1

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)

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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 coolsand 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, O-burning, 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 dimmer

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H

He

(H+He) ejected Fig. III-3: White Dwarf

C+O

Fig. III-1 Forming “Planetary Nebula”

Fig. III-2: WD in globular cluster “M4”

d ~ 7000ly away, 14 billion-year old

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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

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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 - 5000KThey no longer burn the Internal (thermonuclear) fuel – just keep cooling!Less luminous (Not much radiation from surface) - rather hard to detect!Note: Normal Stars : “More mass, larger size” Degenerate Stars : “More mass, smaller size” (see Fig. III-5)

.

Fig. III-5: Mass-radius relation of white dwarfs

FK

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Fig. III-6: Evolution toward white dwarfs

Fig. III-7: Evolution of white dwarfs

Evolution of White Dwarfs

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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.

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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

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 supernova explosion.

Fig. III-8: A Supernova Pictograph?

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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.

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(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.

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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)

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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 such high density.See class notes for further details.

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(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 kmTypical 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.

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Maximum Mass of Neutron Stars:

Like a white dwarf, a neutron star has an upperlimit 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!See class notes for further details.

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Detailed internal structure depends on the nuclear models Interactions among particles

Pressure Ionization

Electron Capture

N core N CORE

`Exotic’ ?

Nuclear Density

Neutron Drip

Fig. III-10: Cross section of a NS

4 x

3 x1017

(iii-b) Structure: (See class notes, Suppl.II)

Surface ~ 103 kg/m3

0.

1 km

10 km

I

II

4 x 1014

1012 kg/m3

1018

107 kg/m3

Outer crust I: ordinary heavy nuclei + e-

Outer crust II: n-rich heavy nuclei + e-

Inner curst:

n-rich heavy nuclei + free e-

+ free n

Internal structure depends on the nuclear models – strong interaction among particles.

n, p, e-

Not drawn to scale.

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(iii-c) Compactness of Neutron Stars: Interactions between nucleons (i.e., neutrons and protons)

Table III-1: Properties of NS - Model dependent!

Nucleon Separation

Fig. III-11: Potential Energy V for a system (eV) Strong Interaction

0

(+)

(–)

(+) : Repulsive Force(-) : Attractive Force

See class notes for details.

Model (B)

Model (A)

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

V

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(iii-d) Mass-Central Density Relation of Dense StarsCompactness (M/R)depends on “nuclear force”

logc

M /M☉ 1.4 M☉

Model (A)Model (B)

White Dwarf

Neutron Star

Stable

Stable Stable

Unstable!

Unstable!

Fig. III-12:Mass-central density relation

of neutron stars and white dwarfs

Unstable!

See class notes for details.

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(iii-e) Superlfluidity and SuperconductivityA 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)!

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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 equationThe temperature of NS decreases in time due to radiation!

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.

Eqn (III-1)

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Dashed : Cool, Non-StandardCooling,

Extotic Particles (Pion-cooling) M ~ 1.4 M☉

with superfluid

Solid : Hot, Standard cooling n+N p+N+e-+, p+N+e- n+N+ M ~ 1.2 M☉

with superfluid (N = n or p)

cooling process superfluidity composition

Tsuruta et al. 2002, ApJ

Fig. III-13: Typical Cooling Curves of a NS

Obs. Data

a: Cas A point source

b: Crab pulsar

1: pulsar PSR J0822

2: Vela pulsar

4: Geminga pulsar

6: Pulsar PSR B1055

Upper limit

Detection

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(v) Pulsar = rotating, magnetic neutron star (Ref.: Class notes; FK Sec. 20-11)

¤ The discovery of pulsars in the 1960s stimulatedinterest 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

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“Lighthouse Effect”

N

S

Magnetic

Field

Radio Emission

Rotation Axis

-rayemission

Radio emission: emitted above the polar regions - whenever the emission cone points towards us, we see a signal! Lighthouse”

Gamma rays emitted from outer magnetosphereX-ray – optical: emitted

from inner magnetosphere

Fig. III-14: Pulsar radiation

X-ray emissionN

S

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•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

Fig.III-15: Light Curve of PSR 0329-54

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Fig. III-17: Crab Nebula and Pulsar – optical

Note: 1000 pulsars have been found. Could be as high as 105.

“Crab Pulsar”: Optical

d = 2000 pc ~ 6600 lyP ~ 33 msL ~ 1031 watt (~ 5 x the solar luminosity)

“Crab Pulsar” - x-rays (Chandra X-ray Obs.)

Fig. III-16: Pulsar Environment

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Fig. III-18: Crab Nebula and Pulsar

26Fig. III-19: Crab Pulsar (detail)

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Fig. III-20: “Crab Pulsar” seen in space

X-ray (Chandra) Optical (Hubble)

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Emit radiation in Radiao/Optical/X-ray/-ray band Rotational Period: P ~ msec-sec

More Properties of Pulsars

B1937+21(1.6ms)

Crab (33ms)

Fig. III-21: Voice from Pulsars…

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.

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Relativistic Electrons(*1) Synchrotron Radiation

X-ray Magnetic Field

Fig. III-22: Spectrum (Number of Photons/sec-keV vs Photon Energy)

X-ray Emission: 2 components(1) Blackbody radiation = Thermal emission (~ kT)(2) Power-law radiation = Non-thermal emission (independent of temperature T)

**************************************************************************************************

Fig. III-23: Synchrotron radiation

(1)

(2)

Photon Energy

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III-1c. Black Holes (Ref.: Lecture notes; FK p. 603, Sec. 21-1, 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

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(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 them-

selves 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

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*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 CurvatureFig. III-26: Formation of a black hole

B

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The general theory of relativity predicts black holes

Fig. III-27: Formation of a Black Hole

b

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★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!)

EX 54: 10M☉ Star, Rs = 30 km.

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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

singularity

Fig. III-28: Interior of a Black Hole

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•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

•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 horizonWe can extract energy from theErgoregion (see class notes)

Fig. III-29: A Rotating Black Hole

Ergosphere

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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

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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.

Fig. III-32: PSR B1757-24

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(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 fields. Then, the magnetic fields can funnel the gas onto the

40Fig. III-33: A Binary X-Ray Pulsar

xxxxxxxxxxxx

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

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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

Lagrange Point

Equi-potential Contour Curve

Fig. III-34: Binary Stars and Roche Lobe Overflow

●

Compact star

Neutron star

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Fig. III-37: Light Curve of Cen X-3

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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