ASTR 1040 Recitation: White Dwarfs and Supernovae Ryan Orvedahl Department of Astrophysical and Planetary Sciences March 10 & 12, 2014
This Week Observing Session: Tonight Mar 10 (8:00 pm) MIDTERM: Thurs Mar 13 (regular class time, 9:30 am) Review Session: Wed Mar 12 (5:00 - 7:00 pm) R. Orvedahl (CU Boulder) WD & SNe Mar 10 & 12 2 / 18
Today’s Schedule Past / Current Homework Questions? White Dwarfs and Degeneracy Pressure Supernovae and Nuclear Reactions R. Orvedahl (CU Boulder) WD & SNe Mar 10 & 12 3 / 18
“Basic” Quantum Mechanics Heisenberg Uncertainty Principle Pauli Exclusion Principle Planck’s Constant: h ≈ 10 − 34 J s or � ≡ h / (2 π ) J s R. Orvedahl (CU Boulder) WD & SNe Mar 10 & 12 4 / 18
“Basic” Quantum Mechanics Heisenberg Uncertainty Principle ∆ x ∆ p ≥ � / 2 ∆ t ∆ E ≥ � / 2 p is momentum and E is energy Werner Heisenberg R. Orvedahl (CU Boulder) WD & SNe Mar 10 & 12 5 / 18
“Basic” Quantum Mechanics Pauli Exclusion Principle No two fermions (protons, electrons, neutrons) can occupy the same quantum state Fermions have half-integer spin and Bosons (photons) have integer spin Wolfgang Pauli R. Orvedahl (CU Boulder) WD & SNe Mar 10 & 12 6 / 18
Degeneracy Pressure White Dwarf: ∼ size of Earth, ∼ mass of Sun Supported by Electron Degeneracy Pressure � 5 / 3 � Z � 5 / 3 � P NR = � 2 ρ m e A m p R. Orvedahl (CU Boulder) WD & SNe Mar 10 & 12 7 / 18
How did you get that result? R. Orvedahl (CU Boulder) WD & SNe Mar 10 & 12 8 / 18
White Dwarf Mass-Radius Relationships Is there a relationship between Mass and Radius? R. Orvedahl (CU Boulder) WD & SNe Mar 10 & 12 9 / 18
White Dwarf Mass-Radius Relationships Is there a relationship between Mass and Radius? Yes! How do we find it? R. Orvedahl (CU Boulder) WD & SNe Mar 10 & 12 9 / 18
White Dwarf Mass-Radius Relationships Is there a relationship between Mass and Radius? Yes! How do we find it? Use Hydrostatic Equation (who remembers what that even means?) R. Orvedahl (CU Boulder) WD & SNe Mar 10 & 12 9 / 18
White Dwarf Mass-Radius Relationships Is there a relationship between Mass and Radius? Yes! How do we find it? Use Hydrostatic Equation (who remembers what that even means?) R ∝ M − 1 / 3 Set P HSE = P Deg ⇒ R. Orvedahl (CU Boulder) WD & SNe Mar 10 & 12 9 / 18
Relativistic Result We used P = nvp , what happens when v ≈ c ? R. Orvedahl (CU Boulder) WD & SNe Mar 10 & 12 10 / 18
Relativistic Result We used P = nvp , what happens when v ≈ c ? Simply replace v → c � 4 / 3 � Z � 4 / 3 � ρ P R = � c A m p R. Orvedahl (CU Boulder) WD & SNe Mar 10 & 12 10 / 18
Degeneracy Pressure with Numbers For Z / A = 1 and ρ = 1 g/cm − 3 Non-Relativistic: P NR = 9 . 9 × 10 12 dyn cm − 2 Relativistic: P R = 1 . 2 × 10 15 dyn cm − 2 R. Orvedahl (CU Boulder) WD & SNe Mar 10 & 12 11 / 18
Short Project – Units! Unit conversions are good for the soul, so ... Convert dyn cm − 2 (cgs) to SI/MKS unit of pressure: Pascal Remember P = F / A and a dyn is cgs unit of force R. Orvedahl (CU Boulder) WD & SNe Mar 10 & 12 12 / 18
Short Project – Units! Unit conversions are good for the soul, so ... Convert dyn cm − 2 (cgs) to SI/MKS unit of pressure: Pascal Remember P = F / A and a dyn is cgs unit of force 1 dyn cm − 1 = 0.1 Pa R. Orvedahl (CU Boulder) WD & SNe Mar 10 & 12 12 / 18
Short Project – Units! Unit conversions are good for the soul, so ... Convert dyn cm − 2 (cgs) to SI/MKS unit of pressure: Pascal Remember P = F / A and a dyn is cgs unit of force 1 dyn cm − 1 = 0.1 Pa 1 dyn cm − 2 = g cm 1 s 2 cm 2 10 − 3 kg g s 2 m = 0 . 1 kg m kg 1 s 2 cm = s 2 10 − 2 m = 0 . 1 m 2 = 0 . 1 Pa s 2 R. Orvedahl (CU Boulder) WD & SNe Mar 10 & 12 12 / 18
Classifying Supernovae – It’s Complicated R. Orvedahl (CU Boulder) WD & SNe Mar 10 & 12 13 / 18
Supernova Onion Shell Burning R. Orvedahl (CU Boulder) WD & SNe Mar 10 & 12 14 / 18
Why Stop at Iron ( Z = 26)? R. Orvedahl (CU Boulder) WD & SNe Mar 10 & 12 15 / 18
Naturally Occurring Elements with Z > 26 Exist! For high Z elements it is hard to get another charged particle close due to the high Coulomb potential barrier A +1 Not for neutrons: A Z X + n → X + γ Z Results in more massive nucleii that are stable or unstable against beta-decay: A +1 A +1 Z +1 X + ? X → Z R. Orvedahl (CU Boulder) WD & SNe Mar 10 & 12 16 / 18
Naturally Occurring Elements with Z > 26 Exist! For high Z elements it is hard to get another charged particle close due to the high Coulomb potential barrier A +1 Not for neutrons: A Z X + n → X + γ Z Results in more massive nucleii that are stable or unstable against beta-decay: A +1 A +1 Z +1 X + ? X → Z Z +1 X + e − + ¯ A +1 A +1 X → ν e + γ Z R. Orvedahl (CU Boulder) WD & SNe Mar 10 & 12 16 / 18
Neutron Processes If beta-decay half-life is short compared to timescale for neutron capture slow process or s-process reactions tends to produce stable nucleii If beta-decay half-life is long compared to timescale for neutron capture rapid process or r-process reactions tends to produce neutron rich nucleii R. Orvedahl (CU Boulder) WD & SNe Mar 10 & 12 17 / 18
Neutron Processes s-process tend to occur in normal phases of stellar evolution r-process can occur during a supernova Neither process plays a significant role in energy production Accounts for abundances of nucleii with A � 60, ( Z � 26) R. Orvedahl (CU Boulder) WD & SNe Mar 10 & 12 18 / 18
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