Detecting the Sagittarius Stream with LAMOST DR4 M Giants and Gaia DR2

The LAMOST Telescope is a 4 m Schmidt telescope at the Xinglong Observing Station; this National Key Scientific facility was built by the Chinese Academy of Sciences (Cui et al. 2012; Zhao et al. 2012). The main goal of the LAMOST spectroscopic survey is to provide A-, F-, G-, K-, and M-type stars to improve our understanding of the structure of the Milky Way (Deng et al. 2012). Although the standard data processing pipeline provides an accurate estimation of the stellar atmospheric parameters for the AFGK-type stars, it does not reliably identify M-type stars (Luo et al. 2015). Zhong et al. (2015) selected a large sample of M-giant and M-dwarf stars from the LAMOST DR1 catalog using a template fitting method. Using this method and selecting only spectra with a signal-to-noise (S/N) > 5, we find over 490,000 spectra that show the characteristic molecular titanium oxide(TiO), vanadium oxide(VO), and calcium hydride(CaH) features typical of M-type stars in LAMOST DR4 data. The TiO and CaH spectral indices were defined by Reid et al. (1995) and Lépine et al. (2007), and the distribution of the spectral indices is a good indicator for separating M-dwarf stars with different metallicities (Gizis 1997; Lépine et al. 2003, 2007, 2013; Mann et al. 2012). Zhong et al. (2015) showed that M giants generally have weaker CaH molecular bands for a given range of TiO5 values. This spectral index distribution of M-type stars can be used to separate giants from dwarfs with little contamination. Following the method in Zhong et al. (2015), we selected 33,000 M giants from the LAMOST DR4 sample.

Next, we calculated the heliocentric radial velocity (RV) of all M-giant stars by using a cross-correlation method with a template spectrum in a zero-velocity rest frame; the same method is used in Zhong et al. (2015). This procedure was repeated until the measured RV for each corrected training spectrum was less than ±5 kms⁻¹ from the published value.

Finally, using the TiO and CaH spectral indices we identified 33,000 M-giant stars from the LAMOST DR4 sample. Then we cross-matched this sample to the ALLWISE Source Catalog (Wright et al. 2010) in NASA/IPAC Infrared Science Archive, using a search radius of 3''. More than 99% of the M giants from LAMOST DR4 had search radii less than 3'' in the ALLWISE Source Catalog, and we obtained five photometric bands for these stars (J, H, K, W1, and W2). The details for our selection criteria are the same as those in Section 3.1 of Li et al. (2016). The interstellar reddening is corrected using the same spatial model of the extinction mentioned in Li et al. (2016). We adopt the E(B − V) maps of Schlegel et al. (1998), in combination with A_r/E(B − V) = 2.285 from Schlafly & Finkbeiner (2011) and A_λ/A(r) from Davenport et al. (2014).

Thanks to the presence of the gravity-sensitive CO bands in Wide-field Infrared Survey Explorer (WISE) photometry, metal-rich giants stands out from the dwarfs (Meyer et al. 1998; Koposov et al. 2015). We purify our sample by excluding a few contaminating K-giant stars and M-dwarf stars using the photometric selection criteria of the WISE color index (W₁ − W₂)₀; for more details see Equation (1) of Li et al. (2016). Finally we get 22,999 M-giant stars. We also removed contamination from 894 carbon stars by cross-matching with the latest LAMOST carbon star catalog (Ji et al. 2016; Li et al. 2018).

Li et al. (2016) has constructed a new photometric distance relation using a large sample of M giants from the Sagittarius (Sgr), LMC, and SMC structures. The variation in these distance relations (see the parameters in Table 1 of Li et al. 2016) reflects the differing chemical composition of these structures. The distances were computed using the color index (J − K)₀ to get the absolute J-band magnitude, M_J, using the relation described in Li et al. (2016). In the ALLWISE Source Catalog, the mean photometric errors for our M giants are δJ = ±0.238 mag, δK = ±0.029 mag, δW1 = ±0.008 mag, and δW2 = ±0.008 mag. The J-band magnitude error is much larger in our full M-giant sample than the sample selected by Li et al. (2016) because most LAMOST observed regions are located at lower Galactic latitudes, close to the plane where the extinction uncertainty has a larger effect on the accuracy of J-band magnitude. In this work we only consider the Sgr stream members (Sgr stream member selection is described in Section 3.1), and as such most of the candidates are located at higher galactic latitude. Since we are working at high galactic latitude where the extinction is low, the J-band magnitude error is smaller than the LAMOST average. For Sgr member candidates, the mean δJ = 0.0298 mag, δK = 0.009 mag, δW1 = 0.004 mag, and δW2 = 0.003 mag, and therefore are negligible in our distance uncertainty computation.

In Li et al. (2016), the (J − K)₀ color–distance relation for M-giant stars was shown to have some uncertainty due to an absolute magnitude dispersion around their best-fit model. This absolute magnitude dispersion was found to be around 0.36 mag and translates to a distance uncertainty of about 20%. Since we use the same color–distance relation in our work, we also expect to have a distance uncertainty of 20%. Although the distance uncertainty for an individual M giant is relatively large, for structures like the Sgr stream, we should have relatively high precision because the distance relation is calibrated with the Sgr core member stars (Li et al. 2016).

Figure 1 shows the heliocentric-distance and RV distribution for all of our selected M giants. As we can see, the distance of most of the M-giant stars is smaller than 20 kpc, with only 700 stars having distances larger than 20 kpc. For these 700 stars we checked the spectra by eye to ensure they are true M-giant stars. Of these ~700 stars, about 50 were not true M giants, and they were removed from the sample. We only select the stars with distances larger than 20 kpc as candidates for selecting Sgr members.

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Since Gaia published its DR2 data consisting of astrometry, photometry, RVs, astrophysical parameters, and the unprecedentedly high accuracy proper motion, we have the chance to determine 6D phase-space information for our catalog of M giants (Gaia Collaboration et al. 2018). We cross-matched our M giants with Gaia DR2 data using a cross-match radius of 3''. We found 94% of the stars in our Sgr candidate sample had matching stars in the Gaia data. The mean proper motion error in pmra is 0.14 mas yr⁻¹ and pmdec is 0.10 mas yr⁻¹ with a dispersion in these means of 0.08 and 0.06, respectively.

For each star, we calculated the line-of-sight Galactic standard of rest velocity from the heliocentric RV using the formula: V_gsr = RV + 10 cos l cos b + 225.2 sin l cos b + 7.2 sin b kms⁻¹. This formula removes the contributions from the 220 kms⁻¹ (Dehnen 2000) rotation velocity at the solar circle as well as the solar peculiar motion (relative to the local standard of rest) of (U, V, W)₀ = (10.0, 5.2, 7.2) kms⁻¹ (Dehnen & Binney 1998).

To determine the energy and angular momenta of the stars in our sample, we first convert from proper motion and RV to Cartesian velocity (Johnson & Soderblom 1987). The XYZ coordinates we use are left-handed, where the X-axis is positive toward the Sun and the Y-axis is positive in the the direction of Galactic rotation. We also propagate the errors in distance, RV, and proper motion into the errors in our Cartesian velocities using a Monte Carlo method.

To calculate the energy and angular momentum for each of our M giants, we assume that the Galactic potential is represented by three components: a spherical bulge, an exponential disk, and an NFW dark matter halo (Navarro et al. 1996). Based on the Galactocentric (X, Y, Z, V_x, V_y, V_z) and potential Φ_tot(X, Y, Z), the four integrals of motion $(E,{\boldsymbol{L}})$ can be calculated as follows:

$$\begin{eqnarray}\begin{array}{rcl}E & = & \displaystyle \frac{1}{2}({V}_{x}^{2}+{V}_{y}^{2}+{V}_{z}^{2})+{{\rm{\Phi }}}_{\mathrm{tot}}(\sqrt{{x}^{2}+{y}^{2}+{z}^{2}})\\ {L}_{x} & = & {{YV}}_{z}-{{ZV}}_{y}\\ {L}_{y} & = & {{ZV}}_{x}-{{XV}}_{z}\\ {L}_{z} & = & {{XV}}_{y}-{{YV}}_{x}\\ L & = & \sqrt{{L}_{x}^{2}+{L}_{y}^{2}+{L}_{z}^{2}}.\end{array}\end{eqnarray} \tag{ 1 }$$

Figure 4 shows the orbit distribution of the Sgr stream in the XYZ plane. In the XZ plane, we can see a clear stream orbit trend.

Li et al. (2016) shows that the metallicities of M giants have a strong correlation with (W1 − W2) and can be fit with the linear relation: [M/H]_phot = −13.2 × (W1 − W2)₀ − 2.28 dex, with an uncertainty of 0.35 dex. Clearly (W1 − W2)₀ is an acceptable proxy for [M/H]. So using this relation we calculate photometric [M/H] for each M-giant star.

We tried recalibrating our color–metallicity relation using data from APOGEE DR13 (Holtzman et al. 2018). The linear relationship we fit to the APOGEE data was similar to the result Li et al. (2016) found using APOGEE DR12.

For all of our M-giant stars, we now have heliocentric RV, proper motion, S/N determined from the spectrum, distance, and metallicity determined from photometry.

To select candidate members of the Sgr stream from the LAMOST M-giant stars, we first did a broad cut on the total M-giant sample using the selection criteria: $-15^\circ \lt {\tilde{B}}_{\odot }\lt 15^\circ$, D_helio > 20 kpc, and S/N > 5. This selection gives a large population of Sgr candidate members that are in the correct region of the sky, and have good enough spectra to determine if they are M giants. Through the distance and velocity distribution, we can easily separate the Sgr stream member from the disk component. We remove stars that are more than 20 kpc from the Sgr orbit in distance and 50 kms⁻¹ from the Sgr orbital velocity. Then with these selected stars, we also remove stars that are outside the 2σ distribution in L_x, L_y, and L_z angular momentum distribution. Our final Sgr sample contains a total of 164 candidates, which we are very confident belong to the Sgr stream. We list these stars in Table 1.

Table 1.  The Parameters for Sagittarius Stream Members

	R.A.	Decl.	${\tilde{{\rm{\Lambda }}}}_{\odot }$	${\tilde{B}}_{\odot }$	J0	H0	K0	W10	W20	RV
	(deg)	(deg)	(deg)	(deg)	(mag)	(mag)	(mag)	(mag)	(mag)	(kms−1)
1	−184.98	14.71	2.03	268.39	11.25	11.88	11.06	10.84	10.85	10.97
2	−152.44	20.12	−2.73	266.00	4.44	12.04	11.12	10.93	10.85	10.96
	Vgsr	D⊙	[Fe/H]	S/N	XGC	YGC	ZGC	Vx	Vy	Vz
	(kms−1)	(kpc)	(dex)	⋯	(kpc)	(kpc)	(kpc)	(kms−1)	(kms−1)	(kms−1)
1	−106.08	23.45	−1.62	14.75	15.14	9.17	−20.46	−291.55	−2.65	14.75
2	−100.29	28.99	−0.83	24.28	17.82	7.97	−26.19	−327.34	−47.52	−27.84
	pmRA	pmRAerror	pmDec	pmDecerror	E	L	Lx	Ly	Lz
	(masy−1)	(masy−1)	(masy−1)	(masy−1)	(km2s−2)	(km2s−2)	(km2s−2)	(km2s−2)	(km2s−2)
1	−0.86	0.07	−2.79	0.04	−42303.85	6318.78	81.06	5743.09	2633.87
2	−0.625	0.08	−2.87	0.05	−23328.86	9355.16	−1466.55	9069.79	1762.69

(This table is available in its entirety in FITS format.)

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Figure 2 shows the distance and V_gsr distribution of the pure Sgr stream candidates. The left panels show the distance distribution of the Sgr stream, and the right panels show the velocity distribution of the Sgr stream. In the upper panels, we compare our stars with the Dierickx & Loeb (2017) N-body model, and in the lower panels, we compare our stars with the Law & Majewski (2010) N-body model. From the figure we can see the leading arm covers a large ${\tilde{{\rm{\Lambda }}}}_{\odot }$ range of 60°–160°, and the trailing arm covers a range of 160°–270°. From the left panel we find many stars extended to the anti-center region and that these stars have a distance of about 100 kpc. Sesar et al. (2017b) find a "spur" structure with RR Lyrae stars that is consistent with the distance to our M-giant detection. Unfortunately, our Sgr sample does not trace the turning back branch feature 1 for the trailing arm from Sesar et al. (2017b).

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While we compared our results to many N-body models (Law & Majewski 2010; Peñarrubia et al. 2010; Dierickx & Loeb 2017), we limit our discussion to the two that were most consistent with our data; the model from Dierickx & Loeb (2017) and the model from Law & Majewski (2010). L&M model is the first numerical model of the Sgr–Milky Way system that is capable of simultaneously satisfying the majority of major constraints on the angular positions, distances, and radial velocities of the dynamically young tidal debris streams (Law & Majewski 2010). Model from Dierickx & Loeb (2017) is the first to accurately reproduce existing data on the 3D positions and radial velocities of the debris detected 100 kpc away in the MW halo. From the upper panel of Figure 2 we can see the Dierickx & Loeb (2017) model matches the observed data well in distance versus ${\tilde{{\rm{\Lambda }}}}_{\odot }$. We have one star consistent with the "spur" structure in trailing arm apo-center. The velocity distribution in our observed data does not match the model as well as the distance distribution. We can see that the trailing arm velocity matches well, but the leading tail velocity is significantly undervalued compared to our data.

The L&M model was created to reproduce the distance and position of the 2MASS Sgr M giants. In the lower panel of Figure 2, we can see that our M-giant candidates match the distance and velocity of the L&M model's leading and trailing arms well, but they are inconsistent toward the apo-center of the trailing arm (${\tilde{{\rm{\Lambda }}}}_{\odot }\sim 180^\circ$) both the distance and velocity distribution. The apo-centric distance of our M giants in the trailing arm extend to 120 kpc.

From the above discussion, we can see that none of the models can perfectly match with observation. For L&M's N-body model, which has no disk rotation and the key element in the success of this model is the introduction of a nonaxisymmetric component to the Galactic gravitational potential, the distance for the trailing is obviously a lower estimation, and the velocity for the trailing tail that crosses to the north hemisphere is significantly shifted. Another model is derived by Dierickx & Loeb (2017), which combined analytic modeling and N-body simulations. This model can be well compared to the observation in the distance distribution, even the "spur" structure out to the 100 kpc detected by RRly and our M giants. We actually also compared our data to the N-body model originally with a late-type, rotating disk galaxy (Peñarrubia et al. 2010), but both the velocity and the distance are not consistent.

With distances estimated from photometry (to ∼20%), radial velocities from spectroscopy (to ∼7 kms⁻¹), and proper motions uncertainty (to ∼0.13 masy⁻¹ and ∼0.09 masy⁻¹ in R.A. and decl. derictions separately) from Gaia DR2, we are able to analyze the phase-space distribution of the 164 Sgr stream candidates. The proper motion distribution is shown in Figure 3. The colors show the ${\tilde{{\rm{\Lambda }}}}_{\odot }$ value of each star, which helps identify the leading and trailing arms. From this figure, we can see that leading and trailing arms have different proper motion distributions and most stars have small proper motion error in both R.A. and decl. directions.

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We are showing "the 3D orbit precession" in Figure 4. The X, Y, and Z positions with arrows representing the direction and magnitude of the V_x, V_y, and V_z velocities. We can see the Sgr stream stars as clumps on this figure. In the middle of the Figure 4, we can see the Sgr stream orbit well because the (X,Z) plane is mostly aligned with the orbital plane of the stream. From the orbit distribution we can see leading and trailing arms have a significant velocity segregation. In the (X, Z) plane, both the leading and trailing arms have opposite velocity distributions. The red small dots show stars having a V_y > 0 kms⁻¹, and the blue dots show stars having a V_y < 0 kms⁻¹. In the (X, Y) and (Y, Z) plane it is hard to see orbital direction clearly. Thanks to the Gaia proper motion we are capable of tracing the 3D orbit precession for the whole Sgr stream. We also illustrate the V_x, V_y, and V_z velocity distribution along the ${\tilde{{\rm{\Lambda }}}}_{\odot }$ in Figure 5.

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In Figure 6, we examine the angular momentum (L) versus energy (E) space of the Sgr stream candidates. This is the first time that this stream has been inspected using this method. From Figure 6 we can see that the leading and trailing arms have slightly different distributions in angular momentum versus energy space, but are coincident in L_x versus L_y and L_x versus L_z space. This figure makes us confident that the stars we are selecting all belong to the same substructure, and thus our Sgr selection method was good.

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As noted, a velocity separation is seen for the leading and trailing arms in the (X, Z) plane. For the leading arm, we can see that the components of angular momentum show two distinct parts especially in the (L_x, L_z) and (L_y, L_z) planes. For the trailing arm we did not see clear component separation.

Recently, Gibbons et al. (2017) demonstrated that the Sgr stream has two subpopulations with distinct chemistry and kinematics. Using our photometric metallicity estimation relation, we are able to estimate metallicities for our Sgr stars in a large ${\tilde{{\rm{\Lambda }}}}_{\odot }$ range. Figure 7 presents the metallicity distribution of the leading and trailing arms in six ${\tilde{{\rm{\Lambda }}}}_{\odot }$ bins (three for the leading arm and three for the trailing arm). As we can see from the left panel, the trailing arm has a broad metallicity distribution, but considering the Poisson error, it is hard to say whether there is an obvious metallicity gradient along the trailing arm. In the right panel, the leading arm stars show a slight metallicity gradient in all three ${\tilde{{\rm{\Lambda }}}}_{\odot }$ bins (peak shift from upper panel to lower panel). Thus we did not see an obvious [Fe/H] gradient in either the leading and trailing arm. When comparing the [Fe/H] between leading and trailing arms, we also did not see a significant difference. This could be because our data is not complete and we still need more data to do the analysis.

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