ASTRONOMY 304. Research Topics in Astronomy and Astrophysics EXTRASOLAR PLANETS. Paul Hickson

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1 ASTRONOMY 304 Research Topics in Astronomy and Astrophysics EXTRASOLAR PLANETS Paul Hickson 2006

2 ASTR 304 Research Topics in Astronomy and Astrophysics 2006 EXTRASOLAR PLANETS COURSE INFORMATION Section, Time and Location: Instructor: ASTR , MWF , MATH 225 Professor Paul Hickson Department of Physics and Astronomy Office: HENN 305, Telephone: Office hours: M , WF Teaching Assistant: Mr. Saul Davis Department of Physics and Astronomy Office: HENN 310B sdavis@phas.ubc.ca Office hours: TBD Course web site: Background assumed: Evaluation: 2nd year physics, introductory astronomy weekly quizzes 100% 2

3 COURSE OUTLINE 1. Background Astronomical quantities and units Radiative measurements Types and sources of radiation The Solar System Stars and stellar evolution 2. Detection of Extrasolar Planets Doppler methods Astrometric methods Transits, occultations and gravitational lensing Direct imaging and interferometry 3. Properties of Extrasolar Planets Sizes, masses, orbital parameters Structure and composition Correlations with stellar properties 4. Formation and Evolution of Planetary Systems The protoplanetary disk Condensation Planetary dynamics and migration 5. Future Directions Extremely-large ground-based telescopes Space telescopes Interferometers Search for life 3

4 General References: Hartmann 2005, Moons & Planets, Thomson Phillips 1999, Physics of Stars, Wiley Carroll & Ostlie 1995, Introduction to Modern Astrophysics, Addison Wesley Van der Hucht & Oddbjorn 2005, Dynamics of Planetary Systems, IAU Symp. 197, Cambridge Recent Conferences: Beaulieu, Lecavelier des Etangs & Terquem 2004, Extrasolar Planets: Today and Tomorrow, ASP Conference Series, Vol 321, Astronomical Society of the Pacific Penny et al 2006, Planetary systems in the Universe Observation, Formation and Evolution, IAU Symp. 202, ASP Conference Series, Astronomical Society of the Pacific, in press Review Papers: Web: Marcy et al. 2005, Observed Properties of Exoplanets: Masses, Orbits, and Metallicities, astro-ph/ Guillot 2005, The Interiors of Giant Planets: Models and Outstanding Questions, Annual Review of Earth and Planetary Sciences, Vol. 33, p Bodenheimer & Lin 2002, Implications of Extrasolar Planets for Understanding Planet Formation, Annual Review of Earth and Planetary Sciences, Vol. 30, p arxiv.org/archive/astro-ph 4

5 1 Background This section provides some essential background that will be helpful in understanding the concepts and research papers that we will be discussing. The material here is necessarily brief. You are encouraged to refer to introductory astronomy and physics books for more detail. 1.1 Astronomical quantities and units Astronomers generally use SI units (meter, kilogram, second, etc). One also sees CGS units (centimeter, gram, second), so you should be aware of the conversion factors. Often, neither of these systems are convenient, so quantities are expressed in terms of certain astronomical measures. The most important are summarized in Table 1.1. For convenience, some commonly-used physical constants are listed in Table 1.2. Table 1.1. Units commonly used by astronomers Unit Abbreviation SI value astronomical unit AU m parsec pc m Solar mass M kg Earth mass M kg Jupiter mass M A kg Solar radius R m Earth radius R m Jupiter radius R A m Solar Luminosity L W year yr s Hertz Hz 1 s 1 Jansky Jy Wm 2 Hz 1 radian rad dimensionless degree or deg π /180 rad arcminute or arcmin π / rad arcsecond or arcsec π / rad steradian sr dimensionless square degree or sq deg (π /180) 2 sr 5

6 Table 1.2. Commonly-used physical constants Constant Symbol SI value Speed of light c ms 1 Gravitational constant G Nm 2 kg 2 Planck s constant h Js Boltzmann s constant k JK 1 Stefan-Boltzmann constant σ Wm 2 K 4 proton mass m p kg electron mass m e kg 1.2 Radiative measurements The fundamental quantity of electromagnetic radiation is the photon. A photon is uniquely characterized by its energy E, momentum p and spin s. More than one photon can have the same values of these quantities. Such photons are indistinguishable. The energy of a photon is proportional to its frequency ν (the frequency of oscillation of the associated electric and magnetic fields), where h is Planck s constant. Each photon has a wavelength λ, related to the momentum by E = hν, (1.1) p = h / λ. (1.2) Photons travel at the speed of light c. The frequency and wavelength are related by λν = c. (1.3) Light emitted by astronomical objects generally consists of large numbers of photons having a range of wavelengths. We are primarily interested in the power emitted or received, often as a function of frequency or wavelength. The primary radiation quantities of interest to astronomers are shown in Table 1.3. Table 1.3. Fundamental Radiation Quantities Name Symbol Units Description Luminosity L W Emitted power Specific Luminosity L ν WHz 1 Power per unit frequency interval Flux F Wm 2 Radiant power per unit area Specific Flux F ν Wm 2 Hz 1 Flux per unit frequency interval Intensity I Wm 2 sr 1 Flux per unit solid angle Specific Intensity I ν Wm 2 Hz 1 sr 1 Intensity per unit frequency interval 6

7 The luminosity is the total power emitted by an object, at all frequencies and in all directions. Usually the radiation is isotropic (the radiation is emitted equally in all directions) although this is not always the case. Flux generally is dependent on position. It almost always decreases with distance from the source. For a source of luminosity L emitting isotropically, the flux of radiation at a distance d from the source is F = L 4πd 2. (1.4) Intensity is affected only by absorption or emission of light and by frequency shifts (Doppler effect). If there is no emission or absorption along the line of site, the intensity is constant and independent of the distance. It is often more convenient to talk about flux or intensity per unit wavelength, F λ and I λ. These are related to F ν and I ν by the equations F λ = ν λ F ν, I λ = ν λ I ν. (1.5) A measurement of the flux or intensity emitted by an object as a function of wavelength or frequency is called a spectrum of the object Astronomical magnitudes It is convenient to use a logarithmic measure of flux called astronomical magnitude. Magnitudes were first introduced by Hipparchos and Ptolemy to describe the relative brightness of stars (the human eye has a logarithmic response to light). The modern magnitude scale was defined by Pogson in He found that a logarithmic base equal to the fifth root of 100, which has a value of about 2.51, matched the ancient Greek system quite well. The zero point of the magnitude system is chosen in such a way that the magnitude of a particular standard star is exactly zero. This leads to the definition where m = 2.5log(F / F Vega ) (1.6) F F ν W (ν)dν (1.7) and the function W (ν) describes the response of the measuring instrument as a function of the frequency of the incident radiation. Vega is a star (spectral type A0V) defined to have m = 0 in all wavelength bands (actually, Vega has now been superceded by a set of several standard stars). For reference, the brightest star in the sky (Sirius) has a magnitude (at visible wavelengths) of m 1.4. The faintest stars visible by eye have m 6. At its brightest, the planet Venus has m 4. The full moon has m 12.6 and the sun has m

8 By analogy, on can define a logarithmic measure of intensity called surface brightness and usually denoted by the symbol µ. µ = 2.5log(I / I Vega ) (1.8) where I Vega is the intensity that would result if the light from Vega was spread uniformly over 1 square arcsec of sky Absolute magnitude Astronomers often use a logarithmic measure of luminosity called absolute magnitude. The absolute magnitude M is defined to be the apparent magnitude m that an object would have if it were at a distance of 10 pc. Since the flux decreases as the inverse square of the distance (Equation (1.4)) we have, M = m 5logd 5 (1.9) where d is the actual distance to the object in pc. Substituting Equations (1.4) and (1.6) into (1.9) we find that M = 2.5 log L + const (1.10) which shows that absolute magnitude is indeed a measure of luminosity Photometric bands The wavelength band of a photometric system is the spectral region over which the function W (ν) is large enough to make a significant contribution to the integral in (1.7) Wavelength bands are often characterized by central wavelength and bandwidth. If the bandwidth is sufficiently small, and the specific flux of the object is a slowly varying function of frequency, we can take F ν outside the integral to get a direct relationship between magnitude and the average specific flux (over the wavelength band). m = 2.5log F ν + const (1.11) where const denotes a constant which depends both on the choice of wavelength band and the units of F ν. Clearly, the magnitude defined in this way is meaningful only if the wavelength band is specified. The corresponding relation for surface brightness is µ = 2.5log I ν const (1.12) where the numerical factor converts steradians to square arcsec and const has the same value as in Equation (1.11). Many standard wavelength bands are in use today. Most common is the Johnson (or UBV... ) system, summarized in Table 1.4, which divides the optical and near-infrared spectral region into nine relatively broad bands. The resolving power, defined by R = λ / Δλ (1.13) 8

9 where λ is the central wavelength and Δλ is the bandwidth, is about 5 for the Johnson system. Figure 1.1 shows the wavelength response of the Johnson UBV filters. Band Central λ (um) Table 1.4. Johnson Photometric Bands Bandwidth (um) F ν (m = 0) (Wm -2 Hz -1 ) m AB m U e B e V e R e I e J e K e L e M e Differences between magnitudes obtained in different bands, for the same source, are called colors. These are clearly a measure of flux ratios between different wavelengths, and are therefore related to the slope of the spectrum. Figure 1.1. Transmission curves of the Johnson U, B and V filters as a function of wavelength in Angstroms. (Adapted from Johnson, 1952, ApJ 114, 522.) 9

10 1.2.4 AB magnitudes While standard photometric systems provide a convenient way to measure broadband fluxes and colours of objects, they are not well suited to observations at higher spectral resolution. The measurement of flux as a function of frequency or wavelength is called spectrophotometry. The result can be described by specifying F ν or I ν as a function of frequency, or F λ or I λ as a function of wavelength. However, it is often more convenient to use a logarithmic measure. For this reason, the AB magnitude system is defined by m AB = 2.5log F ν 56.1 (1.14) The constant is chosen so that the AB magnitude of Vega is zero at a wavelength of 550 nm. It therefore corresponds approximately to the Johnson V magnitude at that wavelength. Like F ν, the AB magnitude is a continuous function of frequency or wavelength. It deviates from the broadband magnitudes at other wavelengths. The approximate differences between AB magnitudes and Johnson magnitudes are listed in the last column of Table Types and sources of radiation The spectrum of radiation is an important diagnostic of physical conditions in the source. The following types of radiation are most important in astrophysics. A detailed description can be found in Tucker, Radiation Processes in Astrophysics Line radiation Electronic transitions within atoms result in the emission or absorption of radiation at specific frequencies, primarily in the visible, UV and near infrared (NIR) regions of the spectrum. Emission lines are produced by a hot gas and absorption lines occur when radiation with a continuous spectrum passes through a gas. The frequency of the line is related to the transition energy E by Equation (1.1). Examples of emission and absorption lines are shown in Figure 1.2 and Figure 1.3. Individual lines have an intrinsic width Δν that is inversely related to the lifetime Δt of the excited state according to the Heisenberg uncertainty principle, Therefore, ΔEΔt h. (1.15) Δν = ΔE h 1 Δt. (1.16) Further broadening occurs from atomic motions, electrostatic effects, Doppler shifts, etc. Analysis of the resulting spectra can provide information about the chemical composition, temperature, pressure, and velocity of the object. 10

11 Figure 1.2. Infrared spectrum of Jupiter showing molecular absorption bands. The top curve is a model, the bottom curve is the data (Ridgeway et al. 1976, ApJ, 207, 1002). Figure 1.3 Spectra of hot stars, showing absorption and emission lines. The Balmer series of Hydrogen is particularly prominent. (Silva & Cornell, 1992, ApJS, 81, 865). 11

12 Rotational and vibrational transitions in molecules produce lines in the infrared region of the spectrum. These provide an important diagnostic of the densities and temperatures of molecules in interstellar space, and the composition of planetary atmospheres Black-body radiation Black body radiation is emitted by any perfectly absorbing body or gas cloud that is in thermal equilibrium at some temperature T. The specific intensity of this radiation is given by the Planck formula where k is Boltzmann s constant. I ν = 2hν 3 c 2 1 exp(hν / kt ) 1 (1.17) By integrating this expression over frequency and solid angle, one obtains the flux passing through a surface, F = dν dω 0 I 2π ν cosθ (1.18) = σt 4 where σ = 2π 5 k 4 / 15h 3 c 2 is the Stefan-Boltzman constant. The cosine factor appears because I ν is the flux per steradian perpendicular to the direction of propagation. This means that the surface of a black body, at temperature T, emits a flux F of radiation given by Equation (1.18) Bremsstrahlung In an ionized gas, electrons move freely, but are subject to electrostatic deflection when they pass near ions. Such an encounter results in a net acceleration of the electron in a direction perpendicular to its motion. As a result, electromagnetic radiation is produced, known as bremsstrahlung (German for braking radiation ) or free-free emission. This radiation is generally important only for very hot gas ( T 10 6 K ), such as is found in the outer atmospheres of stars, or in clusters of galaxies, where it produces X-ray photons Synchrotron radiation Synchrotron radiation is produced by relativistic electrons (electrons moving with speed v c ) in a strong magnetic field. The Lorentz force causes the electrons to move in a helical orbit along magnetic field lines. The resulting acceleration produces radiation, usually at radio frequencies. Synchrotron radiation is thought to be the source of radio emission observed from Jupiter. It is also the primary source of radiation from radio galaxies, pulsars, and some supernova remnants. 12