Monday. At your option it could be returned to its original date of Friday Nov 30.

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Shawn Casey
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1 1 Monday Exam grading ramping up, results Wednesday I hope. Problem Set 7 will appear on Wednesday. Next Quarter Moon opportunity is around October 31. Next Exam is scheduled for Wed Nov 28. At your option it could be returned to its original date of Friday Nov 30.

2 2 Disks are Seen Directly

3 3 Disks Should Fade As Planets Grow As planets grow the disk should begin to clear. Simulations/calculations say that within 10 million years most of the small dust should be gone. This age corresponds well with observations of young stars showing the infrared excesses go away before an age of 10 million years.

4 4 Faint Disks Should Linger Leftover comets and asteroids should continue to collide and generate faint dust signatures. We see it in our solar system and elsewhere.

5 Beta Pictoris Review Article on Debris Disks Beta Pic is a star with 1.8 times the mass of the Sun (spectral type A6) located 20 parsecs away. 5

6 6 Fomalhaut (Alpha Piscis Austrini) Structure in debris disks suggests the gravitational influence of planets. Hubble ALMA Go looking for Fomalhaut due South in the evening (declination -30).

7 7 Structured Debris Disks Using wavelength of peak excess as a clue, it is becoming evident that some systems have inner and outer debris zones just like the solar system. Vega shows excesses at temperatures of 170K (asteroid belt analog) and 50K (Kuiper belt analog)

8 8

9 9 ALMA Nearby forming stars are typically 100 parsecs away. At a distance of 100 parsecs a typical disk with size 100AU = one arcsecond. No wonder it is so difficult to study the solar system formation process directly... until now.

10 10 ALMA

11 11 ALMA

At small radius magnetic pressure begins to dominate other forces.

12 12 Getting Material Onto the Star Turbulence and magnetic fields lead to viscosity that permits material to lose angular momentum and reach the star. At small radius magnetic pressure begins to dominate other forces. Accretion flows likely follow magnetic field lines onto the star. Click on the right figure for an excellent review article.

13 13 Timescales For revealed T-Tauri stars we can use evolutionary models to estimate the age of the star. Disked stars tend to have ages up a few hundred thousand to a few million years. Few T-Tauri stars (a.k.a. YSO's for young stellar objects) older than 3 million years have disks. Protostars are about 10 times less common and thus must evolve to TTauri phase in about 1/10th the time ( thousand years), consistent with collapse predictions. But what about cloud support in general. If protostars are forming on a freefall time, why are there molecular clouds at all? Turbulence, magnetic fields...

14 14 Disk Masses The disk is the conduit for material on its way into the star. At any given time the disk mass is limited to a few hundredths of a solar mass by gravitational instabilities. Indeed, sub-millimeter measurements are used to infer disk masses of order solar masses around young stars.

15 15 Star Formation Efficiency Possibly illuminated by noting the similarity of the molecular core mass function to the stellar initial mass function. Alves et al. 2007

16 16 Making Planets via Accretion The disk concentrates small grains (sub-micron sized) so that they will collide (gently) frequently. Initially, electrostatic sticking builds millimeter sized clumps. Gravity then comes into play and permits the assembly of true planetesimals - asteroid size. Gravity and collisions build larger bodies until collisions become rare. Golden Rule: Only solid particles take part in the accretion process.

17 Making Planets via Accretion The disk concentrates small grains (sub-micron sized) so that they will collide (gently) frequently. Initially, electrostatic sticking builds millimeter sized clumps.

17 17 Making Planets via Accretion The disk concentrates small grains (sub-micron sized) so that they will collide (gently) frequently. Initially, electrostatic sticking builds millimeter sized clumps. Gravity then comes into play and permits the assembly of true planetesimals - asteroid size. Gravity and collisions build larger bodies until collisions become rare. Golden Rule: Only solid particles take part in the accretion process.

18 18

19 19 Making Planets via Accretion The disk concentrates small grains (sub-micron sized) so that they will collide (gently) frequently. Initially, electrostatic sticking builds millimeter sized clumps. Gravity then comes into play and permits the assembly of true planetesimals - asteroid size. Gravity and collisions build larger bodies until collisions become rare.

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21 21 Making Planets via Accretion The disk concentrates small grains (sub-micron sized) so that they will collide (gently) frequently. Initially, electrostatic sticking builds millimeter sized clumps. Gravity then comes into play and permits the assembly of true planetesimals - asteroid size. Gravity and collisions build larger bodies until collisions become rare.

22 23 Interesting Subtleties The gas that goes along for the ride (but that does not directly participate in accretion) likely plays an important role. The gas orbits at less than Keplerian velocity because it has pressure and thus requires less centripetal acceleration to maintain an orbit. Particles themselves must follow Kepler's laws all particles feel a headwind. Smaller particles are more significantly influenced than larger ones. Differential drift velocity aids in collisions needed for accretion until those relative velocities become too large. Around a meter in size those relative velocities begin to lead to disruptive collisions. Gravity is still weak for these particles so crossing the meter barrier requires some collective gravitational instability collapsing clumps of planetesimals. Watch this Hal Levison s talk on the subject. Lucy Mission

23 24 Wednesday Exam 2 grades should appear today or tomorrow Posted scores will be out of 100% rather than raw points on the Exam We will provide some statistics on mean and standard deviation at the time of posting. Problem Set 7 available late today.

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25 26 One arcsecond at 25 parsecs corresponds to a separation of 25 AU.

26 27 One arcsecond at 25 parsecs corresponds to a separation of 25 AU. Orbital speed around a solar-mass star at 25 AU is 30 km/s / sqrt(25) = 6 km/s

27 28 One arcsecond at 25 parsecs corresponds to a separation of 25 AU. Orbital speed around a solar-mass star at 25 AU is 30 km/s / sqrt(25) = 6 km/s The Doppler Shift is one nm or one part in 600 (v/c) corresponding to ~500 km/s

28 29 One arcsecond at 25 parsecs corresponds to a separation of 25 AU. Orbital speed around a solar-mass star at 25 AU is 30 km/s / sqrt(25) = 6 km/s The Doppler Shift is one nm or one part in 600 (v/c) corresponding to ~500 km/s That s no planet.

29 30 Recap The interstellar medium is mostly H and He gas (99%; individual atoms) with traces of all heavier elements (1%; sub-micron dust grains). Gravitation contraction of a cloud to form a star results in a thin flat disk remaining around the forming star due to angular momentum conservation. Within this disk solid particles (i.e. the 1% that is dust ) can stick and grow to larger sizes. This process continues (likely in complicated ways) until much of the dust mass is concentrated into a small number of larger planet-sized objects on largely non-crossing orbits. The local temperature determines what sort of particles can survive in solid form and thus participate in the accretion process. Close to the star rock +metal Far from the star rock + metal + a whole lot of ice With ice as a building material cores can grow quickly to large size (10 times the mass of the Earth) and begin gravitationally attracting the gas ultimately leading the Neptunes and Jupiters

30 31 The Jovian/Terrestrial Distinction Planets accrete from the solid particles in the disk. The local temperature of the disk determines what types of particles can survive in solid form. The obvious temperature gradient is likely connected to compositional differences with radius in the Solar System.

31 32 The Jovian/Terrestrial Distinction Planets accrete from the solid particles in the disk. The local temperature of the disk determines what types of particles can survive/condense in solid form.

32 33 Condensation/Survival vs. Temperature

33 34 The Jovian/Terrestrial Distinction Close to the Sun, rock and metal are the primary building materials. Ice dominates at greater distance (and in a big way, note the relative abundance of silicates vs. ices).

34 35 Icy Moons (likely with significant volatile content) Ariel (Uranus) Enceladus (Saturn)

gas. Core growth must happen quickly enough so

35 36 Origin of the Gasballs Ice/Rock core accretion followed by gravitational accretion of nebular gas. Core growth must happen quickly enough so that the core reachs critical size before gas removal.

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38 39

Radioactivity is prevalent in everyday life Stars forged virtually all of the

39 40 Natural Radioactivity Measuring the relative amounts of radioactive elements and their isotopes in a rock reveals the time since solidification. Radioactivity is prevalent in everyday life Stars forged virtually all of the atomic nuclei in the Earth. Exploding stars produce vast quantities of radioactive debris.

The heat generated by the decay of this material still warms

40 41 Natural Radioactivity The Earth formed from stellar debris and incorporated a small portion of radioactive material. The heat generated by the decay of this material still warms the Earth's interior to temperatures high enough for volcanic activity.

41 42 Short and Long Lived Isotopes Radioactive isotopes were incorporated at the time of formation of the planets. Isotopes with short (millions of years or less) half lives have decayed entirely by now. Some evidence (short-lived isotope decay products) points to the injection of fresh radioactivity just prior to the formation of the Solar System a nearby supernova? Winds from massive stars? Their extinct isotopic signatures illuminate events early in the history of the Solar System/Earth. Long lived isotopes of uranium, thorium, and potassium with half lives around a billion years or more power the Earth's interior.

42 43 Radiometric Dating and Half Life Over time a radioactive sample becomes less radioactive as unstable atoms decay to stable forms. The decay is a random event for any atom resulting in ½ of the remaining radioactive atoms decaying in a fixed time interval. Each radioactive isotope has its own characteristic half-life U 207Pb (704 million years) Rb 87Sr (48.8 billion years) C 14N (5730 years) ½ will remain after one half life ¼ will remain after two half lives 1/8 will remain after three half lives. * The number of protons in a nucleus establishes the elemental identity (8 protons = oxygen), however the nucleus can carry different numbers of neutrons ( 16O, 17O, 18O)

43 44 Radiometric Dating and Half Life Over time a radioactive sample becomes less radioactive as unstable atoms decay to stable forms. The decay is a random event for any atom resulting in ½ of the remaining radioactive atoms decaying in a fixed time interval. Each radioactive isotope has its own characteristic half-life U 207Pb (704 million years) Rb 87Sr (48.8 billion years) C 14N (5730 years) ½ will remain after one half life ¼ will remain after two half lives 1/8 will remain after three half lives. ( N (t ) = N 0 exp ln 2 t t half ) * The number of protons in a nucleus establishes the elemental identity (8 protons = oxygen), however the nucleus can carry different numbers of neutrons ( 16O, 17O, 18O)

44 45 Friday Exam 2 grades have been posted. Posted scores are out of 100% Mean is 74; Standard deviation is 14. Problem Set 7 available, due next Wednesday. Next quarter moon opportunity about mid-month Exam 3 is officially Friday November 30

45 46 Exponential Decay Why is radioactive decay characterizable by half-lives Any multiplicative (halving or doubling) process is an exponential process. For radioactive decay, the exponential process arises because there is a fixed probability that any given particle will decay in any given time interval. The number of decays per unit time is simply proportional to the number of particles. dn = λ N (t ) dt The equation above is the differential form of an exponential law with solution. N (t) = e λ t +c = N oe λ t

46 48 Radioactive Decay The decay constant, l, maps to half life simply by requiring λ T No = N oe 2 The number of daughter atoms at time, t, is No N(t) N D = N o (1 e ln (2) T1 = λ λ t λt ) = N (t )(e 1) In simple terms then ND t = ln (1+ )/ λ N (t ) This equation works if you start with a pure sample of the radioactive isotope. What if there is already a component of stable daughter atoms in the sample on day one.

47 49 Radiometric Dating: Slightly More Complicated than Just Half Lives How do you account for the amount of decay product in the rock on day one? Different elements fractionate chemically. Isotopes of the same element don't. At time zero all rock crystals have the same ratio of 87Sr to 86Sr, but different ratios of 87Rb to 86 Sr. t N (t ) = N 0 exp ln 2 t0 ( )

$50 Radiometric Dating: Slightly More Complicated than Just Half Lives How do you account for the amount of decay product in the rock on day one? Elements fractionate Isotopes don't.$

48 50 Radiometric Dating: Slightly More Complicated than Just Half Lives How do you account for the amount of decay product in the rock on day one? Elements fractionate Isotopes don't. At time zero all rock crystals have the same ratio of 87Sr to 86 Sr, but different ratios of 87 Rb to 86Sr. Melting an aged rock (sloped isochron) mixes the grain content and re-levels the isotope ratio for 87Sr/ 86Sr. t N (t ) = N 0 exp ln 2 t0 ( )

49 51 Interpretation of the Isochron Slope Writing a simple statement that the present number of strontium atoms is the original number plus the rubidiums that have decayed Sr (t ) = Sr 0 +( Rb0 Rb(t )) Rb(t ) = 87 Sr (t ) = Sr Sr 0 Sr (t ) = Sr Sr intercept 87 ( Rb(t ) (exp ln 2 87 Rb 0 = t t half ) 87 1) slope ) ( Rb (t ) exp ln 2 t Rb(t ) + (exp ln 2 1) 86 t half Sr ( ( Rb 0 exp ln 2 t t half t t half ) )

time. Earth rocks date as relatively young having melted and re-solidified mostly in the

50 52 The Oldest Rocks in the Solar System Melting resets the isochron clock by homogenizing isotope ratios, erasing the ratios that have evolved as atoms have decayed in place over time. Earth rocks date as relatively young having melted and re-solidified mostly in the last billion years. Asteroids have been largely unmelted since the formation of the Solar System.

51 53 Terrific Uniformity in Meteorite Radiometric Ages

52 54 Radioactive Dating Applied to Impact Melted Spherules in Lunar Soil

53 55 Calcium/Aluminum Rich Inclusions (CAI) These highly refractory grains form at the highest temperatures and earliest times in the Solar Nebula They have radiometric ages of about a million years older than the rest of the meteorite matrix (chondrules).

54 56 Calcium/Aluminum Rich Inclusions (CAI) These inclusions show an excess of Magnesium-26 which is the decay product of Aluminum-26. Aluminum-26 decays energetically with a half life of 0.7 million years Suggests injection just prior to solar system formation (a supernova trigger? Winds from massive stars?) Provides more than enough energy to melt small bodies if incorporated early differentiated asteroids.

55 57 Iron Meteorites Pieces of Differentiated Asteroid Parent Body Cores

56 58 Iron Meteorites Pieces of Differentiated Asteroid Parent Body Cores Known as Widmanstätten patterns these are iron/nickel crystals formed by slow cooling of molten metal. To form the crystals seen here cooling rates have to be slower than about one degree per thousand years.

57 59 Extinct Radioactivities Short-lived radionuclides have all decayed away, but their isotopic signatures can illuminate processes happening in the earliest stages of Solar System development during the first several half lives. Aluminum-26/Magnesium-26 (0.7 million years) Hafnium-182/Tungsten-182 (9 million years) Hafnium (Hf) is a lithophile element while Tungsten (W) is a siderophile Physics Today Article on Timing of Formation of Earth's Core based on Hafnium/Tungsten isotope ratios.

58 62 Formation of the Earth's Core Material was cooked at great pressure in a deep magma ocean precipitating siderophiles onto the core, including Tungsten. Differentiation

59 63 Formation of the Earth's Core Infall continues resupplying fresh Hafnium/Tungsten to a Hafnium enriched/tungsten depleted surface layer. Applying this technique in different environments give a core formation time of 2 Myr in asteroids, 7 Myr for Mars, and 30 Myr for Earth.

60 64 Why Should We Expect to Find Other Planets? Planetary system formation is a natural by-product of star formation

61 66 Detecting Jupiter from Afar Consider our Solar System seen from a distance of 20 parsecs (a distance large enough that from the Earth's perspective there would be thousands of stars, and dozens of sun-like stars to examine). How separated (in an angular sense) would Jupiter be from our Sun. How bright would Jupiter be? How bright would the Sun be? Important numbers There are AU in a parsec. The Earth is 1 AU from the Sun, Jupiter is typically 5 AU from the Earth.

67 Detecting Jupiter from Afar Consider our Solar System seen from a distance of 20 parsecs (a distance large enough that from the Earth's perspective there would be thousands

62 67 Detecting Jupiter from Afar Consider our Solar System seen from a distance of 20 parsecs (a distance large enough that from the Earth's perspective there would be thousands of stars, and dozens of sun-like stars to examine). How separated (in an angular sense) would Jupiter be from our Sun. How bright would Jupiter be? How bright would the Sun be?

Regular Features of the Solar System

1 Regular Features of the Solar System All of the planets orbit the Sun in the same plane All planetary orbits are nearly circular All planets orbit the Sun in the same direction Most planets rotate in