3. n
Neutron stars
•We saw how some stars can explode violently as a supernova and neutron core remains
after supernova.
What are the properties of neutron stars?
4. n
Neutron stars
•We saw how some stars can explode violently as a supernova and neutron core remains
after supernova.
What are the properties of neutron stars?
7. Neutron stars
•Although the size of a neutron star is small, the mass of
a neutron star is typically ∼ M⊙ = 2 × 1030
kg
•Thus, the mass density is…
ρ ∼
2.0 × 1030
kg
(20 × 103m)3
∼ 1017−18
kg/m3
8. Neutron stars
•Although the size of a neutron star is small, the mass of
a neutron star is typically ∼ M⊙ = 2 × 1030
kg
•Thus, the mass density is…
ρ ∼
2.0 × 1030
kg
(20 × 103m)3
∼ 1017−18
kg/m3
9. Neutron stars
•Although the size of a neutron star is small, the mass of
a neutron star is typically ∼ M⊙ = 2 × 1030
kg
•Thus, the mass density is…
ρ ∼
2.0 × 1030
kg
(20 × 103m)3
∼ 1017−18
kg/m3
Blue whale(蓝鲸)
10. Neutron stars
•Although the size of a neutron star is small, the mass of
a neutron star is typically ∼ M⊙ = 2 × 1030
kg
•Thus, the mass density is…
ρ ∼
2.0 × 1030
kg
(20 × 103m)3
∼ 1017−18
kg/m3
Blue whale(蓝鲸) ×10万
11. Neutron stars
Neutron star has other important properties
•Neutron stars rotate extremely rapidly. The period of rotation is 1/100-30 seconds!
•Neutrons stars have a strong magnetic field. Its strength is times larger than Earth’s
magnetic field.
1012
12. Neutron stars
Neutron star has other important properties
•Neutron stars rotate extremely rapidly. The period of rotation is 1/100-30 seconds!
•Neutrons stars have a strong magnetic field. Its strength is times larger than Earth’s
magnetic field.
1012
13. Pulsars
•Can you believe the objects as strange as neutron stars really exist?
Yes, we can believe it! We observed it
•In 1967, Jocelyn Bell, who was a graduate student, first discovered surprising object.
•Since the signal is very periodic, they first thought “Is this signal from an Alien?” And
they call these objects pulsar.
•Bell could not win the Nobel prize although his supervisor won it….
14. Pulsars
•In order to explain why the signal is periodic, they expect that this signal comes from rotating
neutron stars very rapidly. It’s evidence of rotating neutron stars!
•Currently, more than 1500 pulsars
have been discovered.
15. Pulsars
•In order to explain why the signal is periodic, they expect that this signal comes from rotating
neutron stars very rapidly. It’s evidence of rotating neutron stars!
•Currently, more than 1500 pulsars
have been discovered.
16. Pulsars
•In order to explain why the signal is periodic, they expect that this signal comes from rotating
neutron stars very rapidly. It’s evidence of rotating neutron stars!
•Currently, more than 1500 pulsars
have been discovered.
17. Neutron star binary
•As we studied before, most of the stars are binary. Some neutron stars are also binary.
•By gravitational wave observation, we have directly observed gravitational wave
from neutron star binary.
18. Gamma-ray burst
•In the 1960s, military satellites are looking for violators of the “Nuclear Test Ban Treaty”
•In 1967, they found irregular flashes of gamma rays
typically lasting only a few seconds
•This phenomenon is called “Gamma-ray bursts(GRBs)”
•Currently, we observe ~ 1 GRBs per day.
19. Gamma-ray burst
•For 9 years of operating observation by
Compton observatory, it detected 2704 GRBs.
Properties of GRBs
•Some GRBs flash lasts for more than 10s
(long period GRB), while some others last for
less than 1s (short period GRB).
•Some GRBs are discovered at high redshift
( )
z > 6
23. Fast radio burst (FRB)
•Not only Gamma-ray bursts, but we also discovered “Fast Radio Bursts (FRBs)”. We first
discovered FRB in 2006.
•FAST telescope has detected some FRBs.
•The mechanism of FRBs has been not understood well (Magnetar ?? Merging neutron stars??)
•The lasting time is less than milli second.
*Magnetar is a neutron star that has a very strong magnetic field.
24. Black holes
Einstein equation
Rμν −
1
2
gμνR + Λgμν =
8πG
c4
Tμν
物质（能量）
时空的扭曲
•More energy (or mass) generates
more distorted space-time.
Remember the density of neutron stars. ρ ∼
2.0 × 1030
kg
(20 × 103m)3
∼ 1017−18
kg/m3
Such high-density objects generate very distorted space-time. This is called “blackhole”.
25. Black holes
ds2
= −
(
1 −
2GM
c2r )
c2
dt2
+
(
1 −
2GM
c2r )
−1
dr2
+ r2
(dθ2
+ sin2
θdϕ2
)
Rμν −
1
2
gμνR + Λgμν =
8πG
c4
Tμν
Schwarzschild solved Einstein's equation
and obtained a solution.
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ds
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dx
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dy
•Let’s briefly understand the meaning of the Schwarzschild solution!
Schwarzschild solution
•In flat space, we can calculate the distance between
two points by
ds2
= dx2
+ dy2
Or
ds2
= dr2
+ r2
dθ2
26. Black holes
ds2
= −
(
1 −
2GM
c2r )
c2
dt2
+
(
1 −
2GM
c2r )
−1
dr2
+ r2
(dθ2
+ sin2
θdϕ2
)
Rμν −
1
2
gμνR + Λgμν =
8πG
c4
Tμν
Schwarzschild solved Einstein's equation
and obtained a solution.
•Let’s briefly understand the meaning of the Schwarzschild solution!
Schwarzschild solution
•Then, how can we measure the distance between
two points around a black hole in space-time?
The answer is the Schwarzschild solution!
27. Black holes
ds2
= −
(
1 −
2GM
c2r )
c2
dt2
+
(
1 −
2GM
c2r )
−1
dr2
+ r2
(dθ2
+ sin2
θdϕ2
)
r =
2GM
c2
Schwarzschild radius
If an object which has mass becomes a Schwarzschild radius, that object becomes a
black hole.
M
(Question) How big does the Earth have to be to become a black hole?
G = 6.68 × 10−11
[m3
kg−1
s−2
]
c = 3.0 × 108
[m/s]
Mearth = 6.0 × 1024
[kg]
28. Black holes
ds2
= −
(
1 −
2GM
c2r )
c2
dt2
+
(
1 −
2GM
c2r )
−1
dr2
+ r2
(dθ2
+ sin2
θdϕ2
)
r =
2GM
c2
Schwarzschild radius
If an object which has mass becomes a Schwarzschild radius, that object becomes a
black hole.
M
(Question) How big does the Earth have to be to become a black hole?
G = 6.68 × 10−11
[m3
kg−1
s−2
]
c = 3.0 × 108
[m/s]
Mearth = 6.0 × 1024
[kg]
r =
2 × 6.68 × 10−11
× 6.0 × 1024
(3.0 × 108)2
∼ 8.9 × 10−3
m = 0.89cm
29. Black holes
Stellar size blackhole( )
∼ 1 − 100M⊙
•Such blackholes are observed by gravitational
wave
Super massive blackholes(SMBH) ( )
∼ 105
− 1010
M⊙
•Stellar size blackhole is generated at the end
stage of stellar objects
•The formation mechanism has not been clear.
•SMBH in M87 was first observed by EHT in
2019. They also observed SMBH in our galaxy
(Sgr A*).
•Galaxies usually have SMBH in the center of it.
33. Summary
• After a supernova explosion, neutron stars are generated.
Its density is extremely high.
• Occasionally, Pulsar, Gamma-ray bursts, and Fast radio
bursts are discovered.
• Blackholes are generated at the end stage of stellar
evolution.
