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Constraining the Properties of Milky Way Dwarf Spheroidals with Surface Brightness & Velocity Dispersion Data Introduction Justin Craig, Casey R

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Constraining the Properties of Milky Way Dwarf Spheroidals with Surface Brightness & Velocity Dispersion Data Introduction Justin Craig, Casey R Constraining the Properties of Milky Way Dwarf Spheroidals with Surface Brightness & Velocity Dispersion Data Introduction Justin Craig, Casey R. Watson Department of Physics & Astronomy, Millikin University, Decatur, IL, USA. Dark matter (DM) is the dominant form of matter in the universe [1]. Observations of Results Table 1. The star-related quantities derived from observations and steps I and II with the values for 푛, 훾, and 푅푒 from Ref. [7] and 푦푒 = 푅푒/푅∗. rotation curves (Fig. 1), suggest that every galaxy is embedded within a large DM halo (Fig. (B) (NFW) Abstract Galaxy 풏 휸 풚풆 푹풆/(pc) 푹∗/(pc) 휶 (B) 휶 (NFW) 휷ퟎ 휷ퟎ 휷∞ (B) 휷∞ (NFW) 푫 (B) 푫 (NFW) 2), that comprises, on average, 84% of the mass of each galaxy and the same fraction of CVI 5 0.60+0.08 0.785+0.050 452 ± 13 576 ± 17 1.0 ± 0.1 0.7 ± 0.1 0.27 ± 0.05 0.97 ± 0.01 -1.51 ± 0.57 -12.15 ± 0.01 7.7 ± 2.2 3.6 ± 1.2 Using a combination of surface brightness and velocity dispersion data, we simultaneously −0.06 −0.032 matter in the universe as a whole [1,2,3]. CVII 5 0.53+0.12 0.756+0.024 70.7 ± 11.2 93.6 ± 14.8 1.1 ± 0.1 0.9 ± 0.1 0.29 ± 0.05 0.93 ± 0.02 0.23 ± 0.20 −7.90 ± 1.16 3.5 ± 1.5 1.6 ± 0.7 constrain the velocity anisotropy and dark matter mass profiles of Milky Way dwarf spheroidals −0.10 −0.031 +0.02 +0.001 (dSphs). Our findings indicate strong correlations between the distributions of visible and dark Draco 9 0.27−0.01 0.559−0.003 214 ± 2 383 ± 4 1.0 ± 0.1 0.7 ± 0.1 0.11 ± 0.05 0.75 ± 0.02 -0.83 ± 0.29 −3.89 ± 0.67 8.3 ± 2.5 5.0 ± 1.0 +0.01 +0.002 matter within the dSphs and provide further insights into the cusp vs. core debate. Fornax 9 0.27−0.01 0.504−0.002 838 ± 3 1662 ± 6 1.0 ± 0.1 0.7 ± 0.1 0.11 ± 0.05 0.75 ± 0.02 0.92 ± 0.23 −3.76 ± 0.45 11.1 ± 1.1 5.9 ± 1.3 +0.01 +0.002 Leo I 9 0.20−0.01 0.456−0.001 270 ± 2 592 ± 4 1.2 ± 0.1 1.8 ± 0.3 0.17 ± 0.04 0.94 ± 0.05 -1.52 ± 0.35 −16.42 ± 2.76 8.0 ± 1.2 3.1 ± 0.5 +0.03 +0.002 Leo II 9 0.48−0,03 0.368−0.003 171 ± 2 465 ± 5 1.5 ± 0.1 0.7 ± 0.1 0.43 ± 0.04 0.87 ± 0.02 -1.30 ± 0.18 -5.49 ± 0.73 7.4 ± 1.3 4.5 ± 1.2 II. Spherical Jeans Equation Analysis +0.01 +0.002 Ret2 9 0.11−0.01 0.544−0.002 55 ± 5 101 ± 9 1.0 ± 0.1 0.7 ± 0.1 0.03 ± 0.05 0.72 ± 0.02 -1.63 ± 0.40 −9.32 ± 1.30 3.1 ± 0.2 1.5 ± 0.2 Given 푅 and Eqn. (2), we can now use the Spherical Jeans Equation (SJE: Eqn. 4) to determine other +0.05 +0.017 ∗ Sextans 5 0.81−0.05 0.553−0.018 413 ± 3 747 ± 5 1.1 ± 0.1 0.7 ± 0.1 0.43 ± 0.04 1.00 ± 0.01 -0.08 ± 0.02 −3.42 ± 1.64 7.6 ± 2.1 4.7 ± 1.5 parameters of interest [18] +0.02 +0.004 U Minor 5 0.27−0.01 0.863−0.007 407 ± 2 472 ± 2 1.0 ± 0.1 0.9 ± 0.1 0.11 ± 0.05 0.06 ± 0.05 −0.11 ± 0.19 0.02 ± 0.13 9.6 ± 1.9 9.9 ± 1.9 푑푙푛휎2(푦) 푑푙푛휈(푦) Fig. 1: Rotation curves reveal the need for extra, unseen mass in galaxies [4]. Fig. 2: DM Halo [5] 푦휎2(푦) 푟 + + 2훽(푦) = −휎2퐼(푥) . (4) 푟 푑푙푛푟 푑푙푛푟 0 Table 2. The DM quantities derived in step III for both the Burkert profile (B) and the NFW profile. In column 8, 9 and 10, we show the mass at 푅 (푀 ) found from an equation derived in Ref. [14] (denoted as W09), the Burkert profile (B), and the NFW profile. The final three As the most DM-dominated systems in the universe, dwarf galaxies serve as excellent DM 2 푒 푒 We adopt the following forms of the radial velocity dispersion profile and velocity anisotropy profile, 휎푟 (푦) columns show the error in our models relative to the data (SD푟푒푙) for the Burkert (B) and NFW profiles and the ratio of NFW/B uncertainties. laboratories [1,2]. In this poster, we use stellar velocity dispersion and surface brightness and 훽(푦), respectively, for our analysis: 푴ퟎ/ 푴ퟎ/ 푴풆/ 푴풆/ 푴풆/ 퐒퐃 퐒퐃 퐒퐃풓풆풍 (퐍퐅퐖) profile data to infer the DM properties of 9 Milky Way dwarf spheroidal galaxies (dSphs). 푠 2 (푡−푠)/2 Galaxy 풓 /(pc) 풓 /(pc) 흆 /(푴 풑풄−ퟑ) 흆 /(푴 풑풄−ퟑ) (ퟏ풆ퟖ푴 ) (ퟏ풆ퟖ푴 ) (ퟏ풆ퟕ푴 ) (ퟏ풆ퟕ푴 ) (ퟏ풆ퟕ푴 ) 풓풆풍 풓풆풍 휎 푦 = 퐷푦 (1 + 푦 ) , (5) 풐 풔 ퟎ ⊙ 풔 ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ (B) (NFW) 퐒퐃 (퐁) 푟 (B) (NFW) (W09) (B) (NFW) 풓풆풍 Data and Galaxy Selection where D is a normalization constant, and t and s are free parameters, and CVI 576 ± 52 883 ± 103 0.087 ± 0.019 0.037 ± 0.008 2.09 ± 1.02 2.62 ± 1.49 1.68 1.61 ± 0.79 2.18 ± 1.24 1.133 1.354 1.195 CVII 85.1 ± 8.5 104 ± 13 0.464 ± 0.035 0.315 ± 0.060 0.04 ± 0.02 0.04 ± 0.03 0.04 0.03 ± 0.02 0.05 ± 0.03 0.645 0.663 1.028 In this work, we only consider Milky Way (MW) dSphs for which both high quality surface 훽 +훽 푦2 훽 푦 = 표 ∞ , (6) Draco 383 ± 35 547 ± 68 0.307 ± 0.044 0.095 ± 0.026 2.17 ± 0.74 1.97 ± 0.90 0.79 0.76 ± 0.26 0.96 ± 0.44 0.856 0.970 1.134 brightness (SB) and velocity dispersion data exist. We make further cuts based on 3 1+푦2 additional factors: 1. Tidal disruption, 2. Spherical Symmetry, and 3. Constraints on the Fornax 1662 ± 151 2374 ± 297 0.020 ± 0.003 0.007 ± 0.002 11.35 ± 3.00 11.51 ± 5.58 4.11 3.09 ± 0.82 4.76 ± 2.18 0.523 1.149 2.198 inner slope, g, of the stellar density profile, 휈 푟 . where 훽표 and 훽∞ are free parameters that describe b at the center of a dSph and at large radii, respectively Leo I 493 ± 38 328 ± 66 0.180 ± 0.020 0.227 ± 0.062 2.71 ± 0.76 1.01 ± 0.51 1.23 0.91 ± 0.26 1.50 ± 0.76 0.770 0.890 1.155 2 2 [16].The coefficient 휎 in Eqn. (4) is given by 휎 = 퐺푀 Τ푅 , where 푀 = 4휋휌 푟 3 , 휌 and 푟 are, Leo II 310 ± 19 664 ± 83 0.358 ± 0.014 0.063 ± 0.016 1.34 ± 0.38 2.31 ± 1.15 0.65 0.46 ± 0.13 0.56 ± 0.28 0.806 1.129 1.401 1. Tidal disruption 0 0 0 ∗ 0 퐷푀 퐷푀 퐷푀 퐷푀 respectively, the density and scale radius parameters of the chosen DM halo model, and 푥 = 푟Τ푟 . The two Ret2 101 ± 9 144 ± 18 0.683 ± 0.095 0.214 ± 0.058 0.09 ± 0.02 0.08 ± 0.03 0.04 0.03 ± 0.01 0.04 ± 0.01 0.114 0.231 2.035 MW dSphs are often tidally disrupted by the gravitational influence of the much larger MW 퐷푀 DM density models we consider are the Burkert (푟 = 푟 ; [19]) and NFW (푟 = 푟 ; [20]) profiles, and the Sextans 679 ± 57 1068 ± 133 0.037 ± 0.004 0.016 ± 0.002 1.45 ± 0.62 2.38 ± 1.22 0.89 0.62 ± 0.27 1.14 ± 0.59 0.972 1.115 1.147 that they orbit, e.g., [6]. Tidal disruption disturbs the equilibrium that is assumed in the 퐷푀 표 퐷푀 푠 mass integrals over these profiles (퐼(푥) in Eqn. (4)) are shown in Eqns. (7) and (8). U Minor 471 ± 43 524 ± 52 0.135 ± 0.025 0.114 ± 0.020 1.78 ± 0.67 2.07 ± 0.77 2.22 1.67 ± 0.63 1.55 ± 0.58 0.992 0.973 0.980 orbital analysis we will conduct, so we must discard dSphs undergoing disruption. 2 ∞ 푥 푑푥 푟 (7) 2000 2000 = Spherical Symmetry 퐼퐵푢푟푘푒푟푡 푥 = ׬ 2 , 푥 .2 0 (1+푥)(1+푥 ) 푟0 1750 1750 Due to increased and uncertain projection effects, analysis of velocity dispersion data is 1500 1500 ∞ 푥2푑푥 푟 skewed for dSphs that are more ellipsoidal. We therefore restrict our galaxy sample to 1250 1250 (퐼푁퐹푊 푥 = ׬ 2 , 푥 = (8 0 푥(1+푥) 푟푠 (pc) dSphs that are statistically well-described by only 1 axial radius (spherical) rather than 3 (pc) 1000 1000 s 0 r = 1.72R r r r = 2.40R independent axial radii (ellipsoidal), according to the analysis of Ref.
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