Post on 04-Oct-2021
Maurizio Falanga mfalanga@issibern.ch
White Dwarfs, Neutron Stars, and Black Holes
Einführung und Überblick: Donnerstag, 20. Februar 2020
Specialist Course - Compact Objects In Galaxies
Einführung und Überblick 19. September 2017
Organisation der Vorlesung
Webseite:
Zeit & Ort: Donnerstag 10:15 – 12:00 Uhr; Physik, Hörsaal B78
Voraussetzung (ECTS 4):
• regelmässige und aktive Teilnahme an der Vorlesung • regelmässige und aktive Teilnahme an den Übungen
Lectures
General introduction to high energy astrophysics Stellar structure equations, Equation of States White dwarfs, npe-gas, Equation of states for WD Chandrasekhar limit Equation of States for dense matter Neutron Stars observational signatures Pulsars, Radio, X-ray Conditions for mass flow through an accretion disks and or wind Single aspect of General relativity Black holes observational aspects Radiation processes
- 6 Exercises for different topics to solve during the whole period - One Numerical Project to work on. Write a simple code, using
only analytical equations, to trace (in the Schwarzschild metric) the photons emitted around a black hole as seen from an distant observer.
Exercises
Objectives
Formation and observation of compact stars and stellar black holes in the context of stellar evolution. Astrophysical phenomena related to compact objects. Properties and description of dense matter. Simple applications of the theory of relativity.
Literatur
Frank, King & Raine: Accretion Power in Astrophysics
Rosswog & Brüggen: Introduction to High-Energy Astrophysics
Shapiro & Teukolsky: Black Holes, White Dwarfs, and Neutron Stars
Seward & Charles: Exploring the X-ray Universe
Rybicki & Lightman: Radiative Processes in Astrophysics
Chandrasekhar: The Mathematical Theory of Black Holes
Sternentwicklung
S. Chandrasekhar 1910-1995
A massive star can collapse into something denser WD (1930)
R. Oppenheimer & H. Snyder predict that massive stars can collapse into black holes (1939)
Weisse Zwerge
White Dwarfs:
• 1844: F. Bessel noticed that Sirius had a slight back and forth motion, as if it was orbiting an unseen object. In 1863, the astronomer A. Clark spotted this mysterious object (Radius, period). This companion star was later determined to be a white dwarf (Radius, Mass).
Magnetic Cataclysmic Variables
Polars Intermediate Polars Classical/Dwarf Novae
(Prototype AM Her)
B ~ 108 –106 G
Energy Sources: CN: nuclear burning DN: through gravity
Non MCVs
Porb ~ 1-10 hrs
Pspin = Porb Pspin « Porb
Synchronous Rotation Asynchronous Rotation
Porb (P) < Porb (IP)
Lacc = ηMc2 η ~ 0.7% (CV); ~ 20% (NS)
(For a review see B. Warner 1995)
Types of CV binaries:
Neutronenstern
Radio Astronomy in the 30’s-60’s
Discovery (1961-63) Quasi-Stellar Radio Sources as the most energetic and distant members of a class of objects
3C273
Karl Jansky 1933
1967
Radio Signals from the Sky
Jocelyn Bell (1943-)
- They soon realized that the best clocks of the time were not accurate enough to time the object. It seemed very unnatural to receive such a perfectly regular signal from space!
Period of 1.337 s 1.3372866576 s
LGM-1 (Little Green Men)
- It could originate from extra terrestrial intelligence?
M. Falanga
A massive star can collapse into something denser (1930). He was awarded the 1983 Nobel Prize in Physics for this fundamental prediction!
In 1934, F. Zwicky and W. Baade and that a stellar collapse of a heavy star during a supernova event should lead to the formation of a dense core of neutrons (NS) at the center of the SN remnant.
S. Chandrasekhar (1910-1995)
Fritz Zwicky (1898 –1974)
In 1932, James Chadwick, then at the Cavendish Laboratory in Cambridge, England, discovers the neutron. He got the Nobel physics prize in 1935.
James Chadwick (1891-1974)
During the course of the next few months, J. Bell discovered 3 more pulsating radio sources (or pulsars). These pulsars were proposed to be rapidly rotating neutron stars.
PULSARS are NEUTRON STARS Anthony Hewish, won the Nobel Prize in Physics for the discovery in 1974.
R ~ 10 km ρ ~1014g/cm3 M ~ 1.4 Msun - Magnetic dipole - Electromagnetic radiation - Pulsar slowdown
Properties of neutron stars:
Core collapse of an evolved star • Stellar core collapse => conservation of angular momentum => fast
spinning neutron star! • Stellar core collapse => conservation of magnetic flux => highly
magnetized neutron star
• Pacini (1967) proposed the existence of a highly magnetized, rapidly spinning neutron star as the power source of the nebula. This would radiate a very powerful EM wave with the rotational frequency of the star. This is below the plasma frequency of the nebula, therefore all this energy will be absorbed and re-radiated by the plasma of the nebula.
1968: The discovery of PSR B0531+21 (Crab Pulsar) These extremely short bursts (~33 ms) proved the
existence of a pulsar at the center of the Nebula. (This is the compact radio source detected by
Hewish and Okoye in 1964)
PSR 0531+21
Crab Nebula In 1968, at the height of the “pulsar fever”, giant radio pulses originating in the Crab Nebula were detected.
1054
Schwarze Löcher
The existence of “dark stars” (in Newtonian mechanics)
Pierre-Simon Laplace (1749–1827)
John Michell (1724–1793)
V =
1/2
R 2GM
A Treatise of the System of the World, London (1728)
Escape Velocity
Earth: 11.2 km/s Moon: 2.3 km/s Sun: 600 km/s
Isaac Newton (1643-1727)
K. Schwarzschild 1873-1916
The event horizon Rs = 2 M
R. P. Kerr 1934 -
Finds the solution for rotating black holes (1963)
Finds black holes as a solution to Einstein’s equations (1916)
J. A. Wheeler 1911-2008
No Hair Theorem
1967 Black Holes
Black Escape velocity c Hole singularity in space-time
Black Holes
J. A. Wheeler
BH have NO HAIR
X-ray Astronomy 1962
1970
1972
§ Bright X-ray emission § Rapid X-ray variability
Sloa
n D
igita
l Sky
Sur
vey
§ 30 M¤ Blue supergiant main-sequence star (optically bright, X-ray dim)
Optical Astronomy
§ Orbits, 5.6 days, an unseen optically (but bright X-ray) object
X-ray Binary System § The companion has a mass between of ~ 10 M¤
What is it?
Cygnus X-1
§ Can’t be a Neutron star because M > 3 M¤
By elimination, we are left with a Black Hole
§ A red giant would be easily seen
§ A main-sequence star would be seen with a little effort
§ Can’t be a White Dwarf because M > 1.4 M¤
§ The companion has a mass between of ~ 10 M¤
Black Hole in our Galactic Center ?
NIR Evidences of a SM-BH at the GC
h Enclosed Dark Mass ≈ 3-4 106 M¤ within 124 AU = 17 l. h. ≈ 2000 RS
NIR adaptive optics at VLT & Keck h Proper motions of the stars of the central
cluster h Orbital parameters of the closest star S2 to
the GC: P ≈ 15.2 yr, V ≈ 5000 km s-1 h Dynamical center in Sgr A*
Stellar-mass Must be at least 3 solar masses (~1031 kg)
Supermassive Millions to billions of solar masses; located in
the centers of galaxies
We cannot see black holes directly, but their influence on the matter around them reveals their presence
Types of Black Holes
Intermediate mass A few thousand to a few tens of thousands of solar
masses; possibly the agglomeration of stellar mass holes
Energy released onto the Black Hole as X-ray Luminosity
LX ≈ ~1035 -1038 erg s-1 RNS
M G MNS
Disk Accretion Shakura & Sunyaev, 1973, A&A
Artist impression
(Kepler’s Law)
€
P =2π a 3/2
G1/2 [m1 +m2 ]1/2
v1 = 2πa1P , m1a1 = m2a2, a = a1 + a2
v1 =2πa m2
P(m1 +m2 )
v1,obs = v1 sini =2πa m2 sin iP(m1 +m2 )
P =P 3/2 (m1 +m2 )
3/2 v1,obs3/2
(2π )1/2 (m2 sin i)3/2G1/2 [m1 +m2 ]
1/2 =P 3/2 (m1 +m2 ) v1,obs
3/2
(2π )1/2 (m2 sin i)3/2G1/2
Pv1,obs3
2πG = (m2 sin i)3
(m1 +m2 )2
a: semi-major axis P: orbital period i: orbital inclination angle v1,obs: line of sight speed
With the mass ratio (m1/m2); we still need the orbital inclination in order to determine the masses individually.
Mass determination in binary systems
Center of the Gravity
a1
a2
©http://mc2.gulf-pixels.com/ 35
What is X-ray?
• X-ray = high-energy photon o hν = 0.1 keV – 100 keV o λ = 0.1 – 100Å (λ1keV = 12.4Å) o kT = 106 – 1010 K (kT1keV = 107K)
• We can see o Extremely high temperature o Non-thermal particle acceleration o Atomic process
Radiation processes
Bremsstrahlung:
Synchrotron radiation:
Compton Scattering:
Multi temperature and density post-shock model for CVs
Magnetic Field
NS geometry of the emission region
XTE J1807-294
Thermal disk emission
The plasma is heated by the accretion shock as the material collimated by the hotspot on to the surface. The seed photons for Comptonization are provided by the hotspot.
Seed photons from the hotspot
Thermal Comptonization in plasma of Temperature ~ 40 keV
B ~ 108 G
Rm
θ
Detected in 1969 Cen X-4 with Vela 5b (Belian et al. 1972)
Discovery paper 3U 1820-30 with ANS (Grindlay et al. 1976)
Kuulkers, in ’t Zand & Lasota 2009 Falanga et al. 2008
Type of X-ray Bursts
M Iron reflection line
M
Relativistic Iron line
Accretion disk model
X-ray Sources in the Galaxy observed with INTEGRAL
Over 700 hard X-ray sources ranging from CV to AGN
White dwarfs: R~10,000 km, Vesc~0.02 c, density~ 106 g/cc Neutron stars: R~15 km, Vesc~0.32 c, density~ 1014 g/cc Schwarzschild radius = 2.95 km M/Mo Efficiency of energy production 6% to 42%.
Energy released onto the Black Hole as X-ray Luminosity
LX ≈ ~1035 -1038 erg s-1 RNS
M G MNS
Disk Accretion Shakura & Sunyaev, 1973, A&A
Artist impression
Stellar-mass Must be at least 3 solar masses (~1031 kg)
Supermassive Millions to billions of solar masses; located in
the centers of galaxies
We cannot see black holes directly, but their influence on the matter around them reveals their presence
Types of Black Holes
Intermediate mass A few thousand to a few tens of thousands of solar
masses; possibly the agglomeration of stellar mass holes