THE LEAST-LUMINOUS GALAXY: SPECTROSCOPY OF THE MILKY WAY SATELLITE SEGUE 1

Targets were selected for spectroscopy based on gri photometry of Segue 1 from the SDSS DR6 public database (Adelman-McCarthy et al. 2008). As discussed in SG07, we set the target priorities to preferentially observe stars with a high likelihood of being Segue 1 members. Using the theoretical isochrones of Clem et al. (2008) and Girardi et al. (2004), we chose targets whose color and apparent magnitudes minimize the distance from the best-fitting Segue 1 isochrone. The highest priority targets were those located within 0.1 mag of the red giant branch (RGB) tracks, or within 0.2 mag of the horizontal branch, with additional preference being given to brighter stars (Figure 1). Stars farther from any of the fiducial sequences were classified as lower-priority targets. We designed the slitmask so as to maximize the number of high-priority targets: a total of 59 targets were placed on the Segue 1 mask, 26 of which were in our highest priority category. Slitmasks were created using the DEIMOS dsimulator package in IRAF.

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One multislit mask was observed for Segue 1 using the Keck II 10 m telescope and the DEIMOS spectrograph (Faber et al. 2003) on the night of 2007 November 12. The mask was observed for a total of 5400 s through the 1200 line mm⁻¹ grating covering a wavelength region 6400–9100 Å. The spatial scale is 012 per pixel, the spectral dispersion of this setup is 0.33 Å, and the resulting spectral resolution is 1.37  Å (FWHM). Slitlets were 07 wide. The minimum slit length was 5'' to allow adequate sky subtraction; the minimum spatial separation between slit ends was 04 (3 pixels).

Spectra were reduced using a modified version of the spec2d software pipeline (version 1.1.4) developed by the DEEP2 team at the University of California-Berkeley for that survey. A detailed description of the two-dimensional reductions can be found in SG07. The final one-dimensional spectra are rebinned into logarithmic wavelength bins with 15  km s⁻¹ per pixel.

Radial velocities were measured by cross-correlating the observed science spectra with a set of high signal-to-noise stellar templates. The method is the same as that described in SG07 and briefly repeated here. Stellar templates were observed with Keck/DEIMOS using the same setup as described in Section 2.2 and covering a wide range of stellar types (F8 to M8 giants, subgiants, and dwarf stars) and metallicities ([Fe/H] = −2.12 to +0.11 dex). We calculate and apply a telluric correction to each science spectrum by cross correlating a hot stellar template with the night sky absorption lines following the method in Sohn et al. (2007). The telluric correction accounts for the velocity error due to mis-centering the star within the 07 slit caused by small mask rotations or astrometric errors. We apply both a telluric and heliocentric correction to all velocities presented in this paper.

The random component of the velocity error is calculated using a Monte Carlo bootstrap method. Noise is added to each pixel in the one-dimensional science spectrum, we then recalculate the velocity and telluric correction for 500 noise realizations. The random error is defined as the square root of the variance in the recovered mean velocity in the Monte Carlo simulations. The systematic contribution to the velocity error was determined by SG07 to be 2.2 km s⁻¹ based on repeated independent measurements of individual stars. Since we are using the same spectrograph setup and reduction methods, we assume the systematic error contribution is constant across the two runs. We add the random and systematic errors in quadrature to arrive at the final velocity error for each science measurement. Radial velocities were successfully measured for 49 of 59 extracted spectra. The median velocity error of these 49 stars is 3.6 km s⁻¹  similar to that of SG07. The median velocity error of the 24 Segue 1 members (see below) is 5.2 km s⁻¹ since these stars are fainter than the sample average. The majority of spectra for which we could not measure a redshift did not have a sufficient signal-to-noise ratio. The fitted velocities were visually inspected to ensure reliability. The resulting velocities and associated errors are listed in Table 2.

In Figure 2, we identify Segue 1 as the overdensity of stars with radial velocities near 206 km s⁻¹. We estimate possible foreground contribution below and then discuss our criteria for Segue 1 membership, which we base only on velocity.

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We expect minimal contamination from foreground Milky Way stars at the position and velocity of Segue 1. Segue 1 lies at a Galactocentric position of (l, b) = (2205, 504. According to the Besancon star count model⁸ of the Milky Way (Robin et al. 2003) at this Galactic position, the velocity distribution of Milky Way foreground stars peaks at a heliocentric velocity of 20 km s⁻¹. The Besancon models include stellar contributions from the Milky Way thin and thick disk, spheroid and stellar halo. The kinematic distribution of foreground stars is roughly approximated by a Gaussian with FHWM of 35 km s⁻¹, however the tails of the distribution extend to significantly positive and negative velocities. The percentage of Milky Way stars expected in the presumed velocity span of Segue 1, between 190 < v < 220  km s⁻¹, is 2.5% of the total distribution. Thus, if we assume that all the stars with velocities less than 100 km s⁻¹ are Milky Way foreground stars (a total of 20 stars, see Figure 2), we predict less than one foreground star in the Segue 1 velocity range.

As noted by Belokurov et al. (2007), Segue 1 is superposed on the leading arm of the Sagittarius stream, ∼100° away from the main body of the Sagittarius dSph. Thus, a second possible source of contamination in our Segue 1 sample is stars associated with the Sagittarius stream. As discussed in Section 4, the predicted velocity of the leading stream at this position is v ∼ −100  km s⁻¹, very far from the radial velocity of Segue 1. While both the trailing arm and possible older wraps of the Sagittarius stream may be present at this position, both components would have much wider velocity distributions than Segue 1. We conclude that there is no contamination from Sagittarius stream stars in the Segue 1 velocity window. Finally, there are four stars at higher velocities (v ∼ 300  km s⁻¹) that do not appear to be associated with Segue 1 as a result of the 100  km s⁻¹ velocity difference which we discuss in Section 4.1.

Since the expected contamination from both foreground Milky Way stars and the Sagittarius stream is low in the velocity region of Segue 1, our criteria for Segue 1 membership are simple: we assign membership based only on velocity. Stars with radial velocities between 190 < v < 220  km s⁻¹ are considered members of Segue 1. This cut provides 24 member stars. The nearest nonmembers in our spectroscopic sample are at v = 155  km s⁻¹ and v = 281  km s⁻¹, so different velocity cuts would identify the same set of members.

The color–magnitude distribution of kinematically selected Segue 1 members is shown in Figure 1. We plot fiducial sequences for the globular clusters M92 ([Fe/H] = −2.3) and M3 ([Fe/H]= −1.6). These ridge lines are based on those of Clem et al. (2008) in g' − r', converted to g − r using the transformations of Rider et al. (2004) and shifted to the distance of Segue 1 (23 kpc). These fiducials are well matched to the kinematic sample. In particular, the spectra of the two bright blue stars (r ∼ 17.5, g − r ∼ −0.1) show strong broad absorption lines of the Paschen series and narrow Ca ii triplet lines consistent with being horizontal-branch stars. The position of these two stars is also well matched to the metal-poor horizontal-branch isochrones at the distance of Segue 1.

We measure the mean velocity and velocity dispersion of Segue 1 using the maximum-likelihood method described by Walker et al. (2006). This method assumes that the observed velocity dispersion is the sum of the intrinsic galaxy dispersion and the dispersion produced by measurement errors. Fitting the full Segue 1 sample based on the 24 member stars identified above, we find a mean heliocentric velocity of 206.4 ± 1.3  km s⁻¹ and a velocity dispersion of 4.3 ± 1.2  km s⁻¹(Figure 2). We do not find evidence for rotation in this system, however, given the small numbers of stars we cannot rule out rotation velocities on the same order as the velocity dispersion. We test this by adding a sinusoidal term to the systemic velocity, varying the amplitude and scale radius (Strigari et al. 2008a). The most likely value for the rotation amplitude is zero, with an upper 1σ limit of 5 km s⁻¹. While this test justifies the mass modeling we use with no streaming motion in the velocities, larger kinematic data sets and smaller velocity uncertainties are necessary to test more conclusively for streaming motion Segue 1.

The gray-shaded region in the right panel of Figure 2 indicates the 1σ width of the Segue 1 velocity distribution. We note that all the member stars lie within 2.5σ of the systemic Segue 1 velocity. The next nearest star in velocity space is over 10σ away. We interpret this cold distribution as evidence that there are no stars currently in the process of being tidally stripped from Segue 1 (Klimentowski et al. 2007). We note here and in Section 3.4, however, that the lack of outliers is not sufficient to prove that tidal processes are not affecting our results (e.g., Muñoz et al. 2008). This interpretation also does not mean that stars have not been previously stripped from Segue 1, and still allows for the possibility that tidal interactions are currently on-going in the dark matter component of this object. We discuss this further in Section 3.4.

We calculate the dynamical mass of Segue 1 using two different methods. In both cases, we assume that Segue 1 is a relaxed, self-gravitating, spherically symmetric system with no rotational motion. We presently ignore any effects on the mass estimates due to tidal interactions between Segue 1 and the Milky Way, leaving that discussion to Section 3.4. We first assume the simplest possible configuration: an isotropic sphere in which mass follows light. Further assuming that the density is described as a King model and is in virial equilibrium, Illingworth (1976) showed that the total mass is then M = 167βr_cσ² where β is a parameter that depends on the concentration of the system and is generally assumed to be 8 for dSphs (Mateo 1998), r_c is the King (1966) profile core radius, and σ is the observed average velocity dispersion. We convert the measured half-light radius of Segue 1 to King core radius as r_c = 0.64*r_eff = 18.6⁺⁵₋₃ pc. Using this method, we estimate the total mass of Segue 1 to be 4.5^+4.7_−2.5 × 10⁵  M_☉.

Our second method to calculate the mass loosens the constraint that mass-follows-light and uses the individual stellar velocity measurements (in contrast to the velocity dispersion averaged over the projected radius as above). The method is described in Strigari et al. (2008a). Similar to the mass-follows-light method, this model assumes spherical symmetry and dynamical equilibrium, i.e., that the kinematic tracer population is related to the mass distribution via the Jeans equation. We assume that the light profile follows the observed Plummer profile with effective radius r_eff = 29 pc, and that the dark matter follows a five-parameter density profile characterized by a scale density, a scale radius, an asymptotic inner slope, an asymptotic outer slope, and a parameter governing the transition between these two slopes. The dark matter density profile allows for both flat central density cores and steep central density cusps, including the CDM-favored NFW-like r⁻¹ central cusps. We also allow for a radially varying stellar velocity anisotropy profile. We then marginalize over these five free parameters, and can estimate the mass at any given radius. Though the data do not constrain any of these parameters separately, the total dynamical mass within the stellar extent of 50 pc is relatively well constrained. Using this model, we find the mass within 50 pc to be 8.7⁺¹³_−5.2 × 10⁵ M_☉. We note that the likelihood distribution of this quantity, shown in Figure 3, is nearly lognormal; the mass is greater than 5 × 10⁴ M_☉with 3σ confidence. In comparison, the total stellar mass is merely 340 L_☉.

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The two masses calculated above agree within errors. In the mass-follows-light method, the majority of the dark matter mass in the galaxy resides within the stellar radius, while the second method leaves open the possibility that the majority of the mass lies outside the observed light distribution. However, determining the total galaxy mass requires knowledge of the total radial extent of the dark matter halo and the profile shape beyond the last observed point. This is clearly difficult to determine observationally and strongly depends on the unknown orbital history of the galaxy. We can only estimate the instantaneous tidal radius of the galaxy, which ranges from a few ten to a few hundred parsecs depending on assumptions detailed in Section 3.4.2. If the tidal radius is large, then it is plausible that the majority of mass lies outside the stellar distribution.

Extrapolating the second estimate of mass to a radius of 300 pc, we find a total dynamical mass of 10⁷ M_☉, which, remarkably, is consistent with the common mass scale of all Milky Way dSphs (Strigari et al. 2008a). This common mass scale has been noted in previous studies (Mateo et al. 1993; Gilmore et al. 2007); we discuss this further in Section 6. If the stellar component of Segue 1 is embedded in a 10⁷ M_☉ dark matter halo, we would expect the luminous component to have experienced very little tidal disruption despite its current proximity to the Galaxy.

Regardless of which estimator is used above, the observed mass of Segue 1 is significantly larger than expected if all its mass were due to a stellar-only component. Since Segue 1 contains little to no HI gas (Putman et al. 2008), the stellar mass likely dominates the total baryonic mass. In the absence of nonbaryonic dark matter, we expect the M/L of Segue 1 to be M/L_V ∼ 3, accounting for stellar remnants in an old stellar population (Maraston 2005). Assuming this M/L, the stellar mass of Segue 1 is ∼1 × 10³ M_☉, translating into an expected velocity dispersion of merely 0.4  km s⁻¹. This is more than 3σ below the measured dispersion of Segue 1 and thus argues strongly for the presence of dark matter.

Finally, we calculate the v-band M/L (M/L_V) within the observed radius. Combining the absolute luminosity of Segue 1 (M_V = −1.5^+0.6_−0.8) with the mass from the first method above (assuming mass-follows-light), we calculate a M/L of ln(M/L_V) = 7.2^+1.1_−1.2 (M/L_V = 1320⁺²⁶⁸⁴₋₉₃₆), and in the second two-component method we calculate ln(M/L_V) = 7.8^+0.5_−1.3 (M/L_V = 2440⁺¹⁵⁸⁰₋₁₇₇₅). In both cases, the error distribution is asymmetric and the M/L is well in excess of that predicted from the stellar mass alone. The two-component model ratios suggests a dark matter-dominated galaxy with a 6σ significance. If the luminous components of dSphs do indeed reside in common mass dark matter halos, we would predict the highest M/Ls in the least luminous dSphs (see the middle panel of Figure 6). Since Segue 1 is the least luminous of the recently discovered ultra-faint Milky Way satellites, this remarkably high M/L is expected in this model. Understanding the processes that lead to this high M/L will be a future challenge to galaxy formation models.

The remarkably high M/L of Segue 1 rests on our interpretation that the measured stellar velocities faithfully trace the gravitational potential. Here we discuss two possibilities that might affect this assumption. First is the presence of unresolved binary stars inflating our measured velocity dispersion. The second is tidal interactions with the Milky Way affecting the kinematics. Both issues are difficult to quantify without further observations, but are worthwhile considering here.

3.4.1. The Effects of Binary Stars

3.4.2. The Effects of Tidal Interactions

We estimate the spectroscopic metallicity of individual stars in our Segue 1 sample via spectral synthesis modeling (Kirby et al. 2008a). The method compares the observed spectrum to a grid of synthetic spectra covering a range of effective temperature, surface gravity, and composition. We estimate effective temperature and surface gravity for each star based on the Johnson–Cousins VI magnitude which we determine by transforming the SDSS gri magnitudes (Chonis & Gaskell 2008). The results are unaffected by using alternative photometric methods to determine these parameters. The best-matching composition is found by minimizing residuals between the observed spectrum and a smoothed synthetic spectrum matched to the DEIMOS spectral resolution. Our method has been tested against high-resolution Keck/HIRES abundances for six RGB stars in the ultra-faint dSphs of SG07 (Kirby et al. 2008b). This comparison yields precisions better than 0.25 dex for DEIMOS spectra with signal-to-noise ratios (S/Ns) greater than S/N>20 Å⁻¹. Although the method can theoretically be applied to all types of stars, it has not yet been tested against high-resolution spectroscopic abundances for horizontal-branch or main-sequence stars.

Our kinematic sample contains a single RGB star (r = 18.4). The above method estimates its metallicity to be [Fe/H] = −3.3 ± 0.2 dex. The effective temperature and surface gravity used to determine the metallicity of this star are T_eff = 5191 K and log g = 2.76, with estimated systematic errors of 150 K and 0.12 dex, respectively. The derived metallicity is much more sensitive to T_eff than log g; Kirby et al. (2008a) estimate that a 150 K change in T_eff incurs an error on [Fe/H] of less than 0.15 dex. While DEIMOS spectra contain some information about α-element abundances, the errors we estimate on this quantity are large. The [Fe/H] value is unchanged whether or not we mask out absorption lines due to the α-elements.

A small portion of the observed Segue 1 RGB star spectrum and synthetic spectra are shown in Figure 4. At this metallicity, the strong absorption lines of Ca ii are clearly visible, but weaker Fe lines are not. In the inset to Figure 4, we compare a small region of the observed spectrum to models at [Fe/H] = −3.3 and −2.0 with the same temperature and surface gravity. For a star with these parameters, the strongest Fe line in the DEIMOS spectral range is Fe I 8689. The observed spectrum in Figure 4 shows no evidence for absorption at 8689 Å, even though a more metal-rich star would display this line.

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At red wavelengths, metallicity is often estimated via the Ca ii triplet absorption lines (e.g., Helmi et al. 2006, SG07). However, Kirby et al. (2008b), Koch et al. (2008) and others note that current implementations of this method fail for metallicities below [Fe/H] ∼ −2.5. The Ca ii triplet method is based an empirical calibration of Galactic globular clusters and is not calibrated for metallicities below [Fe/H] ⩽−2.4 (Rutledge et al. 1997). The metallicities in the ultra-faint dSph are below this limit. We therefore do not use this method and strongly caution the use of this relationship for very low metallicity systems. The remaining analysis is based on the results from the spectral synthesis method above.

While other stars in our kinematic sample have sufficient signal-to-noise to measure metallicity, [Fe/H] estimates for the remainder of the sample are less reliable. The two horizontal-branch stars seen in Figure 1 are too hot to display strong metal absorption and what metal lines exist are overwhelmed by the Paschen series. The main-sequence stellar spectra are more suitable for metallicity measurement, but have much lower S/Ns as compared to the RGB star above and higher surface gravities. The synthesis method has also not yet been tested for stars with log g > 3.3. The main-sequence stars with adequate S/N to measure a metallicity have surface gravities 3.5 < log g < 4.3. The average metallicity for these 13 main-sequence stars is [Fe/H] = −1.8 ± 0.1 dex, with individual measurements ranging from −1.5 to −2.8. This average is significantly more metal rich than above and suggests that the mean metallicity of Segue 1 may be higher than that of the single RGB star. These results also suggest that Segue 1 has a significant internal metallicity spread. In support of this spread, we note that the fiducial isochrones in the color–magnitude diagram of Figure 1 cannot simultaneously fit the RGB and main sequence. While the horizontal-branch and main-sequence turnoff are well fitted in this figure, the single RGB star is slightly too blue, suggesting it is more metal poor than the main sequence, consistent with our spectroscopically measured metallicity. These results, however, should be approached with caution. While there are no obvious reasons the main-sequence metallicities should be biased, we remain aware that the spectral synthesis code has not been tested in this regime. Pending more reliable confirmation, we take the metallicity of the RGB star to be representative of Segue 1.

Kirby et al. (2008b) demonstrate that the luminosity–metallicity relationship is loglinear for Milky Way dwarf galaxies across nearly four decades in luminosities (see Figure 6 and Section 6). Given the luminosity of Segue 1 (M_V = −1.5, L_V = 340 L_☉), the predicted metallicity based on this relationship is [Fe/H] = −2.8 ± 0.2. While our metallicity estimate of the single RGB star in our Segue 1 sample is more metal poor than this prediction, the main-sequence metallicity is more metal rich. The average of these two metallicities is closer to the predicted value. Additional observations are required to securely determine whether or not Segue 1 lies on the luminosity–metallicity relationship, and in Figure 6 we assume that the average metallicity is equal to that of the RGB star. Quantifying the mean metallicity of Segue 1 and the amount of internal metallicity spread is crucial to interpreting the formation history of Segue 1. If this object does indeed lie on the luminosity–metallicity relationship and has a significant internal metallicity spread, this is further evidence for that Segue 1 formed via galaxy, rather than globular cluster, formation processes.

There are four stars in our kinematic sample with v ∼ 300  km s⁻¹, or v_GSR ∼ 200  km s⁻¹(Figure 2). This is unusual in that standard Milky Way models predict that such high-velocity stars are extremely rare (e.g., Robin et al. 2003). These four stars have sufficiently different velocities (Δv = 30  km s⁻¹) that they are not gravitationally bound to each other; however, given their spatial and kinematic proximity they could plausibly be associated with a single stellar stream. To highlight how unusual this grouping is, we note that over the eight fields observed by SG07 (with similar targeting priorities), only seven out of nearly 900 stars had v_GSR ⩾ 200  km s⁻¹, with only one field having more than one higher velocity stars (as compared to four of 59 in Segue 1). Since none of the SG07 fields are near any known streams, we circumstantially associated these four stars with the Sgr stream. However, none of the Sgr models discussed above match the position and velocity of these higher velocity stars (filled circle in Figure 5). We tentatively associate these stars with older Sgr tidal debris or a possibly new stream. More observations and theoretical work are needed in this region to confirm this hypothesis.