PROPER MOTIONS IN TERZAN 5: MEMBERSHIP OF THE MULTI-IRON SUBPOPULATIONS AND FIRST CONSTRAINT ON THE ORBIT^*

We converted the PMs into units of mas yr⁻¹ by multiplying the measured displacements by the pixel scale of the master frame ($0\buildrel{\prime\prime}\over{.} 05$ pixel⁻¹). Since the master frame has been oriented according to the equatorial coordinate system, the X PM component corresponds to that projected along the (negative) R.A. (−μ_α cosδ), and the Y PM component corresponds to that along the decl. (μ_δ). The output of this analysis is summarized in Figure 3, where we show the vector point diagram (VPD) for all of the stars of the final PM catalog. The first clear feature is that more than 70% of the stars are distributed within the innermost 1.5 mas yr⁻¹ from the origin of the VPD (see histograms in Figure 3). The remaining fraction of stars describes a sparser and asymmetric distribution out to about 10 mas yr⁻¹. In order to highlight these features, we selected only stars with m_F606W < 24, which typically have the most accurate PMs, and plotted them as red points in Figure 3. Their distribution in the VPD clearly shows at least two components. One is a symmetric distribution centered around the origin, with PM weighted mean values ${\mu }_{\alpha }\mathrm{cos}\delta =0.02\pm 0.02$ mas yr⁻¹ and μ_δ = −0.01± 0.02 mas yr⁻¹. The other is an asymmetric structure approximately centered around the coordinate (μ_α cos δ ∼ −1.8, μ_δ ∼ −3.5) mas yr⁻¹ in the VPD. The locations of these two components in the CMD clearly reveal their nature (see Figure 4). In fact, the stars of the first component (shown as blue dots in the VPD) describe the cluster evolutionary sequences in the CMD (central lower panel), with a small degree of contamination left. In contrast, the stars belonging to the asymmetric component (red dots) correspond to the blue plume in the CMD (lower right panel), which is essentially populated by young disk stars in the foreground of Terzan 5. This is further confirmed by the comparison with the prediction of the Besançon model (Robin et al. 2003) with only young (t_age < 7 Gyr) Galactic disk stars for a field centered at the coordinates of Terzan 5 and covering the same FOV as that of the ACS/WFC (see Figure 5).

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Many systematic uncertainties may affect the measurement of relative PMs (see Bellini et al. 2014 for a detailed description). It is therefore important to check that the measured PMs of our final catalog do not suffer from such systematic effects. Since we have only two epochs of observations and a relatively small number of images per epoch (only two long exposures were acquired in the first epoch), full control of all of the possible systematics is not achievable. Nonetheless, we have carefully checked for the presence of any systematics that our data sets allow us to verify.

First of all, we looked for any possible chromatic-induced systematics by checking that no trend between PMs and color exists for our sample. Figure 6 shows the results of this test. By selecting stars in a wide magnitude range (23 < m_F606W < 26), we computed the 3σ clipped average value of our PMs (for both the spatial components) in color bins of 0.04 mag (red filled circles). The error bars are within the size of the symbols. Clearly, these values describe a flat relation (shown as a red dashed line). The best least-squares linear fit to these data gives a null angular coefficient within the uncertainty for both of the PM components. Thus, we can safely conclude that no trend with color exists for our measurements.

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We repeated a similar test looking for possible trends with the observed magnitude in the range 19 < m_F606W < 26 in order to exclude extremely faint sources that have intrinsically larger PM errors. Figure 7 shows the result of this test. Also in this case, the best linear fit to the 3σ clipped average PM values computed in bins of 0.3 mag is compatible (within the errors) with a null angular coefficient line, thus demonstrating that no significant trend is found with magnitude either.

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Finally, we also carefully checked the existence of spurious trends with the location of stars on the detector. To do so, we followed the method described in Bellini et al. (2014), by plotting maps of the measured PMs as a function of the position on the sky, where to each star we associated the average motion of the closest 100 neighbors. Overall we found a homogeneous distribution in both of the PM components.

The tests discussed above demonstrate that the derived PMs do not suffer from significant systematic effects. Also, the use of available CTE-corrected images for both epochs (see Section 3) should have minimized the effect of CTE losses on the PM estimate. While we cannot exclude that other systematics can affect our measurements, we can firmly conclude that these are the best PMs we can measure with the available data set.

The two major subpopulations in Terzan 5 were identified in the ($K,J-K$) CMD by Ferraro et al. (2009). Their radial distributions are incompatible with that expected for background field stars, and the measured line-of-sight velocities are consistent with the systemic radial velocity of Terzan 5. However, the membership of the two populations has been questioned (see, e.g., Willman & Strader 2012). To address this concern and to assess their cluster membership from PMs, we cross-correlated the Multi-conjugate Adaptive optics Demonstrator (MAD) catalog with the PM catalog. The result is summarized in Figure 9. The left panel shows the IR CMD of Terzan 5 after the PM-based membership selection (black dots). The sources recognized as contaminating field stars based on the value of their PMs are also plotted in red. The decontaminated CMD clearly exhibits the two red clumps (RCs) originally discovered by Ferraro et al. (2009).

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Figure 10 highlights the CMD and VPDs for subsamples of stars properly selected in the two RCs. As can be seen, the two PM distributions appear quite symmetric, both showing a small (0.5 mas yr⁻¹) dispersion around the origin. Although these PMs cannot be used to reveal possible intrinsic kinematical differences between the two populations, we can solidly conclude that these stars are all members of Terzan 5.

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Overall, the number of contaminants in the IR CMD (selected as stars outside a distance of 1.5 mas yr⁻¹ from the center of the VPD) is much smaller than what is observed in the optical plane. This is because the MAD photometry corresponds to a smaller FOV (with respect to the ACS one) and to the very central region of the system, where the cluster population is expected to dominate. It is also worth noticing that both of the RC subsamples are much more centrally concentrated than the likely Galactic field contaminants selected at the same magnitude level (see the red, blue, and gray lines, respectively, in Figure 10). According to a Kolmogorov–Smirnov test performed on the three samples, the probability of PM-rejected stars having been extracted from one of the two RC populations is always smaller than 10⁻⁴. This further confirms that stars rejected according to our PM-membership selection are field objects, homogeneously distributed in the sampled FOV.

In conclusion, the relative PMs measured in this work and applied to the MAD CMD definitely demonstrate that the two major subpopulations photometrically discovered in Terzan 5 are both members of the system.

In Massari et al. (2014b) we presented the distribution of the iron abundance for the largest sample of stars in Terzan 5. In that work, target membership was inferred from radial velocities, and the fraction of contaminating stars was estimated statistically from the chemical and kinematical characterization of the field surrounding the system itself (Massari et al. 2014a). According to that work, in the innermost 200'' the expected fraction of contaminating field stars is about 16% (18 out of 114 stars).

The measure of relative PMs gives the great opportunity to verify the membership of each single star in the ACS FOV (instead of adopting a statistical approach only) and to check whether the estimate of the contribution from contaminating stars is reliable. To this aim, we cross-correlated them with the iron abundance catalog. We found only 42 out of 135 targets in common because the majority of the spectroscopic targets are either bright RGB stars, which saturate even in the short exposures, or stars located outside the ACS FOV. The locations of these targets in the VPD are shown in Figure 11, where blue circles mark stars with −0.6 ≤ [Fe/H] < 0, and red circles correspond to more metal-rich objects (0 ≤ [Fe/H] < 0.5). Clearly, with only a few exceptions (four targets), all spectroscopic targets appear to be members of the system, having PMs (and radial velocities) well within the characteristic cluster distribution. Also, four stars belonging to the newly discovered metal-poor component of Terzan 5 (with [Fe/H] ≃ −0.8; see Origlia et al. 2013; Massari et al. 2014b) have measured PMs and are shown in the figure (black triangles). As is apparent, they are also members of Terzan 5. Finally, the two magenta filled squares correspond to the super-metal-rich stars ([Fe/H] > 0.5) found in Massari et al. (2014b) and are suggested to be nonmembers. Indeed, their PMs are either outside the distribution of member stars or are just at its edge.

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Overall, six out of 42 spectroscopic targets appear to be field stars. Such a fraction corresponds to the 14% of the sample, in very good agreement with the statistical estimate obtained from our previous spectroscopic studies. Therefore, these results confirm that the iron distribution of Terzan 5 shown in Massari et al. (2014b) is made up of genuine cluster members, showing a huge internal iron spread of more than 1 dex.

One of the most intriguing applications of PM measures is the determination of the absolute motion of a stellar system. The best way is to relate the mean motion of all of the stars in the system⁶ to the absolute reference frame defined by very distant objects, such as background galaxies or quasars, which appear as zero-motion sources (see, e.g., Dinescu et al. 1999; Mahmud & Anderson 2008; Bellini et al. 2010; Lépine et al. 2011; Sohn et al. 2012; Massari et al. 2013). Unfortunately, because of the high stellar density and the very large extinction in the direction of Terzan 5, we have not been able to detect such objects in the ACS FOV.

We then cross-correlated our PM catalog with many public catalogs of stellar PMs, such as NOMAD (Zacharias et al. 2005), the Guide Star Catalog version 2.3, UCAC4 (Zacharias et al. 2012), and the Yale/San Juan Southern Proper Motion catalog (Dinescu et al. 1997, Platais et al. 1998). However, because these catalogs have PMs measured only for very bright sources, we found just four stars in common with our PM sample, all having PM uncertainties larger than 8 mas yr⁻¹ in the public data sets. Hence, no meaningful result about the absolute PM of Terzan 5 can be obtained from this kind of analysis.

An interesting alternative is described in Ortolani et al. (2011; see also Rossi et al. 2015), where the authors anchor the motion of the GC HP1 to that of the underlying bulge population. The bulge PM is the composition of its internal kinematics and the reflex motion of the local standard of rest (LSR). In the direction of Terzan 5, the radial velocity distribution of bulge stars peaks at v_rad = 21.0 ± 4.6 km s⁻¹ (Massari et al. 2014a). Assuming that bulge stars are at the same distance from the Galactic center (here we adopt 8.4 kpc following Ghez et al. 2008 and Ortolani et al. 2011, but see also van der Marel et al. 2012 for a complete overview of the topic), the tangential component of the bulge velocity is ${v}_{\mathrm{tan}}={v}_{\mathrm{rad}}\mathrm{sin}(l)/\mathrm{cos}(l)=1.41\pm 0.31$ km s⁻¹, or in Galactic coordinates ${\mu }_{l}^{\mathrm{bulge}}=0.05\pm 0.01$ mas yr⁻¹. Because the bulge shows cylindrical rotation (Howard et al. 2008; Kunder et al. 2012; Ness et al. 2013; Zoccali et al. 2014), we can assume ${\mu }_{b}^{\mathrm{bulge}}=0$ mas yr⁻¹. By summing these values to the motion of the LSR (${\mu }_{l}\mathrm{cos}(b)=6.10\pm 0.25$ mas yr⁻¹, μ_b = 0 mas yr⁻¹, corresponding to v_LSR = 243 ± 10 km s⁻¹; see Ortolani et al. 2011), we obtain the total motion of the bulge at Terzan 5 coordinates: (μ_l cos(b), ${\mu }_{b}{)}_{\mathrm{bulge}}=(6.15\pm 0.25$, 0) mas yr⁻¹.

As a second step for determining the PM of Terzan 5 relative to that of the bulge, we excluded foreground disk contaminants belonging to the blue plume in the CMD by selecting a subsample of stars with (m_F606W – m_F814W) > 3.9 and m_F606W < 24.5, which do not saturate even in the long exposures. We also applied a selection in terms of PM errors, by excluding stars with uncertainties larger than 0.3 mas yr⁻¹ in the two PM components. We then defined as Terzan 5 members all of the stars located within 2 mas yr⁻¹ from the origin of the VPD.

To select the sample of bulge stars, we followed an iterative procedure similar to that described by Anderson & van der Marel (2010) for the determination of the center of ω Centauri. After the exclusion of all Terzan 5 members, we computed the first-guess mean motion of bulge stars. We then excluded all objects contained within a circle of 2 mas yr⁻¹ radius positioned at the same distance as the "Terzan 5 circle" from the first-guess mean on the symmetrically opposite side in the VPD. A new value of the mean motion has been evaluated from this sample, and the procedure has been repeated until convergence was reached. Once the Terzan 5 and the bulge samples are defined, we determined their weighted mean motion with a 3σ clipping procedure that, after the last step, included 3,853 sources for the Terzan 5 sample and 797 for that of the bulge (black dots in Figure 12). We computed the uncertainty in the weighted mean motions as the standard error in the mean, that is, the dispersion of the surviving stars around the mean PM, divided by the square root of their number.

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The resulting motion of Terzan 5 relative to the bulge (see the blue arrow in Figure 12) expressed in Galactic coordinates (see Ortolani et al. 2011 for the details of the transformations) turned out to be (μ_l cos(b), ${\mu }_{b}{)}_{{\rm{T}}5-\mathrm{bulge}}=(0.26\pm 0.10$, 0.83 ± 0.12) mas yr⁻¹, where the final uncertainties are the sum in quadrature of those computed for the two separated samples. By subtracting the motion of the bulge quoted above, we finally obtained the absolute PM of Terzan 5: (μ_l cos(b), ${\mu }_{b}{)}_{{\rm{T}}5}=(-5.89\pm 0.27$, 0.83 ± 0.12) mas yr⁻¹, where the total uncertainties are the sum in quadrature between that coming from the motion of the bulge and that associated with the motion of the cluster relative to it. This is the first absolute PM estimate ever obtained for Terzan 5.

On the basis of the absolute PM estimate derived in the previous section, we performed a numerical integration of the orbit of Terzan 5 in the Galactic potential. We used the three-component (bulge, disk, and halo) axisymmetric model from Allen & Santillan (1991), which has been extensively used and discussed in the literature to study orbits and dynamical environmental effects on Galactic stellar systems (e.g., Allen et al. 2006; Montuori et al. 2007; Ortolani et al. 2011; Moreno et al. 2014; Zonoozi et al. 2014), thanks to its relative simplicity and fully analytic nature. We adjusted the various model parameters to make the rotation velocity curve match the value of 243 km s⁻¹ measured at the Solar Galactocentric distance of 8.4 kpc (see above). The cluster PMs were reported in the Cartesian Galactocentric reference frame, resulting in a velocity vector (v_x, v_y, v_z) = (−60.4 ± 1.3, 85.7 ± 11.1, 35.0 ± 6.0) km s⁻¹ at the position (x, y, z) = (−2.51 ± 0.30, 0.39 ± 0.02, 0.17 ± 0.01) kpc. We adopted the convention in which the X axis points opposite to the Sun (i.e., the Sun position is (−8.4,0,0)). The orbit was then time-integrated backwards for 12 Gyr, starting from the given initial (current) conditions and using a second-order leapfrog integrator (e.g., Hockney & Eastwood 1988) with a rather small and constant time step (∼100 kyr, corresponding to $\sim 1/300$ of the dynamical time at the Sun distance, computed as ${({R}_{0}^{3}/{{GM}}_{g})}^{1/2}$, where ${M}_{g}\sim 1.7\times {10}^{11}{M}_{\odot }$ is a characteristic Galactic mass parameter). During the >10⁵ time steps used to describe the entire orbit evolution, the errors on the conservation of both the energy and the Z component of angular momentum were kept under control and never exceeded one part over 10⁵ and 10¹³, respectively. To take into account the uncertainties on the kinematic data, we generated a set of 1,000 orbits starting from the phase-space initial conditions normally distributed within a 3σ range around the cluster velocity vector components and the current position, with σ being equal to the quoted uncertainties on these parameters. For all of these orbits we repeated the backward time integration. The probability densities of the resulting orbits projected on the equatorial and meridional Galactic planes are shown in Figures 13 and 14, respectively. Darker colors correspond to more probable regions of the space, that is, to Galactic coordinates crossed more frequently by the simulated orbits. As is apparent, the larger distances reached by the system during its evolution are R = 3.5 kpc and $| Z| =1.6$ kpc at a 3σ level of significance, which roughly correspond to a region having the current size of the bulge.

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In a forthcoming study, we plan to quantify the possible influence of a central nonaxisymmetric component (the bar or the spiral arms). Indeed, although triaxial potentials are expected to facilitate the onset of very radial orbits (because of the lack of conservation of any angular momentum component) with a possible prolongation of the system orbital motion in much farther out regions, a recent study by Moreno et al. (2014) demonstrated (using a sophisticated and realistic model) how this intuitive picture could be wrong, due to the complex interplay between the gravitational potentials generated by the various components. The relatively small perigalactic distance (<500 pc) that Terzan 5 could have achieved during its orbit could imply a significant mass loss due to tidal erosion and thus represents a further strong motivation for studying in more detail the dynamical history of this system.

Based on the current results, we can conclude that the integration of the Terzan 5 orbit performed by means of this simple axisymmetric Galactic static model suggests an in situ formation for the cluster within the Galaxy, rather than an external accreted origin. This supports the interpretation (Ferraro et al. 2009) of this system as the remnant of one of the massive stellar clumps that may have contributed to forming the Galactic bulge (Noguchi 1999; Immeli et al. 2004).