. A.A.A. acknowledges support from the Herchel Smith Fellowship at the University of Cambridge and a Fitzwilliam College research fellowship supported by the Isaac Newton Trust. E.S. acknowledges funding through the VIDI grant “Pushing Galactic Archeology to its limits” (with project number VI.Vidi.193.093), which is funded by the Dutch Research Council (NWO). This research has been partially funded by a Spinoza award by NWO (SPI 78-411). This research was supported by the International Space Science Institute (ISSI) in Bern, through ISSI International Team project 540 (The Early Milky Way).
We gratefully acknowledge the High Performance Computing Center of the Université de Strasbourg for the very generous time allocation and for its support of the development of this project.

We wish to thank Pablo Galán, Rosa Hoogenboom, Sara Vitali, Clár-Bríd Tohill, Sara Vitali, and Paige Yarker for their invaluable help in supporting the INT observations reported here.

This work has made use of data from the European Space Agency (ESA) mission Gaia,<fnref n="24" /> processed by the Gaia Data Processing and Analysis Consortium (DPAC).<fnref n="25" /> Funding for the DPAC has been provided by national institutions, in particular, the institutions participating in the Gaia Multilateral Agreement.

This work is based on observations collected at the European Southern Observatory under ESO programs 105.20AL.001, 110.246A.001, and 111.2517.001.

Funding for SDSS-III<fnref n="26" /> has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation, and the US Department of Energy Office of Science.

SDSS-III is managed by the Astrophysical Research Consortium for the Participating Institutions of the SDSS-III Collaboration including the University of Arizona, the Brazilian Participation Group, Brookhaven National Laboratory, Carnegie Mellon University, University of Florida, the French Participation Group, the German Participation Group, Harvard University, the Instituto de Astrofísica de Canarias, the Michigan State/Notre Dame/JINA Participation Group, Johns Hopkins University, Lawrence Berkeley National Laboratory, Max Planck Institute for Astrophysics, Max Planck Institute for Extraterrestrial Physics, New Mexico State University, New York University, Ohio State University, Pennsylvania State University, University of Portsmouth, Princeton University, the Spanish Participation Group, University of Tokyo, University of Utah, Vanderbilt University, University of Virginia, University of Washington, and Yale University.

Guoshoujing Telescope (the Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST)) is a major national scientific project built by the Chinese Academy of Sciences. Funding for the project has been provided by the National Development and Reform Commission. LAMOST is operated and managed by the National Astronomical Observatories, Chinese Academy of Sciences.

Software: Python corner (Foreman-Mackey 2016), STREAMFINDER (Malhan & Ibata 2018), Armadillo (Sanderson & Curtin 2016), IRAF (Tody 1986, 1993), Gal-Pot (Dehnen & Binney 1998).

## Data Availability

The sample of stream stars will be available online at the VizieR service.<fnref n="27" />

## ORCID iDs

Rodrigo Ibata https://orcid.org/0000-0002-3292-9709

Khyati Malhan https://orcid.org/0000-0002-8318-433X

Wassim Tenachi https://orcid.org/0000-0001-8392-3836

Anke Ardern-Arentsen https://orcid.org/0000-0002-0544-2217

Michele Bellazzini https://orcid.org/0000-0001-8200-810X

Paolo Bianchini https://orcid.org/0000-0002-0358-4502

Piercarlo Bonifacio https://orcid.org/0000-0002-1014-0635

Elisabetta Caffau https://orcid.org/0000-0001-6011-6134

Benoit Famaey https://orcid.org/0000-0003-3180-9825

Salvatore Ferrone https://orcid.org/0000-0003-1623-6643

Nicolas F. Martin https://orcid.org/0000-0002-1349-202X

Florent Renaud https://orcid.org/0000-0001-5073-2267

Guillaume Thomas https://orcid.org/0000-0002-2468-5521

Zhen Yuan https://orcid.org/0000-0002-8129-5415

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Baumgardt, H., & Vasiliev, E. 2021, MNRAS, 505, 5957

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Bianchini, P., Sills, A., van de Ven, G., & Sippel, A. C. 2017, MNRAS, 469, 4359

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Bovy, J., & Rix, H.-W. 2013, ApJ, 779, 115

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Buder, S., Asplund, M., Duong, L., et al. 2018, MNRAS, 478, 4513

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Dehnen, W., & Binney, J. 1998, MNRAS, 294, 429

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Errani, R., & Navarro, J. F. 2021, MNRAS, 505, 18

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Ferrone, S., Di Matteo, P., Mastrobuono-Battisti, A., et al. 2023, A&A, 673, A44

Foreman-Mackey, D. 2016, JOSS, 1, 24

Fukushige, T., & Heggie, D. C. 2000, MNRAS, 318, 753

Gaia Collaboration, Helmi, A., van Leeuwen, F., et al. 2018, A&A, 616, A12

Gaia Collaboration, Prusti, T., de Bruijne, J. H. J., et al. 2016, A&A, 595, A1

Gaia Collaboration, Vallenari, A., Brown, A. G. A., et al. 2023, A&A, 674, A1

Goodman, J., & Weare, J. 2010, CAMCS, 5, 65

GRAVITY Collaboration, Abuter, R., Amorim, A., et al. 2019, A&A, 625, L10

Grillmair, C. J. 2017, ApJ, 847, 119

Grillmair, C. J., & Dionatos, O. 2006, ApJL, 643, L17

Hammer, F., Puech, M., Chemin, L., Flores, H., & Lehnert, M. D. 2007, ApJ, 662, 322

Harris, W. E. 2010, arXiv:1012.3224

Helmi, A. 2004, ApJL, 610, L97

<footnote n="24">²⁴ https://www.cosmos.esa.int/gaia</footnote>

<footnote n="25">²⁵ https://www.cosmos.esa.int/web/gaia/dpac/consortium</footnote>

<footnote n="26">²⁶ http://www.sdss3.org/</footnote>

<footnote n="27">²⁷ https://vizier.unistra.fr</footnote>
We gratefully acknowledge the High Performance Computing Center of the Université de Strasbourg for the very generous time allocation and for its support of the development of this project.

We wish to thank Pablo Galán, Rosa Hoogenboom, Sara Vitali, Clár-Bríd Tohill, Sara Vitali, and Paige Yarker for their invaluable help in supporting the INT observations reported here.

This work has made use of data from the European Space Agency (ESA) mission Gaia,<fnref n="24" /> processed by the Gaia Data Processing and Analysis Consortium (DPAC).<fnref n="25" /> Funding for the DPAC has been provided by national institutions, in particular, the institutions participating in the Gaia Multilateral Agreement.

This work is based on observations collected at the European Southern Observatory under ESO programs 105.20AL.001, 110.246A.001, and 111.2517.001.

Funding for SDSS-III<fnref n="26" /> has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation, and the US Department of Energy Office of Science.

SDSS-III is managed by the Astrophysical Research Consortium for the Participating Institutions of the SDSS-III Collaboration including the University of Arizona, the Brazilian Participation Group, Brookhaven National Laboratory, Carnegie Mellon University, University of Florida, the French Participation Group, the German Participation Group, Harvard University, the Instituto de Astrofísica de Canarias, the Michigan State/Notre Dame/JINA Participation Group, Johns Hopkins University, Lawrence Berkeley National Laboratory, Max Planck Institute for Astrophysics, Max Planck Institute for Extraterrestrial Physics, New Mexico State University, New York University, Ohio State University, Pennsylvania State University, University of Portsmouth, Princeton University, the Spanish Participation Group, University of Tokyo, University of Utah, Vanderbilt University, University of Virginia, University of Washington, and Yale University.

Guoshoujing Telescope (the Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST)) is a major national scientific project built by the Chinese Academy of Sciences. Funding for the project has been provided by the National Development and Reform Commission. LAMOST is operated and managed by the National Astronomical Observatories, Chinese Academy of Sciences.

Software: Python corner (Foreman-Mackey 2016), STREAMFINDER (Malhan & Ibata 2018), Armadillo (Sanderson & Curtin 2016), IRAF (Tody 1986, 1993), Gal-Pot (Dehnen & Binney 1998).

## Data Availability

The sample of stream stars will be available online at the VizieR service.<fnref n="27" />

## ORCID iDs

Rodrigo Ibata https://orcid.org/0000-0002-3292-9709

Khyati Malhan https://orcid.org/0000-0002-8318-433X

Wassim Tenachi https://orcid.org/0000-0001-8392-3836

Anke Ardern-Arentsen https://orcid.org/0000-0002-0544-2217

Michele Bellazzini https://orcid.org/0000-0001-8200-810X

Paolo Bianchini https://orcid.org/0000-0002-0358-4502

Piercarlo Bonifacio https://orcid.org/0000-0002-1014-0635

Elisabetta Caffau https://orcid.org/0000-0001-6011-6134

Benoit Famaey https://orcid.org/0000-0003-3180-9825

Salvatore Ferrone https://orcid.org/0000-0003-1623-6643

Nicolas F. Martin https://orcid.org/0000-0002-1349-202X

Florent Renaud https://orcid.org/0000-0001-5073-2267

Guillaume Thomas https://orcid.org/0000-0002-2468-5521

Zhen Yuan https://orcid.org/0000-0002-8129-5415

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Avila-Reese, V., Firmani, C., Klypin, A., & Kravtsov, A. V. 1999, MNRAS, 310, 527

Baumgardt, H., & Hilker, M. 2018, MNRAS, 478, 1520

Baumgardt, H., & Vasiliev, E. 2021, MNRAS, 505, 5957

Beasley, M. A., Leaman, R., Gallart, C., et al. 2019, MNRAS, 487, 1986

Bekki, K., & Freeman, K. C. 2003, MNRAS, 346, L11

Bell, E. F., McIntosh, D. H., Katz, N., & Weinberg, M. D. 2003, ApJS, 149, 289

Belokurov, V., Evans, N. W., Irwin, M. J., et al. 2007, ApJ, 658, 337

Bianchini, P., Sills, A., van de Ven, G., & Sippel, A. C. 2017, MNRAS, 469, 4359

Bianchini, P., Varri, A. L., Bertin, G., & Zocchi, A. 2013, ApJ, 772, 67

Binney, J., & Tremaine, S. 2008, Galactic Dynamics (2nd ed.; Princeton, NJ: Princeton Univ. Press)

Bland-Hawthorn, J., & Gerhard, O. 2016, ARA&A, 54, 529

Bovy, J. 2015, ApJS, 216, 29

Bovy, J., & Rix, H.-W. 2013, ApJ, 779, 115

Bressan, A., Marigo, P., Girardi, L., et al. 2012, MNRAS, 427, 127

Buder, S., Asplund, M., Duong, L., et al. 2018, MNRAS, 478, 4513

Caldwell, N., Bonaca, A., Price-Whelan, A. M., Sesar, B., & Walker, M. G. 2020, AJ, 159, 287

Carlberg, R. G. 2012, ApJ, 748, 20

Carlberg, R. G. 2020, ApJ, 889, 107

Carlberg, R. G., & Agler, H. 2023, ApJ, 953, 99

Cerny, W., Martínez-Vázquez, C. E., Drlica-Wagner, A., et al. 2023, ApJ, 953, 1

Clementini, G., Ripepi, V., Garofalo, A., et al. 2023, A&A, 674, A18

Cole, D. R., & Binney, J. 2017, MNRAS, 465, 798

Combes, F., Leon, S., & Meylan, G. 1999, A&A, 352, 149

Correa Magnus, L., & Vasiliev, E. 2022, MNRAS, 511, 2610

Cui, X.-Q., Zhao, Y.-H., Chu, Y.-Q., et al. 2012, RAA, 12, 1197

Dehnen, W. 2002, JCoPh, 179, 27

Dehnen, W., & Binney, J. 1998, MNRAS, 294, 429

Dodd, E., Callingham, T. M., Helmi, A., et al. 2023, A&A, 670, L2

Dodd, E., Helmi, A., & Koppelman, H. H. 2022, A&A, 659, A61

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Drimmel, R., & Spergel, D. N. 2001, ApJ, 556, 181

Eilers, A.-C., Hogg, D. W., Rix, H.-W., & Ness, M. K. 2019, ApJ, 871, 120

Erkal, D., Belokurov, V., Laporte, C. F. P., et al. 2019, MNRAS, 487, 2685

Errani, R., & Navarro, J. F. 2021, MNRAS, 505, 18

Errani, R., Navarro, J. F., Smith, S. E. T., & McConnachie, A. W. 2024, ApJ, 965, 20

Ferrone, S., Di Matteo, P., Mastrobuono-Battisti, A., et al. 2023, A&A, 673, A44

Foreman-Mackey, D. 2016, JOSS, 1, 24

Fukushige, T., & Heggie, D. C. 2000, MNRAS, 318, 753

Gaia Collaboration, Helmi, A., van Leeuwen, F., et al. 2018, A&A, 616, A12

Gaia Collaboration, Prusti, T., de Bruijne, J. H. J., et al. 2016, A&A, 595, A1

Gaia Collaboration, Vallenari, A., Brown, A. G. A., et al. 2023, A&A, 674, A1

Goodman, J., & Weare, J. 2010, CAMCS, 5, 65

GRAVITY Collaboration, Abuter, R., Amorim, A., et al. 2019, A&A, 625, L10

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Harris, W. E. 2010, arXiv:1012.3224

Helmi, A. 2004, ApJL, 610, L97

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<footnote n="26">²⁶ http://www.sdss3.org/</footnote>

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