Download AN INTRODUCTION TO ASTRONOMY Dr. Uri Griv •

BEN-GURION UNIVERSITY
AN INTRODUCTION TO ASTRONOMY
Dr. Uri Griv
Department of Physics, Ben-Gurion University
Tel.: 08-6428226 Email: [email protected]
2
2
1
1
0
0
−1
−1
−2
t=0.5
−2
3
2
1
t=1.0
0
−1
−2
−3
t=1.5
3.5
2.5
1.5
0.5
−0.5
−1.5
−2.5
−3.5
t=3.0
• Computer simulated formation of a “sun”
and “planets” around it: disk (Jeans)
instability model (G RIV ET AL . Planetary
and Space Science, 2007)
Star Clusters
• Open clusters: ∼ 103 stars; total number of
open clusters in the Galaxy N ∼ 104
• Globular clusters: ∼ 106 stars; total number
of globular clusters in the Galaxy N ∼ 103
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Star Clusters
• Open cluster M 67, ∼ 103 stars
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Star Clusters
• Globular cluster M 13, ∼ 106 stars
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Open Clusters – Galactic Distribution
• In the Galactic plane – They are “young”
• The typical age of open clusters t ∼ 108
years
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Globular Clusters – Galactic Distribution
• Spherical distribution – They are “old”
• Typical age of globular clusters t ∼ 1010
years
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Dynamics of Star Clusters
• The stars move freely past one another
without direct collisions
• A cluster is made of a discrete number of
stars → random velocities → no rotation
• The thermodynamic Maxwell–Boltzmann
(MB) distribution of velocities
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Dynamics of Star Clusters
• The velocity dispersion V ≈ (3kT /m)1/2
• A true MB distribution has a “tail”
• Stars will be lost from the cluster
• The escape speed ve = 2V
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Open Clusters – Stellar Orbits
• No rotation !
• Let us consider a cluster of stars with
random stars’ velocities → Our aim is to
define the relaxation time trelax
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Dynamics of Star Clusters
Number of stars
1
0.8
0.6
0.4
0.2
0
−1
−0.5
0
Velocity
0.5
1
• The velocity dispersion V ≈ (3kT /m)1/2
• A true MB distribution has a “tail”
• Stars will be lost from the cluster
• The escape speed ve = 2V
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Relaxation Time
• The stars move freely past one another
without collisions
• The relaxation time trelax is the time to
establish the MB distribution
• Long-range ∝ 1/r2 gravitational force
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• A rougth estimate of trelax !
• Imagine each star to have a sphere of
influence of cross-sectional area πr2 : any
other star were to enter this sphere suffered
a strong encounter
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Dynamics of Star Clusters – Relaxation
• The relaxation time trelax is defined to be the
time between successive encounters
• A naive estimate!
• Let us assume that the number density of
stars n and the typical random velocity V
• The cylindrical volume swept out by that
star’s sphere of influence πr2 V trelax
• This volume must contain one other star
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Dynamics of Star Clusters – Relaxation
• Thus, n(πr2 V trelax ) = 1. So
trelax
1
= 2
πr V
(1)
• What should we choose for r here?
Obviously, the radius at which the
gravitational potential energy of a pair of
stars is equal to the typical random kinetic
energy per star:
Gm2
mV 2
=
r
2
• This is a rough estimate of r!
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(2)
Dynamics of Star Clusters – Relaxation
• Substitute the above value of r from Eq. (2)
into Eq. (1):
V3
trelax ≈
4πG2 m2 n
• A more accurate estimate gives
(3)
V3
trelax ≈
and ln(2R/r) ≈ 1
2
2
4πG m n ln(2R/r)
(4)
where 2R is the cluster-core diameter
• Observations: N = 103 , m = 1M⊙ , V = 1
km/s (open clusters) and N = 106 ,
m = 0.5M⊙ , V = 20 km/s (globular
clusters)
• Accordingly, trelax ≈ 107 and 109 years
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Binary Stars
• About 50% of all stars are binary
• Only a very small minority of binary stars
can be detected as visual binaries
• The bound orbits of binary stars are ellipses
when viewed from either star, and are two
ellipses when viewed by an observer at a
rest with respect to the center of mass
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Binary Stars
• Only a very small minority of binary stars
can be detected as visual binaries
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Binary Stars
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Accretion Disks
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Accretion Disks
• Roche lobe
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Accretion Disks
• Accretion disks: mass transfer from a
lobe-filling star toward a compact
companion (white dwarf, neutron star, or
black hole)
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Accretion Disks
• Schematic diagram of accretion disk
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Accretion Disks
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Accretion
• Gas flow from a protostar
• “Individual” rotation
• “Total” rotation around the center of mass
• Formation of a dense core
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Galaxies
• Hubble “fork” diagram
• Elliptical galaxies
• S0 galaxies
• Spiral galaxies (normal and barred ones)
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Elliptical Galaxies
• Elliptical galaxy
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Spiral Galaxies
• Spiral galaxies – face-on view
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Spiral Galaxies
• Spiral galaxy M83 – face-on view
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Spiral Galaxies
• Spiral galaxy M101 – face-on view
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Spiral Galaxies
• Spiral galaxy NGC 891 – edge-on view
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Ring Galaxies
Astronomy Picture of the Day
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Discover the cosmos! Each day a different image or photograph of our fascinating universe is featured,
along with
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written(MTU)
by a professional
astronomer.
Authors
& editors:
Robert Nemiroff
& Jerry Bonnell
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NASA Web Site Statements, Warnings, and Disclaimers
2004
AprilSpecific
26
NASA Official: Jay
Norris.
rights apply.
A service of: LHEA at NASA / GSFC
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Ring Galaxy AM 0644-741 from Hubble
Image Credit: Hubble Heritage Team (AURA / STScI), J. Higdon (Cornell) ESA, NASA
Explanation: How could a galaxy become shaped like a ring? The rim of the blue galaxy pictured on
the right is an immense ring-like structure 150,000 light years in diameter composed of newly formed,
extremely bright, massive stars. That galaxy, AM 0644-741, is known as a ring galaxy and was caused
by an immense galaxy collision. When galaxies collide, they pass through each other -- their individual
stars rarely come into contact. The ring-like shape is the result of the gravitational disruption caused by
an entire small intruder galaxy passing through a large one. When this happens, interstellar gas and dust
become condensed, causing a wave of star formation to move out from the impact point like a ripple
across the surface of a pond. The intruder galaxy has since moved out of the frame taken by the Hubble
Space Telescope and released to commemorate last Saturday’s fourteenth anniversary of Hubble’s
launch. Ring galaxy AM 0644-741 lies about 300 million light years away.
Tomorrow’s picture: spinning einstein
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Ring Galaxies
• The ring galaxy – “Cartwheel galaxy”
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Our Own Galaxy – Milky Way
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Our Own Galaxy – Milky Way
• The center of the Galaxy
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Our Own Galaxy – Milky Way
• The gas-layer of the Galaxy
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Spiral Galaxies
• The galactic orbit of a star
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Spiral Galaxies
• Actual galactic orbit of a star
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Spiral Galaxies
• Epicyclic motion of a star
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Spiral Galaxies
• Differential galactic rotation
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Spiral Galaxies
• Rotation curve
• Vrot = ω · R → ω ≡ 2π/T ∝ 1/R
Period T ∝ Distance R
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