GD-1: The Relic of an Old Metal-poor Globular Cluster

Figure 1 shows the proper motions of stars in the Gaia DR2 sample within −60° < ϕ₁ < −20° and −02 < ϕ₂ < 02. The overdensity at the bottom left corner clearly stands out. We select the GD-1 candidates with proper motions in the red polygon in Figure 1. Their CMDs from SDSS DR9 and Gaia DR2 are shown in the left and right panels of Figure 2, respectively. Overlaid in the left panel, the red line is the best-fit isochrone from the Dartmouth isochrone library (Dotter et al. 2008) with [Fe/H] = −2.3, an age of 13 Gyr, and a distance of 8 kpc. The area enclosed by the blue lines in Figure 2 is

$$\begin{eqnarray}&&\left\{\begin{array}{l}{{gr}}_{0}\gt -36.755917+6.1373654\times {g}_{0}-0.34166210\\ \,\times \,{g}_{0}^{2}+0.0063657131\times {g}_{0}^{3}\\ {{gr}}_{0}\lt 26.910462-3.9900350\times {g}_{0}+0.19378849\\ \,\times \,{g}_{0}^{2}-0.0030286203\times {g}_{0}^{3}\\ 18.3\lt {g}_{0}\lt 21\end{array}\right..\end{eqnarray} \tag{ 1 }$$

Stars in this area are dwarfs, whose parallax distribution is shown in Figure 3, where we can also see that almost all stars have $| \varpi | \lt 1$ mas. The red line is the fitting Gaussian function with a mean of 0.071 mas and a variance of 0.48 mas. Because of the big uncertainty, we cannot estimate the distance of GD-1 stream from the distribution. If we apply the parallax correction recommended in Stassun & Torres (2018), which is ∼−0.08 mas, we obtain an estimated typical distance to the stream center from the Sun of ∼8 kpc.

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We use the CMD of these dwarfs with $| \varpi | \lt 1$ mas and −5° < ϕ₂ < 1° to select GD-1 member candidates with distances in 8–10 kpc. We divide the full range where GD-1 candidate stars are detected ϕ₁: [−85°, 5°] into 18 regions each with a 5° interval. Their diagrams of μ_α cos δ − μ_δ are shown in Figure 4. The red circle in each panel is where we select GD-1 candidates. The radius of each circle is 2 mas yr⁻¹, which is large enough to cover most GD-1 members, while their fiducial centers are given in Table 1.

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Table 1.  Circle Centers in Figure 4 and Distances in Figure 10

ϕ1 Range	$({\mu }_{\alpha }\,\cos \,\delta ,{\mu }_{\delta })$	Distance
(deg)	(mas yr−1)	(kpc)
[−85, −80]	(−2.2, −10.0)	8.5 ± 0.1
[−80, −75]	(−2.4, −10.7)
[−75, −70]	(−2.4, −11.2)
[−70, −65]	(−2.8, −12.0)
[−65, −60]	(−3.5, −12.6)	8.0 ± 0.4
[−60, −55]	(−4.2, −13.0)	8.0 ± 0.2
[−55, −50]	(−4.4, −13.0)	7.6 ± 0.1
[−50, −45]	(−4.8, −12.8)	8.0 ± 0.1
[−45, −40]	(−5.4, −12.8)	8.0 ± 0.2
[−40, −35]	(−5.8, −12.6)	8.6 ± 0.2
[−35, −30]	(−6.3, −11.7)	8.5 ± 0.2
[−30, −25]	(−6.9, −11.0)	8.0 ± 0.2
[−25, −20]	(−7.0, −10.2)	8.5 ± 0.1
[−20, −15]	(−7.5, −8.7)	9.2 ± 0.1
[−15, −10]	(−7.9, −7.6)	9.2 ± 0.1
[−10, −5]	(−8.5, −6.0)	9.7 ± 0.4
[−5, 0]	(−8.0, −4.4)	10.4 ± 0.2
[0, 5]	(−7.6, −3.3)

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We select the overdensities in Figure 4 by hand, then convert the circle centers in Figure 4 to (μ_ϕ1, μ_ϕ2) coordinates. We also use the correction formula in Koposov et al. (2010) to correct the Sun's reflex motion (note that there is a typo in ${\mu }_{{\phi }_{\mathrm{1,2},c}}\,={\mu }_{\alpha ,\delta }-{\mu }_{\mathrm{reflex}}$, which should be ${\mu }_{{\phi }_{\mathrm{1,2},c}}={\mu }_{\alpha ,\delta }+{\mu }_{\mathrm{reflex}}$) by assuming the distance along ϕ₁: d(ϕ₁) = 8 kpc if ϕ₁ < −20°, (ϕ₁ + 20) × 0.1 kpc, otherwise, and V_⊙ = 220 km s⁻¹. Figure 5 shows the circle centers in Figure 4 in (ϕ₁, μ) coordinates. In each panel, asterisks are μ_ϕ1s, while diamonds are μ_ϕ2s, and these circle centers are shown in red, while the data from Table 4 in Koposov et al. (2010) are shown in blue. The proper motions μ_ϕ1 and μ_ϕ2 in the right panel have been corrected for the Sun's reflex motion, while those in the left panel are not corrected. The left panel shows that these circle centers coincide well with data from Table 4 in Koposov et al. (2010), while the right panel shows that ${\mu }_{{\phi }_{2}}\sim 0$ mas yr⁻¹, which implies that GD-1 stars move along the GD-1 trace.

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Figures 6 and 7 show the μ_α cos δ and μ_δ of the stars in the circles in Figure 4 along ϕ₁, respectively. We fit these μ_α cos δ and μ_δ by polynomials with the lowest orders that visually go right through the centers of these data along ϕ₁ in Figures 6 and 7, respectively. The resulting polynomials are

$$\begin{eqnarray}&&\begin{array}{l}{f}_{1}({\phi }_{1})=-7.482+6.392\times {10}^{-2}\times {\phi }_{1}+4.553\times {10}^{-3}\\ \quad \times \,{\phi }_{1}^{2}+5.167\times {10}^{-5}\times {\phi }_{1}^{3}+1.950\times {10}^{-7}\times {\phi }_{1}^{4}\end{array}\end{eqnarray} \tag{ 2 }$$

and

$$\begin{eqnarray}\begin{array}{rcl}{f}_{2}({\phi }_{1}) & = & -3.698+2.450\times {10}^{-1}\times {\phi }_{1}-5.795\\ & & \times \,{10}^{-3}\times {\phi }_{1}^{2}-2.550\times {10}^{-4}\times {\phi }_{1}^{3}-2.858\\ & & \times \,{10}^{-6}\times {\phi }_{1}^{4}-1.121\times {10}^{-8}\times {\phi }_{1}^{5},\end{array}\end{eqnarray} \tag{ 3 }$$

respectively. The red central line in Figure 6 is ${f}_{1}({\phi }_{1})$, while that in Figure 7 is ${f}_{2}({\phi }_{1})$. These two equations can correct small deviations of the circle centers in Figure 4 selected by hand.

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Now, we map the GD-1 stream using stars by the criteria: (1) they should be in the GD-1 dwarf CMD of 8–10 kpc, (2) $| \varpi | \lt 1$ mas, and (3) they should be covered by the circles in Figure 4. Figure 8 shows positions of these stars, where the GD-1 overdensity clearly stands out and follows the trace. We select some fiducial points along the GD-1 trace in (ϕ₁, ϕ₂), which is listed in Table 2, then fit them by a quadratic polynomial

$$\begin{eqnarray}\begin{array}{rcl}{f}_{3}({\phi }_{1}) & = & -1.057-7.030\times {10}^{-2}\times {\phi }_{1}\\ & & -\,1.033\times {10}^{-3}\times {\phi }_{1}^{2},\end{array}\end{eqnarray} \tag{ 4 }$$

which is the red line in Figure 8. We also introduce

$$\begin{eqnarray}&&{\phi }_{2}^{c}({\phi }_{1})\equiv {\phi }_{2}-{f}_{3}({\phi }_{1})\end{eqnarray} \tag{ 5 }$$

to help us further study the GD-1 stream.

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To determine the distances of different parts of the GD-1 stream, we select stars by the criteria: (1) $| \varpi | \lt 1$ mas, (2) $| {\phi }_{2}^{c}| \lt 0\buildrel{\circ}\over{.} 5$, (3) $| {\mu }_{\alpha }\,\cos \,\delta -{f}_{2}({\phi }_{1})| \lt 1$ mas yr⁻¹, and (4) $| {\mu }_{\delta }-{f}_{3}({\phi }_{1})| \lt 1$ mas yr⁻¹. The matched filter algorithm in Willett et al. (2009) is used to estimate the distances. We find that the stars of the GD-1 stream in Figure 2 within 17 < g₀ < 21 can be well bounded by $| {{gr}}_{0}({g}_{0})-{\text{}}\mathrm{ISO}({g}_{0})| \lt -0.312+0.019\,\times {g}_{0}$ (${\text{}}\mathrm{ISO}({g}_{0})$ is the Dartmouth isochrone with [Fe/H] = −2.3, an age of 13 Gyr and a distance of 8 kpc), which is shown in Figure 9, where the bound lines are shown in blue, stars are shown by black symbols, and the red line is the Dartmouth isochrone with [Fe/H] = −2.3, an age of 13 Gyr and a distance of 8 kpc. Thus, we use σ(g₀) = 0.5 × (−0.312 + 0.019 × g₀) for Gaussian profiles to broaden the Dartmouth isochrone to generate the template filter at the distance of 8 kpc.

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We generate Hess diagrams of 18 regions each with a 5° interval along the ∼90° GD-1 trace by convolving the SDSS photometric errors on their CMDs. We select the Hess diagrams on which the GD-1 dwarfs obviously overwhelm the background stars as shown in Figure 10. In each Hess diagram, we shift the filter from −0.3 mag to 0.9 mag in g₀ by the step of 0.01 mag, then use the Equations (2)–(6) in Willett et al. (2009) with assuming the Hess diagram of the background ∼0 to calculate the distance and error of the region (there is a typos in Equation (6) in Willett et al. 2009, which should be ${\sigma }_{\delta r}=\sqrt{-\tfrac{{\sigma }^{2}(a)}{a(\delta {r}_{m})\tfrac{{d}^{2}a}{d\delta {r}^{2}}}}{| }_{\delta r=\delta {r}_{m}}$, because the second derivative $\tfrac{{d}^{2}a}{d\delta {r}^{2}}$ should be not greater than 0 at the maximum). In each panel of Figure 10, the red line is a Dartmouth isochrone with [Fe/H] = −2.3 and an age of 13 Gyr, and the distance with error is shown in red. All distances with Gaussian errors are listed in Table 1.

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We select the GD-1 candidates in the spectral data of SDSS DR14 and LAMOST DR6 by the criteria: (1) $| \varpi | \lt 1$ mas, (2)$| {\phi }_{2}^{c}| \lt 1^\circ$, (3) $| {\mu }_{\alpha }\,\cos \,\delta -{f}_{1}({\phi }_{1})| \lt 2$ mas yr⁻¹ (4) $| {\mu }_{\delta }-{f}_{2}({\phi }_{1})| \lt 2$ mas yr⁻¹ and (5) [Fe/H] < −1.9 dex. For a star that has multiple spectra and multiple measurements, its parameters with errors are the mean values of these measurements. In panel (A) of Figure 11, the spectral radial velocities of SDSS DR14 along ϕ₁ are shown by black asterisks, while those of LAMOST DR6 are shown by red circles, and the central red line is

$$\begin{eqnarray}&&{f}_{4}({\phi }_{1})=-273.4-6.5\times {\phi }_{1}\end{eqnarray} \tag{ 6 }$$

km s⁻¹, while the dotted lines are ${f}_{4}({\phi }_{1})\pm 50$ km s⁻¹. We can see that stars are crowded in this range, where GD-1 members are located. The spectroscopic stars in SDSS DR14 and LAMOST DR6 that meet all of the above four criteria and also have radial velocities $| {RV}-{f}_{4}({\phi }_{1})| \lt 50$ km s⁻¹ are selected as GD-1 spectroscopic stream member candidates. One hundred and thirty-six spectra for 116 individual stars from SDSS DR14 and 32 spectra for 20 individual stars from LAMOST DR6 are given in Tables 3 and 4, respectively.

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Panel (B) of Figure 11 shows the [Fe/H] distributions of these spectroscopic member candidates. The black histogram is for SDSS stars, which is fitted by a Gaussian function and indicated by a dotted profile, while the red histogram is for LAMOST stars. The fitted value of [Fe/H] histogram for SDSS stars is −2.20 ± 0.12 dex, while the peaks of [Fe/H] histograms for SDSS and LAMOST stars are all at ∼−2.25 dex, which are well consistent with −2.3 dex that the photometric data give in Figure 2. Gao et al. (2015) has shown that for low metal stars, [Fe/H] ((Wu et al. 2014) less than −1.5 dex in LAMOST DR1, which are determined by LASP with ELODIE interpolator) are systematically measured higher when compared with those in the PASTEL catalog (Soubiran et al. 2010). Thus, the actual intrinsic metallicity of the GD-1 stream we estimate no more than −2.20 dex, with an estimated error of about 0.12 dex.

Panel (C) of Figure 11 shows the sky positions of these candidates, while their CMD is shown in panel (D). In these two panels, SDSS stars are indicated by black asterisks, while LAMOST stars are indicated by red circles. The red line in panel (D) is the Dartmouth isochrone with [Fe/H] = −2.3, an age of 13 Gyr, and a distance of 8 kpc. The former panel shows that SDSS stars are distributed along the whole GD-1 trace, while LAMOST stars are only extended to ϕ₁ ∼ −52° from ϕ₁ ∼ 5°. The latter panel shows most LAMOST stars are giants or subgiants, while SDSS stars are mostly G dwarfs and F turnoff stars.

The parallax distributions of these spectroscopic candidates from SDSS and LAMOST catalogs are shown in panel (E) by black and red histograms, respectively. The parallax distribution of SDSS is fitted by a Gaussian function, which is shown by a dotted profile, with a mean of 0.18 mas and a variance of 0.21 mas. Panel (F) shows the proper motions of these spectroscopic candidates. The μ_α cos δ and μ_δ of SDSS spectroscopic candidates are shown by black asterisks and black crosses, respectively, while those of LAMOST spectroscopic candidates are shown by red circles and red diamonds, respectively. Equations (2) and (3) are overplotted by black lines as guidelines.

In this refined CMD (in $({{gr}}_{0},{g}_{0}^{c})$ coordinates), we use Equation (1) to select GD-1 dwarfs, where g₀ is replaced by g₀^c. The sky positions of these dwarfs are shown in the upper panel of Figure 13, where the blue line is ${\phi }_{2}^{c}=0^\circ$ and the blue dotted lines are ${\phi }_{2}^{c}=\pm 0\buildrel{\circ}\over{.} 5$. The stellar counts with Poisson error along GD-1 between the two blue dotted lines are shown in the bottom panel. While we acknowledge that because we use Gaia DR2 to select candidate stream members and that the catalog is limited to g ∼ 21 and the statistical significance of suspect over or underdensities may also be limited, we do find that:

• (1)  
  There are four candidate overdensities along the GD-1 trace. These four overdensities are at ϕ₁: [−54°, −43°], [−37°, −23°], [−17°, −11°], and [−3°, 2°], which are denoted as O1, O2, O3, and O4, respectively.
• (2)  
  There is a gap centered around ϕ₁ ∼ −21°, which has no GD-1 candidate member star.
• (3)  
  There are two candidate underdensities at ϕ₁ ∼ −40° and ${\phi }_{1}\sim -8^\circ .$
• (4)  
  The width of stream visually broadens along the GD-1 trace from O3 along two directions.
• (5)  
  There is a noticeable wobble in O1.
• (6)  
  The stellar density drops suddenly to background level at ϕ₁ ∼ 2°.
• (7)  
  A spur originates at ϕ₁ ∼ −40°, where the O1 and O2 are separated, which is discussed by Price-Whelan & Bonaca (2018) and also shown in Figure 10 of Koposov et al. (2010). We conjecture that it results from GD-1 stars pulled out of the stream by an encounter. Thus, O1 and O2 were once on a single overdensity, but separated later.

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Figure 14 shows the density profiles of four overdensities O1, O2, O3, and O4 along ϕ₂^c. We fit these profiles by Gaussian functions, and in each panel, the Gaussian width σ, center and full width at half maximums (FWHMs) are also given in red. Their lengths along ϕ₁ and FWHMs in degrees along the ϕ₂^c are shown by the red rectangles in the upper panel of Figure 13. All information about these four overdensities are given in Table 5, where the areal densities of dwarfs are the ratios of dwarf number (calculated from Gaussian fitting) divided by areas of rectangles in the upper panel of Figure 13. Their Gaussian centers are 0039, −0051, 0147, and −0115 in ϕ₂^c, respectively, while Gaussian widths are 0290, 0147, 0119, and 0247, respectively, which correspond to FWHMs of 91.9 pc, 49.4 pc, 44.6 pc, and 104.7 pc, respectively by the distance of Equation (7). These FWHMs show that the narrowest place of the GD-1 stream is in O3, and then broadens gradually along two directions. Besides, the O3 has the highest areal density of dwarfs as shown in Table 5. For stars stripped from the progenitor cluster earlier would move away further both in position and velocity from the progenitor (Bovy 2014). So O3 centered $({\phi }_{1},{\phi }_{2}^{c})\sim (-14^\circ ,0\buildrel{\circ}\over{.} 15)$ ((α, δ) ∼ (17818, 5219)), which has the narrowest stream width, highest stellar areal density and also shows a noticeable wobble, is the most likely candidate for the GD-1 stream progenitor.

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Systems at the end of their bound lifetime like GD-1 are not expected to be stripped smoothly, so at least some fluctuations from the normal trace are expected to simply be the result of the last few stripping episodes being stochastic and erratic. But given the overall density structure, it seems possible that the local density is affected by the encounters that created the underdense features. After all, the energy of the stars is redistributed, and shocks and caustics could mess up the smooth stream density. A more detailed dynamical model of the stream over time including encounters with dense structures and tracing the stream as it passes through the plane of the disk will help determine the nature of these encounters.

In this subsection, we require select stars satisfying the following criteria: (1) $| \varpi | \lt 1$ mas; (2) −85° < ϕ₁ < 5°; (3) $| {\mu }_{\alpha }\,\cos \,\delta -{f}_{1}({\phi }_{1})| \lt 2$ mas yr⁻¹; (4) $| {\mu }_{\delta }-{f}_{2}({\phi }_{1})| \lt 2$ mas yr⁻¹; (5) $-1^\circ \lt {\phi }_{2}^{c}\lt 1^\circ$. Their CMD is shown in Figure 15.

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Because the spectroscopic parameters for hot stars are more difficult to derive, due to less characteristic spectral lines, different physical mechanism, and sparse templates, we only give radial velocities for stars with gr₀ < 0.1 from LAMOST DR6 and SDSS DR14, which are shown in Figure 16, where one symbol represent one spectrum, so a star may have several symbols. From the figure we can see that the radial velocities of all blue stars are well within the radial velocity range of GD-1 stream, so we believe all of these spectroscopically observed stars are GD-1 members. All blue stars with gr₀ < 0.1 from spectroscopic catalogs of LAMOST DR6 and SDSS DR14 are listed in Tables 6 and 7, respectively.

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We overplot all spectroscopic GD-1 member stars from LAMOST DR6 and SDSS DR14 by red and blue circles in Figure 15, respectively—the positions of BHB and BS stars of the GD-1 stream are clearly shown. We select BHB stars by the criteria of 0.3 < M_g < 0.8 and −0.3 < gr₀ < −0.1, and BS stars by the criteria of 1.5 < M_g < 4 and −0.2 < gr₀ < 0.1. There are total of seven BHB and 21 BS stars of the GD-1 stream, which are listed in Table 8. In LAMOST DR6 and SDSS DR14, there are six and two spectroscopic BHB stars, respectively, and four and eight spectroscopic BS stars, respectively. Not counting spectra of the same star, we have a total of six new spectroscopic BHB and ten new spectroscopic BS candidate stream members.