Our Galaxy

The Milky Way

Credit & Copyright Barney Magrath

History of Understanding: The Milky Way

• Milky Way – bright band of light across sky

• Galileo– First to use telescope to study MW– Found it was made of millions of faint stars

• What is the Milky Way?– Thomas Wright (1750) suggested that solar system was embedded

in enormous shell of stars…– Emmanuel Kant (1755) realized that the MW is a giant disk of

stars– Kant also hypothesized that space was full of other, similar disks

of stars.

• Nebulae– Fussy blobs in the sky– First systematically catalogued by Messier– Messier was mainly interested in comets…

Credit : A. Dimai

• What were Messier’s objects?

• Possibilities…– Glowing clouds of gas in between the stars– Large collections of stars in our own Galaxy– Whole other galaxies

• Turns out that all of these possibilities are represented…

The Orion Nebula (M42)

Glowing gascloud

Andromeda “Nebula” (M31)

Another galaxy…

The Nature of Fuzzy Objects

• But, this was vigorously debated in early 1900s…

• The Great Debate (1920)– NAS – downtown DC– Debate between Harlow Shapley and Heber Curtis– Shapley argued for nebula all being local (i.e. within the Milky

Way)– Curtis argued for “island universe” hypothesis (i.e., there are many

islands of stars like the Milky Way in the universe)

• Really need a good distance indicator to solve the problem…

Coordinate Systems

Regions of the Milky Way Galaxy

radius of disk = 50,000 l.y. (20 kpc)

number of stars = 200 billion

thickness of disk = 1,000 l.y. (300 pc)

Sun is in disk, 8kpc out from center

Spherical Galactic Coordinates, l, b

• Coordinate system centered on Sun

• Galactic Plane is plane in which most of material lies

• Galactic coords, l, b are angular coords on sphere

• b is Galactic latitude, angular dist of source from Gal plane

• b=0 defines a circle on the Galactic disk

Spherical Galactic Coordinates, l, b

• l is Galactic longitude 0-360o

• b=0 defines a circle on the Galactic disk

• l,b only define where something appears on the sky, to define actual position we also need distance from Sun

Cylindrical Galactic Coordinates, R,,z

• 3-D system with Gal center at origin

• R dist from Gal center• z height above disk is angle from the Sun-

Gal Center line• Dist of object from Gal

center is

R2 + z2

Distance Determination within Milky Way

• Need distances of objects to:• Map out galaxy in 3-D• Understand physics of some sources

Measuring Distances to Stars

Trigonometric parallax – apparent wobble of a star due to the Earth’s orbiting of the Sun

D

r

p

Measuring Distances to Stars

If parallax angle p is in radians

Parallax also used to define the parsec (pc) as the distance of a hypothetical source for which p=1”

From math on the triangle we can get

r/D = tan p p

D = (p/1”)-1 pc

Measuring Distances to Stars

r/D = pIf parallax angle p is in arcsec and distance D is in

parsecsA star with a parallax of 1 arcsec is 1 parsec distant

From math on the triangle we can get

1 parsec 206,265 A.U. = 3.26 light years

Measuring Distances to Stars

Practical limit on how small an angle can be measured - ground based obs can measure

distances out to 30 pc Using the HIPPARCOS satellite got past some limitations extending use of method to 300 pcGAIA will extend the range of the method by another factor of ~5

Proper Motion

• Star velocities can be handled component by component

• Radial v>0 motion away from us

• ‘Proper motion’ is denoted and measures angular velocity, a tangential vector, ie change in position of star against backdrop (separate from parallax) typically mas/yr

• Earth/Sun is a moving frame of reference that needs to be corrected for - heliocentric velocity

v =Δλλ0

c

Main Sequence Fitting

• The further a star is from you, the dimmer it appears. Bright stars are close, and faint stars are farther away. This simple idea would work perfectly if all stars had the same intrinsic brightness. They don't.

Main Sequence Fitting• Studying stars en masse has taught us hot stars

are very luminous and cool stars are relatively dim, so star temperature/color tell us something about luminosity…and hence distance

• So measure stellar temperature-get intrinsic lum, use inverse square law and apparent luminosity to

get distance

Flux = L / 4d2

Star Clusters

• What are the two major types of star cluster?

• Why are star clusters useful for studying stellar evolution?

• How do we measure the age of a star cluster?

Open Clusters

• 100’s of stars

• 106 - 109 years old

• irregular shapes

• gas or nebulosity is sometimes seen

Pleaides (8 x 107 yrs)

Globular Clusters

• 105 stars

• 8 to 15 billion years old (1010 yrs)

• spherical shape

• NO gas or nebulosity

M 80 (1.2 x 1010 yrs)

Clusters are useful for studying stellar evolution!

• all stars are the same distance• use apparent magnitudes

• all stars formed at about the same time• they are the same age

Plot an H-R Diagram!

Pleiades H-R Diagram

Globular Cluster H-R Diagram

Palomar 3

Cluster H-R Diagrams Indicate Age

• All stars arrived on the MS at about the same time.

• The cluster is as old as the most luminous (massive) star left on the MS.

• All MS stars to the left have already used up their H fuel and are gone.

• The position of the hottest, brightest star on a cluster’s main sequence is called the main sequence turnoff point.

Older Clusters have Shorter Main Sequences

Main Sequence Fitting• In reality the stars age affects luminosity too, so want to

take account of that

• Plot HR diagram for the cluster• Determine age from main sequence cut-off point• Correct stellar luminosities to be as though they were in

zero-age stars• Then slide cluster main sequence until it overlays

calibrated “zero-age main sequence” -the amount of luminosity shift gives the distance

(App. Brightness) Flux = L / 4d2

Recap: Magnitude System

apparent magnitude

• brightness of a star as it appears from Earth

= -2.5 log (app bright)

• each step in magnitude is 2.5 times in brightness

absolute magnitude• the apparent magnitude a star would have if it were 10 pc away

Main Sequence Fitting

• Often magnitudes are used instead of flux/luminosity

m-M = 5 log (D/pc) - 5

m is the apparent magnitudeM is the absolute magnitude

Astronomical Dust dust grains: Not the dust one finds around the house, which is typically

fine bits of fabric, dirt, or dead skin cells!!

Interstellar dust grains are much smaller clumps, on the order of a fraction of a micron across, irregularly shaped, and composed of carbon and/or silicates. Dust is most evident by its absorption, causing large dark patches in regions of our Milky Way Galaxy and dark bands across other galaxies.

The exact nature and origin of interstellar dust grains is unknown, but they are clearly associated with young stars

Extinction & Reddening

• So extinction by dust gives a color change in the stellar spectrum, consider specific intensity I at freq v for material with abs coefficient (absn coeff has unit of 1/length)

=− vIν + jv

d ln Iν =d Iν

Iν

= −κ vds

Over distance ds a fraction v ds of photons of freq v are scattered/absorbed

Integrate from 0 to s

dIv

ds

ln Iv (s)−lnIv(0) =−0

s

∫ds' v(s') ≡−τ v(s)

ln Iv (s)−lnIv(0) =−0

s

∫ds' v(s') ≡−τ v(s)

• where t is the optical depth, that depends on frequency

• This reduces to

τ v

Iv (s) =Iv(0)e−τv (s)

specific intensity is reduced by factor compared to the case of no absorption

Exactly the same for flux (ie integrated over all directions for isotropic source)

e−τv

Iν (s) =Iν (0)e−τv (s)

Recall the relation between flux and magnitude

m =−2.5 logS+ constant S ∝10-0.4m

S

Sv,o

=10-0.4(m−m0 ) =e−τv =10−log(e)τv

Flux

v m −m0

m

m0

the apparent magnitude

the apparent magnitude without absorption

S

Sv,o

=10-0.4(m−m0 ) =e−τv =10−log(e)τv

Thus can also define an extinction coefficient that describes change of apparent magnitude due to absorption

Av =m−m0 =−2.5 logS

Sv0

=2.5 log(e)τ v = 1.086τ v

Frequency dependence of extinction means it changes spectral color, and thus often described in terms of the ratio of amounts of flux in different frequency ranges

v

v

Av is the extinction coefficient that describes change of apparent magnitude due to absorption

Av =m−m0 =−2.5 logS

Sv0

v

Absorption always linked to a color change in the stars spectrum, this is described by the color excess (CE)

So color excess defined as:

E(X −Y ) =AX −AY =(X−X0 )−(Y −Y0 ) =(X−Y )−(X−Y )0Ratio depends on physical properties of dust

AX

AY

E(X −Y ) =AX −AY =AX(1−AY

AX

) ≡AXRX−1

Nicely separated out a factor of proportionality between extinction coefficient and the color excess -depends on ‘colors’ considered and the composition of the dust in the system

Blue (B) and visual (V) common colors used in astronomy so commonly see Av = Rv E(B - V)

for the dust in the Milky Way

Av =1mag D

1kpcin the neighborhood of the Sun

Av = (3.1+/-0.1) E(B - V)

≈

Color-Color Diagram

• Sometimes color ‘differentials’ are plotted, like (U-B) v (B-V)

• The relative suppression of the two bands depends on dust composition (assume known)

• Then we see how big the shift is to estimate extinction

• m-M = 5 log (D/pc) - 5 + A

Distance determination

• Another way to get distance (or mass) …..track a binary star system

Reminder: Newton’s version Kepler’s 3rd Law

• Consider isolated system of 2 bodies mass m1, m2 orbiting at distances r1, r2 from mutual center of gravity

• Bodies complete one orbit in same period, P

• Centripetal force F = mv2/r

Reminder: Centripetal Force

• The centripetal force is the external force required to make a body follow a circular path at constant speed

• The force is directed inward, oriented toward the axis of rotation (force which is directed outward is centrifugal force)

• Centripetal force is a force requirement, not a particular kind of force. Any force (gravitational, electromagnetic, etc.) can act as a centripetal force

Reminder: Newtonian physics• Consider isolated system of 2 bodies mass m1, m2 orbiting at distances

r1, r2 from mutual center of gravity

• Bodies complete one orbit in same period, P, vel in orbit=2r/P

• Centripetal forces of the orbits are:

F1=m1v12/r1=42m1r1/P2 (1)

F2=m2v22/r2=42m2r2/P2

Reminder: Newtonian physics

F1=m1v12/r1=42m1r1/P2 (1)

F2=m2v22/r2=42m2r2/P2

• Newton’s 3rd Law has F1= F2 giving

r1/ r2=m2 /m1 more massive body orbits closer to center of mass

separation of two bodies a= r1+ r2 which gives us

r1=m2 a/(m1 + m2) (2)

Mutual gravitational force F=G m1 m2 / a2 (3)

Combine 1,2,3 -> P2=42 a3 /G(m1 + m2)

Distances of Visual Binary Stars

• Period, p, and apparent orbit diameter (a is semi-major axis) are direct observables

• orbit may be inclined to sight-line

• If know masses can get true separation, a

• True versus apparent separation gives distance

P2 =4 2

G(m1 + m2 )a3

Keplers 3rd law

Cepheid Variables

Henrietta Leavitt(1868-1921)

She studied the light curves of variable stars inthe Magellenic clouds.

Same distance

Cepheid Variables

The brightness of the stars varied in a regular pattern.

Cepheid Variables

prototype: Cephei

F - G Bright Giants (II) whose pulsation periods (1-100 days) get longer with increased luminosity

Distance Indicator!!

Cepheid Variables

Recap: Luminosity of Stars

Flux = L / 4d2

Luminosity – the total amount of power radiated by a star into space.

The Instability Strip

There appears to be an almost vertical region on the H-R Diagram where all stars within it (except on the Main Sequence) are pulsating and

variable.

Distances of pulsating starsPulsations -radial density waves propagating with speed of sound, cs

Period comparable to sound-crossing time P~ R/ cs

Speed of sound ~ thermal vel of gas particles so kBT~mp cs

2 (mp is the mass of a proton, ie characteristic mass of particles in the stellar plasma; kB is Boltmann’s constant)

Virial Theorem - gravitational binding energy of the star is twice the kinetic (thermal) energy ->

Distances of pulsating starsVirial Theorem - gravitational binding energy of the star is twice the kinetic (thermal) energy -> k.e.=1/2 m v2 twice k.e. is thus mp cs

2

GMmp

R: kBT

Use kBT~mp cs2

P :

R

cs

:R mp

KBT:

R3

2

GM∝ ρ

−12

ρPulsation period depends only on mean density

Distances of pulsating stars

P :

R

cs

:R mp

KBT:

R3

2

GM∝ ρ

−12

ρPulsation period depends only on mean density

Also know L M3 and L R2T4 so

P ∝R

32

M∝ L

712

Metallicity

In astrophysics all elements heavier than H, He are called metals

These elements, with the exception of traces of Li, were not formed in the big bang, but rather in stellar interiors

Often the abundance of an element is defined scaled to abundances in the Sun and one can use a metallicity index that compares the log of the ratio of element X to Hydrogen in the star, and in the Sun, ie:

[X

H] =log(

n(X)n(H )

)* −log(n(X)n(H )

)Metallicity Index

Metallicity

where n is the number density of the species

[Fe/H]=-1 means Fe is at 1/10 solar abundance

Metallicity, Z defines the mass fraction of ALL elements heavier than helium

The Sun has Z 0.02 - means 98% of mass of Sun is H plus He

[X

H] =log(

n(X)n(H )

)* −log(n(X)n(H )

)

≈