天文觀測 I

Crab & Pulsar

Crab – Chinese Astronomer’s Record

• The supernova was noted on July 4, 1054 A.D. by Chinese astronomers.

• It was about four times brighter than Venus, or about mag -6.

• it was visible in daylight for 23 days, and 653 days to the naked eye in the night sky

宋史天文志有關天關客星的記載

Supernova Explosion

Crab Nebula -- Discovery

• The nebulous remnant was discovered by John Bevis in 1731, who added it to his sky atlas.

• Charles Messier independently found it on August 28, 1758, when he was looking for comet Halley on its first predicted return, and first thought it was a comet. Of course, he soon recognized that it had no apparent proper motion, and cataloged (M1) it on September 12, 1758.

Crab Nebula inBevis’ catalog

Crab Nebula = SNR of SN 1054

• J.C. Duncan of Mt. Wilson Observatory compared photographic plates taken 11.5 years apart, and found that the Crab Nebula was expanding at an average of about 0.2" per year; backtracing of this motion showed that this expansion must have begun about 900 years ago (Duncan 1921).

• Also the same year, Knut Lundmark noted the proximity of the nebula to the 1054 supernova

Radio Band: Discovery and Pulsar

• In 1948, the Crab nebula was identified as a strong source of radio radiation, named and listed as Taurus A and later as 3C 144.

• On November 9, 1968, a pulsating radio source, the Crab Pulsar (also cataloged as NP0532, "NP" for NRAO Pulsar, or PSR 0531+21), was discovered in M1 by astronomers of the Arecibo Observatory 300-meter radio telescope in Puerto Rico.

X-ray Band: Discovery and Position

• X-rays from this object were detected in April 1963 with a high-altitude rocket of type Aerobee with an X-ray detector developed at the Naval Research Laboratory.

• the X-ray source was named Taurus X-1. Measurements during lunar occultations of the Crab Nebula on July 5, 1964, and repeated in 1974 and 1975, demonstrated that the X-rays come from a region at least 2 arc minutes in size.

Crab: Luminosity

• Emitted in X-rays by the Crab nebula is about 100 times more than that emitted in the visual

light.

• Its apparent brightness corresponds to an absolute magnitude of about -3.2, or more than 1000 solar luminosities.

• Its overall luminosity in all spectral ranges was estimated at 100,000 solar luminosities or 5x1038 erg/s !

What is Crab ?

• Supernova

• Supernova Remnant

• Nebula

• Pulsar (young)

• Variable star

Aliases of CrabMessier Object

X-ray old name X-ray name

Radio: Cambridge CatalogNGC

γ-ray name

Pulsar: J name

Infrared name

Pulsar: B name

Supernovaname

SNR name

Radio: NRAOcatalog

Common name

Crab: Multi-wavelength Observation• Crab is the one of few astrophysical objects being able to b

e seen in all the EM wave bands (from radio to γ–ray)

X-ray: Chandra UV: ASTRO 1 Optical: VLA Near IR: 2MASS

Mid IR: IRAS Far IR: IRAS Radio: NRAO Composed

Crab: Pulsar, Multi-wavelength

• Not only the emission but also pulsar ……

Optical

X-ray

γ-ray Optical

Radio

Infrared

Pulsar: Discovery

• Pulsars were discovered by Jocelyn Bell and Antony Hewish in 1967 while they were using a radio array to study the scintillation of quasars.

• They found a very regular signal, consisting of pulses of radiation with period of 1.34 sec

• The original name for the object was "LGM", Little Green Men, thinking of it as a beacon made by some extraterrestrial intelligence.

• Thomas Gold analyzed the results of these observations, determining that the only natural object that could be responsible was a neutron star, a type of stellar object up to then only hypothesized.

Why Pulsar Must Come from Neutron Star ?

222

2 3

1 32 2

1 32 2

Breaking frequency:

4

4

21701.4 10

0.461.4 10

bkrot

bkrot

bkrot

GMR

R

GM

R

RMHz

M km

RMP ms

M km

Breaking Period

Mass Radius Breaking period

Sun 1 M 7x1010cm 2.8 hours

White dwarf 1 M 6x108cm 8 sec

Neutron star 1.4 M 1x106cm 0.46 ms

Pulsars:• Pulsar period : 1.6 ms to ~300 sec

• Types of pulsars• Radio pulsar

• X-ray pulsar

• Millisecond pulsar

• Isolated pulsar

• Binary pulsar

• Rotational-powered pulsar

• Accretion-powered pulsar

• Nuclear-powered pulsar

• Anomalous X-ray pulsar

Sound of Pulsar

PSR B0329+54P=0.714519 s

f=1.4 Hz

Sound of Pulsar

Vela pulsarP=89 msf=11 Hz

Sound of Pulsar

Crab pulsarP=33 msf=30 Hz

Sound of Pulsar

PSR J0437-4715P=5.747 msf=174 Hz

Sound of Pulsar

PSR B1937+21P=1.55780644887275 ms

f=642 Hz

Properties of Neutron Star

• Lower limit of mass : 1.4 M

• Upper of mass: limit of mass : < 3.2 M

• Radius: ~10-15 km

• Mean density: 1x1014 g/cm3

• Rotational period: 1.6 msec to ~300 sec (from pulsar_

• Magnetic field: 108 to 1014 Gauss

Why Neutron Star Rotates so Fast ?

2 2

2

2

2

2

Conservation of angular momentum

1Suppose

10

10

24days (Sun's rotational period)

brfore before after after

beforeafter before

after

afterafter before

before

before solar

after

before

af

MR MR

R

R

RP P

R

R R

R km

P

P

42ter ms

Pulsar: Light House Effect

• Consider the neutron star as a magnetic dipole. The poles has strongest magnetic filed and also the large radiation as the result of strong interaction on them.

• However, if the magnetic dipole is aligned on the rotational axis, no pulsation can be detected

Pulsar: Light House Effect

• If the magnetic dipole misaligned to the rotational axis, the strong emission from the pole (or poles) may be shining to the observer with periodically with rotational period, which is somewhat like a light house on sea. Thus, it is named “light house effect”.

Crab Pulsar: X-ray Band

Isolated Pulsar: Rotation-powered

• Since dipole is a vector, changing the direction is also changing the dipole moment.

• Our EM knowledge tells us that when a magnetic dipole moment change with the time, there are EM wave emission.

• The energy supply for the radiation is the rotational energy of the neutron star for the isolated pulsar.

Pulsar: Braking Index

2

2 2 4 3

122

sin3

: Magnetic dipole mement

: the angle rotational axis and dipole

: braking index

3: Pure dipole radiation

For Crab n=2.515 0.005

Breaking constant can be yield

n

d II M c

dtM

k

n

n

21

2 2

through

2

nn k

kn n n

PPn

P

Pulsar: Age

1 10

1 1

1 1

1

1

i

1 1 1 1

1

1 11 1

11

If ;

age now

i

nn

t

n n nnow i

n nnow now now now

n n nnow i i

nnow now

age nnow i

nownow age

d dk dt

dt k

ddt

k n k

n k n

tn

tn

1

1 1

For n=3; 2

Characteristic age

=2

now

now now

nowage

now

now

now

P

n P

Pt

P

P

P

Pulsar: a Precise Clock

• Astronomers found that the (isolated) pulsars are precise clocks, which can compete to atom clock.

• Pulsar period (frequency) ephemeris:

0 0 0

0

0 0 0

0

2

0 0

3

0

2

0 0

3

0

0

-13 -19

1

21

61

21

6Crab's ephemeris

T MJD48734

P=0.0334033474094 0.0000000000002 sec

P=4.209599 10 2 10

T T T

T

T T T

T

P t P P t T P t T

P t T

t t T t T

t T

Crab: Age, Magnetic Field and Flux

2 2 4 3

22

3 3

19

12

45 2

2 49

38

Characteristic age

P1250 years

2P2

sin3

1/

3.3 10

For Crab: B=3.9 10

10

11.8 10

2

4.6 10 /

121000

rot

rot

Crab sun

I M c

P PB PP

P

B PP Gauss

Gauss

I g cm

E I erg

dEI erg s

dt

L L

X-ray Pulsar

• Most of the pulsars are detected in radio band but of a few of them whose pulsations can be detected in X-ray band.

• The X-ray pulsation can be originate:

• Magnetospheric Emission

• Cooling Neutron Stars

• Accretion

X-ray Pulsar: Magnetospheric Emission:

• X-ray pulsars can be produced when high-energy electrons interact in the magnetic field regions above the neutron star magnetic poles.

• Pulsars seen this way, whether in the radio, optical, X-ray, or gamma-ray, are often referred to as "spin-powered pulsars," because the ultimate source of energy comes from the gradual slowing down of the neutron star rotation.

X-ray Pulsar: Cooling Neutron Stars

• When a neutron star is first formed in a supernova, its surface is extremely hot (more than 109 degrees). Over time, the surface cools.

• While the surface is still hot enough, it can be seen with X-ray telescopes.

• If some parts of the neutron star are hotter than others (such as the magnetic poles), then pulses of thermal X-rays from the neutron star surface can be seen as the hot spots pass through our line of sight.

• Some pulsars, including Geminga , show both thermal and magnetospheric pulses.

X-ray Pulsar: Accretion Power

• If a neutron star is in a binary system with a normal star, the powerful gravitational field of the neutron star can pull material from the surface of the normal star.

• As this material spirals around the neutron star, it is funneled by the magnetic field toward the neutron star magnetic poles. In the process, the material is heated until it becomes hot enough to radiate X-rays.

• As the neutron star spins, these hot regions pass through the line of sight from the Earth and X-ray telescopes see these as X-ray pulsars. Because the gravitational pull on the material is the basic source of energy for this emission, these are often called "accretion powered pulsars."

Pulsar Evolution

• Basically, normal pulsars have intrinsically precise periods modulated only by slow monotonic increase (spin down) due to graduate loss (radiated away) of rotational energy.

12

12

Supernova

Pulsar period ~50 ms; B~10

spin-down, magnetic field decay

Pulsar period ~sec; B<10 G

Massive star Young Pulsar +Supernova Remnant

Isolate Pulsar

G

Millisecond Pulsar

• However, there are very fast-rotating pulsar whose periods are less or equal to ~10 ms. The new category of pulsars is called millisecond pulsars or “recycled” pulsars.

• The extreme small period change rates (much smaller than normal pulsars) imply that the millisecond pulsars have weak magnetic fields (~109G) and their characteristic ages are about 109 years.

• The millisecond pulsars can be either isolated or in binary systems with low mass companion.

P-B Diagram

Millisecondpulsars

Youngpulsars

Evolution

Model

• The millisecond pulsar started as an normal pulsars which lost most of its magnet field and was “spun up” to millisecond pulsars by accreting matter from their companion star in an X-ray binary.

• Two kinds of X-ray binaries – High Mass X-ray Binary (HMXB) and Low Mass X-ray Binary (LMXB)

• HMXB is hardly to be the candidate because:

(1) Nearly spherical accretion provides little angular momentum to spin-up the neutron star.

(2)To spin-up normal pulsar to millisecond pulsar requires ~0.1 solar mass. Even at Eddington accretion rate (10-8 M⊙ per year), it would take ~107 years, which much larger than the mass transfer phase of most HMXBs.

HMXB and LMXB

HMXB LMXB

LMXB and Millisecond Pulsar• The companion transfers large amount angular momentum to

neutron star through accretion.• Millisecond pulsar in low mass secondary binary system –

The binary was once an accreting LMXB but terminate mass transfer due to the secondary sink into Roche lobe.

• Isolated millisecond pulsar –

The accretion process eventually consumed the all the matter in secondary and left an fast rotating neutron star.

• This model implies that there should be coherent millisecond X-ray pulsars in ~150 LMXBs. People tried to search but failed to find any millisecond pulsar in LMXBs until April 1998.

(The fastest pulsar in LMXB discovered before 1995 was A0538-66 (P=69 ms)).

Millisecond Pulsar in LMXB ????

• Although the recycle model was reasonable and wildly believed, there was no direct evidence that the LMXB is the progenitor of millisecond pulsars

• DO WE SEE MILLISECOND PULSAR IN LMXB ?????