A COMPLETE SPECTROSCOPIC SURVEY OF THE MILKY WAY SATELLITE SEGUE 1: THE DARKEST GALAXY^*

As a complement to ongoing deep, wide-field photometric surveys of the ultra-faint dwarfs (e.g., Muñoz et al. 2010), we embarked upon a spectroscopic search for evidence of tidal stripping or extratidal stars. The ideal target for such a search would be a galaxy that (1) is nearby, to maximize the tidal forces it is currently experiencing,⁹ (2) is moving at a high velocity relative to the Milky Way, to minimize the degree of contamination by foreground stars, and (3) has a small angular size, to minimize the area that the survey needs to cover. Out of all the known Milky Way dwarf galaxies, the clear choice according to these criteria is Segue 1. At a distance of 23 kpc from the Sun (28 kpc from the Galactic center), Segue 1 is the closest dwarf galaxy other than Sagittarius, which of course is the prototype for a dwarf undergoing tidal disruption. Its heliocentric velocity of 207 km s⁻¹ (the largest of the Milky Way satellites within 200 kpc) and relatively small velocity dispersion give Segue 1 the lowest expected surface density of Milky Way foreground stars within 3σ of its mean velocity (according to the Besançon model; Robin et al. 2003). Finally, if Segue 1 is not surrounded by a massive dark matter halo—and it can only host visible tidal features if no extended halo is present—its instantaneous Jacobi (tidal) radius based on the stellar mass estimated by Martin et al. (2008) is ∼30 pc, or 45, which is an observationally feasible area to search. This calculation conservatively assumes that Segue 1 has never been closer to the Milky Way than it is now; if its orbital pericenter is less than 28 kpc, its baryon-only tidal radius would be even smaller. The properties of Segue 1 are summarized in Table 1.

Table 1. Summary of Properties of Segue 1

Row	Quantity	Value
(1)	R.A. (J2000) (h m s)	10:07:03.2${\,\pm\,} 1\mbox{$.\!\!^{\mathrm s}$}7$
(2)	Decl. (J2000) (° ' '')	+16:04:25 ± 15''
(3)	Distance (kpc)	23 ± 2
(4)	MV	−1.5+0.6 − 0.8
(5)	LV (L☉)	340
(6)		0.48+0.10 − 0.13
(7)	μV, 0 (mag arcsec−2)	27.6+1.0 − 0.7
(8)	reff (pc)	29+8 − 5
(9)	Vhel (km s−1)	208.5 ± 0.9
(10)	VGSR (km s−1)	113.5 ± 0.9
(11)	σ (km s−1)	3.7+1.4 − 1.1
(12)	Mass (M☉)	5.8+8.2 − 3.1 × 105
(13)	M/LV (M☉/L☉)	3400
(14)	Mean [Fe/H]	−2.5

Notes. Rows (1)–(2) and (4)–(8) are taken from the SDSS photometric analysis of Martin et al. (2008) and row (3) from Belokurov et al. (2007a). Values in rows (9)–(14) are derived in this paper.

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To select targets for the survey, we focused on the area within ∼15' (100 pc) of the center of Segue 1 as determined by Martin et al. (2008). Guided by the 24 member stars identified by G09, we tweaked the color of the (appropriately shifted and reddened) M92 isochrone from Clem et al. (2008) so that it passed through the center of the member sequence at all magnitudes (this adjustment was only needed for the subgiant branch and main sequence, not the red giant branch). The Segue 1 main sequence appears to be slightly redder than that of M92, with the offset increasing toward fainter magnitudes (see Figure 1). The full G09 member sample is located within 0.25 mag of the adjusted fiducial track (0.2 mag for r ⩽ 21 and 0.1 mag for r ⩽ 20).

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Using positions and magnitudes extracted from DR5 of the SDSS (Adelman-McCarthy et al. 2007), we selected stars within a narrow range of colors around the adopted fiducial sequence. Red giants (r ⩽ 20) were required to be within 0.1 mag of the sequence, and the selection window was gradually widened toward fainter magnitudes, reaching 0.235 mag at r = 21.7. Horizontal branch (HB) candidates were allowed to be 0.2 mag away from the fiducial track. A small number of stars located near a metal-poor asymptotic giant branch (AGB) isochrone from Girardi et al. (2004) were also selected. Within 10' (67 pc) of Segue 1, we identified 112 stars lying within the color–magnitude selection box (down to a magnitude limit of r = 21.7) that we consider to be our primary target sample. Stars up to a factor of two farther away from the fiducial sequences or within the primary color–magnitude selection region but at larger distances from Segue 1 were targeted with reduced priorities. We also included as many of the known member stars as possible on multiple slit masks to obtain repeated velocity measurements for constraining the binary population.

We observed 12 new slit masks, including at least one slit placed on each of the 112 candidate member stars (plus repeat observations of 18 of the 24 members from G09), with the DEIMOS spectrograph (Faber et al. 2003) on the Keck II telescope. The observations took place on the nights of 2009 February 18, 26, and 27 and 2010 February 12 and 13.

The spectrograph setup and observing procedures were identical to those described by Simon & Geha (2007, hereafter SG07): we used the 1200 ℓ mm⁻¹ grating with an OG550 filter to cover the wavelength range 6500–9000 Å at a spectral resolution of R = 6000 (slit width of 07). An internal quartz lamp and Kr, Ar, Ne, and Xe arc lamps were employed for flat-fielding and wavelength calibration, respectively. Total integration times for the science masks ranged from 10 minutes for a mask targeting very bright stars to ∼2 hr for most of the masks aimed at fainter stars. The masks are summarized in Table 2. Conditions during the observing nights were generally good, with seeing ranging from 07 to 10 and thin cirrus at times.

As with the observations, data reduction followed the outline given in SG07. We used a modified version of the data reduction pipeline developed for the DEEP2 galaxy redshift survey. The additional improvements we made to the code since SG07 were to redetermine the wavelength solution for slits that were initially not fit well and to identify and extract serendipitously observed sources more robustly. The pipeline determines a wavelength solution for each slit, flat-fields the data, models and subtracts the sky emission, removes cosmic rays, co-adds the individual frames, and then extracts the spectra.

In the spring of 2009, the DEIMOS CCD array was experiencing an intermittent problem wherein one of the eight chips (corresponding to the blue half of the spectral range at one end of the field of view) would fail to read out completely on some exposures. In a few cases, the affected chip was completely blank, while in others only the top or bottom of the chip was absent and the remainder of the pixels were saved normally. We dealt with this problem conservatively by excluding all of the data from the temperamental chip from our reduction any time it exhibited abnormal behavior. As a result, a fraction of our targets have lower signal-to-noise ratio (S/N) in the blue than would be expected from the total mask observing times, but since most of the key spectral features for our analysis are on the red side of the spectra, the overall impact is minor.

After reducing the data, we used the custom IDL code described by SG07 to measure the radial velocity of each star. We first corrected each spectrum for velocity offsets that could result from miscentering of the star in the slit by cross-correlating the telluric absorption features against those of a telluric standard star specially obtained for this purpose (Sohn et al. 2007; SG07). The spectra were then cross-correlated with a library of high S/N templates with well-known velocities obtained with DEIMOS in 2006 and 2007. The template library contains 15 stars ranging from spectral type F through M, mostly focusing on low-metallicity giants but also including representative examples of subgiants, HB stars, main-sequence stars, and more metal-rich giants. We also fit four extragalactic templates, identifying a total of 69 background galaxies and quasars. The velocity of each target spectrum is determined from the cross- correlation with the best-fitting template spectrum. We estimate velocity errors using the Monte Carlo technique presented in SG07: we add random noise to each spectrum 1000 times and then redetermine its velocity in each iteration. We take the standard deviation of the Monte Carlo velocity distribution for each star as its measurement uncertainty. Previous analysis of a sample of stars observed multiple times with the same instrument configuration and analysis software indicates that our velocity accuracy is limited by systematics at the 2.2 km s⁻¹ level. We have now confirmed the magnitude of the systematic errors with a much larger sample of repeat measurements than were used by SG07.

As discussed in Sections 1 and 2.2, one of the main goals of this study is to determine the effect of binary stars on the observed velocity dispersion of Segue 1. Accomplishing this task requires making multiple velocity measurements of stars, verifying that the derived velocity uncertainties are accurate, and searching for individual binaries. The bulk of our analysis of the repeat observations is presented in Paper II, but in Figure 2(a) we illustrate the agreement between subsequent velocity measurements and the initial one for each star observed more than once. Figure 2(b) shows the distribution of velocity differences for each pair of measurements, normalized by their uncertainties. The good match to a Gaussian distribution for $-2 < (v_{2} - v_{1})/\sqrt{\vphantom{A^A}\smash{\hbox{${\sigma _{1}^2 + \sigma _{2}^2}$}}} < 2$ indicates that the uncertainties are accurate, and the excess in the wings of the distribution provides evidence for velocity variability (see Section 4.2 and Paper II). A total of 93 stars, including approximately half of the member sample, were observed at least twice during the course of our survey.

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In Section 2.3, we described obtaining a spectrum of each one of the 112 stars within our primary photometric selection region and not more than 67 pc from the center of Segue 1. We successfully measured velocities for 109 of these stars. One target star (SDSSJ100707.12+160022.4) did not have any identifiable features in its spectrum, one spectrum (SDSSJ100700.75+160300.5) suffered from reduction difficulties (see the Appendix), although it appears to be a member, and the remaining one (SDSSJ100733.12+155736.7) was not detected in our data. The magnitude of this latter star should have made it easily visible in the exposures we obtained, but a check of the SDSS images showed no source at this position, and the target was flagged in the SDSS catalog as a possible moving object. We conclude that this source was actually an asteroid that happened to have the right colors and position to be selected for our survey. After excluding it, our completeness is 98.2%. We also targeted a fraction of Segue 1 member candidates as far out as 16' (107 pc). Within 11', 12', and 13', our overall completeness is 97.0%, 96.7%, and 92.3%, respectively. Only a few stars at larger radii were observed.

We consider three different membership selection techniques: a subjective, star-by-star selection using velocity, metallicity, color, magnitude, and the spectrum itself, a slightly modified version of the algorithm introduced by Walker et al. (2009b), and a new Bayesian approach presented in Paper II. For the remainder of the paper, we adopt the third method as defining our primary sample except where explicitly noted.

We first select member stars using the parameters listed above. Candidate members must have colors and magnitudes consistent with the photometric selection region displayed in Figure 1 and described in Section 2.2, must have velocities within a generous ∼4σ window around Segue 1 based on the systemic velocity and velocity dispersion measured by G09, and should have low metallicities. We can then iteratively refine the member selection by examining the stars near the boundaries of the selection region more carefully. With this process, we classify 65 stars as definite members, six additional stars as probable members, and five more as likely (but not certain) non-members. The remaining stars are clearly not members. The sample selected in this way is displayed in Figure 3.

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While the flexibility afforded by this subjective approach is useful and allows all available information to be taken into account, a rigorous and objective method is also desirable to avoid the possibility of bias. Walker et al. (2009b) recently developed such a statistical algorithm to separate two potentially overlapping populations. This technique, known as expectation maximization (EM), allows one to estimate the parameters of a distribution in the presence of contamination, with specific application to the case of identifying dwarf galaxy member stars against a Milky Way foreground. Given a set of velocities, radial distances, and a third parameter in which dwarf galaxy stars and Milky Way stars are distributed differently, the EM algorithm relies on the distinct distributions of the two populations in each property to iteratively assign membership probabilities to each star until it converges on a solution. Walker et al. (2009b) use the pseudo-EW of the Mg triplet lines at 5180 Å as their third parameter, but we find that the reduced EW of the CaT lines works as well. Rutledge et al. (1997a, 1997b) define this reduced EW as W' = ΣCa − 0.64(V_HB − V), where ΣCa is the weighted sum of the EWs of the CaT lines: ΣCa = 0.5EW₈₄₉₈ + 1.0EW₈₅₄₂ + 0.6EW₈₆₆₂. Note that since the EM algorithm does not incorporate photometric information, it must be run on a sample of stars that has already passed the color–magnitude selection. Also, EM may fail to select HB stars because their broad hydrogen lines interfere with measurements of the CaT EW; fortunately, the HB members of Segue 1 are obvious.

We display the distribution of observed stars in radius, velocity, and reduced CaT EW in Figures 4 and 5. Segue 1 stands out as the large overdensity of stars with velocities just above 200 km s⁻¹ and smaller than average radii and W' values. We caution that W' is only a properly calibrated metallicity indicator for stars on the red giant branch (RGB), which constitute a small minority of the data set examined here. Nevertheless, experiments with globular cluster stars reaching several magnitudes below the main-sequence turnoff from the compilation of Kirby et al. (2010) show that while W' does increase at constant metallicity toward fainter main-sequence magnitudes, this increase is less than 2 Å for stars within 2 mag of the turnoff. We therefore conclude that including both RGB and main-sequence stars may broaden the Segue 1 distribution toward higher values of W' (perhaps accounting for the clear presence of Segue 1 stars in Figure 4(b) up to W' ≈ 6 Å), but should not significantly affect the performance of EM.

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The EM algorithm selects 68 stars as definite members of Segue 1 (membership probability p ⩾ 0.9). An additional three stars have 0.8 ⩽ p < 0.9 and are classified as members by eye, yielding 71 very likely members. These 71 stars correspond to 70 of the 71 subjectively classified members.¹¹ Finally, three stars have membership probabilities of 0.5 ⩽ p < 0.8.

Our final results are based on a Bayesian analysis that allows for both contamination by Milky Way foreground stars and the contribution of binary orbital motions to the measured velocities. These calculations are a natural generalization of the Walker et al. (2009b) EM method. The method is described in more detail in Paper II and is summarized here in Section 5. In this framework, we find 53 definite members (〈p〉 ⩾ 0.9) and nine further probable members (0.8 ⩽ 〈p〉 < 0.9), plus the two RR Lyrae variables (see Section 4.2), but seven of the stars considered likely members by the other two techniques receive lower probabilities of 0.4 ⩽ 〈p〉 < 0.8 here. With the exception of the discussion in Section 4.3, where we mention the range of velocity dispersions that can be obtained for different member samples, the main results of this paper (including the velocity dispersion, mass, and density of Segue 1) rely on this Bayesian analysis. It is important to note that unlike previous studies, we include all stars that pass our photometric cuts in the Bayesian calculations, not just the ones with high membership probabilities. Each star is weighted according to its probability of being a member of Segue 1. This approach allows us to account correctly for the significant number of stars with membership probabilities that are neither close to zero nor close to one.

One of the defining differences between galaxies and globular clusters is that dwarf galaxies universally exhibit signs of internal chemical evolution and contain stars with a range of metallicities, while globulars generally do not. Recent work has shown that multiple stellar populations with different chemical abundance patterns are in fact present in some globular clusters, but these differences tend to be subtle (which is why they are only being recognized now) and are preferentially found in luminous clusters that are often argued to be the remnants of tidally stripped dwarf galaxies (e.g., Lee et al. 1999; Marino et al. 2009; Da Costa et al. 2009; Ferraro et al. 2009; Cohen et al. 2010).

We use the spectral synthesis method introduced by Kirby et al. (2008a) and refined by Kirby et al. (2009, 2010) to measure iron abundances¹² in Segue 1 directly from our medium-resolution spectra. Kirby et al. (2010) showed that the metallicities measured in this way are reliable for stars with log g < 3.6. Thus, we can only determine metallicities for the six red giant members of Segue 1; the fainter stars are all at or below the main-sequence turnoff. The metallicities of these six stars span an enormous range, with two stars at [Fe/H] > −1.8 and two others at [Fe/H] < −3.3 (see Table 4). One of the two extremely metal-poor (EMP) stars does not have a well-defined metallicity measurement because no Fe lines are detected in its spectrum. The upper limit on its metallicity therefore depends on the assumptions, but it is certainly well below [Fe/H] = −3. The mean metallicity of the Segue 1 red giants is [Fe/H] = −2.5, comparable to the most metal-poor galaxies identified so far (Kirby et al. 2008b), and the standard deviation, while not well constrained with such a small sample, is ∼0.8 dex. Using a completely independent data set, Norris et al. (2010b) reach essentially identical conclusions regarding the Segue 1 abundance range and identify yet another EMP member star at [Fe/H] = −3.5 (Norris et al. 2010a).

The very large star-to-star spread in metallicities and the presence of EMP stars with [Fe/H] < −3.0 each independently argue that Segue 1 cannot be a globular cluster, contrary to initial suggestions (Belokurov et al. 2007a; Niederste-Ostholt et al. 2009). Only ω Centauri among globular clusters has a comparable metallicity spread (e.g., Norris & Da Costa 1995; Hilker et al. 2004), and that object is widely regarded to be the remnant of a dwarf galaxy (Lee et al. 1999; Majewski et al. 2000b; Carraro & Lia 2000; Hilker & Richtler 2000; Tsuchiya et al. 2003; Mizutani et al. 2003; Rey et al. 2004; Ideta & Makino 2004; McWilliam & Smecker-Hane 2005; Carretta et al. 2010) rather than a true globular. The lowest metallicity Segue 1 giants are also at least a factor of four more metal-poor than any known star in a globular cluster (e.g., King et al. 1998; Kraft & Ivans 2003; Preston et al. 2006; Carretta et al. 2009). We conclude that the metallicities of stars in Segue 1 provide compelling evidence that, irrespective of its current dynamical state, Segue 1 was once a dwarf galaxy.

Before attempting to determine the velocity dispersion and mass of Segue 1, we consider the impact of variable stars and binaries that could be in our sample. The G09 members include two HB stars in Segue 1. Our repeated measurements demonstrate that the velocities of both of these stars vary with time, leading us to conclude that they are RR Lyrae variables. Follow-up photometry with the Pomona College 1 m telescope at Table Mountain Observatory confirms that one of these stars, SDSSJ100644.58+155953.9, is a photometric variable with a characteristic RR Lyrae period of 0.50 days.¹³ We do not detect variability in the second star, SDSSJ100705.60+160422.0, but the limits we can place are not inconsistent with the low amplitude variability that might be expected for such a blue star. Given their blue colors, the stars are probably type c variables pulsating in the first overtone mode. Because the light curve phases at the times our spectra were acquired are not known, we cannot measure the center-of-mass velocities of these stars and must remove them from our kinematic sample even though they are certainly members of Segue 1.

We also obtained multiple measurements of five of the six Segue 1 red giants in order to check whether any of them are in binary systems. For four of the stars, the velocity measurements do not deviate by more than 2σ from each other, providing no significant indication of binarity, although long period or low amplitude orbits cannot be ruled out. SDSSJ100652.33+160235.8, however, shows clear radial velocity variability, with the velocity decreasing from 216.1 ± 2.9 km s⁻¹ on 2007 November 12 to 203.0 ± 2.3 km s⁻¹ on 2009 February 27, and then rising back to 210.8 ± 2.3 km s⁻¹ on 2010 February 13. Assuming that these observations correspond to a single orbital cycle, we infer a period of ∼1 yr and a companion mass of ∼0.65 + 0.25(1/sin³i − 1) M_☉.

With at least one out of the brightest six stars (excluding the even more evolved HB stars) in the galaxy in a binary system, the binary fraction of Segue 1 is likely to be significant, as has been found for other dwarf galaxies (Queloz et al. 1995; Olszewski et al. 1996) and some, although not all, globular clusters (Fischer et al. 1993; Yan & Cohen 1996; Rubenstein & Bailyn 1997; Clark et al. 2004; Sollima et al. 2007). For main-sequence stars, which dominate our sample, the binary fraction can only be larger since the tight binary systems will not yet have been destroyed by the evolution of the more massive component. We have a limited sample of repeat observations of some of the main-sequence members, in which two additional stars, SDSSJ100716.26+160340.3 and SDSSJ100703.15+160335.0, are detected as probable binaries. However, these binary determinations are almost certainly quite incomplete, and proper corrections for the inflation of the observed velocity dispersion of Segue 1 by binaries must be done in a statistical sense, as we discuss in Section 5.

Because the issues of membership and binary stars are so critical to our results, we must experiment with different samples of member stars and methods of determining the velocity dispersion. Inspection of Figure 4 makes clear that for W' ⩽ 3 Å, the expected contamination by Milky Way foreground stars is negligible (1–2 stars). Very conservatively, then, we can select the stars with W' ⩽ 3 Å and 190 km s⁻¹ ≲ v ≲ 225 km s⁻¹ as an essentially clean member sample (the exact velocity limits chosen do not matter, since the next closest stars are at v = 175 km s⁻¹ and v > 300 km s⁻¹). With the two RR Lyrae variables and the one obvious RGB binary removed, the velocity dispersion of the other 34 stars is 3.3 ± 1.2 km s⁻¹. (Note that we calculate the velocity dispersion using a maximum likelihood method following Walker et al. 2006.) This value can be regarded in some sense as a lower limit to the observed dispersion of Segue 1 (prior to any correction for undetected binaries).

Since this conservative approach involves discarding nearly half of the data, we would also like to consider alternatives. The largest member sample that we can define is the 71 stars selected using either our holistic, subjective criteria in Section 3.1 or the EM algorithm. After again excluding the two RR Lyraes and the RGB binary, the raw velocity dispersion of these stars is 5.5 ± 0.8 km s⁻¹, which we take as an upper limit to the observed dispersion of Segue 1 (as before, prior to correcting for undetected binaries). However, the dispersion in this case is dominated by a single star (SDSSJ100704.35+160459.4; see Section 4.4). If we remove this object from the sample, the dispersion of the remaining stars falls to 3.9 ± 0.8 km s⁻¹, corresponding to a factor of two decrease in the mass of the galaxy. Other stars that are borderline members or non-members have negligible effects on the derived dispersion (see the Appendix).

We note at this point a curious finding regarding the brightest stars in Segue 1. If we isolate the evolved stars (six giants and two HB stars) in the sample, their velocity dispersion appears to be quite small. For the HB stars and the binary on the giant branch, we cannot assume that we have enough measurements to average out the effects of the binary orbit and RR Lyrae pulsations, but we estimate a dispersion of 1.3^+2.4 _{− 0.7} km s⁻¹ for the other five RGB stars. Using our full Bayesian analysis (Section 5) and including the binary, the intrinsic dispersion of the giants is 2.0^+3.1 _{− 1.7} km s⁻¹. Given the substantial error bars, these values are formally consistent with the larger dispersion obtained for the full data set, even though they are also close to zero. Nevertheless, the velocity dispersion we determine for the remaining stars is not significantly affected by the inclusion or exclusion of the giants and HB stars. Without any known physical mechanism that could change the kinematics of Segue 1 for stars in different evolutionary states, we conclude that the apparently small dispersion of these stars is most likely a coincidence resulting from small number statistics.

Next, we use the sample defined by the Walker et al. (2009b) EM algorithm. Since this sample is nearly identical to that considered in the previous paragraphs, the results are unchanged: a dispersion of 5.7 ± 0.8 km s⁻¹ for all 71 stars minus the RR Lyraes and the RGB binary, and 4.1 ± 0.9 km s⁻¹ when SDSSJ100704.35+160459.4 is removed. It is worth noting that all of these measurements and those described above are consistent within 1σ with the original velocity dispersion of 4.3 ± 1.2 km s⁻¹ determined by G09.

The above two methods make various assumptions about how membership is defined, but do not allow for a fully self-consistent statistical treatment. The method described in Paper II (Martinez et al. 2010) and summarized in Section 5 treats these assumptions and the data analysis in a fully Bayesian manner. This analysis identifies a total of 61 stars (excluding the two RR Lyrae variables) as likely members with 〈p〉 > 0.8. This method arrives at significantly lower membership probabilities for eight stars compared to the EM and subjective analyses. These stars fall into three partially overlapping categories: velocity outliers, frequently with large velocity uncertainties as well (such that there is a significant chance that the star's true velocity is far away from the systemic velocity of Segue 1); stars with large reduced CaT EWs (W' > 4 Å); and stars at large radii (r > 10'). The only one of these stars that has an appreciable effect on the velocity dispersion is SDSSJ100704.35+160459.4. Removing each of the seven other stars from the sample changes the dispersion by less than 0.2 km s⁻¹. With only the 61 most likely members included in the calculation, we find a velocity dispersion of 3.4 ± 0.9 km s⁻¹.

Despite our best efforts to define a member sample that is both clean and complete, there are fundamental uncertainties that cannot be avoided in determining whether any given star is a member of Segue 1. In particular, we know that Segue 1 is an old, metal-poor stellar system located 23 kpc from the Sun, and moving at a heliocentric velocity of ∼207 km s⁻¹. Unfortunately, the Milky Way halo also contains old, metal-poor stars that span ranges in distance and velocity that encompass Segue 1. Given a large enough search volume, it is therefore inevitable that some halo stars with the same age, metallicity, distance (and hence the same colors and magnitudes), and velocity as Segue 1 will be found. We can use observations and models to estimate the expected number of such stars included in our survey, but that does not help us in ascertaining the provenance of individual stars.

As a result, we are left with a small number of stars whose membership status is necessarily uncertain. The algorithms discussed in Section 3.1 allow us to assign membership probabilities to these objects, which is the best statistical way to deal with our limited knowledge. Nevertheless, each star that we observed either is or is not a member, and with a small sample, the assumption that a particular star has a membership probability of, e.g., 0.6 can produce different results than if it were known absolutely to be a member or not. Most of the stars in this category do not have an appreciable effect on the derived properties of Segue 1 (most importantly the velocity dispersion), either because they lie near the middle of the distribution or because their velocity uncertainties are relatively large. One object, however, can make a significant difference, as discussed in the following paragraph. A few other stars that cannot be classified very confidently in one category or the other are listed in the Appendix, but their inclusion or exclusion has minimal impact on the properties of Segue 1 or the results of this paper.

The one star that can individually affect the kinematics of Segue 1 is SDSSJ100704.35+160459.4. This star is a major outlier in velocity, with a mean velocity from two measurements of 231.6 ± 3.0 km s⁻¹. It is therefore located more than 6σ (where σ is estimated from the rest of the stars) away from the systemic velocity of Segue 1, but because its position is extremely close (38'') to the center of the galaxy and it has a CaT EW that could plausibly be associated with Segue 1 (although on the high side), the EM method returns a membership probability of 1. The membership probability from our full Bayesian analysis (see Paper II) is lower, but far from negligible, at 0.49. The high velocity of this star relative to the systemic velocity of Segue 1 could be explained if it is a member of a binary system, but our two velocity measurements of it (separated by 1 yr) do not show a significant change in velocity, so the period would have to be ≳ 5 yr. In addition to its disproportionate effect on the velocity dispersion, for an equilibrium model a star that is a 6σ outlier from the mean velocity but is located so close to the center of the galaxy implies strongly radial orbits. None of the other stars in the sample lead to a preference for extreme velocity anisotropy.

Given a sample of stars that may be members of Segue 1, we allow for the possibility that some of the observed stars are likely members of binary star systems rather than single stars. We therefore must treat the (unknown) velocity of the star system's center of mass v_cm and the measured velocities themselves as distinct quantities. For each star system of absolute magnitude M_V, we have a set of measured velocities v_i, where i runs over the number of repeat observations of the star under consideration at times t_i, and the associated measurement uncertainties e_i. We write the likelihood of obtaining the observed data for each star assuming it is a member of Segue 1 (S1) in terms of a joint probability distribution in the measured velocities v_i and the unknown center-of-mass velocity v_cm:

$$\begin{eqnarray} &&\mathcal {L}_{\mathrm{S1}}(v_{i}|e_{i},t_{i},M_{V};\sigma,\mu,B, \mathscr {P}) \nonumber \\ && \quad = \int _{-\infty }^{\infty } P(v_{i}|v_{{\rm cm}},e_{i},t_{i},M_{V};B, \mathscr{P})P(v_{{\rm cm}}|\sigma,\mu) dv_{{\rm cm}}\nonumber \\ && \quad \propto (1-B) \frac{e^{-\frac{(\langle v\rangle -\mu)^{2}}{2\sigma ^{2}}}}{\sqrt{\sigma ^2 + \sigma _{m}^2}} + BJ(\sigma,\mu | \mathscr{P}), \end{eqnarray} \tag{ 1 }$$

where the first factor in the integrand is the probability of drawing a set of velocities v_i given a center-of-mass velocity v_cm and certain values for the binary parameters B and $\mathscr{P}$. B represents the binary fraction and $\mathscr{P}$ is the set of binary parameters [μ_log P, σ_log P] (see below). The second factor is the probability distribution of center-of-mass velocities given an intrinsic velocity dispersion of Segue 1, σ, and a systemic velocity, μ. In the last line of Equation (1), 〈v〉 is the average velocity weighted by measurement errors and σ_m is the uncertainty on this weighted average for the combined measurements of each star. Note that we assume that the center-of-mass velocity distribution of Segue 1 is Gaussian. We also use metallicity (W') and position to help determine membership, so that the full likelihood is of the form $\mathcal {L}(v_{i},W^{\prime },r)$, but we omit the metallicity and position dependence in the equations presented here for simplicity. The absolute magnitude of each star is taken into account so that its radius can be calculated and only binaries with separations larger than the stellar radius are allowed, as described in Minor et al. (2010) and Paper II.

For each star, the $J(\mu,\sigma |\mathscr{P})$ factor is generated by running a Monte Carlo simulation over the distribution of binary properties, which include the orbital period, mass ratio, and orbital eccentricity. Unfortunately, the characteristics of binary populations in dwarf galaxies are completely unknown at present. The best empirical constraints on binary properties come from studies of the Milky Way, but there is no guarantee that the small-scale star-forming conditions in the Milky Way and those that prevailed in Segue 1 many Gyr ago are similar, especially since Segue 1 has a metallicity two orders of magnitude below that of the Galactic disk population. In principle, a lower metallicity could change the probability of forming binary systems (and higher order multiples) and the properties of those systems, but binaries with separations in the range that can affect our observations (≲ 10 AU) are expected to form via disk fragmentation (e.g., Kratter et al. 2010) or interactions between protostellar cores (e.g., Bate 2009), neither of which should be very sensitive to metallicity (M. Krumholz 2010, private communication).

In the Monte Carlo simulations, we fix the distributions of the mass ratio and eccentricity to follow that observed in solar neighborhood binaries. However, since the period distributions of binary populations have been observed to differ dramatically from cluster to cluster (e.g., Brandner & Koehler 1998; Patience et al. 2002), we allow for a range of period distributions. Specifically, we assume that the distribution of periods has a log-normal form similar to that of Milky Way field binaries (Duquennoy & Mayor 1991; Raghavan et al. 2010). We take the mean log period μ_log P and the width of the period distribution σ_log P as free model parameters. We further assume that the period distribution observed in Milky Way field binaries is the result of superposing narrower binary distributions from a variety of star-forming environments. Thus, our prior on the period distribution is that it is narrower than, but consistent with being drawn from, the Duquennoy & Mayor (1991) period distribution with μ_log P = 2.23 and σ_log P = 2.3. To accomplish this, we choose a flat prior in σ_log P over the interval [0.5, 2.3] and a Gaussian prior in μ_log P centered at μ_log P = 2.23, with a width chosen such that when a large number of period distributions are drawn from these priors, they combine to reproduce the Milky Way period distribution of field binaries. We can then write the likelihood of each star being a member of Segue 1 or the Milky Way as

$$\begin{eqnarray} && \mathcal {L}(v_{i}|e_{i},t_{i},M_{V};f,B,\sigma,\mu,\mathscr{P}) = (1-f)\mathcal {L}_{{\rm MW}}(v_{i}|e_{i})\nonumber\\ && \qquad \quad + f\mathcal {L}_{S1}(v_{i}|e_{i},t_{i},M_{V};B,\sigma,\mu,\mathscr{P}), \end{eqnarray} \tag{ 2 }$$

where f is the fraction of the total sample that are Segue 1 members. The second term in Equation (2) is given by Equation (1), and the likelihood of membership in the Milky Way is

$$\begin{equation} \mathcal {L}_{{\rm MW}}(v_{i}|e_{i}) \propto \int \frac{e^{-\frac{(v_{{\rm cm}} - \langle v\rangle)^2}{2\sigma _{m}^2}}}{\sqrt{2\pi \sigma _{m}^2}} P_{{\rm MW}}(v_{{\rm cm}}) dv_{{\rm cm}}. \end{equation} \tag{ 3 }$$

The expected Milky Way velocity distribution is taken from a Besançon model (Robin et al. 2003) after the same photometric criteria used to select Segue 1 stars have been applied.

By applying the above analysis to our full Segue 1 data set, we can correct for the likely presence of binaries in the sample and derive the intrinsic velocity dispersion of the galaxy. All observed stars (not only the likely members) that meet the photometric selection cut described in Section 2.2 are included in this calculation, with the weight for each star determined by its likelihood of membership in Segue 1. Our posterior probability distribution for the dispersion is maximized at σ = 3.7 km s⁻¹, ∼12% smaller than what we measure without a binary correction. The 1σ uncertainties on the dispersion are +1.4 km s⁻¹ and −1.1 km s⁻¹. We find a 90% lower limit on the dispersion of 1.8 km s⁻¹, and the probability of the true velocity dispersion being less than 1 km s⁻¹ is ∼4%. The differential and cumulative probability distributions for σ are displayed in Figure 6. If the gravitational potential of Segue 1 were provided only by its stars, the velocity dispersion would be ≲ 0.4 km s⁻¹ (G09). Our lower limit on the dispersion therefore allows us to conclude with high confidence that Segue 1 is dynamically dominated by dark matter unless it is currently far from dynamical equilibrium. We discuss the implausibility of large deviations from equilibrium caused by tidal forces later in Section 7.2.

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We further note that small intrinsic velocity dispersions (σ ≲ 2 km s⁻¹) can only be obtained if the binary period distribution is skewed toward short periods. In particular, mean periods of less than ∼40 yr are required to produce such a small dispersion (Paper II); for comparison, the mean period in the solar neighborhood is 180 yr (Duquennoy & Mayor 1991). The posterior distribution we derive for the mean period in Segue 1 is in fact weighted toward quite short periods (∼10 yr). This result is not an artifact of the short time baseline of our multi-epoch data (observations on timescales of ∼1 yr cannot constrain periods of centuries or longer), because our priors allow for flatter period distributions than the posterior for the mean period. Despite this preference for shorter periods, the data strongly indicate only a modest contribution to the velocity dispersion from binaries because the period distribution is still wide and the small number of detected binaries indicates that the fraction of stars in close binary systems is not large.

To provide reassurance that our priors on the period distribution are not biasing the posterior period distribution toward longer periods (and hence the corrected velocity dispersion toward higher values), we repeated the calculations above with a flat prior on the mean period μ_log P. The best-fit mean period barely changed, and while somewhat shorter periods are allowed in this case, the probability of an intrinsic velocity dispersion less than 1 km s⁻¹ does not increase (see Figure 7). Even with a more extreme logarithmic μ_log P prior, the likelihood of a small dispersion is unchanged despite the resulting very short mean period. The reason for this outcome is that when the mean period is forced to be short, the binary fraction is then constrained to be low and the width of the period distribution is similarly constrained to be small to fit the observed changes in the velocities and the observed velocity distribution. Hence, the tail of the probability distribution toward low velocity dispersions cannot be made significantly larger by having a prior that biases the result to shorter mean periods.

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These results contrast with the findings of McConnachie & Côté (2010), who conclude that galaxies like Segue 1 could have very low intrinsic velocity dispersions that are inflated substantially by the presence of binary stars. While we agree with their results given the assumptions they make, two primary factors are responsible for the different conclusions from our analysis. First, McConnachie & Côté ignore binaries with periods longer than 10–100 yr. This cutoff appears reasonable from an observational perspective, since such binaries will not be detectable in current data sets, but it has the effect of making the binary fractions they require very large because the majority of Milky Way binaries have periods longer than 100 yr. Second, they analyze only single-epoch velocity data sets, whereas the multiple measurements we have for a number of stars give us much greater leverage with which to determine the inflation of the velocity dispersion caused by binaries. Our Bayesian analysis including the multi-epoch data and all the information in the tail of the velocity distribution shows that a substantial inflation by binaries is disfavored for the Segue 1 data set presented here (see Paper II for more details).

The same Bayesian machinery described in Section 5.1 for determining the velocity dispersion of Segue 1 can also be employed to calculate the mass of the galaxy (again including a correction for binary stars). Wolf et al. (2010; also see Walker et al. 2009a) derived a simple formula for the mass within the half-light radius of a system: M_1/2 = 3σ²r_1/2/G. For a flat prior on σ (see Paper II for a discussion of the effect of the choice of priors), we find a posterior probability distribution on the mass within the three-dimensional half-light radius of Segue 1 (38 pc) of 5.8^+8.2 _{− 3.1} × 10⁵ M_☉, consistent with the mass determined by G09 from the original data set.¹⁴ Because the uncertainties on the mass are not Gaussian, this measurement disagrees with the stellar mass of Segue 1 (∼1000 M_☉) at much more than 1.8σ significance; the 99% confidence lower limit on the mass is 16, 000 M_☉ (however, the magnitude of this low-mass/low-σ tail in the probability distribution is prior-dominated). The V-band mass-to-light ratio within the half-light radius is ∼3400 M_☉/L_☉. Since there is no evidence that the dark matter halo of Segue 1 is truncated at such a small radius, this value represents a lower limit on the total mass-to-light ratio of the galaxy, which could be 1–2 orders of magnitude larger.

7.1.1. Extended Tidal Debris Near Segue 1

7.1.2. The Surface Brightness Profile of Segue 1

7.1.3. Ancient Wraps of the Sagittarius Stream

7.1.4. Does the Sagittarius Stream Overlap in Velocity With Segue 1?

7.1.5. Contamination of the Segue 1 Member Sample

Relying on the line of reasoning examined above, NO09 proposed that Segue 1 is actually a star cluster whose derived properties have been distorted by contamination from Sgr stream stars. Such contamination is a difficult issue to quantify, because by definition any stars that could be contaminating the member sample must have very similar velocities, metallicities, distances, and ages to Segue 1 stars. The only way to assess definitively the expected number of contaminants would be with an even wider field survey to identify Segue 1-like stars that are far enough away from the galaxy so as to be very unlikely to be associated. While SDSS includes some of the desired data, the SDSS spectroscopic coverage of stars at faint magnitudes is very sparse, so the vast majority of stars do not have velocity measurements. Nevertheless, some do, and those observations can be used to estimate the significance of the contamination.

The NO09 estimate of the contamination depends critically on the assumptions discussed in Section 7.1.4 that the BHB stream they identify with Sagittarius is exactly coincident in both position and velocity with Segue 1. However, as noted in Section 7.1.4, the surface density of BHB stars in the higher velocity component appears to be down by a factor of at least a few by the time it reaches Segue 1 (their Figure 10), and the velocity offset compared to Segue 1 further reduces the contribution of these stars within the Segue 1 velocity selection window.

To take into account these effects, we repeat the analysis described by NO09. Using DR7 data, if we select the BHB stars according to their heliocentric velocities, the positive velocity stream component has a mean velocity of v_hel = 195 km s⁻¹. Since the stream is extended spatially, and therefore likely has a velocity gradient along its length, it is more concentrated in the GSR velocity system, where its velocity is v_GSR = 132 km s⁻¹ and its velocity dispersion is 12.2 km s⁻¹ (corresponding to an intrinsic dispersion of 10 km s⁻¹ after the 7 km s⁻¹ median velocity errors are removed). Given the velocity window spanned by the likely Segue 1 members (not including SDSSJ100704.35+160459.4) of 194.6 km s⁻¹ ⩽ v_hel ⩽ 224.2 km s⁻¹, only 41% of stars in the positive velocity stream would be expected to have velocities consistent with membership in Segue 1. Applying our actual photometric selection criteria (Section 2.2) instead of the broader selection box used by NO09 reduces our estimate of the surface density of Sgr stream stars at the declination of Segue 1 to 120 deg⁻² (for stars with r magnitudes between 17.5 and 21.7). The complete region of our spectroscopic survey covers 0.087 deg², and the effective area of the full survey (including the incompleteness at larger radii) is ∼0.14 deg². Assuming, as NO09 did, that half of these stars are in the negative velocity stream component, and removing the 59% of the positive velocity stream stars that would still lie outside the Segue 1 velocity range, suggests that a total of 2–3 Sgr stream stars could be in our sample.

The next question is what effect including a few Sgr stars in an analysis of Segue 1 would have. We repeat the Monte Carlo simulation carried out by NO09 to answer this question. Using the same setup they did, with assumed velocity dispersions of 1 km s⁻¹ for Segue 1 and 10 km s⁻¹ for the Sgr stream (and putting them both at the same mean velocity, contrary to the argument above), we find that five Sgr stars must be included in the 71 star Segue 1 sample to have a significant chance (∼20%) of boosting the apparent velocity dispersion of Segue 1 to at least 3.9 km s⁻¹. Given the smaller number of contaminating stars estimated above, we conclude that the inclusion of Sgr stream stars in the Segue 1 member sample is not likely to provide the dominant component of the observed velocity dispersion.

Also, when significant numbers of such contaminants are present they tend to have an easily visible effect on the velocity distribution (as they must if they are going to alter the dispersion). Visually, the simulated velocity histograms frequently appear to be composed of a narrow central peak containing most of the stars, surrounded by a few well-separated outliers (see Figure 9 for an example). These outliers would raise suspicions in any membership classification scheme like the ones outlined in Section 3.1 and might well be discarded from the sample. Interlopers that happen to fall within the main peak of the velocity distribution (and are therefore more difficult to identify) do not have a significant impact on the velocity dispersion; only stars in the wings of the distribution can both be mistaken for members and substantially change the apparent dispersion. However, our analysis shows that any such contaminating population cannot be large, and in Paper II we demonstrate that including an additional population does not change the derived parameters for Segue 1.

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Moreover, a closer examination of the positive velocity stream component calls into question the assumption that it is associated with Sagittarius at all. Newberg et al. (2010) used BHB stars in SDSS and the SEGUE survey to trace the Orphan Stream across the sky and noted that it passes slightly north of Segue 1, at a distance of ∼25 kpc and a velocity of v_GSR = 130 km s⁻¹. Isolating the SDSS BHB stars within 1σ of the positive velocity stream's mean velocity, we find that their spatial distribution closely matches the track of the Orphan Stream determined by Belokurov et al. (2007b) and Newberg et al. (2010), as shown in Figure 10. The good correspondence between the path of the Orphan Stream and the BHB stars at the same velocity is highly suggestive that these stars are members of the Orphan Stream rather than an old (and heretofore undetected) wrap of the Sagittarius stream. If this peak is indeed related to the Orphan Stream, which is narrow and spatially confined, and not Sagittarius, then it is quite unlikely that any main-sequence stars associated with this feature would be located close enough to Segue 1 to appear as contaminants in our survey. That would then imply that most or all of the Sgr stars near Segue 1 are at negative velocities, as suggested in Section 7.1.3, which would further reduce our estimate of the possible contamination by Sgr above.

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After considering each piece of evidence in concert, we thus conclude that contamination by the Sgr stream does not provide a very plausible explanation for the large velocity dispersion of Segue 1.

Having determined the nature of Segue 1, the effect of binary stars on the velocity dispersion, and the level of contamination by the Sgr stream, the final issue we must analyze is the impact of Milky Way tides. Unfortunately, while the presence of tidal tails would be incontrovertible evidence of tidal effects, the contrapositive is not true: there are no observations that can conclusively rule out tidal disruption. We therefore consider several possible signatures of tides.

• 1.  
  First, our spectroscopic survey shows there are no obvious tidal tails connected to Segue 1 (see Figure 3). Although the spatial distribution is not uniform, we find Segue 1 members in every direction around the galaxy rather than the bipolar pattern that tidal tails would be expected to produce. The apparent clumpiness of the member stars toward the western edge of the galaxy may simply be the result of small number statistics (Martin et al. 2008). While the spectroscopic member sample confirms that Segue 1 has an elliptical shape, nonzero ellipticities are not necessarily associated with tidal influences (Muñoz et al. 2008) and may just reflect the shape with which the galaxy formed. We also note that the tidal tails seen in the SDSS photometry in the Segue 1 discovery paper (Belokurov et al. 2007a) have not been confirmed by deeper follow-up (Belokurov et al. 2007a; NO09; R. Muñoz et al. 2011, in preparation).
• 2.  
  Velocity gradients are a commonly used indicator of tidal disruption, although like tidal tails they may only be visible in particular geometries and at large radii (Piatek & Pryor 1995; Muñoz et al. 2008; Łokas et al. 2008). We see no velocity gradient across Segue 1; the mean velocities of the stars in the eastern and western halves of the galaxy agree within their uncertainties. The inclusion or exclusion of the ambiguous members, RR Lyraes, and binaries does not affect this result. There are also no apparent trends in the mean velocity from one end of the galaxy to the other (unlike, e.g., Willman 1; Willman et al. 2010). Using the methodology described by Strigari (2010) to calculate completely general constraints on the rotation of Segue 1, we derive a 90% confidence upper limit of 5.0 km s⁻¹ on the rotation amplitude, but we note that samples a factor of two larger than ours are typically required to detect rotation.
• 3.  
  A velocity dispersion profile that rises at large radii is often regarded as a possible result of tidal stripping, although the same behavior can be interpreted as evidence for an extended dark matter halo as well. Our member sample is not large enough to divide the data into more than a few radial bins, but we can begin to investigate the shape of the dispersion profile. Velocity dispersion profiles with two different binnings are displayed in Figure 11. As seen in the left panel of Figure 4, the velocity dispersion appears to reach a local minimum at a radius of ∼3' before increasing back to its central value at larger radii. This shape seems to be independent of the exact binning chosen (and in fact is visible in the unbinned data), but as the error bars in the figure show, it is not statistically significant. While it is possible that the dispersion increase could suggest that the stars beyond ∼8' from the center of the galaxy have been stripped, we caution that apparent features in other data sets of similar size (or even larger) have often disappeared when larger samples of velocity measurements become available (Wilkinson et al. 2004; Kleyna et al. 2004). With the modest number of bins possible for a sample of 71 members, we view the shape of the dispersion profile of Segue 1 as possibly interesting but not necessarily meaningful at this point. It is also worth pointing out that the mass implied by the central velocity dispersion, even if the decline at ∼3' is real, is enough to put the tidal radius beyond the observed extent of the galaxy (see below), suggesting a consistency problem for the tidal interpretation.
• 4.  
  Finally, "extratidal" excesses of stars at large radii are frequently considered to be indicative of tidal disturbances. The King (1962) tidal radius or limiting radius of Segue 1 is not well known because of the lack of deep enough wide-field photometry (although NO09 estimate a value of ∼26'), but our complete spectroscopic sample enables us to investigate the stellar profile out to r ∼ 13'. Our observations are effectively complete within two half-light radii of the center of the galaxy (Section 2.6), where we identify 61 member stars. Between two and three times the half-light radius, we obtained successful spectra for 62 out of 75 stars located in the highest priority photometric selection region, for a completeness of 83%. We therefore adjust the nine observed members in that annulus to a projected total of 11 members, yielding 72 member stars within 3 half-light radii (132). We find 39 member stars within 1r_half (54% of the total), 22 member stars between 1r_half and 2r_half (31%), and estimate 11 member stars between 2r_half and 3r_half (15%), compared to the expected numbers of 56%, 33%, and 11% for a Plummer profile (once the 10% of the stars that should lie beyond 3r_half are removed from consideration). The radial profile of Segue 1 thus does not show any excess out to at least 3r_half (88 pc).

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The above arguments demonstrate an absence of evidence in favor of tidal disruption, but as mentioned at the beginning of this section and discussed in detail by Muñoz et al. (2008), none of them (singly or in concert) are sufficient to prove that Segue 1 is not being tidally disrupted. Perhaps the strongest evidence for the absence of tidal effects results from consistency checks between the mass we measure for Segue 1, the corresponding tidal radius, and the timescale for tidal disruption.

As discussed by G09, the current position of Segue 1 is difficult to reconcile with a scenario in which it is in the final stages of disruption. Segue 1 has a crossing time of ∼10⁷ yr, and at a velocity of ∼200 km s⁻¹ it will travel less than 2 kpc per crossing time. In order for the observed kinematics of Segue 1 to be significantly distorted by tides, the galaxy must be within a few crossing times of its orbital pericenter. Conservatively, then, Segue 1 should be no more than ∼10 kpc past pericenter. Segue 1 is located 28 kpc from the Galactic center, which would place its pericenter at a Galactocentric distance of at least 18 kpc, inconsistent with the closest approach to the Milky Way that would be required to disrupt it (see below).

For the IAU value of the Milky Way rotation velocity (220 km s⁻¹), the mass enclosed at the position of Segue 1 is 3 × 10¹¹ M_☉. The mass of Segue 1 is best constrained at the half-light radius of the galaxy (Wolf et al. 2010), where we obtain M_half = 5.8^+8.2 _{− 3.1} × 10⁵ M_☉. Even if we assume (without any physical basis) that the mass distribution is arbitrarily truncated at the half-light radius, the instantaneous Jacobi radius (e.g., Binney & Tremaine 2008, Equation (8.91)) for Segue 1 would be ∼250 pc. If we use the Jacobi radius as an estimate of the tidal radius, then all of the stars we observed are well within the present-day tidal radius. Although Binney & Tremaine present a detailed discussion of why the Jacobi radius is necessarily an imperfect estimator, it is worth noting that subhalos in the Aquarius simulation (Springel et al. 2008) show a strong correlation between the radius of the subhalo and the Jacobi radius, supporting the use of the Jacobi radius as the tidal radius in practice. In order to bring the tidal radius in to the position of our outermost confirmed member, the pericenter of Segue 1's orbit must be less than ∼10 kpc. Substantially, disturbing stars at the half-light radius, where the mass is being measured, requires an orbital pericenter of less than ∼4 kpc (eccentricity greater than 0.75, since Segue 1 is clearly not near its apocenter at the present time). The Jacobi radius scales as M^1/3_Segue 1, so even major revisions to the derived mass do not affect our conclusion. This calculation is quite conservative, because it relies most strongly on the central kinematics of the galaxy where the observational uncertainties are smallest and tidal effects are weakest.

Incorporating reasonable assumptions about the extent of the dark matter halo of Segue 1 only strengthens this result. In the Via Lactea II simulation (Diemand et al. 2008), subhalos with V_max > 10 km s⁻¹ (see Section 8) that currently reside between 20 and 40 kpc from the host halo have median tidal truncation radii of ∼500 pc. Since these simulations self-consistently include tides and orbital trajectories, there is good reason to suspect that the mass of Segue 1 extends well past r_half. If we extrapolate the Segue 1 mass beyond the observed region using cold dark matter (CDM) priors (since current simulations cannot resolve radii smaller than ∼100 pc), we find a mass within 100 pc of M₁₀₀ = 2.2 × 10⁶ M_☉ and a mass within 300 pc of M₃₀₀ = 1.4 × 10⁷ M_☉, consistent with the common mass scale of Milky Way satellites (Strigari et al. 2008a). With these larger masses, the current tidal radius would increase to 400–700 pc, making the center of Segue 1 nearly impervious to tides for any plausible orbit.