Masses of Dwarf Satellites of the Milky Way
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1 Masses of Dwarf Satellites of the Milky Way Manoj Kaplinghat Center for Cosmology UC Irvine Collaborators: Greg Martinez Quinn Minor Joe Wolf James Bullock Evan Kirby Marla Geha Josh Simon Louie Strigari Beth Willman
2 Milky Way circa 2008 LeoIV CVnII Name Year Discovered LMC 1519 SMC 1519 Sculptor 1937 Fornax 1938 Leo II 1950 Leo I 1950 Ursa Minor 1954 Draco 1954 Carina 1977 Sextans 1990 Sagittarius 1994 Ursa Major I 2005 Willman I 2005 Ursa Major II 2006 Bootes 2006 Canes Venatici I 2006 Canes Venatici II 2006 Coma 2006 Segue I 2006 Leo IV 2006 Hercules 2006 Leo T 2007 Bootes II 2007 LeoIV 2008 Carina Sextans LMC BootesI/II Coma Segue1 Milky Way SMC Sculptor Fornax UMaI Ursa Minor W1 Herc UMaII Sag Draco 100,000 light years J Bullock, M Geha and L Strigari
3 stellar velocities in dwarfs Observation: Line of sight velocity of individual stars Infer: Intrinsic dispersion Estimate: Gravitational potential well that results i n t h i s d i s p e r s i o n assuming equilibrium -- mass of dark matter halo There is a fundamental degeneracy with the velocity dispersion anisotropy of stars that prevents the slope of the mass profile from being measured well. Plots from Walker, Mateo, Olszewski, Penarrubia, Evans, Gilmore ApJ 2009
4 What can we measure in the satellites with line of sight velocity measurements? Answer: Mass within the half-light radius of stars. An excellent fit is: M 1/2 = 3r 1/2σLOS 2 G r1/2 : 3D half-light radius M1/2 : total mass within r1/2 No dependence on stellar velocity anisotropy and this was derived in Wolf et al 2010 From likelihood analysis Fit Plot from Wolf, Martinez, Bullock, Kaplinghat, Geha, Munoz, Simon, Avedo MNRAS 2010 Also see Walker, Mateo, Olszewski, Penarrubia, Evans, Gilmore ApJ 2009
5 What can we measure in the satellites with line of sight velocity measurements? Answer: Mass within the half-light radius of stars. An excellent fit is: M 1/2 = 3r 1/2σLOS 2 G r1/2 : 3D half-light radius M1/2 : total mass within r1/2 No dependence on stellar velocity anisotropy and this was derived in Wolf et al 2010 From likelihood analysis Fit The fact that mass within about twice half-light radius is well constrained was suggested in Strigari, Bullock and Kaplinghat, Astrophys.J.657:L1-L4,2007 Plot from Wolf, Martinez, Bullock, Kaplinghat, Geha, Munoz, Simon, Avedo MNRAS 2010 Also see Walker, Mateo, Olszewski, Penarrubia, Evans, Gilmore ApJ 2009
6 1 0.1 Density of dark matter at half light radius Segue 1 estimate Dashed line is Einasto profile with Vmax ~ 18 km/s 0.01! -2 =0.007 M sun /pc 3 r -2 =1kpc Half light radius in parsec Wolf, Martinez, Bullock, Kaplinghat, Geha, Munoz, Simon, Avedo MNRAS 2010 (except Segue 1) Also see Walker, Mateo, Olszewski, Penarrubia, Evans, Gilmore ApJ 2009
7 1 0.1 Density of dark matter at half light radius Segue 1 estimate Dashed line is Einasto profile with Vmax ~ 18 km/s M 1/2 = 3r 1/2σ 2 LOS G 0.01! -2 =0.007 M sun /pc 3 r -2 =1kpc Half light radius in parsec Wolf, Martinez, Bullock, Kaplinghat, Geha, Munoz, Simon, Avedo MNRAS 2010 (except Segue 1) Also see Walker, Mateo, Olszewski, Penarrubia, Evans, Gilmore ApJ 2009
8 Density of dark matter at half light radius Segue 1 estimate! -2 =0.007 M sun /pc 3 r -2 =1kpc Dashed line is Einasto profile with Vmax ~ 18 km/s M 1/2 = 3r 1/2σ 2 LOS G Turn this into an average density within the stellar half light radius Half light radius in parsec Wolf, Martinez, Bullock, Kaplinghat, Geha, Munoz, Simon, Avedo MNRAS 2010 (except Segue 1) Also see Walker, Mateo, Olszewski, Penarrubia, Evans, Gilmore ApJ 2009
9 Density in solar masses per unit parsec cube Density of dark matter at half light radius Segue 1 estimate! -2 =0.007 M sun /pc 3 r -2 =1kpc Dashed line is Einasto profile with Vmax ~ 18 km/s Half light radius in parsec M 1/2 = 3r 1/2σ 2 LOS G Turn this into an average density within the stellar half light radius ρ 1/2 σ2 LOS r 2 1/2 Wolf, Martinez, Bullock, Kaplinghat, Geha, Munoz, Simon, Avedo MNRAS 2010 (except Segue 1) Also see Walker, Mateo, Olszewski, Penarrubia, Evans, Gilmore ApJ 2009
10 Density in solar masses per unit parsec cube Density of dark matter at half light radius Segue 1 estimate! -2 =0.007 M sun /pc 3 r -2 =1kpc Dashed line is Einasto profile with Vmax ~ 18 km/s /r Half light radius in parsec M 1/2 = 3r 1/2σ 2 LOS G Turn this into an average density within the stellar half light radius ρ 1/2 σ2 LOS r 2 1/2 Wolf, Martinez, Bullock, Kaplinghat, Geha, Munoz, Simon, Avedo MNRAS 2010 (except Segue 1) Also see Walker, Mateo, Olszewski, Penarrubia, Evans, Gilmore ApJ 2009
11 Another way to see this: A Common Mass Strigari, Bullock, Kaplinghat, Geha, Simon, Willman 2008 Density consistent with basic LCDM predictions for objects that collapse early (before full reionization)
12 Another way to see this: A Common Mass Strigari, Bullock, Kaplinghat, Geha, Simon, Willman pc is a good radius at which to compare the ensemble to theory (which doesn t yet predict half-light radius) Density consistent with basic LCDM predictions for objects that collapse early (before full reionization)
13 Another way to see this: A Common Mass Strigari, Bullock, Kaplinghat, Geha, Simon, Willman pc is a good radius at which to compare the ensemble to theory (which doesn t yet predict half-light radius) subhalos Springel et al. 08 Density consistent with basic LCDM predictions for objects that collapse early (before full reionization) ~tidal radius r max [ kpc ] Aq-A-5 Aq-A-4 Aq-A-3 Aq-A-2 Aq-A V max [ km s -1 ] Maximum rotation speed (km/s)
14 Another way to see this: A Common Mass Strigari, Bullock, Kaplinghat, Geha, Simon, Willman pc is a good radius at which to compare the ensemble to theory (which doesn t yet predict half-light radius) subhalos Springel et al. 08 Density consistent with basic LCDM predictions for objects that collapse early (before full reionization) ~tidal radius r max [ kpc ] pc Aq-A-5 Aq-A-4 Aq-A-3 Aq-A-2 Aq-A V max [ km s -1 ] Maximum rotation speed (km/s)
15 What does M 300 ~ 10 7 M sun tell you?! Massive subhalos VL2 subhalos Slide from James Bullock
16 What does M 300 ~ 10 7 M sun tell you?! Massive subhalos VL2 subhalos Vast majority of subhalos in VL2 have M 300 < 10 7 M sun! Slide from James Bullock
17 What does M 300 ~ 10 7 M sun tell you?! Massive subhalos VL2 subhalos Relation is steep for Vmax < 10 km/s 2 M Vmax M 5km/s Vast majority of subhalos in VL2 have M 300 < 10 7 M sun! Slide from James Bullock
18 What does M 300 ~ 10 7 M sun tell you?! Massive subhalos VL2 subhalos While massive halos have weak relation between M300 and total mass, we don t care about massive (MW-size) halos! Relation is steep for Vmax < 10 km/s 2 M Vmax M 5km/s Vast majority of subhalos in VL2 have M 300 < 10 7 M sun! Slide from James Bullock
19 What does M 300 ~ 10 7 M sun tell you?! Massive subhalos Strigari plot VL2 subhalos While massive halos have weak relation between M300 and total mass, we don t care about massive (MW-size) halos! Relation is steep for Vmax < 10 km/s 2 M Vmax M 5km/s Vast majority of subhalos in VL2 have M 300 < 10 7 M sun! Slide from James Bullock
20 What does M 300 ~ 10 7 M sun tell you?! Massive subhalos Strigari plot VL2 subhalos While massive halos have weak relation between M300 and total mass, we don t care about massive (MW-size) halos! Relation is steep for Vmax < 10 km/s 2 M Vmax M 5km/s Vast majority of subhalos in VL2 have M 300 < 10 7 M sun! Slide from James Bullock
21 preliminary remarks: case for dark matter in segue 1 (found in sdss at about 23 kpc from the sun) Tidal radius without dark matter about the same as the radius that contains half the light. At relative velocity of 4 km/s, stars will move apart about 400 pc in the time the dwarf takes to move about 20 kpc Existence of extremely metal poor stars and large metallicity spread: not found in star clusters
22 Measuring mass in Segue 1! About 70 members with multi-epoch measurements for about half M(r <r 1/2 )= 3r 1/2σLOS 2 G 3 38pc (3.8km/s)2 = pc M 1 (km/s) 2 = M Intrinsic dispersion ~3.8 km/s ρ(r <r 1/2 )=1.7 M pc 3 Simon, Geha et al, arxiv: Martinez, Minor et al, in prep
23 Segue 1 analysis: new method to handle membership and binaries A fully Bayesian method that extends the expectation maximization method of Walker, Mateo, Olszewski, Sen, & Woodroofe, M. 2009, AJ, 137, 3109 { } Stellar populations: L(D i M )=FL gal (D i M gal ) + (1 F )L MW (D i M MW ). (1)
24 Segue 1 analysis: new method to handle membership and binaries A fully Bayesian method that extends the expectation maximization method of Walker, Mateo, Olszewski, Sen, & Woodroofe, M. 2009, AJ, 137, 3109 { } Stellar populations: L(D i M )=FL gal (D i M gal ) + (1 F )L MW (D i M MW ). (1) Separability: L gal,mw (v, w, r) =L gal,mw (w)l gal,mw (v r)l gal,mw (r) (2) [ ]
25 Segue 1 analysis: new method to handle membership and binaries e A fully Bayesian method that extends the expectation maximization method of Walker, Mateo, Olszewski, Sen, & Woodroofe, M. 2009, AJ, 137, 3109 { } Stellar populations: L(D i M )=FL gal (D i M gal ) + (1 F )L MW (D i M MW ). (1) Separability: L gal,mw (v, w, r) =L gal,mw (w)l gal,mw (v r)l gal,mw (r) No spatial bias: (2) L(v, w r)=f(r)l gal (w)l gal (v r) + (1 f(r)) L MW (w)l MW (v r) n gal (r) n gal (r)+n MW (r) [ ] ( ) f(r) is the = fraction of stars that are dwarf g ne gal selection (r) ( 1+(r/r bias affects s ) 2) α/2.0 the for the standard Plummer profi Can now constrain halflight radius independent of photometry
26 Segue 1 analysis essentials: binaries Likelihood for each star assuming it is in Segue 1: L(v i σ i,t i,m; σ, µ, B, P) = = P (v i,v cm σ i,t i,m; σ, µ, B, P)dv cm P (v i v cm, σ i,t i,m; B,P)P (v cm σ,µ)dv cm ( Binary orbital parameters Intrinsic dispersion
27 Segue 1 analysis essentials: binaries Likelihood for each star assuming it is in Segue 1: L(v i σ i,t i,m; σ, µ, B, P) = = P (v i,v cm σ i,t i,m; σ, µ, B, P)dv cm P (v i v cm, σ i,t i,m; B,P)P (v cm σ,µ)dv cm ( Binary orbital parameters P (v i v cm, σ i,t i,m; B,P) n e (v i v cm ) 2 /2σ 2 i = (1 B) + BP 2πσ 2 b (v i v cm, σ i,t i,m; P) i i=1 Intrinsic dispersion = (1 B)N (v i, σ i ) e (v cm v ) 2 /2σ 2 m 2πσ 2 m + BP b(v i v cm σ i,t i,m; P) (12) where ( ; ) is the likelihood in the
28 Segue 1 analysis essentials: binaries Likelihood for each star assuming it is in Segue 1: L(v i σ i,t i,m; σ, µ, B, P) = = P (v i,v cm σ i,t i,m; σ, µ, B, P)dv cm P (v i v cm, σ i,t i,m; B,P)P (v cm σ,µ)dv cm ( Mass ratio distribution Ellipticity distribution Period distribution (Mean period, Dispersion in period, Binary fraction) P (v i v cm, σ i,t i,m; B,P) n = (1 B) i=1 Binary orbital parameters Intrinsic dispersion e (v i v cm ) 2 /2σ 2 i 2πσ 2 i + BP b (v i v cm, σ i,t i,m; P) = (1 B)N (v i, σ i ) e (v cm v ) 2 /2σ 2 m 2πσ 2 m + BP b(v i v cm σ i,t i,m; P) (12) where ( ; ) is the likelihood in the
29 Test of binary likelihood code intrinsic dispersion 0.4km/s intrinsic dispersion 0.4km/s (a) 0.4 km/s intrinsic dispersion, 10 year mean period (b) 0.4 km/s intrinsic dispersion, 10 year mean period intrinsic dispersion 3.7km/s intrinsic dispersion 3.7km/s (c) 3.7 km/s intrinsic dispersion, 10 year mean period (d) 3.7 km/s intrinsic dispersion, 10 year mean period
30 Measuring dark matter mass in Segue 1: effect of binary stars Some part of the measured velocity of a star is due to orbital motion Repeat measurements at about 1 year interval for many stars needed to constrain binary properties well enough to estimate dark matter mass Simon, Geha et al, arxiv: Martinez, Minor et al, in prep
31 Measuring dark matter mass in Segue 1: Measuring the period of binaries Martinez, Minor et al, in prep
32 Measuring dark matter mass in Segue 1: membership Can compute probability density of membership: p i = f(r i )L gal (w i,v i r i ) f(r i )L gal (w i,v i r i ) + (1 f(r i )) L MW (w i,v i r i ) Mean values agree well with the Walker et al 2009 method. The power of the present method is in expanding the model space, discussing priors and disentangling binaries in the tail from members. (9
33 Measuring dark matter mass in Segue 1: membership Can compute probability density of membership: p i = f(r i )L gal (w i,v i r i ) f(r i )L gal (w i,v i r i ) + (1 f(r i )) L MW (w i,v i r i ) Mean values agree well with the Walker et al 2009 method. The power of the present method is in expanding the model space, discussing priors and disentangling binaries in the tail from members. Model space explored is large {R, σ, µ, w, σ w, w MW, σ w,mw, δ,s,r s, α} l paramet (9
34 Measuring dark matter mass in Segue 1: membership Can compute probability density of membership: p i = f(r i )L gal (w i,v i r i ) f(r i )L gal (w i,v i r i ) + (1 f(r i )) L MW (w i,v i r i ) Mean values agree well with the Walker et al 2009 method. The power of the present method is in expanding the model space, discussing priors and disentangling binaries in the tail from members. Model space explored is large {R, σ, µ, w, σ w, w MW, σ w,mw, δ,s,r s, α} l paramet (9
35 Measuring dark matter mass in Segue 1: further work More epochs for a star help enormously in constraining the binary orbit. Estimate the effect of binaries on measuring higher order moments like kurtosis. We already know the contribution is large and this is important if you are trying to extract the intrinsic kurtosis (much more than for the attempt here to extract the dispersion).
36 Gamma rays from DM annihilation in the satellites: Fermi constraints Our previous discussion has been somewhat divorced from CDM priors. When interpreted in the context of CDM simulations, the estimates of mass and flux are more constrained. Segue 1 not included Fermi/LAT collaboration, Bullock, Kaplinghat, Martinez 2010
37 Gamma-ray flux from annihilation in segue 1 From Greg Martinez; Preliminary
38 Probing the small scale matter power spectrum is interesting Perturbations are erased below the free-streaming length/damping length Transfer Function (k) CMB SUSY Cluster Galaxies CDM 50% from decay 100% from decay 1 kev sterile neutrino MW satellites Lya Galaxy lensing (OMEGA) k (h/mpc)
39 conclusions Detailed Segue 1 analysis leads to the conclusion that it is a highly dark matter dominated galaxy with an intrinsic dispersion of about 3.7 (spread of about 1 km/s). Estimated central density within 40 pc has a mean value of about 1 Msun/pc^3 -- the highest measured density in the dwarfs. Interpreted in the context of LCDM, it should be among the brightest sources of dark matter annihilation products.
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