ASTR 1040 Recitation: White Dwarfs and Supernovae Ryan Orvedahl - - PowerPoint PPT Presentation

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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

SLIDE 1

ASTR 1040 Recitation: White Dwarfs and Supernovae

Ryan Orvedahl

Department of Astrophysical and Planetary Sciences

March 10 & 12, 2014

SLIDE 2

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

SLIDE 3

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

SLIDE 4

“Basic” Quantum Mechanics

Heisenberg Uncertainty Principle Pauli Exclusion Principle Planck’s Constant: h ≈ 10−34 J s or ≡ h/(2π) J s

R. Orvedahl (CU Boulder)

WD & SNe Mar 10 & 12 4 / 18

SLIDE 5

“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

SLIDE 6

“Basic” Quantum Mechanics

Pauli Exclusion Principle No two fermions (protons, electrons, neutrons) can

ccupy 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

SLIDE 7

Degeneracy Pressure

White Dwarf: ∼size of Earth, ∼mass of Sun Supported by Electron Degeneracy Pressure PNR = 2

Z

5/3

ρ mp

5/3

R. Orvedahl (CU Boulder)

WD & SNe Mar 10 & 12 7 / 18

SLIDE 8

How did you get that result?

R. Orvedahl (CU Boulder)

WD & SNe Mar 10 & 12 8 / 18

SLIDE 9

White Dwarf Mass-Radius Relationships

Is there a relationship between Mass and Radius?

R. Orvedahl (CU Boulder)

WD & SNe Mar 10 & 12 9 / 18

SLIDE 10

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

SLIDE 11

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

SLIDE 12

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?) Set PHSE = PDeg ⇒ R ∝ M−1/3

R. Orvedahl (CU Boulder)

WD & SNe Mar 10 & 12 9 / 18

SLIDE 13

Relativistic Result

We used P = nvp, what happens when v ≈ c?

R. Orvedahl (CU Boulder)

WD & SNe Mar 10 & 12 10 / 18

SLIDE 14

Relativistic Result

We used P = nvp, what happens when v ≈ c? Simply replace v → c PR = c Z

4/3

ρ mp

4/3

R. Orvedahl (CU Boulder)

WD & SNe Mar 10 & 12 10 / 18

SLIDE 15

Degeneracy Pressure with Numbers

For Z/A = 1 and ρ = 1 g/cm−3 Non-Relativistic: PNR = 9.9 × 1012 dyn cm−2 Relativistic: PR = 1.2 × 1015 dyn cm−2

R. Orvedahl (CU Boulder)

WD & SNe Mar 10 & 12 11 / 18

SLIDE 16

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

SLIDE 17

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

SLIDE 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

s2 1 cm2 g s2 cm = 10−3kg s210−2m = 0.1 kg s2m = 0.1 kg m s2 1 m2 = 0.1 Pa

R. Orvedahl (CU Boulder)

WD & SNe Mar 10 & 12 12 / 18

SLIDE 19

Classifying Supernovae – It’s Complicated

R. Orvedahl (CU Boulder)

WD & SNe Mar 10 & 12 13 / 18

SLIDE 20

Supernova Onion Shell Burning

R. Orvedahl (CU Boulder)

WD & SNe Mar 10 & 12 14 / 18

SLIDE 21

Why Stop at Iron (Z = 26)?

R. Orvedahl (CU Boulder)

WD & SNe Mar 10 & 12 15 / 18

SLIDE 22

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 Not for neutrons: A

ZX + n → A+1 Z

X + γ Results in more massive nucleii that are stable or unstable against beta-decay: A+1

X →

A+1 Z+1X + ?

R. Orvedahl (CU Boulder)

WD & SNe Mar 10 & 12 16 / 18

SLIDE 23

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 Not for neutrons: A

ZX + n → A+1 Z

X + γ Results in more massive nucleii that are stable or unstable against beta-decay: A+1

X →

A+1 Z+1X + ? A+1 Z

X →

A+1 Z+1X + e− + ¯

νe + γ

R. Orvedahl (CU Boulder)

WD & SNe Mar 10 & 12 16 / 18

SLIDE 24

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

SLIDE 25

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