I

EF

CO

DRI

L

AI

N

R

DN

XAEA

ESII

C

M LMV

A

AI

AD

R

E

LGE

14–1

End

-Sta

ges

ofS

tella

rE

volu

tion

I

EF

CO

DRI

L

AI

N

R

DN

XAEA

ESII

C

M LMV

A

AI

AD

R

E

LGE

14–2

Whi

teD

war

fs1

Whi

teD

war

fs

Siri

usA

+B

:Cha

ndra

(X-r

ays;

WD

isbr

ight

)

McD

onal

dO

bser

vato

ry(o

ptic

al;W

Dis

fain

t)

Whi

teD

war

fs:

Siri

usB

•C

ompa

nion

toth

ebr

ight

ests

tar

Siri

us

•ca

nnot

bese

enw

ithth

ena

ked

eye.

•A

naly

zing

the

mot

ion

ofS

irius

from

1833

to

1844

,Frie

dric

hW

ilhel

mB

esse

l(18

44)

conc

lude

d

that

Siri

usm

usth

ave

anun

seen

com

pani

on.

•S

irius

Bw

asno

tact

ually

obse

rved

until

1862

Janu

ary

31by

Alv

anG

raha

mC

lark

.

•S

tar

B’s

pecu

liar

high

tem

pera

ture

,sm

alls

ize,

and

grea

tden

sity

wer

eno

test

ablis

hed

until

1925

byW

alte

rA

dam

s.

I

EF

CO

DRI

L

AI

N

R

DN

XAEA

ESII

C

M LMV

A

AI

AD

R

E

LGE

14–3

Whi

teD

war

fs2

Whi

teD

war

fs

mas

sdi

strib

utio

nof

1733

whi

tedw

arfs

(Kep

ler

etal

.20

07,M

NR

AS

375,

1315

)

Whi

teD

war

fs

1.E

ndst

ages

ofev

olut

ion

ofst

ars

born

with

M.

8M

⊙

2.ty

pica

llyM

∼0.

6M⊙

3.m

ainl

yco

nsis

tofC

and

O

4.R

adiu

s∼

Ear

th

5.ty

pica

lden

sity

ρ∼

106

gcm

−3

I

EF

CO

DRI

L

AI

N

R

DN

XAEA

ESII

C

M LMV

A

AI

AD

R

E

LGE

14–5

Whi

teD

war

fs4

Whi

teD

war

fs

Col

or-m

agni

tude

diag

ram

ofth

eN

GC

6397

Whi

teD

war

fseq

uenc

e(R

iche

ret

al.

2006

,Sci

ence

313,

936)

glob

ular

clus

ters

are

the

old-

estb

uild

ing

bloc

ksof

the

Gal

axy

=⇒

man

yst

ars

have

alre

ady

died

=⇒

GC

sm

usth

osta

larg

e

num

ber

ofw

hite

dwar

fs

I

EF

CO

DRI

L

AI

N

R

DN

XAEA

ESII

C

M LMV

A

AI

AD

R

E

LGE

14–6

Whi

teD

war

fs5

Whi

teD

war

fs

whi

tedw

arfc

oolin

gtr

acks

Cha

brie

yer

etal

.20

05(A

pJ54

2,21

6)

•w

hite

dwar

fsar

est

abili

zed

byth

epr

essu

reof

the

de-

gene

rate

elec

tron

gas

•th

eyca

nno

tshr

ink

•co

olin

gof

the

ioni

cga

s

take

sa

very

long

time

•at

low

tem

pera

ture

:cr

ys-

taliz

atio

n,cr

ysta

lstr

uctu

re

sim

ilar

todi

amon

d

Whi

tedw

arfs

are

diam

onds

inth

esk

y

I

EF

CO

DRI

L

AI

N

R

DN

XAEA

ESII

C

M LMV

A

AI

AD

R

E

LGE

14–7

Whi

teD

war

fs6

Whi

teD

war

fs

For

ade

gene

rate

gase

,the

equa

tion

ofst

ate:

(P=

P(T

,ρ))

for

is

P∝

{

ρ5/

3(n

on-r

elat

ivis

tic)

ρ4/

3(r

elat

ivis

tic)

(14.

1)

inde

pend

ento

fT!

WD

stru

ctur

eca

nbe

dete

rmin

edfr

omhy

dros

tatic

equi

libriu

mal

one:

Mas

sst

ruct

ure

Pre

ssur

est

ruct

ure

(mas

sco

nser

vatio

n)(h

ydro

stat

iceq

uilib

rium

)

dM dr=

4πr2

ρ(r

)dP dr

=−

ρ(r

)GM

(r)

r2

I

EF

CO

DRI

L

AI

N

R

DN

XAEA

ESII

C

M LMV

A

AI

AD

R

E

LGE

14–8

Whi

teD

war

fs7

Whi

teD

war

fs

C/OHe

8500

km

200k

m

10 k

m

HW

hite

dwar

fsco

me

intw

ofla

-

vors

:

DA

:H

pres

enti

nsp

ectr

um

(∼80

%of

allW

D)

DB

:H

epr

esen

tin

spec

trum

(∼

the

rest

)

plus

afe

wod

dbal

ls

Str

uctu

re:

grav

itatio

nally

settl

ed,s

oD

B’s

real

lydo

noth

ave

any

Hsi

nce

itw

ould

“sw

imon

top”

=⇒

laye

red,

“oni

on-li

ke”

stru

ctur

e

I

EF

CO

DRI

L

AI

N

R

DN

XAEA

ESII

C

M LMV

A

AI

AD

R

E

LGE

14–9

Whi

teD

war

fs8

Whi

teD

war

fs •S

ubra

hman

yan

Cha

ndra

sekh

ar,

1910

–199

5

•N

obel

priz

e19

83

•R

adiu

sde

crea

ses

with

incr

eas-

ing

mas

s:R

∝M

1/3

•C

hand

rase

khar

limit:

rela

tivis

tic

limit:

Mas

sm

ustb

ele

ssth

an1.

4M

⊙

Type

IIS

N20

01cm

inN

GC

5965

(2.5

6m

NO

T,H

åkon

Dah

le;N

OR

DIT

A)

Evo

lutio

nof

mor

em

assi

vest

ars:

fusi

onup

to56

Fe,

then

noen

ergy

gain

=⇒

nopr

essu

reba

lanc

ein

cent

re=⇒

supe

rnov

aex

plos

ion

ofty

peII.

ener

gyre

leas

e:10

46W

(1020

L⊙

;abo

ut1%

inlig

ht,r

esti

nne

utrin

os)

I

EF

CO

DRI

L

AI

N

R

DN

XAEA

ESII

C

M LMV

A

AI

AD

R

E

LGE

14–1

1

Neu

tron

Sta

rs1

Neu

tron

Sta

rs

Neu

tron

star

sfo

rmaf

ter

the

core

colla

pse

ofm

assi

vest

ars.

See

late

rfo

rph

ysic

sof

supe

rnov

ae.

Dur

ing

the

colla

pse

the

dens

ities

gets

ohi

ghth

atne

utro

niza

tion

sets

in:

p+

e−−→

n+

ν e

Gen

eral

prop

ertie

s:

•P

ress

ure

mai

nly

thro

ugh

dege

nera

tene

utro

ns(s

imila

rto

dege

nera

teel

ec-

tron

sfo

rW

D!)

.

•Ty

pica

lden

sity

:ρ∼

1014

gcm

−3

(nuc

lear

dens

ities

)

•Ty

pica

lrad

ius:

10..

.15

km(N

urem

berg

!)

•su

rfac

egr

avity

∼10

11×

Ear

th

•D

etai

led

stru

ctur

eno

tyet

fully

unde

rsto

od

I

EF

CO

DRI

L

AI

N

R

DN

XAEA

ESII

C

M LMV

A

AI

AD

R

E

LGE

14–1

2

Neu

tron

Sta

rs2

Neu

tron

Sta

rs:

Str

uctu

re

4.3x

10

g c

m11

−3

9.7km

0.6km0.3km

Out

er c

rust

: nuc

lei &

e−

2x10

g

cm

14−

3

Sup

erflu

id n

eutr

ons

Inne

r cr

ust:

nucl

ei &

e−

Sup

erflu

id n

Sup

erflu

id p

Nor

mal

e−

1.3x

10

g c

m15

−3

unkn

own

(pio

n co

nden

sate

?)(q

uark

mat

ter?

)

Cru

st:

perh

aps

crys

talli

zed?

Ato

ms

beco

me

elon

gate

dal

ong

B-fi

eld

line

onsu

rface

Inte

rnal

stru

ctur

eun

clea

r:

•S

upra

cond

uctin

gm

atte

r

•S

upra

fluid

ity(i.

e.,fl

uid

with

novi

scos

ity)

•ce

ntra

lcom

posi

tion

unkn

own

(afte

rS

hapi

ro&

Teuk

olsk

y)

I

EF

CO

DRI

L

AI

N

R

DN

XAEA

ESII

C

M LMV

A

AI

AD

R

E

LGE

14–1

3

Neu

tron

Sta

rs3

Neu

tron

Sta

rs:

Rot

atio

n

Dur

ing

colla

pse,

angu

lar

mom

entu

mis

cons

erve

d(E

xplo

sion

:sy

mm

etric

)

Tota

lang

ular

mom

entu

mof

hom

ogen

eous

sphe

re:

J=

Iω

whe

reI

=2 5M

R2

I

EF

CO

DRI

L

AI

N

R

DN

XAEA

ESII

C

M LMV

A

AI

AD

R

E

LGE

14–1

3

Neu

tron

Sta

rs4

Neu

tron

Sta

rs:

Rot

atio

n

Dur

ing

colla

pse,

angu

lar

mom

entu

mis

cons

erve

d(E

xplo

sion

:sy

mm

etric

)

Tota

lang

ular

mom

entu

mof

hom

ogen

eous

sphe

re:

J=

Iω

whe

reI

=2 5M

R2

Ang

ular

mom

entu

mco

nser

vatio

n(J

befo

re=

JN

S):

2 5M

befo

reR

2 befo

reω

befo

re=

2 5M

NSR

2 NSω

NS

or

ωN

S=

(

Mbe

fore

MN

S

)(

Rbe

fore

RN

S

)

2

ωbe

fore

orP

NS∼

(

RN

S

Rbe

fore

)

2

Pbe

fore

(whe

reP

:ro

tatio

npe

riod)

I

EF

CO

DRI

L

AI

N

R

DN

XAEA

ESII

C

M LMV

A

AI

AD

R

E

LGE

14–1

3

Neu

tron

Sta

rs5

Neu

tron

Sta

rs:

Rot

atio

n

Dur

ing

colla

pse,

angu

lar

mom

entu

mis

cons

erve

d(E

xplo

sion

:sy

mm

etric

)

Tota

lang

ular

mom

entu

mof

hom

ogen

eous

sphe

re:

J=

Iω

whe

reI

=2 5M

R2

Ang

ular

mom

entu

mco

nser

vatio

n(J

befo

re=

JN

S):

2 5M

befo

reR

2 befo

reω

befo

re=

2 5M

NSR

2 NSω

NS

or

ωN

S=

(

Mbe

fore

MN

S

)(

Rbe

fore

RN

S

)

2

ωbe

fore

orP

NS∼

(

RN

S

Rbe

fore

)

2

Pbe

fore

(whe

reP

:ro

tatio

npe

riod)

Exa

mpl

e:R

befo

re=

7000

00km

(sun

),R

NS

=15

km,P

Sun

=27

d=⇒

PN

S=

0.00

1s

Neu

tron

Sta

rsar

eex

trem

ely

fast

rota

tors

.

clos

eto

brea

k-up

spee

d!

I

EF

CO

DRI

L

AI

N

R

DN

XAEA

ESII

C

M LMV

A

AI

AD

R

E

LGE

14–1

4

Neu

tron

Sta

rs6

Pul

sars

Dis

cove

ry:

Bel

l&H

ewis

h(1

967)

:

Rad

ioP

ulsa

r

radi

oem

issi

onis

puls

ed,

very

shor

tper

iods

:m

illis

econ

dsto

afe

w

seco

nds

I

EF

CO

DRI

L

AI

N

R

DN

XAEA

ESII

C

M LMV

A

AI

AD

R

E

LGE

14–1

5

Neu

tron

Sta

rs7

Pul

sars

Pul

sars

atdi

ffere

ntw

avel

engt

hs

Pul

satio

nsno

tonl

yin

the

radi

ore

gim

e,bu

tals

oat

optic

al,X

-ray

,and

γ-r

ay

wav

elen

gth,

butn

otin

allc

ases

.

I

EF

CO

DRI

L

AI

N

R

DN

XAEA

ESII

C

M LMV

A

AI

AD

R

E

LGE

14–1

6

Neu

tron

Sta

rs8

Pul

sars

Pul

ses

due

toth

elig

htho

use

effe

ctca

used

byra

pid

rota

tion.

Rot

atio

npe

riod:

P=

2πR

v rot

(14.

2)

Rot

atio

nsp

eed

atth

esu

rfac

em

ustb

esm

alle

rth

esp

eed

oflig

ht.=⇒

R<

Pc

2π

Sho

rtes

tper

iods

obse

rved

:P

∼1

ms

=⇒

R<

50km

Pul

sars

are

neut

ron

star

s!

I

EF

CO

DRI

L

AI

N

R

DN

XAEA

ESII

C

M LMV

A

AI

AD

R

E

LGE

14–1

7

Neu

tron

Sta

rs9

Pul

sars

Axi

s of

Rot

atio

n

Rad

iatio

nbe

am

Rad

iatio

nbe

am

“Lig

htho

use

mod

el”

for

puls

ars

Ano

ther

cons

erve

dob

serv

able

:

mag

netic

flux:

Φ=

BR

2

Mag

netic

field

afte

rS

N:

BN

S=

(

Rbe

fore

RN

S

)

2

Bbe

fore

=⇒

neut

ron

star

sha

vest

rong

mag

netic

field

s(t

ypic

al:B

∼10

6..

.108

T)

Rad

iopu

lsar

sar

efa

stro

tatin

g(is

o-

late

d)ne

utro

nst

ars

with

stro

ng

mag

netic

field

s.

I

EF

CO

DRI

L

AI

N

R

DN

XAEA

ESII

C

M LMV

A

AI

AD

R

E

LGE

14–1

8

Neu

tron

Sta

rs10

The

soun

dsof

puls

ars

•P

SR

0329

–a

norm

alpu

lsar

(P=

0.71

4519

s)

•P

SR

0833

–th

eV

ela

puls

ar,a

fast

er,y

oung

erpu

lsar

inth

eV

ela

supe

rnov

a

rem

nant

(P=

89m

sec)

•C

rab

puls

ar–

the

youn

gest

puls

ar(P

=33

ms)

•B

1937

–on

eof

the

fast

estp

ulsa

rs(P

=0.

0015

5780

6448

8727

5s)

See

/hea

rhttp://www.jb.man.ac.uk/~pulsar/Education/Sounds/sounds.htm

for

mor

eex

ampl

es.

I

EF

CO

DRI

L

AI

N

R

DN

XAEA

ESII

C

M LMV

A

AI

AD

R

E

LGE

14–1

9

Bla

ckH

oles

1

Bla

ckH

oles

Deg

ener

ate

neut

ron

gas:

Cha

ndra

sekh

arth

eory

appl

ies.

How

ever

,mod

ified

hydr

osta

ticeq

uatio

n(G

RT

)

equa

tion

ofst

ate

muc

hm

ore

com

plic

ated

than

for

whi

tedw

arfs

Neu

tron

star

sal

soha

veup

per

mas

slim

it:O

ppen

heim

erV

olko

fflim

it.

Det

aile

dm

ass

limit

unkn

own,

caus

ality

cons

ider

atio

nsgi

veM

∼3M

⊙(f

or“s

tiff

equa

tion

ofst

ate”

the

soun

dsp

eed

beco

mes

grea

ter

than

spee

dof

light

atth

is

mas

s)

Com

pact

obje

cts

with

mas

sab

ove

Opp

enhe

imer

Vol

koff

limit:

Bla

ckH

oles

Mor

eco

nser

vativ

eas

tron

omer

s:“B

lack

Hol

eC

andi

date

s”.

I

EF

CO

DRI

L

AI

N

R

DN

XAEA

ESII

C

M LMV

A

AI

AD

R

E

LGE

14–2

0

Bla

ckH

oles

2

Bla

ckH

oles

Inm

ore

mod

ern

usag

e(b

utst

illN

ewto

nian

!):

Tota

lene

rgy

ofa

mas

sm

:

E=

Epo

t+

Eki

n=

−G

Mm

R+

1 2m

v2

Mas

sm

isun

boun

dif

E>

0,i.e

.,fo

r

v≥

v esc

ape

=

√

2GM R

Bla

ckH

ole:

Bod

yof

mas

sM

and

radi

usR

for

whi

chv e

scap

e>

c,w

here

cis

the

spee

dof

light

.

Thi

sis

the

case

if

R≤

RS

=2G

M

c2∼

3km

M M⊙

the

Sch

war

zsch

ildR

adiu

s.

I

EF

CO

DRI

L

AI

N

R

DN

XAEA

ESII

C

M LMV

A

AI

AD

R

E

LGE

14–2

1

Bla

ckH

oles

3

Ein

stei

n

Alb

ertE

inst

ein

(187

9–19

55)

Spe

cial

Rel

ativ

ity(1

905)

:

•S

peed

oflig

htha

sth

esa

me

valu

ein

all

fram

esof

refe

renc

e

•O

bser

ver

with

cons

tant

velo

city

mea

sure

the

sam

eph

ysic

alla

ws

From

thes

eax

iom

sfo

llow

s:

=⇒

Spa

cean

dtim

ear

ere

lativ

e(“

4D-s

pace

-

time”

)

=⇒

E=

mc2

(“M

ass

and

Ene

rgy

are

equi

vale

nt”)

I

EF

CO

DRI

L

AI

N

R

DN

XAEA

ESII

C

M LMV

A

AI

AD

R

E

LGE

14–2

1

Bla

ckH

oles

4

Ein

stei

n

Alb

ertE

inst

ein

(187

9–19

55)

Gen

eral

rela

tivity

(191

6):

•M

ass

curv

essp

ace

(“M

etric

”)

I

EF

CO

DRI

L

AI

N

R

DN

XAEA

ESII

C

M LMV

A

AI

AD

R

E

LGE

14–2

1

Bla

ckH

oles

5

Ein

stei

n

Alb

ertE

inst

ein

(187

9–19

55)

Gen

eral

rela

tivity

(191

6):

•M

ass

curv

essp

ace

(“M

etric

”)

•Li

ghtm

oves

thro

ugh

curv

edsp

ace

I

EF

CO

DRI

L

AI

N

R

DN

XAEA

ESII

C

M LMV

A

AI

AD

R

E

LGE

14–2

2

Bla

ckH

oles

6

post

-Ein

stei

n

Kar

lSch

war

zsch

ild(1

873–

1916

)

Dire

ctly

afte

rpu

blic

atio

nof

GR

T:

ds2

=

(

1−

2GM

c2r

)

c2dt

2−

(

1−

2GM

c2r

)

−1

dr2

(Sch

war

zsch

ildM

etric

).

Des

crib

es“s

hape

ofsp

ace”

invi

cini

tyof

mas

sM

.

I

EF

CO

DRI

L

AI

N

R

DN

XAEA

ESII

C

M LMV

A

AI

AD

R

E

LGE

14–2

3

Bla

ckH

oles

7

post

-Ein

stei

n

R>

RS

R∼

RS

R<

RS

Beh

avio

rof

light

isde

term

ined

from

loca

tion

ofem

issi

on,i

nde

pend

ence

from

the

Sch

war

zsch

ildR

adiu

s:

RS

=2G

M

c2∼

3km

M M⊙

Sam

eva

lue

asin

New

toni

ande

rivat

ion!

J.N

.Im

amur

a

I

EF

CO

DRI

L

AI

N

R

DN

XAEA

ESII

C

M LMV

A

AI

AD

R

E

LGE

14–2

3

Bla

ckH

oles

8

post

-Ein

stei

n

R>

RS

R∼

RS

R<

RS

Bla

ckho

lein

GR

T:B

odie

ssm

alle

rth

anth

eir

Sch

war

zsch

ildra

dius

.

J.N

.Im

amur

a

Bla

ckho

les

are

very

sim

ple

phys

ical

obje

cts ,

dete

rmin

ed

by

•M

ass

•(C

harg

e)

•A

ngul

arm

omen

tum

X