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Galactic Stellar Population Structure and kinematics. Alessandro Spagna Osservatorio Astronomico di Torino 26 Febbraio 2002. Galactic Structure. Flat disk : 10 11 stars (Pop.I) ISM (gas, dust) 5% of the Galaxy mass, 90% of the visible light Active star formation since 10 Gyr.

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galactic stellar population structure and kinematics
Galactic Stellar PopulationStructure and kinematics

Alessandro Spagna

Osservatorio Astronomico di Torino

26 Febbraio 2002


Galactic Structure

  • Flat disk:
  • 1011 stars (Pop.I)
  • ISM (gas, dust)
  • 5% of the Galaxy mass, 90% of the visible light
  • Active star formation since 10 Gyr.
  • Central bulge:
  • moderately old stars with low specific angular momentum.
  • Wide range of metallicity
  • Triaxial shape (central bar)
  • Central supermassive BH
  • Stellar Halo
  • 109 old and metal poor stars (Pop.II)
  • 150 globular clusters (13 Gyr)
  • <0.2% Galaxy mass, 2% of the light
  • Dark Halo

Thin disk

The galactic disk is a complex system including stars, dust and gas clouds, active star forming regions, spiral arm structures, spurs, ring, ...

However, most of disk stars belong to an “axisymmetric” structure, the Thin disk, which is usually represented by an exponential density law:

  • hz 250 pc vertical scale height W = 20 km/s
  • hR  3.5 kpc radial scale-lenght
  • z0  20 pc Sun position above the plane
  • R0  8.5 kpc Solar galactocentric distance

Thin disk: kinematics

(a) Local Standard of Rest (LSR)

Definition:Ideal point rotating along a circular orbit with radius R

VLSR 220 km/s (Vz=0,Vr=0)

 T  250 Myr

VRot (r) = - [Kr (r,z=0) r]1/2





(b) Galactic velocities:

(U,V,W) components with respect to the LSR

In particular, (U,V,W) = (+10.0, +5.2, +7.2) km/s

(Dehnen & Binney 1998)







Thin disk: kinematics


  • (c) Velocity Ellipsoid
  • Definition:Ellipsoid of velocity dispersions for a Schwarzchildstellar population (1907) with multivariate gaussian velocities, defined by:
  • the dispersions (1 , 2 , 3 ) along the (v1 ,v2 ,v3 ) principal axis
  • lv = vertex deviation, with respect to (U,V,W)







Thin disk: kinematics

(d) Asymmetric drift

Definition: systematic lag of the rotation velocity with respect to the LSR of a given stellar population

va = vLSR - v of stars



Generally, old stars show largervelocity dispersion and asymmetricdrift, but smallervertex deviation, than young stars


Thin disk: kinematics

Velocity ellipsoid of the “old” thin disk

(U , V , W ;va ) = (34, 21, 18; +6 ) km/s

from Binney & Merrifield (1998) “Galactic Astronomy”

For an isotherm population:

where,  (M/pc²) = galactic surface density


Thin disk: metallicity

Range of Metallicity:

0.008 < Z < 0.03 (Z = 0.02)

No apparent age-metallicity relation is present in the Thin disk (Edvardsson et al 1993, Feltzing et al. 2001)

Age-metallicity distribution of 5828 stars with /<0.5 and Mv<4.4

galactic halo
Galactic Halo
  • Spatial density.
  • Axisymmetric, flattened (~0.7-0.9), power law (n~2.5 - 4) function. For instance:
  • halo(z=0)/0 ~ 1/600
  • Age: 12-13 Gyr
  • Metallicity: [Fe/H] ~ (-1, -3) - [Fe/H]~ -1.5
galactic halo kinematics
Galactic Halo: kinematics

Velocity ellipsoid of the “halo”

(U , V , W ;va ) =

(160, 89, 94; +217 ) km/s

from Casertano, Ratnatunga & Bahcall (1990, AJ, 357, 435)

Rotation velocity. Halo - Thick Disk distributions from Chiba & Beers (2001)


T h i c k disk

  • Basic parameters:
  • hz 1000 pc
  • W 40-60 km/s
  • Pop. II Intermediate
  • [Fe/H]-0.6 dex with low metallicity tail down to -1.5
  • Age: 10-12 Gyr
  • thick(z=0)/0  4-6 %

Thick disk

A matter of debate

Spagna et al (1996) 1137 ± 61 pc 0.042 ± 0.005


Thick disk

A matter of debate

Velocity ellipsoid of the “thick” disk

(U , V , W ;va ) = (61, 58, 39; +36 ) km/s

from Binney & Merrifield (1998) “Galactic Astronomy”

  • The various measurements of the velocity ellipsoid are quite consistent, but a controversy concerning the presence of a vertical gradient is still unresolved:
  •  va/  z = i /  z = 0 according to several authors
  •  va/  z = -14 ± 5 km/s per kpc Majewski et al. (1992, AJ)

Thick disk: Formation Process

  • Bottom-up. Dynamical heating of the old disk because of an ancient major merger




V  200 km/s , m/M  0.10  W  60 km/s

  • Top-down. Halo-disk intermediate component. Hypothesis: dissipative phase of the protogalactic clouds at the end of the halo collapse (Jones & Wise 1983)

Heating of a galactic disk by a merger of a high density small satellite. N-body simulations by Quinn et al. (1993, ApJ)

Actually, more recently, Huang & Calberg (1997) found that low density satellites with mass < 20% seem to generate tilted disks instead of thick disks.


Thick disk: Signature of the

Formation Process


Dynamical heating of an ancient thin disk

Intermediate phase Halo-Disk


Discrete component: No vertical chemical and kinematic gradients expected in the Thick Disk

Continuity of the velocity ellipsoids and asymmetric drift


Thick disk: Signature of the

Formation Process

Proper motion survey towards the NGP (GSC2 material)


Types of surveys suitable for Galactic studies:

  • Selective surveys. For examples, stellar samples selected on the basis of the chemical or kinematic properties (e.g. low metallicity and high proper motion stars Pop. II halo stars. Warning: “biased” results)
  • Surveys with tracers. High luminosity objects which can be observed up to great distances, easy to identify and to measure their distance (e.g. globular clusters, giants, variable RR Lyrae, … ) . It is assumed that tracers are representative of the whole population.
  • In situ surveys. These measure directly the bulk of the objects which constitute the target populations (e.g. dwarfs of the galactic Pop.I and Pop.II). These should guarantee “unbiased” results ifsystematic effects due to the magnitude threshold, photometric accuracy, angular resolution, etc. are properly taken into account.
fundamental equation of the stellar statistics von seeliger 1989
Fundamental Equation of the Stellar Statistics(von Seeliger 1989)

(M)=Luminosity function

D(x,y,z)=density distribution

(Integral Fredholm’s equation of the first kind).

Problem: inversion of the integral equation!

galaxy models
Galaxy models
  • An alternative approach: integrate the Eqn of stellar statistics assuming some prior information concerning the stellar population. In practice,
  • (1) They assume discrete galactic components, each parametrized by specific spatial density, (R,z; p), velocity ellipsoid and by a well defined LF/CMD consistent with the age/metallicity of each component.
  • (2) Predicted starcounts (i.e. of stars vs. magnitude, color, proper motion, radial velocity, etc.) are derived by means of the fundamental Eqn. of the stellar Statistics.
  • (3) Comparisons against observations are used to confute or validate and improve the model parameters.
galaxy models22
Galaxy models


Bahcall&Soneira - IASG - Besancon - Gilmore-Reid - Majewski - GM -Barcelona - Mendez - Sky - HDR-GST - … …

galaxy models lf cmd
Galaxy models: LF & CMD

Synthetic HR diagram for thin, thick disk and halo from IASG model (Ratnatunga, Casertano & Bahcall)


Galaxy models: simulated catalogs

All components

Old thin disk

Young thin disk

thick disk


Intermediate thin disk


Halo Luminosity Function(s)

Gizis & Reid (1999)

Gould et al (1998)

Gizis & Reid (1999, ApJ, 117, 508)

galaxy models no unique solutions
Galaxy models:No unique solutions!

The controversy regarding the scale height of the thick disk can be partially explained by means of the (anti)correlations between hz and0 of the thin and thick disks. Similarly, the estimation of the halo flatness is correlated to the power-index, and it is also sensitive to the separation between halo and thick disk stars.


Galaxy models

What are the “optimal” line of sights to avoid model degeneracy?

Answer: use all-sky directions + multiparameters (photometry+astrometry) + multidimensional best-fitting methods

kinematic deconvolution of the local luminosity function
Kinematic deconvolution of the local luminosity function

Recently, Pichon, Siebert & Bienaymè (2001) presented a new method for inverting a generalized Eqn of Stellar Statistics including proper motions.

Multidimensional starcounts N(l,b,lcosb, b) are used with supplementary constraints required by dynamical consistency* in order to derive both (1) the luminosity function and (2) kinematics


* Based on general dynamical models (stationary, axisymmetric and fixed kinematic radial gradients), such as in (a) the Schwatzchild model (velocity ellipsoid anisotropy ,and (b) Epicyclic model (density gradients)