MAMPOSSt modeling of true & mock dwarf spheroidal galaxies

Transcription

1 MAMPOSSt modeling of true & mock dwarf spheroidal galaxies Gary Mamon (IAP), 30 Oct 2014, GAIA Challenge in Heidelberg, MAMPOSSt modeling of true & mock dwarf spheroidals 1

2 Motivations Mass profiles of dwarf spheroidal & giant elliptical galaxies! inner slope: core, NFW or steeper? normalization concentration dependence on galaxy properties Velocity Anisotropy inner anisotropy outer anisotropy radius of transition Gary Mamon (IAP, Paris), IAU 311, Oxford, 21 July 2014, Mass-orbit modeling of ellipticals with globular clusters and more 2

3 Modeling Fornax & Sculptor Jardel & Gebhardt 12 Amorisco+13 Breddels+13 Richardson & Fairbairn 14 Data 2200 stars in Fornax stars in Fornax in 3 metal populations 2200 stars in Sculptor 1300 stars in Sculptor Method orbit Wolf pinch orbit Jeans (dispersion-kurtosis) Assumptions (all spherical) inner DM slope cored or NFW DM cored σlos for 1 of 3 pops!) disagreeements! core or NFW (if very low concentration) unconstrained velocity anisotropy inner: isotropic outer: radial NA disagreeements! inner: radial outer: tangential inner: slightly tangential outer: radial Gary Mamon (IAP, Paris), IAU 311, Oxford, 21 July 2014, Mass-orbit modeling of ellipticals with globular clusters and more 3

4 Mass modeling methods Gary Mamon (IAP), 30 Oct 2014, GAIA Challenge in Heidelberg, MAMPOSSt modeling of true & mock dwarf spheroidals 4

5 Mass anisotropy degeneracy Spherical stationary Jeans equation anisotropic dynamical pressure tracer density d r 2 dr (r) =1 +2 (r) r 2 (r) 2 r(r) 2 r = GM(r) r 2 = velocity anisotropy isotropic orbits: β = 0 radial orbits: β = 1 circular orbits: β Mass / Anisotropy Degeneracy MAD Gary Mamon (IAP ), ESO workshop, 5 Apr 11, Joint mass and anisotropy modeling of dwarf spheroidals 5

6 1. Jeans analysis Data: surface density Σ, los velocity dispersion σlos (& kurtosis κlos) in bins of projected radius R 2 classes of kinematic modelling model fit of los velocity dispersion M & β Σ σlos 2 Tremaine+94; Mamon & Łokas 05b model fit of los velocity dispersion & kurtosis M & β Σ σlos 2 & κlos Łokas 02; Richardson & Fairbairn 13 Anisotropy inversion Σ σlos 2 & M β! Mass inversion Σ σlos 2 & β M Mamon & Boué 10; Wolf Distribution function modeling Data: distribution of tracers in projected phase space g(r,vlos) standard M & β & f(e,j) g(r,vlos) Wojtak+09 Binney & Mamon 82; Solanes & Salvador-Solé 90; orbit modeling M & orbits g(r,vlos) Schwarzschild 79; Syer & Tremaine 94; de Lorenzi+09 elementary distribution funcs M & fi(e,j) g(r,vlos) Merritt & Saha 93; Gerhard+98; MAMPOSSt M & β & f(v3d) g(r,vlos) Mamon, Biviano & Boué 13 R Dejonghe & Merritt 92;... r caustics g(r,vlos) & β M Diaferio & Geller 97 Gary Mamon (IAP, Paris), IAU 311, Oxford, 21 July 2014, Mass-orbit modeling of ellipticals with globular clusters and more 6

7 Jeans analysis involves binning! Richardson & Fairbairn 14 Sculptor Gary Mamon (IAP, Paris), IAU 311, Oxford, 21 July 2014, Mass-orbit modeling of ellipticals with globular clusters and more 7

8 R r Mass inversion Mamon & Boué 10; Wolf et al. 10 Kinematic deprojection & mass inversion of spherical systems with known anisotropy anisotropic kinematic projection p = ν σ r2 = dynamical pressure P(R) = 2 P = Σ σ los2 = observed projected pressure deprojection R $ & 1 β R2 % r 2 Binney & Mamon 82 ' ) p ( r dr r 2 R 2 GM & Boué 10: simple β(r) insert dynamical pressure into Jeans equation mass profile simple β(r): single integral! Gary Mamon (IAP, Paris), IAU 311, Oxford, 21 July 2014, Mass-orbit modeling of ellipticals with globular clusters and more 8

9 Distribution function modeling Density in projected phase space Dejonghe & Merritt 92 R z r g(r,v z ) = 2 R r dr r 2 R 2 + dv R + f & 1 ) ( 2 v2 + Φ(r),J+ ' * dv θ what choice for f(e,j)? ΛCDM halos: f = f(e,j)=f E (E) J 2( 0) 1+ J 2 r 2 av 2 a 0 Wojtak, Łokas, GM, et al. 08 analysis in projection slow (triple integral) Wojtak, Łokas, GM, et al. 09 Gary Mamon (IAP, Paris), IAU 311, Oxford, 21 July 2014, Mass-orbit modeling of ellipticals with globular clusters and more 9

10 Gary Mamon (IAP, Paris), IAU 311, Oxford, 21 July 2014, Mass-orbit modeling of ellipticals with globular clusters and more 2 r(r) = 1 (r) Z 1 r exp apple 2 Z 2 r (t) dt t (s) GM(s) s 2 ds Solution to Jeans equation of local dynamical equilibrium MAMPOSSt: Modeling Anisotropy & Mass Profiles of Observed Spherical Systems 10 Mamon, Biviano & Boué 13 PDF of distribution in projected phase space very fast! R HkpcL v Hkm s -1 L Projected phase space line-of-sight velocity projected radius R r z p(r, v z )= 4 R N p Z 1 R r (r) p r 2 R 2 h(v z R, r)dr Gaussian 3D velocities: h(v z R, r) = z(r, r) exp apple v 2 z 2 2 z(r, r) z(r, r) = s 1 (r) R r 2 r(r)

11 How accurate masses can we hope for? Tests of MAMPOSSt on 3x11 cluster-mass N=500 ΛCDM halos Mamon, Biviano & Boué 13 σ(log M) = 0.12 dex 32% M200 errors principally caused by triaxiality Mamon, Biviano & Boué 13 With non-spherical modeling: could potentially reach accuracy σ(log M) = 0.03 dex 10%!!! /31/2 Gary Mamon (IAP, Paris), IAU 311, Oxford, 21 July 2014, Mass-orbit modeling of ellipticals with globular clusters and more 11

12 Cluster mass challenge Old+14; Old, Wojtak, Mamon+15 Phase I: HOD mock Phase II: better HOD + SAM 1000 clusters with log M200,c > 13.5 halo centers and velocities provided Gary Mamon (IAP), 30 Oct 2014, GAIA Challenge in Heidelberg, MAMPOSSt modeling of true & mock dwarf spheroidals 12

13 Old, Wojtak, Mamon+15 My algorithms: 1) CLE: a) Estimate r200 from σap b) Select galaxies within r200 & v < 2.7 σlos(r) c) Iterate til convergence d) MCLE = 100 H(z) 2 r200 3 / G! 2) NUM: a) robust linear fit log MCLE vs log N(1 Mpc,1333 km/s) [richness] b) log N(1 Mpc,1333 km/s) log MNUM! 3) CLN: a) Input from NUM b) Same as CLE! 4) MPO [MAMPOSSt]: a) Input from CLN b) Fit r200, rs DM, β red, β blue! 5) MP1: same as MPO, but color-blind 25 algorithms: richness projected phase space size abundance matching velocity dispersion Gary Mamon (IAP), 30 Oct 2014, GAIA Challenge in Heidelberg, MAMPOSSt modeling of true & mock dwarf spheroidals 13

14 PCN PFN NUM ESC SAM2 2 0 Old, Wojtak, Mamon+15 2 NR = 0 RMS = 0.38 MPO NR = 0 RMS = 0.49 MP1 NR = 0 RMS = 0.2 RW NR = 8 RMS = 0.41 TAR NR = 3 RMS = 0.28 l o g ( M c,r e c) / l o g ( M c,true ) PCO NR = 9 RMS = 0.31 PFO NR = 0 RMS = 0.3 PCR NR = 48 RMS = 0.3 PFR NR = 22 RMS = 0.41 MVM NR = 30 RMS = 0.62 AS1 NR = 0 RMS = 0.64 AS2 NR = 0 RMS = 0.62 AvL 25 algorithms: richness projected phase space size abundance matching velocity dispersion NR = 0 RMS = 0.29 CLE NR = 27 RMS = 0.54 CLN NR = 27 RMS = 0.53 SG1 NR = 0 RMS = 0.34 SG2 2 NUM: lowest RMS by far MPO: 2nd lowest! 0 2 NR = 8 RMS = 0.31 SG3 NR = 2 RMS = 0.34 PCS NR = 34 RMS = 0.4 PFS NR = RMS = NR = 3 14 RMS = NR = 0 RMS = NR = 1 RMS = l og(m 200c, Tr u e / M ) Gary Mamon (IAP), 30 Oct 2014, GAIA Challenge in Heidelberg, MAMPOSSt modeling of true & mock dwarf spheroidals 14

15 Application to Fornax Gary Mamon (IAP), 30 Oct 2014, GAIA Challenge in Heidelberg, MAMPOSSt modeling of true & mock dwarf spheroidals 15

16 Fornax: at least two populations Mamon, Chevalier, Romanowsky & Wojtak 14, arxiv: metal-poor: W < 0.5A metal-rich: W > 0.5A W = ΣMg (V VHB) see Battaglia+08; Walker & Penarrubia 11; Amorisco & Evans 12 Gary Mamon (IAP, Paris), IAU 311, Oxford, 21 July 2014, Mass-orbit modeling of ellipticals with globular clusters and more 16

17 Fornax: fixed stellar mass model MDM(2Re) inner DM slope core DM slightly preferred tangential outer anisotropy BH mass unconstrained (3x super-magorrian preferred) Z-rich outer anisotropy Z-poor outer anisotropy MBH Gary Mamon (IAP), 30 Oct 2014, GAIA Challenge in Heidelberg, MAMPOSSt modeling of true & mock dwarf spheroidals 17

18 DM inner slope depends on priors! Mamon, Chevalier, Romanowsky & Wojtak 14, arxiv: Gary Mamon (IAP), 30 Oct 2014, GAIA Challenge in Heidelberg, MAMPOSSt modeling of true & mock dwarf spheroidals 18

19 Gaia Challenge 8 of the non-tangential default mock data from Spherical & Triaxial suite Each run using 13 submocks: 3 x N=1000 (3 axes, random stars) 10 x N=100 (random stars) Each of the 8x13=104 mocks run in 3 cases (total of 312 runs) Tracer density Anisotropy Mass density Easy Hard Very Hard Known Known shape Free OM radius gen NFW: free inner slope free scale radius Tiret free outer β Known Transition radius same as Easy = tracer scale gen Plummer free inner slope same as Hard same as Easy Gary Mamon (IAP), 30 Oct 2014, GAIA Challenge in Heidelberg, MAMPOSSt modeling of true & mock dwarf spheroidals 19

20 VeryHard matches better! Gary Mamon (IAP), 30 Oct 2014, GAIA Challenge in Heidelberg, MAMPOSSt modeling of true & mock dwarf spheroidals 20