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

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

Jun 29, 2023 223 likes •565 views

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

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Modelling the velocity distribution functions

  • f main sequence stars

Andreas Just ( ARI / ZAH) with Lionel Veltz ( AI P) Mary W illiam s ( AI P) 12.6.09

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ARI @ ZAH Padua, 12.6.09 - Andreas Just 2

Content

1) Motivation 2) Disc kinematics 3) Vertical disc model 4) RAVE data 5) Summary

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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: Teff, log g, [Fe/H]
  • Radial velocities vrad
  • Spectro-photometric distances
  • + proper motions: (U,V,W)
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Motivation

  • Complementary: SDSS/SEGUE
  • Star counts (N=108) in ugriz and spectra
  • Future:
  • Pan-STARRS: "more and fainter than SDSS"
  • Gaia satellite mission
  • positions, proper motions and photometry of

109 stars

  • + 108 spectra for radial velocity, stellar

parameters

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Motivation

Needed:

Dynamically consistent and detailed model

  • f the stellar components of the Milky Way
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2) Disc kinematics

  • Solar neighbourhood
  • Hipparcos: distances, proper motions
  • Geneva-Copenhagen Survey: F,G stars, vrad
  • CNS4: faint stars: K+M dwarfs, partly vrad
  • Veltz et al. 2008
  • Red clump + K dwarfs (incl. ~550 RAVE stars)
  • N(MK),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
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Disc kinematics

W-velocities

J-Ks=0.2 0.3 0.4 0.5 2MASS-CNS4, d<25pc

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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 σW(z)
  • f(W,z)
  • Fitting shape f(|W|)
  • Non-Gaussianity by Gauss-Hermite-coefficients
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3) Vertical disc model

  • Input
  • SFR(t) + σW(age) + [Fe/H](age)
  • Hipparcos,CNS4: MV 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: ρi(z)
  • MS stars
  • age distributions and N(z,lifetime)
  • [Fe/H] distributions
  • Kinematics above the plane
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Local disc model

SFR(t)

  • input function

AVR: σ(t)

  • β=0.45
  • fits fMS(|W|)

[Fe/H](t)

  • fits local distribution
  • MV, B-V, lifetimes

local enrichment

  • [O/H]=0.375[Fe/H]
  • Instantaneous recycling, prim. gas infall

Age [Gyr]

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Local metalicity

local metalicity distribution

  • GCS: G dwarfs
  • mass bin 0.84≤M/Msun≤0.9; r<40 pc

+0.13dex scatter in [Fe/H]

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Local kinematics

Best fit

  • Z2 statistics
  • Fit: σmax
  • Χ²=1.13

fMS(|W|)

  • MV<0.5
  • MV =
  • 1,2,…,6,8
  • McCormick
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Local kinematics

  • velocity dispersion σW
  • As function of age
  • σW(age)
  • As function of lifetime
  • σW(lifetime)
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Vertical density profiles

thin disc

  • total,gas,DM,stars(all;lifetime=6Gyr)

thick disc: σW=40km/s; ρ0=5%

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Star counts

SDSS: NGP (b>80°)

Hess diagrams: Number densities in CMD

unit: N/square deg/1mag g/0.1mag g-r

Relative difference in %: (data – model)/model Data model

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Metalicity distributions

  • F; K,M stars at z=0;
  • F; K, M stars at z=500pc
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Velocity distribution functions

  • K,M stars
  • z=0, 300, 600, 900 pc
  • F dwarfs
  • z=0, 300, 600, 900 pc
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Velocity dispersions

  • M,K, … A stars
  • Gradient depends on age distribution
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4) RAVE data

N(total)~250,000

  • 1) Spectro-photometric distances N~135,000
  • Main sequence (MS) N~45,000

Blue Green Red

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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: |ΔW|<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~Vrad*sin b only
  • Contribution from pm ignored
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RAVE: velocity dispersions σW

Selection effects

  • Clean/noclean vs. |errW|<10km/s & |W|<60km/s
  • Cleaning is no problem; errW handling important

colour J-Ks |z| in pc

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RAVE: velocity dispersions σW

Latitude dependence

  • σW slightly smaller at b>60˚?
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RAVE: velocity dispersions σW

Deprojection effects

  • W vs. Vrad*sin(b), pmb*cos(b) ignored
  • σW incl. pm smaller at red end (M dwarfs)
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RAVE: σW vertical gradient

Strong gradient in all colour bins

  • Not reproducable by models
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RAVE: velocity dispersions σW

Intermediate b

  • SFR=const. Model with strongest gradient
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RAVE: f(|W|)

  • Comp. with Hipparcos
  • wider core for blue colours?
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RAVE: f(|W|)

Non-gaussian functions

  • Best fit: smaller σ
  • Core even cooler
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RAVE: f(|W|)

Colour dependence

  • Variation not monotonic with colour (N=1000)
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RAVE: f(|W|)

z dependence (N=200)

  • Range of variation consistent z=0 … 300 pc
  • Cool core in more extended (for blue colours)
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RAVE: f(|W|)

Deprojection effects

  • Core cooler with decreasing influence of pm
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RAVE: f(|W|)

Gauss-Hermite coefficients

  • H4=0 for Gaussian
  • <0 for flatter core
  • >0 for peaked core

N=600 N=200

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5) Summary

Rave kinematical data

  • Consistent with Hipparcos data
  • But σW(0) systematically too small
  • Gal. lat. Dependence not excluded
  • Reason: larger pm errors? Or distance errors?
  • σW (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