Download AN INTRODUCTION TO ASTRONOMY Dr. Uri Griv Department of Physics, Ben-Gurion University

BEN-GURION UNIVERSITY
AN INTRODUCTION TO ASTRONOMY
Dr. Uri Griv
Department of Physics, Ben-Gurion University
Tel.: 08-6428226 Email: [email protected]
Gravitational (Jeans) Instability
• Hydrodynamic equation
∂v
+ ρ(v·∇)v = −∇P − ρ∇Φ (1)
ρ
∂t
where ρ is the density, v is the macroscopic
velocity of the “gas,” P is the pressure, and
Φ is the gravitational potential
• The continuity equation: connects ρ and v
∂ρ
+ ∇·(ρv) = 0
(2)
∂t
• The Poisson equation: connects Φ and ρ
∆Φ = −4πGρ
with the boundary condition Φ → 0 for
|r| → ∞
• Equation of state: for example P = c2s ρ
2
(3)
• The condition of instability k 2 c2s < 4πGρ0
where k = 2π/λ is the wavenumber, λ is
the wavelength and ρ0 is the mean density
q 2
cs
• The Jeans wavelength: λj ∝ ρ0
• The gravitational instability can explain the
origin of galaxies, stars, planets, ...
3
Gravitational (Jeans) Instability
4
Gravitational (Jeans) Instability
5
Trigonometric Parallax
1′′
360◦ ×60′ ×60′′
1.5×1013
= 2πdpc
18
• Parsec (pc)
→ 1 pc ≡ dpc = 3.1 × 10 cm
• Light year (ly) = c × 1 yr
= 3 × 1010 × 3.16 × 107 = 9.5 × 1017 cm
• 1 pc = 3.1× ly
6
Trigonometric parallax – Example
• Parallax of α Cen is 0′′ .751
0′′ .751
360◦ ×60′ ×60′′
• Distance to α Cen →
→ dα = 4.1 × 1018 cm =
4.1×1018
1′′
3.1×1018 = 0′′ .751 = 1.3 pc
• Distance to α Cen →
4.1×1018
9.5×1017
7
=
1.5×1013
2πdα
= 4.3 ly
Temperature I: The Spectra of Stars
• The spectral type of a star yields an estimate
of its temperature:
spectral type = function of T
• This is the basic of the Harvard
classification of stars
8
Temperature II: UBV Photometry
• Strictly speaking: L = (4πR2 )(σT 4 ) where
R is the radius of a star. On the other hand,
L = f · (4πr2 ) → T = (f r2 /R2 σ)1/4
• The basic idea of UBV Photometry is to
measure the proportions of radiant energy
put out by a thermal body at ultraviolet (U),
blue (B), and visual (V) wavelength
• fV /fB = function of T
fB /fU = function of T
• In practice, both methods (The Spectra of
Stars and UBV Photometry) are usually
needed
9
Temperatures of Stars
10
The Hertzsprung–Russell Diagram
• O B A F G K M (RNS)
• I: supergiants II: bright giants III: giants
IV: subgiants V: dwarfs
11
The Hertzsprung–Russell Diagram
12
The Hertzsprung–Russell Diagram
• Evolution tracs of protostars
• The main sequence
13
The Hertzsprung–Russell Diagram
• Main sequence stars
14
The Hertzsprung–Russell Diagram
• T Tauri stars: young stars
15
The Apparent Stellar Magnitude
16
The Apparent Stellar Magnitude
• The responce of the human eye works on
the basis of a geometric progression rather
than an arithmetic progression
• The modern magnitude classification: a
difference of 5 magnitudes to equal exactly
a factor of 100 in apparent brightness
• If m1 and m2 are the apparent magnitudes
with apparent brightness f1 and f1
m2 − m1 = 2.5 log10 (f1 /f2 )
(4)
• The fainter star has the bigger apparent
magnitude
• Polar star: mps = +2.0 Sun’s apparent
magnitude msun ≈ −26.7 → fsun /fps = ...
17
The Absolute Magnitude of a Star
• The absolute magnitude of a star is the
apparent brightness that the star would have
if it were placed at a standard distance of 10
pc away
• From the 1/r2 law of radiation
M = m − 5 log10 (r/10 pc)
(5)
• Photometric distances:
Spectrum (observations) → Stellar Class (O,
B, A, ...) → Absolute Magnitude M (theory)
→ Apparent Magnitude m (observations) →
Eq. (??) =⇒ Photometric Distance r
18
The Absolute Magnitude of a Star
19
The Distances of Stars
20
The Hertzsprung–Russell Diagram
21
Variable Stars
• Period-brightness relation for different stars
22
Cepheid Light Curve
• The light curve of a Cepheid variable star:
Brightness vs. Times
23
Cepheid Period–Luminosity Relation
• The period–luminosity relationship for
classical Cepheids
24