Revisit NGC 5466 Tidal Stream with $Gaia$, SDSS/SEGUE and LAMOST

Although we have retrieved the stars inside a rectangle corresponding to the known extent of the stream, there are still too many field stars that need to be cleaned up. We achieve this by fitting the track of the stream with a second-order polynomial and retaining the stars in the region created by moving the polynomial, which is given by equation (1), up and down by $1.5\degr$ along the $\delta$ direction. It can be seen in Fig. 1 that the the stream trajectory is well enclosed, including the “deviation” part at $\alpha\simeq 185\degr$. Through this selection, 3,130 stars inside the region are left.

We then select candidates of member stars in color-magnitude diagram (CMD), as illustrated in Fig. 2. All sources here have been extinction-corrected using the Schlegel et al. (1998) maps as re-calibrated by Schlafly & Finkbeiner (2011) with RV = 3.1, assuming $A_{G}/A_{V}=0.83627$, $A_{BP}/A_{V}=1.08337$, $A_{RP}/A_{V}=0.63439$²²2These extinction ratios are listed on the Padova model site http://stev.oapd.inaf.it/cgi-bin/cmd. The grey dots represent the stars that pass the first selection. The blue dots are those stars within the tidal radius of NGC 5466 $r_{t}=15.68^{\prime}$ (computed from Harris, 1996, 2010 edition). We use them as the “isochrone” of the globular cluster. Considering a possible wide range of distances traced by the stream, we shift the “isochrone” up/down by 1.02 / 0.69 mag, corresponding to moving the cluster to a heliocentric distance of 10 / 22 kpc, which is also the extent inspected by Jensen et al. (2021). We pick out the stars within the area swept by the “isochrone” and show them with the red dots in Fig. 2. This selection yields 1,960 stars.

Given that NGC 5466 has a [Fe/H] of -1.98 dex (Harris, 1996, 2010 edition), we apply a conservative metallicity cut of -2.5 dex < [Fe/H] < -1.5 dex to the remaining candidates, among which there is a maximum of [Fe/H] uncertainty of 0.5 dex. Through this cut, 570 stars are remained.

Fitting the radial velocity distribution to single out the stream stars has been used in previous studies (e.g., Koposov et al., 2010). Here we mainly refer to the Bayesian method in Huang et al. (2019).

We firstly divide the stars in $\alpha-V_{r}$ plane into six regions, as shown in Fig. 3. These divisions are just based on the visual differences in number density of the stars: higher density for A, D and F, lower density for B and E, and moderate density for region C. Unlike Huang et al. (2019), we directly use the heliocentric radial velocities instead of converting them to the Galactic frame. For each region, it is assumed that the velocity distribution can be described as a combination of two Gaussians, one for the stream stars and the other for the Milky Way field stars. The component of stream stars has a mean $V_{r}^{st}$, a dispersion $\sigma_{V_{r}}^{st}$ and a fraction $f^{st}$, while the component of field stars has a mean $V_{r}^{mw}$ and a dispersion $\sigma_{V_{r}}^{mw}$. With the model parameters $\Theta=\{f^{st},V_{r}^{st},\sigma_{V_{r}}^{st},V_{r}^{mw},\sigma_{V_{r}}^{mw}\}$, the likelihood of observing a star with a radial velocity of $V_{r}^{i}$ is given by

where $\mathcal{N}(x|\mu,\sigma)$ denotes a Gaussian function:

By multiplying the likelihood of each star in a certain region, we can obtain the total likelihood of this region $\mathcal{L}(V_{r}|\Theta)$. The posterior distribution is given by

where $\mathcal{I}(\Theta)$ represents the priors of the model parameters. A uniform distribution is adopted for the priors of all parameters of each region and details of them are listed in Table 1.

In order to obtain marginalized posterior distributions of the model parameters, we run the Markov chain Monte Carlo (MCMC) code (Foreman-Mackey et al., 2013) for each region. As an example, Fig. 4 shows the resulting distributions for region D, where the three vertical dashed lines indicate the 16th, 50th and 84th percentiles of the posteriors. The medians of all posteriors are summarized in Table 2.

For region A, B and C, a general prior [0, 150] km s^-1 is adopted for $V_{r}^{st}$ and a monotonous trend that $V_{r}^{st}$ increases when $\alpha$ decreases is obtained after running MCMC. The other priors of $V_{r}^{st}$ especially for region F are aimed to ensure this trend, which is crucial for estimating stream’s parameters. Generally, the radial velocities of a halo stream are supposed to change monotonically along coordinates as long as there is no turning point contained (like apogalacticon), such as Pal 5 (Ishigaki et al., 2016), GD-1 (Bovy et al., 2016), Hríd and Gjöll stream (Ibata et al., 2021). Therefore, an assumption of a monotonous trend in $\alpha-V_{r}$ plane might be more reasonable for NGC 5466 stream than a non-monotonic one and it is also supported by the later model of the cluster’s disruption (see Section 4).

In Fig. 3, we show the trends of $V_{r}^{st}$ and $V_{r}^{mw}$ with the solid and dashed lines based on the results from Table 2. We note that region E has an incompatible $V_{r}^{st}$ = 101.38 km s^-1 which should be between that of region D and F [124.26, 145.18] km s^-1, given the trend assumption above. Furthermore, there are no stars at all in region E located within this $V_{r}^{st}$ range according to Fig. 3. Hence, we consider that no stream members in this region are detected in our samples and the corresponding parameters derived from MCMC do not represent real situation of the stream. Instead, we fit them with one Gaussian giving a mean $V_{r}^{mw}$of -72.85 km s^-1 and a dispersion $\sigma_{V_{r}}^{mw}$ of 109.63 km s^-1.

To validate the derived parameters, synthetic stellar population similar to the data are generated using the Besançon model³³3https://model.obs-besancon.fr (Robin et al., 2003) and fitted with a Gaussian function as well. Comparisons between observed and synthetic data are shown in Fig. 5, in which the distributions of field stars are generally consistent with the simulated ones.

With the model parameters in Table 2, we further select the member stars whose radial velocities satisfy $|V_{r}-V_{r}^{st}|<3\sigma_{V_{r}}^{st}$, with which 89 stars are retained.

As a stellar stream tidally disrupted from NGC 5466, it is expected to show a coherent sequence both in space and kinematics. The rest of contaminators are further rejected based on this, which is illustrated in Fig. 6. The member stars (green) found by Jensen et al. (2021) are employed as an indicator of the stream sequence in {$\alpha$, $\delta$} vs. {$\mu_{\alpha}^{*}$, $\mu_{\delta}$} planes. The outliers (gray) that deviate from the stream sequence are removed. Those stars (red) consistent with the sequence are retained and proceed to be investigated in the next plane. This means that the red plus gray points in plane $N$ come from the red points in plane $N$-1. $V_{r}$ is further used to exclude contaminators. In such a step-by-step manner, 19 highly probable member stars of NGC 5466 are finally obtained, 9 out of which are outside the tidal radius $r_{t}$.

A smooth Galactic potential model is firstly examined, where “smooth” means that the sub-halo is not considered. The model consists of a Plummer bulge (Plummer, 1911), $\Phi_{\rm bulge}$, two Miyamoto-Nagai disks (Miyamoto & Nagai, 1975), $\Phi_{\rm thin}$ and $\Phi_{\rm thick}$, and a spherical NFW halo (Navarro et al., 1996), $\Phi_{\rm halo}$:

where $r$ is the Galactocentric radius, $R$ is the cylindrical radius and $z$ is the vertical height. For the bulge and disks, we adopt the parameters from Pouliasis et al. (2017, Model I). The virial mass $M_{\rm virial}$ and concentration $c$ used to initialize the NFW halo are from McMillan (2017). Those chosen parameters are summarized in Table 3.

As for the internal gravity of the globular cluster NGC 5466, we choose a Plummer potential:

with a $M_{\rm GC}$ of $6\times 10^{4}M_{\sun}$ (Sollima & Baumgardt, 2017) and a $b_{\rm GC}$ of 6.7 pc computed from the core radius of the cluster (Harris, 1996, 2010 edition). Here $r^{\prime}$ denotes the distance to the cluster’s center.

The solar distance to the Galactic center, circular velocity at the Sun and solar velocities relative to the Local Standard of Rest are set to 8 kpc, 220 km s^-1 (Bovy et al., 2012) and (11.1, 12.24, 7.25) km s^-1 (Schönrich et al., 2010), respectively. To generate long enough tidal tails which can completely cover the data, the cluster is initialized 5 Gyr ago and integrated forward from then on, releasing two particles (leading and trailing directions respectively) at Lagrange points (Gibbons et al., 2014) per 1 Myr with a total of 5000 steps. The velocity dispersion is set to 1.6 km s^-1 (Baumgardt & Hilker, 2018) and the cluster mass is fixed during this process. By doing so, a mock NGC 5466 stream is obtained and we then compare it to observed data in phase-space.

In the left panel of Fig. 7, the mock stream, the member stars found by the above selections and Jensen et al. (2021), are shown in the orange dots, red squares and green points, respectively. The black crosses represent two contaminators that are further discerned given their heliocentric distance and metallicity (see Table 4). Additional members marked with the red diamonds are further selected based on the mock stream which will be described in Section 4.2. Those 10 stars inside the tidal radius $r_{t}=15.68^{\prime}$, which are still bound to the cluster, are not shown here. The NGC 5466 cluster is still marked in a blue triangle. The distances can be obtained from Anders et al. (2019) except for the star at $\alpha\simeq 184.40\degr$ (we call it “S1” for convenience). We estimate a distance to S1 of $17.37^{+5.74}_{-3.45}$ kpc using the method from Carlin et al. (2015), which is a Bayesian approach with likelihood estimated via comparison of spectroscopically derived atmospheric parameters to a grid of stellar isochrones, and returns a posterior probability density function for star’s absolute magnitude.

From Fig. 7, our model stream is very similar to that of Fellhauer et al. (2007). At the leading end, the tail is also spread out wider than the part close to the cluster, which is due to approaching the apogalacticon as mentioned in Fellhauer et al. (2007). It can be seen that the mock stream has a trend in phase-space generally in agreement with that of the data within uncertainties. What’s more, S1 has a declination that the mock stream can not reach, implying it might be an outlier as well. However, S1 is exactly located at the “deviation” area mentioned by Grillmair & Johnson (2006), who argued that it might be caused by irregularities of the Galactic halo potential. Therefore, a smooth potential is not enough to reproduce this “deviation” and taking into account sub-halo component might be necessary.

El-Falou & Webb (2022) has discussed the effects of dwarf galaxies on the tidal tails of Globular Clusters. They claimed that NGC 5466 stream could be perturbed due to one or more close interactions with the Large Magellanic Cloud (LMC). Motivated by this, we examine the smooth Galactic potential with an addition of LMC. This is also done through Gala.

Following El-Falou & Webb (2022), we take a Hernquist Potential (Hernquist, 1990) as the internal potential of LMC:

where $r^{\prime}$ is the distance to the LMC center and $M_{\rm LMC}$ and $a_{\rm LMC}$ are set to $10^{11}M_{\sun}$ and 10.2 kpc as well. The position and velocity of LMC are taken from Gaia Collaboration et al. (2018). In the smooth potential of Section 4.1 accompanied with a moving LMC, the cluster is initialized 5 Gyr ago and then integrated forward from then on. The mock stream under this condition is displayed in the right panel of Fig. 7.

As is shown, adding LMC makes the new mock stream more diffuse and a little different from the old one, especially for the end at $\alpha\sim 180\degr$. Unlike the old mock stream that bends down at the end, the counterpart of the new stream is upturned instead, reaching where S1 is. Having also examined other sub-halos such as the Small Magellanic Cloud, Draco, Ursa Minor, Fornax and Sagittarius, it is only adding LMC, the most massive satellite, that can generate a mock stream in concordance with the observation. Hence the “deviation” of NGC 5466 tidal stream is possibly due to the effect from LMC.

We also estimate the pericentre ($R_{per}$), apocentre ($R_{apo}$) and eccentricity ($e$) of NGC 5466 cluster under both conditions. For the smooth potential, $R_{per}=6.52$ kpc, $R_{apo}=41.52$ kpc and $e=0.73$ are very close to those estimated in Jensen et al. (2021). For the LMC-added potential, $R_{per}=4.30$ kpc, $R_{apo}=53.34$ kpc and $e=0.85$ show a more elliptical orbit. We also note that the minimum separation of the cluster and LMC in the past 5 Gyr is about 22 kpc and happened 138 Myr ago, which agrees closely with that of El-Falou & Webb (2022). Such a close interaction also implies that the stream might have been perturbed by LMC.

It is worth nothing that the mock stream has a longer trailing tail than the leading tail, which implies that there might be more member stars on trailing side. Moreover, the stream’s track with $\alpha\ga 230\degr$ has been beyond the sky coverage of data used in both of Grillmair & Johnson (2006) and Jensen et al. (2021). Therefore, we investigate this possibility using the mock stream considering its good consistency with observation. We directly restrict the data according to the mock stream’s trends in phase-space. The data with $180\degr<\alpha<260\degr$⁴⁴4There are no more spectroscopic data overlapping with the stream on the sky when $\alpha$ goes $>260\degr$. overlapping with the mock stream on the sky are retrieved and processed with CMD and metallicity cuts similar to those of Section 3. The remained stars are then selected in the plane of {$\alpha$, $\delta$} vs. {$\mu_{\alpha}^{*}$, $\mu_{\delta}$, $V_{r}$}, similar to the procedure of Fig. 6 but with the mock stream as the indicator. In this way, all members that have been selected in Section 3 can be reproduced and 4 more stars are identified as shown with the red diamonds in Fig. 7. Among those 4 members, one is a blue horizontal branch (BHB) star whose distance can be obtained from Xue et al. (2011) and Mints & Hekker (2017), and one is at $\alpha\simeq 242.65\degr$ (“S2” hereafter) whose distance is obtained using $Gaia$ parallax = 0.0777 mas with a small relative error = 0.1868 < 20%, and the distances of the other two stars still come from Anders et al. (2019). Clearly, while eliminating the field stars, constraining sky position of the data with a narrow area created by the polynomial in Section 3.1 also excludes some stream stars.

We also note that among 9 candidate members outside the tidal radius $r_{t}$ obtained in Section 3, 2 stars are contaminators which have an inconsistent distance or metallicity and 4 stars have been identified in Jensen et al. (2021). Together with 4 additional members, the detailed information of 13 stars are summarized in Table 4.

Consistent trends in phase-space between the model stream and our members have been shown in Fig. 7 and a metallicity of [Fe/H] = -1.98 dex of the cluster is also in concordance with [Fe/H] of stars in Table 4. Another inspection may be about stellar age which can be reflected by the $Gaia$ photometry. Fig. 8 shows the color - absolute magnitude diagram of the cluster and our stars, where the error bars account for uncertainties in $M_{G}$ due to the distance errors. All member stars including S1 (darkest) and S2 (brightest) lie in the cluster’s isochrone well within uncertainties.