Galactic Stellar Population Structure and kinematics

filercaliforniaΜηχανική

14 Νοε 2013 (πριν από 3 χρόνια και 4 μήνες)

62 εμφανίσεις

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.



Central bulge:



moderately old stars with low specific
angular momentum.



Wide range of metallicity



Triaxial shape (central bar)



Central supermassive BH


Stellar Halo



10
9
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
h
R
R
h
z
z
e
e
z
R
/
)
(
/
0
0
0
)
,
(











h
z



250 pc
vertical scale height




W

= 20 km/s



h
R



3.5 kpc
radial scale
-
lenght



z
0



20 pc
Sun position above the plane



R
0



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



V
LSR

220 km/s (Vz=0,Vr=0)





T


250 Myr

V
Rot
(r) =
-

[K
r
(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 (v
1 ,
v
2 ,
v
3
)
principal axis



l
v

= vertex deviation, with respect to (U,V,W)

G.C.

v
2

v
1

U

V

l
v



















2
3
2
3
2
2
2
2
2
1
2
1
3
2
1
2/3
3
2
1
2
v
2
v
2
v
exp
)
(2
1
)
v
,
v
,
v
Pr(







Thin disk: kinematics

(d) Asymmetric drift

Definition
:


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

v
a

= v
LSR
-


v



V

-
v
a

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
;v
a

) = (34, 21, 18; +6 ) km/s

from Binney & Merrifield (1998)
“Galactic Astronomy”


For an isotherm population:

)
0
(
2
2
/
1




z
G
h
W
z


z
h
z
e
z
/
|
|
)
(



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
2
2
0
)
,
(
n
z
R
z
R
















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
;v
a

) =


(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:



h
z


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
;v
a

) = (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:





v
a
/


z =



i

/


z = 0 according to several authors





v
a
/


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)

2
2
Sat
W
V
M
m




V


200 km/s , m/M


0.10



W



60 km/s

M

m

V

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
)
(
)
,
(
)
(
dr
r
r
D
r
M
m
A
r


)
(
log
5
5
r
a
r
m
M




(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 catalogs

All 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
h
z
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

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,

l
cosb,

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