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