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The Milky Way Galaxy
Daniela Carollo
RSAA-Mount Stromlo Observatory-Australia

Lecture N. 1

The Milky Way from the Death Valley


In this lecture:
General characteristic of the Milky Way Reference Systems Astrometry Galactic Structures


The Milky Way
Why it is so important? We live in the Milky Way! Our Galaxy is like a laboratory, it can be studied in unique detail. We can recognize its structures, and study the stellar populations. We can infer its formation and evolution using the tracers of its oldest part: the Halo Near field cosmology


If we could see the Milky Way from the outside it might looks like our closest neighbor, the Andromeda Galaxy.

NGC 2997

Face on view


Ç We live at edge of disk Ç Disadvantage: structure obscured by "dust". It is very difficult to observe towards the center of the Galaxy due to the strong absorption. Ç Advantage: can study motions of nearby stars


COBE Near IR View


Reference Systems
Equatorial Coordinate System

From Binney and Merrifield, Galactic Astronomy.


Some definitions:
Celestial sphere: an imaginary sphere of infinite radius centered on the Earth NCP and SCP: the extension of the Earth's axis to the celestial sphere define the Nord and South Celestial Poles. The extension of the Earth's Equatorial Plane determine the Celestial Equator Great Circle: a circle on the celestial sphere defined by the intersection of a plane passing through the sphere center, and the surface of the sphere. The great circle through the celestial poles and a star's position is that star hour circle Zenith: that point at which the extended vertical line intersects the celestial sphere Meridian: great circle passing through the celestial poles and the zenith The earth rotates at an approximately constant rate. Since a complete

circle has 360 degrees, an hour of right ascension is equal to 1/24 of this, or 15 degrees of arc, a single minute of right ascension equal to 15 minutes of arc, and a second of right ascension equal to 15 seconds of arc


Equatorial Coordinate System
Right ascension, , measured from the vernal equinox (defined below) to the star's hour circle. Measured in hours, minutes of time, seconds of time, Declination: angular distance measured from the celestial equator to the star, along a star's hour circle (positive northward).

Ecliptic Coordinate System The ecliptic is the Earth orbital plane. The obliquity of the ecliptic is 23o 27'. Intersection of the ecliptic and celestial equator define the vernal equinox (location of the Sun on March 21) and autumnal equinox (location of the Sun on Sep. 22). The Vernal equinox defines the zero-point of the right ascension coordinates. Ecliptic longitude, , measured along the ecliptic increasing to the east with zeropoint at the vernal equinox. Ecliptic latitude, , measured from ecliptic to ecliptic poles. Ecliptic Coordinate System commonly used in solar system studies.


Ecliptic Coordinate System

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Galactic Coordinates System
A more natural coordinate system to use in the analysis of the Milky Way (and even extragalactic objects) is the Galactic coordinate system, where: The Galactic equator is chosen to be that great circle on the sky approximately aligned with the Milky Way mid-plane. This plane is inclined by 62o 36' to the celestial equator.

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The North Galactic Pole is at = 12h 49m, = +27o 24' in 1950 equinox, Galactic latitude, b, is measured from the Galactic equator to the Galactic poles (as seen from the Earth!). NGP is at b = 90, SGP is at b = -90.

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Galactic longitude, l, is measured eastward around the e q u a to r i n d e g r e e s . The definition of l = 0o is given
by the location of the Galactic Center. l = 90o in the direction of the motion of the Sun in its rotation about the Galactic Center. l = 180o is called the anticenter direction. l = 270o is sometimes called the anti-rotation direction. It is common to use the shorthand of Galactic quadrants when discussing directions of the Galaxy: First Quadrant: 0 < l < 90o Second Quadrant: 90o < l < 180o Third Quadrant: 180o < l < 270o Fourth Quadrant: 270o < l < 360o
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Galactic Coordinates (cont.)
l = 0 - Galactic center l = 90 - in the direction of Galactic rotation l = 180 - anticenter l = 270 - antirotation

III

II www.thinkastronomy.com

IV

I

l = 0 - 90 l = 90 - 180

first quadrant second quadrant

l = 180 - 270 third quadrant l = 270 - 230 fourth quadrant


The Cartesian system: defined with respect to the Local Standard of Rest (LSR)
X, Y, Z U, V, W positions velocities X, U

Z, W

X, U - positive away from the GC Y, V - positive toward Gal. rotation Z, W - positive toward NGP Left-handed system; right-handed: U= -U Y, V

X = d cos l cos b Y = d sin l cos b Z = d sin b

d - distance to the Sun


Galactic Cartesian Reference Frame
In this picture the XL points towards the galactic center The position of the stars p = (X,Y,Z) at a distance d with respect LSR is derived as X = d cos(b) cos(l) Y = d cos(b) sin(l) Z = dsin(b) Note that in this right-handed system: the Sun has (X,Y,Z) = (0,0,0) the Galactic Center has coordinates: (R0,0,0). Where R0 is the distance to the Galactic Center (8, 8.5 kpc are commonly adopted)
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Right-handed system


Galactic Cartesian Reference Frame
The space position components: : (l,b) = (180, 0), positive outwards : (l.b) = (90,0), positive in the direction of Galactic rotation Z : (l,b) = (0,90), positive northward Z

GC

R Sun

Local Standard of Rest (LSR): Hypothetical rest frame at the Solar position and moving in a circular orbit: (,,Z) = (0,0,0)



Left-handed system


Galactocentric Cilindric Reference Frame
A cylindrical reference frame with origin at the Galactic center The position of a star in this frame: (R,,z) Z
G

Star
r z

r = Galactocentric distance

Gc
R R = projected distance on the Galactic plane YG Sun XG

= rotation angle, positive in the direction of Galactic rotation


Trigonometric Parallax: direct measure of the distance
- The stellar parallax is the apparent motion of a star due to our changing perspective as the Earth orbits the Sun. -parsec: the distance at which 1 AU subtends an angle of 1 arcsec. - Relative parallax - with respect to background stars which actually do move. -Absolute parallax - with respect to a truly fixed frame in space; usually a statistical correction is applied to relative parallaxes.

r tan p p = d

d ( pc ) =

1 p (")

d/d = p/p


Relation between distance and parallax p (") = 206265 p(rad) r = 1 AU d = r/p = AU/p(rad) d = 206265/p(") AU Fundamental Unit of Distance: Parsec Parsec is defined as the distance at which a star would have a parallax of 1" then 1 pc = 206265 AU = 3.086 * 1013 km


Hipparcos CMD - for stars with / < 0.1


Parallax Measurements: The Modern Era
(mas) Á15 mas

Catalog YPC USNO pg USNO ccd Hipparcos Gaia

Date 1995 To 1992 From `92 1997 2016?

#stars 8112 ~1000 ~150 105 109

Comments Cat. of all through 1995

Á2.5 mas Photographic parallaxes Á0.5 mas CCD parallaxes Á1 mas Á10Åas First modern survey "Ultimate" modern survey

As nice exercise, go to: http://cdsweb.u-strasbg.fr/ then click on VizieR catalogue service choice Hipparcos catalogue and give the coordinates. Get real parallax measures!


Parallax Precision and the Volume Sampled
Photographic era: the accuracy is 10 mas -> 100 pc; Hipparcos era: the accuracy is 1 mas -> 1 kpc GAIA era: the accuracy is 10 Åas -> 100 kpc By doubling the accuracy of the parallax, the distance reachable doubles, while the volume reachable increases by a factor of eight (V ~ r3).

Parallax Size to Various Objects

Ç Nearest star (Proxima Cen)
Ç Brightest Star (Sirius) Ç Galactic Center (8.5 kpc) Ç Far edge of Galactic disk (~20 kpc)

0.77 arcsec 0.38 arcsec 0.000118 arcsec 118 Åas 50 Åas 1.3 Åas

Ç Nearest spiral galaxy (Andromeda Galaxy)


Proper Motions
- reflect the intrinsic motions of stars as these orbit around the Galactic center. - include: star's motion, Sun's motion, and the distance between the star and the Sun. - they are an angular measurement on the sky, i.e., perpendicular to the line of sight; that's why they are also called tangential motions/tangential velocities. Units are arcsec/year, or mas/yr (arcsec/century). - largest proper motion known is that of Barnard's star 10.3"/yr; typical ~ 0.1"/yr - relative proper motions; wrt a non-inertial reference frame (e. g., other more distant stars) - absolute proper motions; wrt to an inertial reference frame (galaxies, QSOs) V2 = VT2 + V
2 R

VT ( km / s) Å(" / yr) = 4.74 d ( pc )
4.74 is a conversion factor from as/yr * pc to km/s


Proper Motions
Å - is measured in seconds of time per year (or century); it is measured along a small circle; therefore, in order to convert it to a velocity, and have the same rate of change as Å , it has to be projected onto a great circle, and transformed to arcsec.

d dt d Å = dt

Å =

Å - is measured in arcsec per year (or century); or mas/yr; it is measured along a great circle.


Proper Motions
NCP

Å 2 = (Å cos ) 2 + Å2
Å



Å

VE




Visualization of high proper motion star using photographic plates


Proper Motions - Some Well-known Catalogs
High proper-motion star catalogs > Luyten Half-Second (LHS) - all stars Å > 0.5"/yr > Luyten Two-Tenth (LTT) - all stars Å > 0.2"/year > Lowell Proper Motion Survey/Giclas Catalog - Å > 0.2"/yr High Precision and/or Faint Catalogs HIPPARCOS - 1989-1993; 120,000 stars to V ~ 9, precision ~1 mas/yr Tycho (on board HIPPARCOS mission) - 1 million stars to V ~ 11, precision 20 mas/yr (superseded by Tycho2). Tycho2 (Tycho + other older catalogs time baseline ~90 years) - 2.5 million stars to V ~ 11.5, precision 2.4-3 mas/yr Lick Northern Proper Motion Survey (NPM) - ~ 450,000 objects to V ~ 18, precision ~5 mas/yr Yale/San Juan Southern Proper Motion Survey (SPM); 10 million objects to V ~ 18, precision 3-4 mas/yr.


Fundamental: please take notes!
Distances and proper motions are observable parameters Their measure is a fundamental step for the purpose of galactic studies Distance provides the absolute magnitude Distance + proper motion + radial velocity provide the kinematic parameters of the stars These information combined with the chemical properties of the stars, their physical parameters (Teff, Logg, etc), and photometry, provides important details on the Structure, Formation, and Subsequent Evolution of the Galaxy.

http://www.esa.int/esaSC/120377_index_0_m.html


Photometric Distance
Fundamental relation: m - M = 5logd - 5 ; m- M is called the distant modulus of the object For a sample of stars for which we know the apparent magnitude, and the derived absolute magnitude, then it is straightforward to derive the distance. How we derive the absolute magnitude? 1. Classification of stellar type: Main sequence stars, TO stars, sub-giant stars giant star..etc 2. Then we use the MV vs Color diagram (HR diagram) using data from various Galactic Globular cluster and Open cluster 3. Theoretical calculation provides HR diagram as well. 4. Final step: comparison between the apparent magnitude and the absolute magnitude. Usually the error on the photometric distances is not less than 15-20 %. This is due to the propagation of the error of the magnitudes.
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kinematic parameters: LSR reference frame
The motion of a star with respect the LSR is expressed in term of (U,V,W) velocity components: (U,V,W) = (,-0,Z) 0= 220 km/s Solar motion correction: (U,V,W) = (U-U , V-V ,W-W ) (U , V ,W ) = (-9,12,7) km/s

(Mihalas & Binney 1981) Z
W

Vec

GC



U V

Quantities that we need to derive (U,V,W): a. Position: (, ) b. Distance c. Radial Velocity


Right-Handed coordinate system


kinematic parameters: LSR reference frame
U V W V = G Ç V VR

Where G = TÇA is the transformation matrix between equatorial and galactic coordinates.

sin A = cos 0

cos sin sin sin cos

cos cos sin cos sin

Tangential velocity components in the equatorial reference system V = 4.74 Ç Å cos()Ç d V = 4.74 Ç ÅÇ d
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Where T is the following matrix:

0.0548755604 0.8734370902 0.4838350155 T = 0.4941094278 0.4448296300 0.7469822445 0.8676661490 0.1980763734 0.4559837762




kinematic parameters: Galactocentric Reference Frame
A cylindrical reference frame with origin at the Galactic center The position of a star in this frame: (R,,z) and the velocities (VR,V,Vz) Z
G

VLSR = (V + 220) km/s

r z

R YG



Sun

XG


Dark Halo

Outer Halo

Inner Halo

Thin Disk

Bulge

Thick Disk and Metal-Weak Thick Disk


Stellar Components of the Milky Way: Characteristics
Component Scale height (pc) ~300 800-1000 Mean Vrot [Fe/H] (km/s) -0.3 -0.6 -1.2 -1.6 -2.2 220 150 to 190 150190 ? 20 - 85 : : W (km/ s) 40:30:20 60:40:40 similar to the thick disk = 100 = 145 Age (Gyr) ~10 or less 10-12 10-12 10-12 ??

Thin old disk Thick disk

Metal-weak 1000 thick disk 1200? Inner Halo Outer Halo 10 Kpc? c/a = 0.6 ?? c/a = 0.9 Radius of 2-3 kpc

Bulge

-1.6 to +0.3

100

~80

10-12


Mass Distribution in the Galaxy
The dominant structures are:

M M

Disk

=

1011

M

The galactic disk
Bulge

= 1010 M The Dark Halo

M

BH

= 109 M = 1012 M

M

DH


Stellar populations: summary
Ç The Milky Way thus has at least four distinct populations of stars:
- the spiral arms Ç young objects, including massive blue stars Ç rotating system, second generation (high in heavy elements) - the disc Ç including the Sun; wide age range Ç rotating, high in heavy elements - the halo Ç including the globular clusters Ç non-rotating, low in heavy elements, old - the central bulge Ç of old stars, seen in infra-red light which penetrates the dust Ç slowly rotating, high in heavy elements (with wide spread)


Propagation errors for two non correlated variables
(to be used in the assignments) Given a function dependent from n variables:

y = f ( x1 , x2 ,......, xn )
The error on y will be evaluated by:



2 y

f = x ç 1

2

2 x1

f + x ç 2

2

2 x
2

f + ,........., x ç n

2

2 x
n