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Stellar observations and the Big Bang

Star field image

3 independent quantities

Review of observable properties

Basic parameters to compare theory and observations:

-^ Mass (

M )

-^ Luminosity (

L )

¾^

The total energy radiated per second i.e.

power (in W)

-^ Radius (

R )

-^ Effective temperature (

T e

The temperature of a black body of the same radius as the star thatwould radiate the same amount of energy. Thus where

σ^

is the Stefan-Boltzmann constant (

×^^10

-^

Wm

-2K

d λ

L

L

e

σT

R

L

Stellar luminosities vary from 10

-1^ – 10

8

that of our sun with surface temperaturesvarying from 2000 – 50000 K

Since nearest stars

d^

1pc ; must measure

p^

< 1 arcsec e.g. and at

d^

pc,

p^

= 0.01 arcsec Telescopes on ground have resolution ~1" Hubble has resolution 0.05"

difficult! Tycho 2 satellite measured 10

6 bright stars with

δ p

confident distances for stars with

d^

< 100 pc

Nearest star =

Proxima Centaur

i

Parallax after 6 month is 0.765’’

Æ

d = 1AU/0.765 = 4.27 ly

Compare with Hubble resolution of ~ 0.05 arcsec ⇒

very difficult to measure

R

directly

Radii of ~ 600 stars measured with techniques such asinterferometry and eclipsing binaries. Æ

Radii have to be obtained another way.

2.1.1 Stellar radii^ Angular diameter of sun^ at distance of 10pc:^ θ

R ~

/10pc = 5

×^

radians = 10

-^

arcsec

The Hertzsprung-Russell diagram

e T R

L

∝

Stefan-Boltzmann law

shows that L correlates with T

Æ

Hertzprung-Russell’s idea of plotting L vs. T and find a path in the diagram where some information about R could be found

Æ

discovery of main sequence

stars (large majority of stars along the shaded band).

Examples of HR^ On main sequence:^ 1 – on the left upper corner, a star with L = 6 L

and T = 4 Tʘ

ʘ

Æ

R = 60 R

ʘ

red

, cool

dwarf

stars, right lower corner with

L = 200 L

andʘ

T = 1/2 T

ʘ^

Æ

R = 0.1 R

ʘ

Out of main sequence: 1 -

supergiants

:^ L = 10

4 L

and T = 1/2 Tʘ

ʘ^

Æ

R = 400 R

ʘ

red giants

:^ L = 10

2 L

and T = 1/2 Tʘ

ʘ^

Æ

R = 50 R

ʘ

white dwarfs

L = 1/200 L

and T = 2 Tʘ

ʘ^

Æ

R = 1/50 R

ʘ

M

R

≈

4 M

L

∝

Temperature, Mass and Radii^ - Luminosity vs mass:^ - Lifetime:

3

(^24)

−

=^

M

McM

E L

t^ L

Æ

More massive stars burn hydrogen more quickly

• Considerations of energy balance for stars on main sequence: - combining:

(^2) / 1

(^4) / 1 4 2

(^4) / 1 2 4

M

M M

σ L πR

Te

≈ ⎞ ⎟⎟ ⎠

⎛ ⎜⎜ ⎝

⎞ ⎟ ⎠

⎛ ⎜ ⎝

Æ

stars with larger masses have higher effective temperatures.

We observe star clusters •^ Stars all at same distance •^ Dynamically bound •^ Same age •^ Same chemical composition Can contain 10

6 stars

NGC3603 from Hubble Space Telescope

2.1.3 Star clusters

•^

In clusters,

t and

Z must be

same for all stars

-^

Hence differences must bedue to

M

•^

Stellar evolution assumes thatthe differences in clusterstars are due only (or mainly)to initial

M

Star cluster known as the

Pleiades

Globular cluster NGC 2808

Globular

Open

-^ MS turn-off points in similarposition. Giant branch joining MS •^ Horizontal branch from giantbranch to above the MS turn-offpoint -^ MS turn off point varies massively,faintest is consistent withglobulars •^ Maximum luminosity of stars canget to

Mv

≈^

• -^ Very massive stars found in theseclusters

The differences are interpreted due to age – open clusters liein the disk of the Milky Way and have large range of ages. The Globulars are all ancient, with the oldest tracing theearliest stages of the formation of Milky Way (~ 12

×^

9 yrs)

Globular vs. Open clusters

Summary of observations

-^

Four fundamental observables used to parameterise stars andcompare with models

M, R, L, T

e

-^

M

and

R

can be measured directly in small numbers of stars

-^

Age and chemical composition also dictate the position of starsin the HR diagram

-^

Stellar clusters very useful laboratories – all stars at samedistance, same

t , and initial

Z

-^

We will develop models to attempt to reproduce the

M, R, L, T

e

relationships

The Big Bang model was a natural outcome ofEinstein's

General

Relativity

as

applied

to

a

homogeneous universe. However, in 1917, theidea

that

the

universe

was

expanding

was

thought to be absurd. So Einstein invented thecosmological constant as a term in his GeneralRelativity

theory

that

allowed

for

a

static

universe.

In

1929,

Edwin

Hubble

announced

that his observations of galaxies outside ourown

Milky

Way

showed

that

they

were

systematically

moving

away

from

us

with

a

speed that was proportional to their distancefrom

us.

The

more

distant

the

galaxy,

the

faster it was receding from us. The universewas

expanding

after

all,

just

as

General

Relativity

originally

predicted!

Hubble

observed that the light from a given galaxywas shifted further toward the red end of thelight

spectrum

the

further

that

galaxy

was

from our galaxy.

The specific form of

Hubble's expansion

law is

important: the speed of recession is proportionalto distance. The expanding raisin bread model atleft illustrates why this is important. If everyportion

of

the

bread

expands

by

the

same

amount

in

a

given

interval

of

time,

then

the

raisins

would

recede

from

each

other

with

exactly a Hubble type expansion law. In a giventime

interval,

a

nearby

raisin

would

move

relatively little, but a distant raisin would moverelatively farther - and the same behavior wouldbe seen from any raisin in the loaf. In otherwords, the Hubble law is just what one wouldexpect for a

homogeneous expanding universe

,

as predicted by the

Big Bang theory

. Moreover

no raisin, or galaxy, occupies a special place inthis universe - unless you get too close to theedge of the loaf where the analogy breaks down.

Reading material

Hubble’s discovery

20

Doppler effect:

1 ) 1

(

1 ) 1

(^

2 2 +

−

=^

z z

v c

0

f^0

=

−

=^

f

f

z

where