Download Lecture 13. Black Holes - Politechnika Wrocławska

•Lecture 7
Our Star
What is a Star?
• Large, glowing ball of gas that generates heat and
light through nuclear fusion in its core.
• Stars shine by Nuclear Fusion:
– For the sun and most of the stars: powered by the
reaction:
• 4 Hydrogen nuclei (4 protons)  1 Helium nucleus
(2 protons and 2 neutrons) + energy
• The same process in H bomb
• E=mc2 at work: the total mass of helium is only
99.3% of the mass of 4 protons put together; the
rest, 0.7% of the rest mass is turned into energy the
powers stars
Sun: Our Star
Distance: 1.49 x 108 km
= 1 A.U.
Mass: 1.99 x 1030 kg
Radius: 6.96 x 105 km
Density: 1.41 g/cm3
Luminosity: 3.8 x 1026 watts
How to calculate Sun radius :
• The angle diameter of Sun = 32’ (arcsec).
8
1.49
x
10
• The Earth-Sun distance = 1 A.U.=
km
Radius: 6.96 x 105 km
How to calculate Sun mass :
Fcentripetal
M z v 2z
M zMs

G
 Fgravitational
2
1AU
. .
(1AU
. .)
vz  30km / s
1AU
. .  1.49 x108 km
G  6.67 x1011 m3kg 1s 2
Mass: 1.99 x 1030 kg
AMO: available solar energy for satellite solar cells.
AM 1.5: AMO reduced by gases in earth’s atmosphere.
12-23
UV absorbed by O2 & O3
IR absorptions of H2O & CO2
How to calculate Sun luminosity :
• Solar constant is the intensity of radiation (the flux
of energy riching 1m 2 ) at AMO ( air mass zero)
2 1
S s  1370 Jm s
Ls  4 (1AU
. .) S s  3.86 x10 W
2
26
How to calculate Sun temperature :
• Stefan – Boltzman law:
Ls  4 R  T
2
s
4
T  5800K
Sun density
Composition of the Sun
Percent by Mass
• H 73%
• He 25%
• O 0.8%
• C 0.3%
• N 0.1%
Hydrostatic equilibrium
The Sun’s Internal Structure
Layers of the Sun
Core of the Sun
The core is in the center, where fusion occurs.
•
•
•
•
Temperature:
Pressure:
Plasma
Nuclear Fusion
14 million K
1 billion atm
Transition region
– Convection to Radiation
– 300 km thick
• Convection zone is similar to the Earth’s
mantle.
• It lies between the photosphere and the
radiation zone.
How does the Light Comes Out?
Photons are created in the nuclear fusion cycle.
They collide with other charged particles and
change their direction (random walk).
They also decrease their energy while walking.
It takes ~10 million year to get outside.
The random bouncing occurs in the radiation zone
(from the core to ~70% of the Sun’s radius).
At T<2 million K, the convection zone carries
photons further towards the surface.
How does the Light Comes Out?
Solar Neutrino
Neutrino is a subatomic particle.
It is a by-product of the solar proton-proton cycle.
It barely interacts with anything.
Counts of neutrino coming from the Sun are
crucial to test our knowledge about solar physics.
Neutrino observatories use huge amounts of
different substances to detect nuclear reactions
with neutrino.
So far theory predicts more neutrino than is seen.
Photosphere
Photosphere is the visible surface of the Sun.
It consists of gas and is far less dense than air over the
Earth’s oceans.
• 6000 K
• Sunspots
Sunspots
• Dark areas on the
photosphere
• Cooler –appear dark
• 11.2 year cycle
SOHO
NASA ESA
– Dynamic Magnetic field
SOHO/MDI NASA & ESA
Chromosphere
Chromosphere is a zone below corona, where the
Sun’s UV radiation is produced (T~10,000 K).
•
•
•
•
Hotter
Less dense
Flares
Prominences
SOHO/EIT
NASA/ESA
Chromosphere
SOHO/EIT
NASA/ESA
Corona
• The uppermost layer of the
atmosphere
• Very hot:
• 0.5 - 2 Million K
• very low density:
• 1-2 million km thick
– Visible during eclipse
• Coronal mass ejections
The solar wind
The solar wind is a stream of photons, ions, and
subatomic particles outward from the surface.
YOHKOH
Dynamic Magnetic field
•
•
•
•
Sunspots
Flares
Prominences
Coronal mass
ejections
Effects on the Earth
• Magnetic storms
• Auroras
• Climate
– 1645-1715 few sun spots
– "Little ice age"
Basic Properties of a Star
• Mass: from 0.1 solar mass to > 100 solar mass
• Size: from 0.1 solar radius to > 1000 solar radius
• Luminosity: from 0.01 solar luminosity to a million solar
luminosity
• Life time: from a few million years to longer than tens of
billion years
– Sun: 10 billion years lifetime (~5 billion years old now)
• Surface Temperature: from 3000 degree above absolute
zero (3000 K  4900 F) to 30,000 K (54000 F)
– Sun: ~6000 K
• Color: from violet to red
– Astronomers classify stars based on their colors, or spectral types:
from hot (violet) to cool (red) are:
O, B, A, F, G, K, M
Oh Be A Fine (Girl/Gal/Girl) Kiss Me
The Hertzsprung-Russell Diagram
Luminosity or
The energy output
Temperature or color
Main Sequence Stars
• For more than 90% of a typical star’s lifetime, it is
on the Main Sequence of H-R Diagram
– With stable Hydrogen burning in the core
– The luminosity, temperature and mass of main sequence
star follow simple relation:
• High mass stars:
– Hotter, more luminous, bigger, and have shorter lifetime
• Low mass stars:
– Cooler, less luminous, smaller, and have longer lifetime
– For main sequence stars, if we know the color of the
star, then we know its MASS, temperature and lifetime
as well.
Main Sequence Stars
The most important property:
Mass of a star
• To the first order, the mass of a star determines all
the other properties of a star:
– in particular, determines the lifetime, evolution, and
fate of a star
– Lifetime:
• 10 solar mass star: a few million years
• Sun: 10 billion years
– Fate of a star:
• Low mass (M < a few solar masses)  white dwarf
• High mass star (>5 – 10 solar masses)  supernova
explosion and neutron star
• Very high mass star (> 20 solar masses) 
supernova explosion and Black Holes
Fate of a low-mass star (Sun)
• Main sequence  red giant  planetary nebula 
white dwarf; M(white dwarf) < 1.44 solar mass
Fate of a High-mass star
• Main sequence (short)  supergiant  supernova
 neutron star; M(neutron star) < 3 solar mass or
black hole
Black Holes
• After a massive star supernova, if the core has a mass > 3
M, the force of gravity will be too strong for even neutron
degeneracy to stop.
• The star will collapse into oblivion.
– GRAVITY FINALLY WINS!!
• This is what we call a black hole.
• The star becomes very small.
– it creates a “hole” in the Universe
– That not even light could escape
• Since 3 M or more are compressed into an infinitely small
space, the gravity of the star is HUGE!
• WARNING!!
– Newton’s Law of Gravity is no longer valid !!
– Have to use Einstein’s general relativity to calculate the properties of
black holes