Download Galactic components Structure and kinematics

Galactic Stellar Population
Structure 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:
 ( R, z ) 0 e
 z  z0 / hz
e
 ( R  R0 ) / hR
• 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
GC
(Vz=0,Vr=0)
R
 T  250 Myr
VRot (r) = - [Kr (r,z=0)
LSR
r]1/2
NGP
(b) Galactic velocities:
G.C.
U
Rot.
V
W
(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
lv
G.C.
(c) Velocity Ellipsoid
v1
U
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
v2
• lv = vertex deviation, with respect to (U,V,W)
V
  v12
v 22
v 32 

Pr( v1 , v 2 , v 3 ) 
exp   


2/3
2
2
2 
(2 )  1 2 3
  2 1 2 2 2 3 
1
Thin disk: kinematics
(d) Asymmetric drift
N.ro of stars
Definition: systematic lag of the rotation
velocity with respect to the LSR of a given stellar
population
va = vLSR - v
-va
Generally, old stars show larger velocity
dispersion and asymmetric drift, but
smaller vertex deviation, than young stars
V
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:
 ( z)  e
hz 
|z|/ hz
W
2G   ( z  0)
1/ 2
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
• Spatial density.
Axisymmetric, flattened (~0.7-0.9), power law (n~2.5 - 4)
function. For instance:
 2 z 
 ( R, z )  0   R  2 
 

2
n/2
•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
V
m
M
m 2
  VSat
M
2
W
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
FORMATION PROCESS
Dynamical heating of an
ancient thin disk
Intermediate phase HaloDisk
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)

A(m)    ( Mr, r )  D( r )  r dr
2
0
(M)=Luminosity function
D(x,y,z)=density distribution
M  m  5  5 log r  a ( r )
(Integral Fredholm’s equation of
the first kind).


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.
Galaxy models
Models:
Bahcall&Soneira IASG - Besancon Gilmore-Reid Majewski - GM Barcelona - Mendez
- Sky - HDR-GST ……
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
GSC 2.2 starcounts vs. Mendez’s Galaxy model
Halo Luminosity Function(s)
Gizis & Reid
(1999)
Gould et al
(1998)
Gizis & Reid (1999, ApJ,
117, 508)
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 powerindex, 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
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