Lec. 9
III SELECTED HOT TOPICS IN
MODERN ASTRONOMY
III-1 Dense Stars (Main Ref.: Lecture notes;
FK p. 533, 563, 603, Sec. 20-4 and11, 21-1, 2,
3, 6, 7; Suppl. II; CD photos shown in class)
1
III-1a White Dwarfs (Main Ref.: Lecture notes; FK p. 563,
Sec. 20-4; Suppl. II)
Low mass stars (M < ~ 4M☉): eject outer layers (H + He) 
Planetary Nebula
The leftover burned-out (C + O) core of a low-mass star cools
and contracts until it becomes a white dwarf (WD)
Note: The core temperature is NOT high enough for
thermonuclear reaction (using C+O), e.g., C-burning, Oburning, to take place!
• No further nuclear reactions take place within the exposed core
• Instead, it becomes a degenerate, dense sphere about the size
of the Earth and is called a white dwarf
• It glows from thermal radiation; as the sphere cools, it becomes
2
dimmer
C+O
H
He
Fig. III-1
Forming “Planetary Nebula”
Fig. III-2:
WD in globular cluster “M4”
d ~ 7000ly away, 14 billion-year old
(H+He) ejected
Fig. III-3: White Dwarf
3
What can sustain WD from its gravity?  degenerate
pressure of degenerate electrons. See earlier lectures
– Lec. 7 and class notes, for what degeneracy and
degenerate pressure are.
Note: ~ 4 – 8 M☉ main sequence stars may end up as heavy
white dwarfs with heavier element core, e.g., Mg, Si (see Stellar
evolution section, Lec. 7)
Characteristics of White
Dwarfs
•Supported by “electron
degenerate pressure”
Fig.III-4: Sirius A & B
4
Maxium Mass = Chandrasekher Limit = ~ 1.4M☉
see class notes for details!
Mass M ~ 0.2 – 1.4M☉;
Radius R ~ 5000km;
Central density
c ~ 109 - 12 kg/m3
(~ one cube-sugar size
~ 1-ton)
Surface temperature
.
Ts ~ 50,000 - 5000K
They no longer burn the
Internal (thermonuclear)
FK
fuel – just keep cooling!
Fig. III-5: Mass-radius relation
Less luminous (Not much radiation
of white dwarfs
from surface) - rather hard to detect!
Note: Normal Stars : “More mass, larger size”
5
Degenerate Stars : “More mass, smaller size” (see Fig. III-5)
Evolution of White Dwarfs
Fig. III-7: Evolution of white dwarfs
Fig. III-6: Evolution toward white dwarfs
6
III-1b Neutron Stars and Pulsars (Main Ref.:
Lecture notes; FK Sec. 20-11; Suppl. II)
(i) Introduction (Main Ref.: Class notes; FK Sec.20-11; Suppl. II)
• A neutron star is a dense stellar corpse consisting primarily of
closely packed degenerate neutrons
• A neutron star typically has a diameter of about 20 km, a
mass less than 3 M(solar), a magnetic field 1012 times
stronger than that of the Sun, and a rotation period of roughly
1 second
Historical Background
Early to Mid-1930s: Oppenheimer and Volkopf – theoretical
prediction of the existence of neutron stars; Baade and
Zwicky – predicted that a supernova explosion will leave
behind a compact neutron star.
7
Late 1950s: J.A. Wheeler’s group calculated structure of white
dwarfs and neutron stars for ideal Fermi gas (i.e., no nuclear
interaction); A.G.W.Cameron
Included nuclear force in
calculation of neutron star
structure the first time, and
discussed cooling of neutron
stars.
Early 1960s: Giacconi et al.
discovered Sco X-1, by a
rocket, first thought to be a
neutron star
Fig. III-8: A Supernova Pictograph?
Mid-1960s: S. Tsuruta (PhD thesis) and A.G.W. Cameron - First
detailed calculation of neutron star cooling. Showed that a
neutron star can be observable for ~ a million years after
8
supernova explosion.
1967: J. Bell, etc., discovered the first radio pulsar; Gold and
Pacini suggested it is a rotating, magnetic neutron star.
1970: Launch of UHURU, the first X-ray satellite.
1980: Launch of Einstein X-Ray Observatory , the first X-ray
telescope – found upper limit for neutron star temperatures the
first time.
1990: Launch of ROSAT X-Ray Observatory – first positive
measurement of neutron star temperatures for at least three
pulsars.
1998: Launch of Chandra (July) and XMM/Newton(December)
X-ray Satellite – found many neutron stars.
9
(ii) Composition – Why Neutron Star? (Main Ref.:
Class notes; Suppl. II)
Composition of dense matter (= `zero-temperature’ matter):
Definition: `zero-temperature’ matter means matter where
Fermi energy EF () >> Thermal energy Eth ~ kT, where  is density.
Fermi energy high when density is high. That means density effect is much
larger than temperature effect. Fermi energy is the energy of degenerate
(quantized) particles.
(See class notes for the details.)
Let’s increase density of `zero-temperature’ matter from the terrestrial
value (e.g., ordinary Fe with 26 protons and 30 neutrons (Fe is the most
stable element in that condition) – then what happens?
 < 107 kg/m3: Ordinary atoms, most stable is iron, 26Fe56.
Pressure Ionization, at  ~ 107 kg/m3: Density high enough and
atoms are so close to each other that electrons freed from atoms by
pressure.
Note: This is ionization by pressure due to high density, not by high
temperature.
10
107 <  < 1012 kg/m3) : Matter consists of heavy ordinary ions such as
“Fe ions” + “free electrons (e-)”
“Electron Capture”, at  ~ 1012 kg/m3 : Matter gets so dense and electrons
and heavy nuclei (ions) get so close to each other that free e- are captured by
nuclei!
Then, inside a nucleus, proton and electron combine to become neutron, by
process called -process: p + e-  n +  (where  is neutrino).
Since within nuclei protons change to neutrons in this manner, the heavy nuclei
(heavy ions such as Fe) become `neutron-rich’!
e.g., 26Fe56 (p = 26, n = 30)  24Cr56 (p = 24, n = 32), etc.
~ 1012 <  <~ 4 x 1014 kg/m3: Nuclei become more and more “neutron-rich”
(e.g., 26Fe108 ), and so
Composition = (Neutron-rich nuclei) + (free e-)
“Neutron Dripping” at ~ 4 x 1014 kg/m3: Too many neutrons inside nuclei 
cannot keep all neutrons inside nuclei  so neutrons `drip’ out of nuclei!
 ~ 4 x 1014 <  < 3 x 1017 kg/m3 :
Composition = (free e-) + (free n) + (n-rich nuclei)
11
 Disintegration of Heavy Nuclei, at  ~ 3 x1017 kg/m3 ~
“Nuclear Density” N
Since density inside and outside the neutron-rich heavy nuclei are ~ equal,
the boundary surface disappears  disintegrate to free n + p + e-!
By then (# of n) / (# of p) ~ 95%, and so, the matter consists
predominantly of neutrons  so neutron matter!
So, stars with density higher than the nuclear density are Neutron Stars!
 Neutron Matter, for ~ 3 x 1017 <  < ~ 1018 kg/m3:
Composition is neutron + protons + electrons, but mostly neutrons.
 `Exotic’ Particle Matter, for  > ~ 1018 kg/m3:
Neutrons and protons transform to `exotic’ particles, such as pions, kaons,
hyperons or quarks, since that is more stable (lower energy state) than
neutron matter.
Note: For matter higher than nuclear density, strong (nuclear) force acts
among particles – which is not well-known. So, there are some uncertainties
as to which `exotic’ particles really will exist and exactly at what density the
transition from the neutrons to `exotic’ particles will take place in matter with
12
such high density.
See class notes for further details.
(iii) Structure and Properties of Neutron
Stars (NS) (Main Ref.: Class notes; Suppl.II; FK 20-11)
(iii-a) Properties:
Typical stellar mass:
M ~ 1 - 2 M☉,
Typical stellar radius:
R ~ 8 – 16 km
Typical central density
c ~ 1017 - 18 kg/m3
~ 1 billion ton per
teaspoon!!!
Typical surface temperature
(to be observable):
Ts ~ 105 - 6 K,
Typical magnetic field strength
of a pulsar B ~ 1012 gauss
Fig III-9: Relative size of a NS.
NS vs Manhattan area of NYC.
13
Maximum Mass of Neutron Stars:
Like a white dwarf, a neutron star has an upper
limit on its mass: ~Mn(max) ~ 1 – 3M☉
Note: If no nuclear force, Mmax ~ 0.7M☉.
Note:
•The pressure within a neutron star comes from two sources
•One is the degenerate nature of the neutrons, and the other is
the strong nuclear force that acts between the neutrons (and
protons) themselves
Fermi energy >> thermal energy (~kT), within a neutron star.
So,“Neutron degenerate pressure” is balanced with gravity
(due to “Pauli Exclusion Principle” for neutrons)
 neutron degenerate pressure supports the star! 14
See class notes for further details.
(iii-b) Structure:
Outer crust I: ordinary heavy
nuclei + e-
(See class notes, Suppl.II)
Fig. III-10: Cross section of a NS
Surface ~ 103 kg/m3
Pressure Ionization
107 kg/m3
Neutron Drip
I
Outer crust II: n-rich heavy
nuclei + e-
II
1012 kg/m3
0.
1 km
44xx1014
3 x1017
Nuclear Density
Inner
curst:
Detailed
internal structure
depends on the nuclear models
n, p, e-
n-rich
heavy
nuclei
+
free
e
Interactions
CORE
NNcore
among particles
+ free n
10 km
1018
`Exotic’
Electron Capture
?
Not drawn to scale.
Internal structure depends on
the nuclear models – strong
interaction among particles.
15
(iii-c) Compactness of Neutron Stars: Interactions
between nucleons (i.e., neutrons and protons)
Fig. III-11: Potential Energy V for a system (eV)
Strong Interaction
V
(+)
Model (B)
Nucleon
Separation
0
(–)
Model (A)
(+) : Repulsive Force
(-) : Attractive Force
See class notes for details.
Model
(A)
(B)
(center)
tons/cm3
3 ~ 50
0.2 ~ 7
Mass/M☉
0.2~1.4
0.2~1.7
Radius
(km)
7 ~ 20
15 ~30
Table III-1: Properties of NS Model dependent!
16
(iii-d) Mass-Central Density Relation of Dense Stars
Fig. III-12:
Mass-central density relation
of neutron stars and white
dwarfs
Compactness (M/R)
depends on “nuclear force”
Unstable!
Unstable!
log(c)
Stable
Neutron Star
Stable
Model (A)
Model (B)
Unstable!
Stable
White Dwarf
M /M☉
See class notes for details.
1.4 M☉
17
(iii-e) Superlfluidity and Superconductivity
A neutron star consists of a superfluid and superconducting core surrounded by
a superfluid mantle and a thin, brittle crust.
Superfluidity of neutrons and superconductivity of protons are among the
strange properties of neutron stars
Note: Superfluid particles have no resistance, move freely.
-important for cooling of neutron stars – come back later.
*************************************************************************************
Summary
-For  < ~1012 kg/m3, “e- degenerate pressure” (White Dwarf)
For  > ~1017 kg/m3, “n degenerate pressure” (Neutron Star)
To oppose huge gravity, what if density  > 1019 kg/m3 ?
 “nothing can support stars!”
 Black Hole (BH)!
18
Comment: Are neutron stars (NS) cold? Not really – observable
NS about a million degrees on the surface (emit X-rays). But
density so large that Fermi energy still >> thermal energy, and
hence the zero-temperature limit still applies.
(iv) Thermal (Temperature) Evolution of
Neutron Stars
Energy balance equation
The temperature of NS decreases in time due to radiation!
Eqn (III-1)
where: E = internal energy of NS; T = internal temperature of NS; H = time rate
of heat generation inside NS; CV = specific heat capacity; L = energy/time for
emitted “neutrinos”; L = energy/time for emitted “photons”, t = age of NS. 19
Fig. III-13:
Typical Cooling Curves of a NS
Upper limit
cooling process
superfluidity
composition
Detection
Solid : Hot, Standard cooling
n+N  p+N+e-+,
p+N+e-  n+N+
M ~ 1.2 M☉
with superfluid
(N = n or p)
Obs. Data
a: Cas A point source
b: Crab pulsar
1: pulsar PSR J0822
2: Vela pulsar
4: Geminga pulsar
6: Pulsar PSR B1055
Dashed : Cool,
Non-Standard
Cooling,
Extotic Particles
(Pion-cooling)
M ~ 1.4 M☉
with superfluid
Tsuruta et al. 2002, ApJ
20
(v)
Pulsar = rotating, magnetic neutron star
(Ref.: Class notes; FK Sec. 20-11)
¤ The discovery of pulsars in the 1960s stimulated
interest in neutron stars
¤ Pulsars are rapidly rotating neutron stars with intense
magnetic fields
A neutron star with an intense magnetic field B is spinning about
its rotation axis (B ~ 1012 Gauss).
¤ A pulsar is a source of periodic pulses of radio
radiation
¤These pulses are produced as beams of radio waves
from a neutron star’s magnetic poles sweep past
the Earth
21
“Lighthouse Effect”
Radio emission:
emitted above the polar
regions - whenever the
emission cone points
towards us, we see a
signal!  Lighthouse”
Fig. III-14: Pulsar radiation
Rotation Axis
N
Gamma rays emitted
from outer
magnetosphere
X-ray – optical: emitted
from inner
magnetosphere
S
X-ray emission
-ray
emission
22
Fig.III-15: Light Curve of PSR 0329-54
•Intense beams of radiation emanate from regions near the
north and south magnetic poles of a neutron star
•These beams are produced by streams of charged particles
moving in the star’s intense magnetic field
23
Fig. III-16:
“Crab Pulsar”: Optical
Pulsar Environment
d = 2000 pc ~ 6600 ly
P ~ 33 ms
L ~ 1031 watt
(~ 5 x the solar luminosity)
“Crab Pulsar” - x-rays
(Chandra X-ray Obs.)
Fig. III-17: Crab Nebula and Pulsar – optical
Note: 1000 pulsars have been found.
24
Could be as high as 105.
Fig. III-18: Crab Nebula and Pulsar
25
Fig. III-19: Crab Pulsar (detail)
26
Fig. III-20:
“Crab Pulsar” seen in space
X-ray (Chandra)
Optical (Hubble)
27
More Properties of Pulsars
Emit radiation in Radiao/Optical/X-ray/-ray band
Rotational Period: P ~ msec-sec
Fig. III-21: Voice from Pulsars…
Crab (33ms)
B1937+21
(1.6ms)
Radiation Process : “Synchrotron Radiation”(*1)(p. 29), “Cyclotron Radiation”
“Dipole Radiation” …etc
Thermal Emission = depends on temperature
Non-Thermal Emission = independent of temperature
e.g. Synchrotron Radiation (*1) – see p. 29.
28
Fig. III-22: Spectrum (Number of Photons/sec-keV vs Photon Energy)
(1)
(2)
Photon Energy
X-ray Emission: 2 components
(1) Blackbody radiation = Thermal emission (~ kT)
(2) Power-law radiation = Non-thermal emission (independent of temperature T)
**************************************************************************************************
(*1) Synchrotron Radiation
Relativistic Electrons
X-ray
Magnetic Field
Fig. III-23: Synchrotron radiation
29
III-1c. Black Holes (Ref.: Lecture notes; FK p. 603, Sec. 211, 2, 3, 6, 7; Suppl. II)
The discovery of neutron stars inspired astrophysicists to
examine seriously one of the most bizarre and fantastic
objects ever predicted by modern science, the black hole
(i) Einstein’s Special Theory of Relativity: : (Ref.:Class
notes; FK Sec. 21-1)
Reading assignment: Study FK Sec. 21-1. (Eqns are optional to
non-science majors – the emphasis is on qualitative ideas).
Here, summary only given
Time Dilation: As velocity v of an object in question approaches
velocity of light c, i.e., v c, time gets longer, i.e., things take
longer time
Space Contraction: : As velocity v of an object in question
approaches velocity of light c, i.e., v c, length gets shorter
30
(ii)Einstein’s General Theory of Relativity and
Black Hole: (Ref.: Class notes; FK 21-2, 6, 7; Suppl. II) Emphasis
is on qualitative ideas.
The general theory of relativity is our most accurate
description of gravitation
Published by Einstein in 1915,
this is a theory of gravity
• A massive object causes
space to curve and time
to slow down
• These effects manifest themselves as a gravitational force
• These distortions of space
and time are most noticeable
in the vicinity of large masses
or compact objects
Fig. III-24:A Black Hole
31
*We know that mass M and energy E are related by
Einstein’s Equation:
E = Mc2
Eqn (III-2)
*Now, General Relativity says: Mass means Gravity, which means Curvature
of Space – i.e., Presence of mass means gravitational attraction force to the
mass, which means space around the mass is curved (not straight). (See Fig.
III-25, III-26, and class notes.)  Proved by various experiments. (See FK Sec.
22-2.)
Fig. III-25:Space Curvature
32
Fig. III-26: Formation of a black hole
The general theory of relativity predicts black holes
Fig. III-27: Formation of a Black Hole
33
★Gravitational Radius RG = `Radius’ of Black Hole: When
radius of an object with a given mass M gets so small that the
curvature gets 180o (i.e. the space around the object is bent by
180o), nothing can come out of the object, for it will come right
back to the object along the curved space. That limiting radius is
called Gravitational Radius, which is commonly considered to be
radius of a black hole. It is also called `event horizon’ (See class
notes for the detailed explanation.)
★Schwarzschild Radius Rs: If the black hole is not rotating, the
black hole radius is called Schwarzschild Radius, Rs, which can
be conveniently expressed as:
Rs = 3 ( Mbh / M☉ ) (km).
Eqn (III-3)
EX 53: 1M☉ Star, Rs = 3 km (compare with the radius of a typical
1 M☉ NS, ~ 10 km!)
34
EX 54: 10M☉ Star, Rs = 30 km.
Note: A massive star with main sequence mass larger than ~
25M☉ will become a black hole, because it cannot eject enough
mass and the collapsed core will have mass larger than the
neutron star maximum mass limit ~ 3M☉ So, if the remnant
collapsed mass is larger than ~3M☉, the core keeps collapsing to
singularity, and hence becomes a black hole.
Note: Though nothing can come out of a black hole itself, the gas
around the hole can emit X-rays. It happens when a black hole is
in a binary system, since gas from the
companion can flow to the black hole
creating an accretion disk around the hole.
See next section!
Nonrotating black hole has only a “center”
and a “surface”
•The entire mass of a black hole is
concentrated in an infinitely dense
Fig. III-28: Interior of a Black35Hole
singularity
•The singularity is surrounded by a surface called the event
horizon, where the escape speed equals the speed of light
•Nothing—not even light—can escape from inside the event
horizon
Ergosphere
•Rotating Black Hole
•In the ergoregion, space and
time themselves are dragged
along with the rotation of the
black hole
•A rotating black hole (one with
angular momentum) has an
ergoregion around the outside
of the event horizon
We can extract energy from the
Ergoregion (see class notes)
Fig. III-29: A Rotating Black Hole
36
III-d Observation of Dense Stars (Main
Ref.: Class notes; FK Sec. 20-11, 21-3)
(i) Isolated Neutron Stars (NS):
Temperature of many isolated NS were measured – the
data points are shown in Fig. III-13, and they are
compared with observation.
See class notes for the details.
Fig. III-30: Spectrum of 1E 1207.4
Fig. III-31: 1E 1207.4
37
Many of these stars are radio pulsars which emit non-thermal
power-law radiation in radio, optical, X-ray, and/or -rays – see
Section III-1b (v). Some of them have thermal radiation from
stellar surface superimposed to non-thermal magnetospheric
radiation – see Fig. III-22.
38
Fig. III-32: PSR B1757-24
(ii) X-rays from Dense Stars in Binary System
In a binary system, the gas flowing from the companion star
forms an accretion disk around the compact companion star
(white dwarf, neutron star, or black hole), and the accretion disk
around the compact star emits predominantly X-rays. The
Companion star can be a main sequence star, giant, or compact
star. Some examples are shown below.
As matter (gas) expands from a companion (normal) star, it fills
“Roche Lobe” and spills onto its primary (compact) star through
“Lagrange Point”, forming “Accretion Disk” around the compact
star.
Pulsating X-ray sources – X-ray pulsars
•In a binary system, the neutron star can have strong magnetic
39
fields. Then, the magnetic fields can funnel the gas onto the
neutron star’s magnetic poles, producing hot spots. These hot
spots then radiate intense beams of X rays.
•As the neutron star rotates, the X-ray beams appear to flash on
and off.
•Such a system is called a pulsating X-ray source, or
an X-ray pulsar
xxxxxxxxxxxx
40
Fig. III-33: A Binary X-Ray Pulsar
Neutron star
Fig. III-34: Binary Stars and Roche Lobe Overflow
Compact star
Lagrange Point
●
Fig. III-36: Sco X-1 1st X-ray source
discovered in the
constellation Scorpius
Found in 1962, X-ray binary
Fig. III-35: Roche Lobe & Lagrange Point
Equi-potential Contour Curve
41
Fig. III-37: Light Curve of Cen X-3
42
Cygnus X-1 :
1st (indirect) discovery of a black hole in a binary system
Found in 1972 as an X-ray source
Supergiant HDE 226868 (M ~ 15 M☉)
Compact object (10-15 M☉ > 5 M☉  black hole)
d ~ 14000 ly away
P ~ 5.6 days
Fig. III-38: Cyg. X-1
43