ASTR 2020
Space Astronomy
Week 6
Stars
Pleiades: open star cluster. Age ~ 80 million years
M13
cluster
~ 10
oldof
stars)
M13(Globular
in Hercules:star
(~ 10
billion of
year
oldGyr
swarm
stars)
gravity
v.s.
random
motion
of
stars
Luminosity & Flux
- Luminosity: Energy given off each second
energy is measures in ergs
luminosity is in erg/second
1 Watt = 107 erg /sec
- Flux: flow or energy though a unit area.
[erg sec-1 cm-2]
- Luminosity of a Star:
L = [Surface Area] x  T4
L* = 4  R*2  T4
 = Stephan-Boltzmann constant
 = 5.67 x 10-5 erg s-1 K-4
Flux received on Earth:
- Flux: flow or energy though a unit area.
F* = L / 4  D*2
[erg sec-1 cm-2]
D = Distance to the star
Note: Flux can be diminished by
intervening dust
- Apparent magnitude:
m = -2.5 log [F* / F(Vega)]
- Absolute magnitude = the Apparent magnitude a star
would have at a distance of 10 pc
Examples:
- Sun: RSun ~ 7 x 1010 cm,
T ~ 5778 K
LSun ~ 4  [7 x 1010]2[5.67 x 10-5][5778]4
= 3.89 x 1033 erg/s
~ 4 x 1033 erg/s
= 1 Solar Luminosity = 1 Lo
- Supergiant star: Betelgeuse
Cool (~3000 K), but large (~ 2 AU) !
L ~ 105 Lo ~ 4 x 1038 erg/s
- Red dwarf star: Cool but small
L ~ 10-4 Lo ~ 4 x 1029 erg/s
Sunspots (darker)
T ~ 4,000 K
vs.
T ~ 6,000 K
& Plages (brighter)
T ~ 7,000 K
the Sun
In the UV
Showing
Magnetic
Fields
the Sun
In X-rays
Showing
Coronal
Loops above
sunspots
The 11 / 22 year Solar Cycle :
Differential rotation +
convection =>stretching / amplification
of magnetic fields.
Helio-seismology:
Probe solar interior
Solar oscillations
Measured with precision
Doppler spectrometers
(meters / second precision)
“Spectrum” of oscillation
frequencies:
Frequency vs. size scale
on Sun.
The Sun “rings” like a bell !
Parallax:
Distance, D, where 1 AU subtends 1 arc-second
206265” ~ 2.06 x 105 arc-seconds in a radian
1 pc = [2.06 x 105] [1.50 x 1013 cm]
= 3.086 x 1018 cm
Stars:
The fundamental building blocks of the Universe:
Massive stars:
Lumnious:
Short-lived:
Rare
~8 to > 100 x mass of Sun
103 to 107 x Sun
3 to 30 million years
Moderate mass stars: 2 to 8 x mass of Sun
Bright:
10 to 103 x Sun
Lifetime:
30 million to ~ 1 billion years
Common
Low-mass stars:
0.08 to 2 x mass of Sun
Dim:
10 to 10-4 x Sun
Long-lived:
1 to > 300 billion years !
Very common: 90 % of stars
Brown dwarves to planets: < 0.08 x mass of Sun
No nuclear fusion, cool, faint
Mass of Sun = 2 x 1033 grams; Luminosity of Sun = 4 x 1033 erg/sec
Black-body radiation:
Continuum
(radiates over continuous range of wavelengths)
peak (cm) ~ 0.3 / T(Kelvin)
Flux at al  increases proportional to T(K)
Wien
Rayleigh-Jeans
Stars:
The fundamental building blocks of the Universe:
Massive stars:
Lumnious:
Short-lived:
Rare
~8 to > 100 x mass of Sun
103 to 107 x Sun
3 to 30 million years
Moderate mass stars: 2 to 8 x mass of Sun
Bright:
10 to 103 x Sun
Lifetime:
30 million to ~ 1 billion years
Common
Low-mass stars:
0.08 to 2 x mass of Sun
Dim:
10 to 10-4 x Sun
Long-lived:
1 to > 300 billion years !
Very common: 90 % of stars
Brown dwarves to planets: < 0.08 x mass of Sun
No nuclear fusion, cool, faint
Mass of Sun = 2 x 1033 grams; Luminosity of Sun = 4 x 1033 erg/sec
Black-body radiation:
Continuum
(radiates over continuous range of wavelengths)
peak (cm) ~ 0.3 / T(Kelvin)
Flux at al  increases proportional to T(K)
Wien
Rayleigh-Jeans
Spectra: Refraction (prism):
Snell’s Law:
n1 sin(d1) = n2 sin(d2)
d1
n1 = refractive index in region 1
n2 = refractive index in region 2
n = c / v = vacuum / medium
d2
n2
n1
The Solar Spectrum (from Kitt Peak’s McMath-Pierce Solar Telescope):
2960 – 13000 angstroms
Stellar spectra: Spectral type: O B A F G K M
90% of stars are on
The “Main Sequence”
ASTR 2020
Space Astronomy
Week 6
Energy generation in Stars
Energy Generation in Stars
Main Sequence:
Nuclear fusion (“burning”) of hydrogen into helium
4 H => 4He
2 main reactions:
“Proton-proton chain” (PP-chain)
Mstar < 1.5 Solar masses
“Carbon-Nitrogen-Oxygen Cycle (CNO cycle)
Mstar > 1.5 Solar masses
Stellar energy generation (Main sequence)
L ~ E / t ~ 4 x 1033 erg /sec
E ~ [energy released]
thermonuclear fusion of hydrogen (H) into Helium (He)
1H
- 1 proton
4He - 2 protons + 2 neutrons
The “proton-proton chain” (M < 1.5 Mo) v.s
“CNO cycle” more massive stars
Neutrons (n) formed form energetic collisions between
electrons (e-) and protons (p+)
e + p + energy => n
n + H => 2H
(deuterium - heavy isotope of H)
Atomic Nuclei: neutrons + protons
Size of neutrons & protons ~ 10-13 cm
Size of atoms
Composition:
quarks + gluons
up-quark
down-quark
three types of charge:
“color”
green
red
blue
~10-8 cm
Decay of free neutrons: mn ~ 1.67 x 10-24 g
a Weak Nuclear interaction ….in 15 minutes (880 sec) !
10-23 sec
880 sec
time
The 4 forces of Nature & the quantum realm
Electromagnetic (EM) force:
Acts on charge +e, -e
e=4.8 x 10-10 c.g.s.
Binds molecules (chemistry) & binds electrons to atomic nucleii
like-charges repel, opposite charges attract
protons (+) attract electrons (-):
F = q1q2 / R2
Force exerted by absorption & emission of photons
Strong Nuclear Force: (~100 x EM force:) Protons, neutrons made of quarks
Quarks carry 3 types of “charge”, called “color”
Binds quarks & protons together despite strong EM repulsion
Binds neutrons to protons:.
Force exerted by absorption & emission of color gluons
Weak Nuclear Force:
Changes quark “flavor”; Causes radioactivity
Force exerted by absorption & emission of W+, W-, Zo “bosons”
Gravitational Force:
Attraction between all mass & energy (curves “space-time”)
Force exerted by absorption & emission of “gravitons”
The Quantum World
the “Standard Model” of particle physics:
Three Forces (Interactions):
Electromagnetic, weak, strong
Structure of (Ordinary) Matter:
Balance of opposing forces
Electro-magnetism
wave nature of electrons
Strong nuclear force
vs. quarks waves
Weak nuclear force
“up” v.s. “down”
quarks
Strong Nuclear Force
Fusion of hydrogen (H)
Into Helium (He)
4 1H => 4He + 26.7 MeV
- Occurs at T ~ 1.5 x 107 K
- Main energy source of stars !
- 0.007% of the mass converts
to energy via
E = mc2
E = 0.007 M(He)c2
~ 4 x10-5 erg / He
Proton-proton Chain:
4 1H => 4He + 26.7 MeV
- Occurs at T ~ 1.5 x 107 K
-Main energy source of stars !
- 0.007 (0.7%)
of the mass converts to energy via
E = mc2 ~ 4.3 x 10-5 erg / 4He
4He
formation rate: n(4He) = Lo / E ~ 9.3x1037 s-1
Neutrino luminosity of Solar core:
L ~ 2n(4He) = 1.9x1038 s-1
Neutrino flux at Earth:
F = L/4DAU2 = 6.6 x 1010 s-1 cm-2
1 eV = 1.602 x 10-12 erg :
1 MeV = 1.602 x 10-6 erg
Neutrino
Flux in
# cm-1 MeV-1
Raymond Davis
C-Cl4 +  => Argon
The Carbon-Nitrogen-Oxygen (CNO) Cycle
Dominates energy production in stars with M > ~1.5 Solar masses
The Carbon-Nitrogen-Oxygen (CNO) Cycle
vs.
P-P chain
Low mass stars
High mass stars
~1 Solar mass stars: Post main-sequence evolution
MS = main sequence
H => He
RG = red giant
He => C
HB = horizontal branch
C => O
AG = asymptotic giant branch =>
planetary nebula (PN) => White dwarf