Jupiter PROBLEM SET #5 DUE TUESDAY AT THE BEGINNING OF LECTURE 19 October 2017 ASTRONOMY 111 FALL 2017 1 Jupiter and Io as seen from Cassini as it flew by (JPL/NASA) Jupiter, its atmosphere, and its magnetic field Albedo and emissivity The ice line and the icy domain of the giant planets Introduction to Jupiter Clouds, storms, and magnetism on Jupiter Jupiter s interior 19 October 2017 ASTRONOMY 111 FALL 2017 2 1
Sublimation temperatures At the low pressures of interplanetary space, water ice rapidly sublimates at temperatures above T = 150 K; pure carbon dioxide, likewise at about 80 K. Bodies colder than this can retain lots of ices, so these temperatures should represent a boundary between fundamentally different kinds of solar system bodies. Where is that boundary in our Solar System? Not in one fixed location, because of the wavelength dependence of emissivity. Sublimation temperature (K) Species Gone in minutes Gone in 10 5 yr N 2 22 13 O 2 22 13 CO 25 16 CH 4 30 18 CO 2 83 50 NH 3 95 55 CH 3 OH 140 80 H 2 O 150 90 Tielens (2005) 19 October 2017 ASTRONOMY 111 FALL 2017 3 Blackbody radiation refresher Recall that a blackbody a perfectly absorbing body in thermal equilibrium radiates according to u " = 2hc' 1 λ ) e,- 0 "./ 1 where and h = 6.626 10 6'7 erg s k = 1.381 10 6A erg K 6 f = σt F where σ = 5.67051 10 6) erg s 6 cm 6' K 6F u l (T) (erg sec -1 cm -3 ster -1 ) 1. 10 16 1. 10 15 1. 10 14 1. 10 13 1. 10 12 1. 10 11 1. 10 10 1. 10 9 1. 10 8 0.01 0.1 1 10 100 10000 K 5000 K Wavelength (µm) 2000 K 1000 K 19 October 2017 ASTRONOMY 111 FALL 2017 4 2
Emissivity Bodies that absorb perfectly at any wavelength are rare, and bodies that absorb the same way at all wavelengths are practically nonexistent. Usually, their intensity and total flux have to be written as I " = λ 2hc' 1 λ ) e,- 0 "./ 1 and f = σt F where λ ( 1) is called the emissivity, and is a complicated average of the emissivity over all wavelengths. 19 October 2017 ASTRONOMY 111 FALL 2017 5 Graybodies If λ is the same at all wavelengths, then = λ and the resulting object is called a graybody. Apart from sharp spectral features due to the quantized energy levels of atoms, molecules, and solids, it is a good approximation to consider a given object to be gray over certain wide wavelength ranges and to be a different gray in other wavelength ranges. For instance, lots of Solar System objects are characterized well by One (constant) emissivity value for visible and ultraviolet wavelengths at which the Sun emits most of its energy And another emissivity value for infrared wavelengths at which planets and asteroids emit most of their energy. We will call this one. 19 October 2017 ASTRONOMY 111 FALL 2017 6 3
Albedo Conventionally, the visible and ultraviolet emissivity is instead characterized by the albedo, A = 1 P6QP. The albedo is something like the reflectivity of the object at these wavelengths. Example 1 What is the temperature of a spherical body of mass M and radius R lying a distance r from the Sun that has an albedo A and infrared emissivity, is heated by sunlight and radioactivity, and is cooled by its own thermal emission? Power absorbed and generated: P ST = 1 A L 4πr ' πr' + MΛ^_` Power emitted: P abc = σt F 4πR ' 19 October 2017 ASTRONOMY 111 FALL 2017 7 Example #1: Albedo and emissivity P de = P fgh 1 A L 4πr ' πr' + MΛ^_` = σt F i 4πR ' T i = If radioactive heating is small enough to be neglected, then T i = as you showed in recitation. 1 A L 16πσr ' F = 1 A 1 A L 16πσr ' + MΛ^_` 4πσR ' F Tjk_lmja`n F 19 October 2017 ASTRONOMY 111 FALL 2017 8 4
Example #1 (cont.) Representative cases, neglecting radioactive heating to good approximation: Venus 1 A F A = 0.7, 1, = 0.74 Earth Mars A = 0.37, 1, A = 0.15, 1, 1 A 1 A F = 0.89 F = 0.96 T = 248 K instead of 278 K To return to our original question: where does the surface temperature equal the freezing/sublimation point of water as a function of albedo? 19 October 2017 ASTRONOMY 111 FALL 2017 9 1 10 3 Asteroid belt Ice line Temperature (K) 100 Å 10 0.1 1 10 100 Orbital radius (AU) The ice line T i = 1 A L 16πσr ' F Blackbody A = 0.05 C group A = 0.2 Most S, X group A = 0.5 Shiniest X (E-type) Water-ice sublimation 19 October 2017 ASTRONOMY 111 FALL 2017 10 5
The ice line (cont.) The asteroid belt marks the transition between the Solar System bodies that cannot have a lot of ice and those that can. The ice content of the outermost asteroids most of the C class should be larger than the innermost. Everything solid that is further out than the asteroids can be expected to have a lot of ice. If bodies have lots of ice mixed in with the usual rocks and metals, their bulk densities are less than the 3-6 g cm -3 of the terrestrial planets: the density of uncompressed water ice is just under 1 g cm -3. For example, C-class 1 Ceres: bulk density 2.1 g cm -3, bulk porosity 0.01. 19 October 2017 ASTRONOMY 111 FALL 2017 11 Jupiter s vital statistics Mass 1.8986x10 30 g (318 M ) Equatorial radius 7.1492x10 9 cm (11.2 R ) Average density 1.326 g cm -3 Moment of inertia 0.254 MR 2 Albedo 0.52 Orbital semimajor axis 7.7857x10 13 cm (5.2043 AU) Orbital eccentricity 0.04839 Sidereal revolution period 11.862 years Sidereal rotation period 9.9250 hours Moons 63 Rings 2 Jupiter as seen from Cassini (JPL/NASA) 19 October 2017 ASTRONOMY 111 FALL 2017 12 6
Visits to Jupiter We have learned an awful lot about Jupiter during the past 44 years as a result of the visits by eight NASA planetary probes: Pioneer 10 and 11 (1973-4) Voyager 1 and 2 (1979) Ulysses (1992, 2003-4) Galileo (1995-2003) Cassini (2001) New Horizons (2006-7) The approach of Voyager 1 to Jupiter (JPL/NASA) 19 October 2017 ASTRONOMY 111 FALL 2017 13 Jupiter: structure and composition Jupiter is best thought of as a gaseous planet. It rotates differentially, has a low average density, and a low moment of inertia for its mass. Equator rotates with P = 9h50.5m, but the rotation period is 9h55.7m near the poles. Jupiter might not even have a core: best determination of the range of the core mass is 0-11 M. It is enhanced in elements heavier than H (except O) by factors of 2-4 relative to the Sun. Molecular constituents: 89.5% H 2, 10.2% He, 0.3% CH 4, 0.026% NH 3, 0.0028% HD, 0.00058% C 2 H 6, 0.0004% H 2 O. T = 112 K at P = 1 Earth atmosphere. (101.5 K is expected from heating by starlight.) 19 October 2017 ASTRONOMY 111 FALL 2017 14 7
Jupiter s surface The visible surface turns out to be a deck of clouds in the upper atmosphere. The clouds are arranged in alternating dark and light bands parallel to Jupiter s equator that change their structure with time. Belts: brown/orange bands Zones: blue/white bands The colors result from various chemical compounds in the atmosphere at various heights. Infrared observations show that the zones are cooler than the belts. Zones thus mark the tops of rising regions (higher altitude) of high pressure, and belts mark falling regions of low pressure. True-color image from Galileo (JPL/NASA) The tops of zones contain NH 3 ice (which sublimates at about 150 K at these pressures), then NH 4 SH. Down below are NH 3 vapor and H 2 0 ice clouds. 19 October 2017 ASTRONOMY 111 FALL 2017 15 Jupiter s surface Jupiter s entire disk unpeeled (Cassini, JPL/NASA) 19 October 2017 ASTRONOMY 111 FALL 2017 16 8
Jupiter s surface thermal emission Infrared image of Jupiter (2.2 microns) from the NASA Infrared Telescope Facility in Mauna Kea, showing the hottest parts of the visible atmosphere, i.e. the places we see deepest into the atmosphere. 19 October 2017 ASTRONOMY 111 FALL 2017 17 Cyclones and anticyclones on Jupiter On Earth, a cyclone is local CCW circulation of air in the northern hemisphere, CW in the southern hemisphere. They are results of the rightward Coriolis force deflection of air flowing toward the center of a low-pressure region. Thus anticyclones, too, as air flows away from high pressure centers, spinning the opposite of cyclones. Jupiter s atmospheric storms appear in images as ovals. White ovals have relatively lower temperatures and thus lie above the main cloud deck. Brown ovals in the northern hemisphere are bright at infrared wavelengths and are therefore holes in the clouds (see deep, higher T). 19 October 2017 ASTRONOMY 111 FALL 2017 18 9
Convection of Jupiter s atmosphere Very similar to the Coriolis force seen in the atmosphere here on Earth. 19 October 2017 ASTRONOMY 111 FALL 2017 19 Cyclones and anticyclones on Jupiter (cont.) Voyager 2 picture of the Great Red Spot region on Jupiter, also showing several white and brown oval storms (JPL/NASA). 19 October 2017 ASTRONOMY 111 FALL 2017 20 10
Special case: the Great Red Spot Size: 40,000 x 14,000 km; six-day rotation period, anticyclonic It has been around for at least 300 years (first identified by Cassini in 1665). Most of the Great Red Spot is high altitude clouds. Most of the spot is about 10 K cooler (8 km above) the white clouds that surround it. The Great Red Spot (Galileo/JPL/NASA) 19 October 2017 ASTRONOMY 111 FALL 2017 21 Cyclones & anticyclones on Jupiter (cont.) Movie from Cassini of cloud-deck flows and rotations, including that of the Great Red Spot at the lower left (JPL/NASA). 19 October 2017 ASTRONOMY 111 FALL 2017 22 11
The descent of Galileo s parachute probe Galileo dropped a probe that parachuted in with a heat shield to prevent burn-up. Transmission stopped at a pressure of P = 24 Earth atmospheres. The probe determined that the wind speeds are higher below the cloud deck than at high altitudes. This implies that the energy source for winds is Jupiter s internal heat and certain atmospheric chemical processes (not sunlight, like on Earth). It found no hint of low-lying clouds of H 2 O; the H/He abundance ratio was still the same as that in the Sun when it shut off. 19 October 2017 ASTRONOMY 111 FALL 2017 23 Jupiter s interior I = 0.254 MR 2 : Jupiter s density decreases faster than linearly with radius. (I = 0.267 MR 2 for linear decrease.) The maximum mass of the core is about 4% that of the planet, but it is compressed ( 11 M but only 1 R ). Very large pressure at center due to overlying layers: P = 8x10 7 Earth atmospheres, ρ = 20 g cm -3, T = 25,000 K The high pressure has an unusual effect on H as well: the compression changes hydrogen to a liquid metallic state. This liquid metal either surrounds or comprises the core. Jupiter emits about twice as much power as it receives from the Sun. This is probably an effect of a continuing, slow, internal rearrangement of mass (collapse), and is a characteristic of the other giant planets as well. 19 October 2017 ASTRONOMY 111 FALL 2017 24 12
Jupiter s magnetic field The differentially-rotating liquid metallic hydrogen in the center comprises a dynamo that is responsible for strong magnetic fields. That Jupiter has such a magnetic field has long been known; Jupiter is a strong radio synchrotron emitter, which requires a strong magnetic field (B) to accelerate charged particles that produce the radiation. The Jovian magnetosphere (bounded by solar wind) extends some 10 million km. Magnetic storms and aurorae are also observed, the latter from high-energy charged particles following the converging lines of B toward the Jovian poles. 19 October 2017 ASTRONOMY 111 FALL 2017 25 Jupiter s magnetic field (cont.) Charged particles travel trace out the magnetic field lines connecting Io and Jupiter. 19 October 2017 ASTRONOMY 111 FALL 2017 26 13