Exo-Obs Course: Planet Formation, Disks, and Radio Observations

I will be sharing the slides I developed for a graduate level course on Exoplanets and Observational Astronomy. This is the first completed slide deck for this course. It covers topics on planet formation, protoplanetary disks, disk structure, and radio observations (single dish and interferometry).

Transcript

1. PLANET FORMATION, DISKS, + THE RADIO 1 Created by: Adina Feinstein
2. RELEVANT READINGS Dullemond + Dominik (2005) Alexander (2007) Lodato (2008) 2 Created by: Adina Feinstein
3. FORMATION THEORY 3 Created by: Adina Feinstein
4. 4 Classical Planet Formation HST IR Pontoppidan et al. 2020 HST UV ALMA Radio
5. 5 • Planets form within the surrounding disk Classical Planet Formation
6. 6 • Planets form within the surrounding disk • Colder regions of the disk allow for the formation of dust and ice grains ◦ Other gases may condense onto the surface of the grains Classical Planet Formation
7. 7 • Planets form within the surrounding disk • Colder regions of the disk allow for the formation of dust and ice grains ◦ Other gases may condense onto the surface of the grains • Inner material of the disk is accreted onto the star Classical Planet Formation
8. 8 • Planets form within the surrounding disk • Colder regions of the disk allow for the formation of dust and ice grains ◦ Other gases may condense onto the surface of the grains • Inner material of the disk is accreted onto the star • Grains collide and stick together, growing into pebbles -> planetesimals -> planets ◦ Alternative: Gravitational instability (similar to star formation) Classical Planet Formation
9. 9 Dust Coagulation Determine the collision rate of dust particles R = σ cs · v rel · n cross-section velocity number density
10. 10 Dust Coagulation The relative velocity, v rel , is a combination of multiple components v rel = √ [(Δv br )2 · (Δv z )2 · (Δv t )2 · (Δv r 2)] v br is the motion in a fluid given by random interactions (Brownian motion). This is very effective for very small dust particles with m dust ~ m gas .
11. 11 Dust Coagulation The relative velocity, v rel , is a combination of multiple components v rel = √ [(Δv br )2 · (Δv z )2 · (Δv t )2 · (Δv r 2)] v z is the vertical settling velocity. z r
12. 12 Dust Coagulation The relative velocity, v rel , is a combination of multiple components v rel = √ [(Δv br )2 · (Δv z )2 · (Δv t )2 · (Δv r 2)] Δv t is the velocity due to turbulence in the disk. This is dependent on particle mass (more massive particles don’t move as much as small particles) and the strength of the turbulence.
13. 13 Dust Coagulation The relative velocity, v rel , is a combination of multiple components v rel = √ [(Δv br )2 · (Δv z )2 · (Δv t )2 · (Δv r 2)] Δv r is the radial velocity defined as v r = -2Δv · (τ s + τ s -1)-1 Δv is the difference in velocity between the gas and dust (~10-100 m/s). τ s is a dimensionless stopping time.
14. 14 Radial Drift Fig. 7 in Alexander (2007) As particles grow, they drift into the central star faster.
15. 15 Meter-sized Boundary Problem Define a dimensionless stopping time, τ s τ s = t S · Ω K Where t S is the drag stopping timescale, Ω K is the Keplerian angular momentum. τ s = 1 implies that the object drifts inwards at a rate of Δv. t s = (⍴ d /⍴ g ) · (s / v th ) ⍴ d is the density of the dust, ⍴ d is the density of gas, s is the size of the particle, and v th is the thermal velocity (~ sound speed).
16. 16 Meter-sized Boundary Problem Assuming: • τ s = 1 • ⍴ g = 10-9 g cm-3 • ⍴ d = 1 g cm-3 • Ω K = 10-7 s-1 • c s ~ 105 cm s-1 Calculate s. τ s = t S · Ω K t s = (⍴ d /⍴ g ) · (s / c s )
17. 17 • Planets form within the surrounding disk • Colder regions of the disk allow for the formation of dust and ice grains ◦ Other gases may condense onto the surface of the grains • Inner material of the disk is accreted onto the star • Grains collide and stick together, growing into pebbles -> planetesimals -> planets ◦ Alternative: Gravitational instability (similar to star formation) • Remaining gas in the disk is either accreted onto the planets or dissipated, leaving just the dust, ice, rocks, and planets behind Classical Planet Formation
18. 18 The Nice Model The giant planets formed first Sun Rocky asteroids Icy asteroids 4 2 6 8 10 au
19. 19 The Nice Model Jupiter migrates inwards Sun 4 2 6 8 10 Planets keep growing au
20. 20 The Nice Model Saturn migrates inward Sun 4 2 6 8 10 au
21. 21 The Nice Model Jupiter and Saturn migrate outwards Sun 4 2 6 8 10 19.2 au 30.1 au au
22. 22 The Nice Model The rocky planets form Sun Rocky planets 4 2 6 8 10 au
23. 23 Alternative Formation Models These models don’t work due to a combination of (a) the physics doesn’t work out and/or (b) they do not produce the frequency of exoplanets we observe.
24. DISK STRUCTURE 24 Created by: Adina Feinstein
25. 25 No two disks look the same.
26. 26 No two disks look the same. Cieza et al. (2021)
27. 27 Images are expensive. We search for evidence of disks via SEDs. Furlan et al. (2011)
28. 28 Different Types of Disks Protoplanetary disks • Disk that is present as the central star continues to form • Gas-rich (~99% gas, 1% dust, should be made of the same material as the star) • Optically thick with strong excess infrared absorption • The gas is typically present within the first ~2 Myr
29. 29 Observable Disk Evolution Cieza et al. (2021) Stage Observable characteristic Physical Interpretation I No obvious gaps Disks form without deep gaps II One or multiple narrow/deep gaps Protoplanets grow and form gaps III Bright ring at the disk edge. Inner disk still present New giant planets form strong pressure bumps IV Dissipation of the inner disk Dust accumulates in the ring V Narrow ring/ multiple rings Most mm dust accumulates in rings
30. 30 Observable Disk Evolution Cieza et al. (2021) Stage Observable characteristic Physical Interpretation I No obvious gaps Disks form without deep gaps II One or multiple narrow/deep gaps Protoplanets grow and form gaps III Bright ring at the disk edge. Inner disk still present New giant planets form strong pressure bumps IV Dissipation of the inner disk Dust accumulates in the ring V Narrow ring/ multiple rings Most mm dust accumulates in rings
31. 31 Observable Disk Evolution Cieza et al. (2021) Stage Observable characteristic Physical Interpretation I No obvious gaps Disks form without deep gaps II One or multiple narrow/deep gaps Protoplanets grow and form gaps III Bright ring at the disk edge. Inner disk still present New giant planets form strong pressure bumps IV Dissipation of the inner disk Dust accumulates in the ring V Narrow ring/ multiple rings Most mm dust accumulates in rings
32. 32 Observable Disk Evolution Cieza et al. (2021) Stage Observable characteristic Physical Interpretation I No obvious gaps Disks form without deep gaps II One or multiple narrow/deep gaps Protoplanets grow and form gaps III Bright ring at the disk edge. Inner disk still present New giant planets form strong pressure bumps IV Dissipation of the inner disk Dust accumulates in the ring V Narrow ring/ multiple rings Most mm dust accumulates in rings
33. 33 Observable Disk Evolution Cieza et al. (2021) Stage Observable characteristic Physical Interpretation I No obvious gaps Disks form without deep gaps II One or multiple narrow/deep gaps Protoplanets grow and form gaps III Bright ring at the disk edge. Inner disk still present New giant planets form strong pressure bumps IV Dissipation of the inner disk Dust accumulates in the ring V Narrow ring/ multiple rings Most mm dust accumulates in rings
34. 34 There is a flow of material from the outer disk to the inner disk. In order for the material to flow inwards, it must lose angular momentum, j. But, j must be conserved, which results in an additional outward flow. As the inner gas loses angular momentum, it drifts inward, accreting onto the star. Accretion rates for young stars are on the order of ~ 10-8 - 10-7 M ⊙ yr-1. Inner Disk Evaporation
35. 35 Inner Disk Evaporation Adams et al. (2004) Once accretion slows, photoevaporation dominates. Energetic X-ray/EUV/FUV photons heat the gas, exciting the H/He atoms to velocities where v th >> v esc . We can define a critical radius within which photoevaporation is efficient: r c = (G M star μ avg ) / (k T) G = gravitational constant, M star = mass of central star, μ avg = average gas particle mass, k = Boltzmann constant, T = temperature of the gas
36. 36 Inner Disk Evaporation Alexander et al. (2008)
37. 37 Observable Disk Evolution Cieza et al. (2021) Stage Observable characteristic Physical Interpretation I No obvious gaps Disks form without deep gaps II One or multiple narrow/deep gaps Protoplanets grow and form gaps III Bright ring at the disk edge. Inner disk still present New giant planets form strong pressure bumps IV Dissipation of the inner disk Dust accumulates in the ring V Narrow ring/ multiple rings Most mm dust accumulates in rings
38. 38 Observable Disk Evolution Cieza et al. (2021)
39. 39 Protoplanetary Disk Structure https://alma-maps.info/
40. 40 Different Types of Disks Transition Disks • The inner disk gas has been accreted onto the central star • The outer disk is still gas-rich, but has a smaller gas mass budget than before • Could have some disk structure starting to show (e.g., gaps, overdensities, etc.) • Typical ages of ~2-5 Myr
41. 41 Different Types of Disks Debris Disks • The vast majority of the gas within the disk has dissipated/accreted/trapped in dust • Optically thin and may show some faint infrared excess • Typical ages of 5 - ~30 Myr • Analogous to the Kuiper Belt
42. 42 Temperature Profile • Disks are extensive and full of dust that absorbs radiation. • The farther you go out in the disk, the more radiation the dust absorptions, so the outer disk is much cooler than initial predictions. • Incoming radiation hits the angled surface of the disk. Miotello et al. 2023
43. 43 Temperature Profile E in = E out L s /(4πa2) · A sin(α) = AσT D 4 [replace L s /(4π) = R s 2σT S 4] T D (a) = sin1/4(α) (R s /a)½ T s A α α changes as a function of where you are in the disk.
44. 44 Gaps = Planets? Clumps in gap No clumps in gap
45. 45 Gaps = Planets? No van der Marel (2023) Dust grains that experience radial drift can pile up at certain locations. The streaming instability can also concentrate dust, creating apparent gaps and rings in the disk structure without a gas gap.
46. 46 Gaps = Planets? No van der Marel (2023) Photoevaporation more so results in an inner cavity rather than a deep gap. This is fairly well established, although the exact contribution of different mechanisms shaping the lifetime of this cavity is not well understood.
47. 47 Gaps = Planets? No van der Marel (2023) “Dead zones” are regions of low ionization where magnetorotational instability (MRI) is suppressed. The MRI requires a weak magnetic field to be threaded through the disk, sufficiently ionizing the gas. The differential rotation in the disk winds up the field lines. When the gas is coupled to the magnetic field, the angular momentum changes, resulting in some material moving in and some moving out.
48. 48 Gaps = Planets? No van der Marel (2023) A massive planet embedded in a disk can clear a gap. A planet will accrete the gas in its orbital path, if it’s massive enough. A planet will exert a torque on the surrounding gas, pushing material away from its orbital path.
49. 49 Clumps = Planets? Also no Just as there are multiple explanations for what cause rings and gaps in disks, other than planets, there are multiple mechanisms that could create “planets” or gas over-densities.
50. PLANETARY COMPOSITIONS 50 Created by: Adina Feinstein
51. 51 Snow Lines https://alma-maps.info/
52. 52 What is a snow line? A snow line is a radial location in the disk where the mid-plane temperature is cold enough such that a volatile1 can condense out of the gas phase and become a solid. Exoplanet and disk people typically care about the H 2 O, CO, and CO 2 snow lines. 1 A volatile is any compound that easily evaporates at low temperatures.
53. 53 Calculate the Snow Line Distances Approximate the disk temperature as: T(r) ≈ 280 K (L star /L ⊙ )¼ (r / 1 AU)-1/2 Assume a solar-like star (1 L ⊙ ) and condensation temperatures of: H 2 O = 130 K CO 2 = 50 K CO = 20 K Calculate the radial distances to all three snow lines. Öberg et al. (2011)
54. 54 Where you form determines what’s in your atmosphere. Öberg et al. (2011); Seligman et al. (2022) C/O
55. 55 Runaway Gas Accretion After a rocky core is formed, they accrete their gaseous envelope. The rate of accretion is regulated by the internal cooling of the core and blows up into a gas giant as the gas accretion rate “runs away” in response to the atmosphere’s self-gravity. A planet can only become a gas giant if this runaway process occurs when there is sufficient gas in the disk (< ~5 Myr after the system is born). Runaway accretion is set by the core mass of the planet.
56. 56 Runaway Gas Accretion Pollack et al. 1996
57. Spicy Discussion Question Do you think we can actually use atmospheric compositions to trace where a planet initially formed? 57 5 minutes ⏰
58. 58 Can we make this assumption?
59. WHAT ARE WE LOOKING AT 59 Created by: Adina Feinstein
60. 60 Never limit your research to a single wavelength. Gáspár et al. (2023)
61. 61 Ultraviolet Observations Phenomenon: Accretion shocks Observable: Excess emission in the FUV Carvalho et al. (2024)
62. 62 Ultraviolet Observations Phenomenon: Ionized gas in the disk Observable: Lyman-alpha emission, CII, SiII, OI
63. 63 Ultraviolet Observations (1000-3000 Å) Phenomenon: Stellar winds and outflows Observable: Deviations in expected emission line profiles + blueshifted absorption Phenomenon: Small dust grains Observable: scattered light surrounding the central star
64. 64 Optical Observations (400-900 nm) Schneider et al. (2018) Phenomenon: Small sub-μm to μm sized grains, disk geometry, substructure Observable: Scattered light imaging Phenomenon: Accretion Observable: H-alpha
65. 65 Infrared Observations (1 - 30 μm) Romero-Mirza et al. (2024) Phenomenon: ~μm to several-μm sized grains, disk geometry, substructure Observables: CO bands, silicate emission features, ice absorption bands, PAH (polycyclic aromatic hydrocarbons), organics
66. 66 Infrared Observations (1 - 30 μm) Tazaki et al. (2025) Phenomenon: Accretion Observable: Hydrogen recombination lines
67. 67 Far-Infrared Observations (30 - 200 μm) There is a big push from the disk community to build a far-IR observatory. Why? There are key water lines (warm water, snowline water, cold water, CO) that are only accessible in the far-IR. It is super important to quantify the role of water in driving planet formation. PRIMA Mission Concept
68. 68 Radio Observations (0.3mm - cm) Phenomenon: large, cold dust grains Observable: radio emission
69. 69 What are we missing? Dust
70. 70 Measuring the Gas Budget in Disks We cannot measure the gas budget of a disk directly because it is mostly composed of H 2 and He, which can only be traced at warmer temperatures than disk conditions. We can observe only molecules and atoms, like CO, HCO+, CN, CO isotopologues, etc. which act as tracers for H 2 /He. Our estimates on the gas-mass content of disks typically have order-of-magnitude errors.
71. 71 No direct measurement of the gas budget ➡ No direct measurement on timescales of disk dispersal ➡ No well-defined period of gas giant planet formation. Measuring the Gas Budget in Disks
72. RADIO OBSERVATIONS 72 Slides adapted from Jay Strader + Laura Chomiuk
73. 73 Single-dish radio observatory • Good for mapping specific lines (e.g., H I in galaxies) • Good for conducting surveys • Not good for understanding disk morphology or substructure (poor angular resolution)
74. 74 Non-steerable single-dish observatories • Example: Arecibo (RIP) • The secondary is movable, which allows for some pointing • General field-of-view (FOV) is very limited
75. 75 The construction of radio telescopes A wavefront is a “surface” connecting all points on a wave at the same phase (in the wave) at a given time. To keep wavefront errors low, you need the surface to be 1/10 - 1/20 the wavelength. Thus, it is ok to have a radio telescope working at cm wavelengths accurate to mm scale.
76. Diffraction Limit 76 The diffraction limit is the highest angular resolution a telescope is able to achieve. When light hits an aperture, it bends and spreads, known as diffraction. Point sources, like stars, spread into a small disk with concentric rings (Airy Pattern).
77. Diffraction Limit 77 The scattering process is dependent on the wavelength and the size of the aperture: θ L = 1.22 λ / D [radians] Where D L is the diffraction limit, λ is the wavelength of light, and D is the diameter of the telescope.
78. 78 PSF/Beam A perfect point-spread function (PSF) of a circular aperture is a 2D diffraction pattern. In radio astronomy, the angular resolution of your single dish is determined by diffraction. In radio astronomy, this is called a beam (in optical, it is the PSF).
79. 79 Calculating the beam The Green Bank Telescope (GBT) in West Virginia has a diameter of 100 m and observes at 21 cm. Calculate the resolution of the GBT in arcseconds. You can think of a single-dish like a giant CCD pixel. Any emission observed within ~7’ of the beam will be mixed together.
80. 80 Sideburnslobes Bright sources outside of the primary beam can enhance the sidelobes. They can be challenging to remove from your observations..
81. 81 Limitations of single-dish radio astronomy Signal confusion - If the dish will mix together all signals within a given FOV, then how can you tell what’s coming from your source versus a nearby source? (We face similar problems in optical astronomy, but it’s worse in the radio due to the low image resolution.) Confusion means it is pointless to do deeper surveys with a single dish.
82. 82 How big is too big for a single dish? If you want your dish to have a resolution of 1’’ at 21cm, what would you need the diameter of your dish to be?
83. Low SNR - Due to fluctuations in the number of unresolved sources in any given area of the sky, the SNR for your observations may be reduced. (boo CMB) 83 Limitations of single-dish radio astronomy
84. INTERFEROMETRY 84 Slides adapted from Jay Strader + Laura Chomiuk
85. 85 Correcting the double slit experiment
86. 86 Double slit experiment with a slightly extended source If your source is slightly extended (fraction of λ/D), the fringes add partially destructively, reducing the amplitude of the wave.
87. 87 Double slit experiment with a highly extended source If your source is very extended (> λ/D), the fringes entirely destructively, leaving no signal at all.
88. 88 Double slit experiment with a highly extended source However, if you decrease the distance between the slits, λ/D increases, and the fringes reappear.
89. 89 What does the double slit experiment tell us 1. Fringe strength decreases as source extension increases. 2. Fringe strength increases as slit spacing decreases for a fixed source size. 3. Fringe strength increases as wavelength increases for a fixed source size. But what does it mean??
90. 90 Interferometry The fringe properties are a Fourier transform of the source as observed through two slits. Instead of using slits, we can use telescopes 🤯 Long baselines (the distance between two telescopes; ↑ D) can give us more information about fine details, while large scale structure is lost. Short baselines (↓ D) can give us more information about the large scale structure, but no fine details.
91. 91 Fourier Transform Fourier theory states that any well-behaved signal (1D + 2D) can be expressed as the sum of sinusoids. We can use fourier transforms to decompose the signal into its sinusoidal components. The fourier transform contains all of the information from the original signal.
92. 92 Fourier Transform The fourier transform in radio astronomy relates the measured interference pattern to the radio intensity on the sky. An interferometer measures the interference pattern produced by pairs of apertures. The interference pattern is directly related to the source brightness.
93. 93 Aperture Synthesis If we let the Earth rotate (like we have a choice) rotate while tracking a source, we can fill the (u, v) sky-plane. We can then take the Fourier transform to make an image of the sky.
94. 94 (u,v)-plane sampling Example: Submillimeter Array
95. 95 (u,v)-plane sampling Example: Submillimeter Array
96. 96 (u,v)-plane sampling Example: Submillimeter Array
97. 97 (u,v)-plane sampling Example: Submillimeter Array
98. 98 What happens if our (u,v)-plane sampling is incomplete?
99. 99 Observable Fringe Pattern 2 Antennas (one baseline)
100. 100 Observable Fringe Pattern 3 Antennas (three baselines)
101. 101 Observable Fringe Pattern 4 Antennas (six baselines)
102. 102 Observable Fringe Pattern 8 Antennas (28 baselines)
103. 103 Observable Fringe Pattern 16 compact anennas
104. 104 Observable Fringe Pattern 16 extended antennas
105. 105 Observable Fringe Pattern 32 antennas (instantaneous)
106. 106 Observable Fringe Pattern 32 antennas (8-hour integration)
107. 107 Making a Useable Image The (u, v) coverage is always finite for a given array, but there are an infinite number of images that are consistent with the observed baseline visibilities. So, to create a useful image, you have to make some reasonable assumptions: 1. The image is mostly empty 2. What isn’t empty are point sources 3. You have to make a choice about the weighting of the baselines (there is more data on smaller baselines)
108. 108 Event Horizons Telescope
109. 109 Event Horizons Telescope
110. 110 Radio Data Products The output radio data is in the form of a data cube (like an IFU) - 1. (x, y) spatial information 2. Each image slice is at a given wavelength (third dimension - frequency/spectrum)
111. 111 Spatial Scales The sensitivity is given by the number of antennas x the area. The field of view is given by the beam of a single antenna. The resolution is set by the largest distance between antennas (called the synthesized beam). The largest achievable angular scale that can be imaged is given by the shortest distance between antennas.
112. 112 Radio vs. Optical Interferometry It’s important to note that in radio interferometry, it is possible to record the incoming wave on a per telescope basis and interfere them later. This is regularly done for very long baseline interferometry (New Horizons). This cannot be done for optical interferometry. Monnier et al. 2007
113. 113 CHARA Optical Interferometer
114. 114 Flux Density Radio sources are often characterized by the flux density in Janskys 1 Jansky = 10-23 erg/s/cm2/Hz Flux densities are distant dependent. The more distant the source, the lower the flux density. Since more distant sources are also smaller, the surface brightness (flux density per solid angle) is distance independent.
115. 115 Brightness Temperature We can assume the Rayleigh-Jeans limit in the radio. This does not require the source to be a blackbody, unlike at other wavelengths. We can directly map the surface brightness of a source to its brightness temperature: I v = (2 k B v2 T B ) / c2 Where I v is the surface brightness, v is the frequency, T B is the brightness temperature. k B is the Boltzmann constant. c is the speed of light.
116. 116 Brightness Temperature To measure the flux density, you integrate the surface brightness over the unit solid angle S v = ∫ Ω I v dΩ = (2 k B v2) / c2 ∫ Ω T B dΩ Where I v is the surface brightness, v is the frequency, T B is the brightness temperature. k B is the Boltzmann constant. c is the speed of light.
117. 117 Brightness Temperature If the source fills the beam and is a blackbody, then its actual temperature is its brightness temperature. If the source is smaller than the beam, then the brightness temperature is lower than the actual temperature.