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:

Rz hRRhzz eezR /)(/0

00),(

• 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 LSR

R

GC

W

V

U

Rot.

G.C.

NGP

(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 Schwarzchild stellar 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)

G.C.

v2

v1

U

V

lv

23

23

22

22

21

21

3212/3321 2

v

2

v

2

vexp

)(2

1)v,v,vPr(

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

V-va

N.ro of stars

Generally, old stars show larger velocity dispersion and asymmetric drift, but smaller vertex deviation, than young stars

Local kinematics from Hipparcos data (Dehnen & Binney 1998)

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:

)0(2 2/1

zGh W

z

zhzez /||)(

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

2/

2

22

0),(n

zRzR

• 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

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

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

22SatW V

M

m

V 200 km/s , m/M 0.10 W 60 km/s

M

mV

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

FORMATION PROCESS

Dynamical heating of an ancient thin disk

Intermediate phase Halo-Disk

PHYSICAL PROPERTIES

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 if systematic 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)

0

2)(),()( drrrDrMmA r

)(log55 rarmM (Integral Fredholm’s equation of the first kind).

(M)=Luminosity function

D(x,y,z)=density distribution

Problem: inversion of the integral equation!

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. N.ro 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.

Models:

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

Galaxy models

Galaxy models: LF & CMD

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

Galaxy models: simulated catalogsAll components

Young thin disk

Old thin disk

Intermediate thin disk

thick disk halo

GSC 2.2 starcounts vs. Mendez’s Galaxy model

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

Gould et al (1998)

Gizis & Reid (1999)

Halo Luminosity Function(s)

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 modelsWhat 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

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)

Kinematic deconvolution of the local luminosity function