Modelling the velocity distribution functions of main sequence - PowerPoint PPT Presentation

Modelling the velocity distribution functions of main sequence stars Andreas Just ( ARI / ZAH) with Lionel Veltz ( AI P) Mary W illiam s ( AI P) 12.6.09

Content � 1) Motivation � 2) Disc kinematics � 3) Vertical disc model � 4) RAVE data � 5) Summary ARI @ ZAH Padua, 12.6.09 - Andreas Just 2

1) Motivation � Fundamental properties of the Milky Way disc not well determined • SFR, AVR: locally and global • Vertical profiles, radial scale lengths • chemical enrichment [Fe/H](t)? � Radial velocity experiment (RAVE) • N ~250,000 stars • Stellar parameters: T eff , log g, [Fe/H] • Radial velocities v rad • Spectro-photometric distances • + proper motions: (U,V,W) ARI @ ZAH Padua, 12.6.09 - Andreas Just 3

Motivation • Complementary: SDSS/SEGUE • Star counts (N=10 8 ) in ugriz and spectra • Future: • Pan-STARRS: "more and fainter than SDSS" • Gaia satellite mission • positions, proper motions and photometry of 10 9 stars • + 10 8 spectra for radial velocity, stellar parameters ARI @ ZAH Padua, 12.6.09 - Andreas Just 4

Motivation Needed: Dynamically consistent and detailed model of the stellar components of the Milky Way ARI @ ZAH Padua, 12.6.09 - Andreas Just 5

2) Disc kinematics • Solar neighbourhood • Hipparcos: distances, proper motions • Geneva-Copenhagen Survey: F,G stars, v rad • CNS4: faint stars: K+M dwarfs, partly v rad • Veltz et al. 2008 • Red clump + K dwarfs (incl. ~550 RAVE stars) • N(M K ),3-D kinematics consistently modelled • Aumer & Binney 2009 (astroph 0905.2512) • Model of N(B-V), σ (B-V) • SFR exp. τ =8.5 Gyr • AVR power law β =0.35 (3-D) • No chem. evol.;IMF Kroupa93 • Models of vertical kinematic easier • in plane: asymmetric drift, vertex deviation ARI @ ZAH Padua, 12.6.09 - Andreas Just 6

Disc kinematics � W-velocities 2MASS-CNS4, d<25pc J-Ks=0.2 0.3 0.4 0.5 ARI @ ZAH Padua, 12.6.09 - Andreas Just 7

Disc kinematics � Vertical gradients • Velocity ellipsoid: tilt • RAVE Siebert et al. 2008 (red clump stars) • i=7.3deg at z=-1 kpc (7.2deg to gal.centre) • SDSS Fuchs et al 2009 (MS + proper motions) • i=11.2deg at z=500pc (3.6deg to gal.centre) • Velocity distribution functions in W • MS stars as function of colour J-Ks • Dispersion σ W (z) • f(W,z) • Fitting shape f(|W|) • Non-Gaussianity by Gauss-Hermite-coefficients ARI @ ZAH Padua, 12.6.09 - Andreas Just 8

3) Vertical disc model • Input • SFR(t) + σ W (age) + [Fe/H](age) • Hipparcos,CNS4: M V bins along MS • velocity distribution functions f(|W|) • Independent of IMF • local density, surface densities, local metalicity distribution of G dwarfs • Output • vertical density profiles: ρ i (z) • MS stars • age distributions and N(z,lifetime) • [Fe/H] distributions • Kinematics above the plane ARI @ ZAH Padua, 12.6.09 - Andreas Just 9

Local disc model � SFR(t) • input function � AVR: σ (t) • β =0.45 • fits f MS (|W|) � [Fe/H](t) • fits local distribution • M V , B-V, lifetimes Age [Gyr] � local enrichment • [O/H]=0.375[Fe/H] • Instantaneous recycling, prim. gas infall ARI @ ZAH Padua, 12.6.09 - Andreas Just 10

Local metalicity � local metalicity distribution • GCS: G dwarfs • mass bin 0.84 ≤ M/M sun ≤ 0.9; r<40 pc +0.13dex scatter in [Fe/H] ARI @ ZAH Padua, 12.6.09 - Andreas Just 11

Local kinematics � Best fit • Z 2 statistics • Fit: σ max • Χ ²=1.13 � f MS (|W|) • M V <0.5 • M V = • 1,2,…,6,8 • McCormick ARI @ ZAH Padua, 12.6.09 - Andreas Just 12

Local kinematics • velocity dispersion σ W • As function of age • σ W (age) • As function of lifetime • σ W (lifetime) ARI @ ZAH Padua, 12.6.09 - Andreas Just 13

Vertical density profiles � thin disc • total,gas,DM,stars(all;lifetime=6Gyr) � thick disc: σ W =40km/s; ρ 0 =5% ARI @ ZAH Padua, 12.6.09 - Andreas Just 14

Star counts SDSS: NGP (b>80°) Hess diagrams: Number densities in CMD unit: N/square deg/1mag g/0.1mag g-r Data Relative difference in %: (data – model)/model model ARI @ ZAH Padua, 12.6.09 - Andreas Just 15

Metalicity distributions • F; K,M stars at z=0; • F; K, M stars at z=500pc ARI @ ZAH Padua, 12.6.09 - Andreas Just 16

Velocity distribution functions • K,M stars • z=0, 300, 600, 900 pc • F dwarfs • z=0, 300, 600, 900 pc ARI @ ZAH Padua, 12.6.09 - Andreas Just 17

Velocity dispersions • M,K, … A stars • Gradient depends on age distribution ARI @ ZAH Padua, 12.6.09 - Andreas Just 18

4) RAVE data � N(total)~250,000 • 1) Spectro-photometric distances N~135,000 • Main sequence (MS) N~45,000 Blue Green Red ARI @ ZAH Padua, 12.6.09 - Andreas Just 19

RAVE data • 1) + proper motions • 3-D velocities U,V,W • Subdivision in galac. Lat. Ranges for testing on systematics due to distance errors • Restriction on stars with small error: | Δ W|<10km/s • 2) high lat. stars b>70 (N=8,788) and >80 (N=2,170) • Log g > 4 and |errW|<10km/s • No distance information used • W~V rad *sin b only • Contribution from pm ignored ARI @ ZAH Padua, 12.6.09 - Andreas Just 20

RAVE: velocity dispersions σ W � Selection effects • Clean/noclean vs. |errW|<10km/s & |W|<60km/s • Cleaning is no problem; errW handling important colour J-Ks |z| in pc ARI @ ZAH Padua, 12.6.09 - Andreas Just 21

RAVE: velocity dispersions σ W � Latitude dependence • σ W slightly smaller at b>60 ˚ ? ARI @ ZAH Padua, 12.6.09 - Andreas Just 22

RAVE: velocity dispersions σ W � Deprojection effects • W vs. V rad *sin(b), pm b *cos(b) ignored • σ W incl. pm smaller at red end (M dwarfs) ARI @ ZAH Padua, 12.6.09 - Andreas Just 23

RAVE: σ W vertical gradient � Strong gradient in all colour bins • Not reproducable by models ARI @ ZAH Padua, 12.6.09 - Andreas Just 24

RAVE: velocity dispersions σ W � Intermediate b • SFR=const. Model with strongest gradient ARI @ ZAH Padua, 12.6.09 - Andreas Just 25

RAVE: f(|W|) � Comp. with Hipparcos • wider core for blue colours? ARI @ ZAH Padua, 12.6.09 - Andreas Just 26

RAVE: f(|W|) � Non-gaussian functions • Best fit: smaller σ • Core even cooler ARI @ ZAH Padua, 12.6.09 - Andreas Just 27

RAVE: f(|W|) � Colour dependence • Variation not monotonic with colour (N=1000) ARI @ ZAH Padua, 12.6.09 - Andreas Just 28

RAVE: f(|W|) � z dependence (N=200) • Range of variation consistent z=0 … 300 pc • Cool core in more extended (for blue colours) ARI @ ZAH Padua, 12.6.09 - Andreas Just 29

RAVE: f(|W|) � Deprojection effects • Core cooler with decreasing influence of pm ARI @ ZAH Padua, 12.6.09 - Andreas Just 30

RAVE: f(|W|) � Gauss-Hermite coefficients • H4=0 for Gaussian • <0 for flatter core • >0 for peaked core N=600 N=200 ARI @ ZAH Padua, 12.6.09 - Andreas Just 31

5) Summary � Rave kinematical data • Consistent with Hipparcos data • But σ W (0) systematically too small • Gal. lat. Dependence not excluded • Reason: larger pm errors? Or distance errors? • σ W (z) steep gradient z<200pc • F(|W|) measureable • General agreement with Hipparcos • N~1000 needed for systematic variations • Vertical gradient only for blue colour bins • Disk model roughly consistent, but • Width of cool core too large • Vertical gradient too strong ARI @ ZAH Padua, 12.6.09 - Andreas Just 32