1 The first exam will be one week from today at the regular class time. It is closed book but you may bring in one 8 1/2 X 11 inch cheat sheet with writing on both sides. It will cover everything I have covered in class up to and including last Monday. There will not be a homework assignment today.
2 Balmer Temperature Hydrogen emits photons in infrared, visible, and ultraviolet wavelengths - series named after scientists that studied them and came up with equation that calculated frequency of each - Paschen - infrared - Balmer - visible - Lyman - ultraviolet Balmer series only lines emitted by astronomical objects visible from Earth s surface - produced by electrons in second energy level
3 Strength of Balmer lines gives more accurate estimation of stellar temperature - produced by electrons in second energy level - if star is cool - most electrons in ground state - can t absorb photons in Balmer series - weak absorption - if star is hot - electrons excited to high energy levels, even ionized - few hydrogen atoms have electrons in second energy level - weak absorption - absorption strongest at medium temperatures where most electrons in second energy level Strength of lines of other elements also dependent on temperature - can be used together to get accurate estimate of temperature
4 Spectral classes of stars - based on stellar temperature Spectral Intrinsic Effective Class color temperature* O electric blue 38,000 B blue 30,000 A blue white 10,800 F yellow white 7,240 G yellow 5,920 K orange 5,240 M red 3,920 *For the hottest spectral type in class, such as A0 in class A. Each class is divided into 10 subgroups labeled 0-9. For example, B0 (hottest), or B9 (coolest) in class B.
5 Spectral Type Classification System O B A F G K M Oh Be A Fine Girl/Guy, Kiss Me! 50,000 K 3,000 K Temperature Other stellar classes have be added as new stars types are discovered. Class "W" stars are very hot stars known as "Wolf-Rayet" Stars."R", "N", "S" stars are cool stars with particular types of molecular bands. "L" stars - brown dwarfs - are possibly not truly stars at all, in the sense that they may not have nuclear reactions at their cores.
6 Stellar spectra - hottest stars at top, coolest stars at bottom - strongest Balmer absorption - A0
7 Digital spectra usually represented by line graphs of intensity vs wavelength Hottest stars at top, coolest at bottom
8 The Doppler Effect
9 The Doppler Effect - Wavelength Shift Due to Motion. Sound Each circle represents the crests of sound waves going in all directions from the train whistle. The circles represent wave crests coming from the train at different times, say, 1/10 second apart. If the train is moving, each set of waves comes from a different location. Thus, the waves appear bunched up in the direction of motion and stretched out in the opposite direction.
10 Doppler Shift for Light We get the same effect for light as for sound.
11 The Doppler Effect 1. Light emitted from an object moving towards you will have its wavelength shortened. 2. Light emitted from an object moving away from you will have its wavelength lengthened. 3. Light emitted from an object moving perpendicular to your line-ofsight will not change its wavelength.
12 The amount of spectral shift tells us the velocity of the object: Δλ = v λ c
13 The Doppler shift only tells us part of the object s full motion - the radial part or the part directed toward or away from us.
14 Spectral Line Shapes In classical picture of the atom as the definitive view of the formation of spectral lines: - spectral lines should be delta functions of frequency - appear as infinitely sharp black lines on stellar spectra However, many processes tend to broaden these lines - lines develop a characteristic shape or profile - quantum mechanical effects - natural or radiation broadening - according to Heisenberg's uncertainly principle, product of the uncertainty in the measurement of energy, ΔE, and time Δt is: ΔEΔt h 2π - results in a natural spread of photon energies around the spectral line. The longer an excited state exists (Δt), the narrower the line width so that metastable states can have very narrow lines. - intrinsic to atom itself - natural width ~ nm
15 Spectral Line Broadening - Zeeman effect - the splitting of a spectral line into several components in the presence of a static magnetic field. - used by astronomers to measure the magnetic field of the Sun and other stars - collisions with neighboring particles - potential of charged particles interacts with that of the atomic nucleus which binds the orbiting electrons. - perturbs the energy levels of the atom in a time-dependent fashion - broadens the spectral line. - motions of the atoms giving rise to the line - macroscopic - highly ordered, i.e. stellar rotation - microscopic - random, i.e., thermal motions, turbulence - Doppler broadening
16 Collisional Broadening Occurs when atoms absorb or emit photons while colliding with other atoms, ions, or electrons - potential of charged particles interacts with that of the atomic nucleus which binds the orbiting electrons. - perturbs the energy levels of the atom - can absorb slightly wider range of wavelengths - dependent on temperature and density of gas Balmer nm line (H γ ) from two A1 stars (same temperature) - differences in width due to differences in density of gas
17 Doppler Broadening Caused by motions of individual atoms in gas - some moving towards observer (blueshift), some moving away (redshift) - some moving faster, some moving slower - broadens spectral line - dependent on temperature Cool gas Hot gas
18 Measuring Rotational Velocity Doppler shift can be used to tell us how fast an object is rotating: As an object rotates, light from side rotating toward us is blueshifted - light from side rotating away from us is redshifted. Spectral lines appear wider - the faster it rotates, the wider are the spectral lines.
19 Extrasolar Planets Planets which orbit other stars are called extrasolar planets. Over the past century, we have assumed that extrasolar planets exist, as evidenced from our science fiction. We finally obtained direct evidence of the existence of an extrasolar planet in the year A planet was discovered in orbit around the star 51 Pegasi. To date: 3518 Confirmed Planets around 2635 Stars 595 Systems with Multiple Planets 4706 Kepler Candidates FYI: Most of the information I give here came from the NASA Exoplanet Archive ( and the Kepler spacecraft website ( There is a lot more information on those sites (and others) if you are interested
20 Detecting Extrasolar Planets Can we actually make images of extrasolar planets? No, this is very difficult to do. The distances to the nearest stars are much greater than the distances from a star to its planets. The angle between a star and its planets, as seen from Earth, is too small to resolve with our biggest telescopes. A star like the Sun would be a billion times brighter than the light reflected off its planets. As a matter of contrast, the planet would be lost in the glare of the star. Improved techniques of interferometry may solve this problem someday.
21 Detection Methods Astrometry - precisely measure star's position in the sky and observe the ways in which that position changes over time - gravitational influence of the planet causes the star to move in a tiny orbit about common center of mass Radial velocity or Doppler method - variations in the speed with which the star moves towards or away from Earth deduced from the displacement in the parent star's spectral lines due to the Doppler effect. Pulsar timing - slight anomalies in the timing of observed radio pulses used to track changes in the pulsar's motion caused by the presence of planets. Transit method - observed brightness of the star drops by a small amount as a planet crosses in front of its parent star's disk. Gravitational microlensing - gravitational field of a star acts like a lens, magnifying the light of a distant background star. Possible planets orbiting the foreground star cause detectable anomalies in the lensing event light curve.
22 Detection Methods Circumstellar disks - disks of space dust are detected because dust absorbs ordinary starlight and re-emits it as infrared radiation. Features in dust disks may suggest the presence of planets. Eclipsing binary planet detected by finding variability in light curve minima as it goes back and forth - most reliable method for detecting planets in binary star systems. Orbital phase observing planetary orbital phases - depends on inclination of the orbit. By studying orbital phases scientists can possibly calculate particle sizes in the atmospheres of planets (using albedo calculations). Two planets have been discovered by Kepler using this method. Polarimetry - stellar light becomes polarized when it interacts with atmospheric molecules, which could be detected with a polarimeter. So far, one planet has been studied by this method.
24 Radial Velocity Doppler shift allows detection of slight motion of star caused by orbiting planet
25 Determining Star s Velocity Animation
26 A plot of the radial velocity shifts forms a wave. Its wavelength tells you the period and size of the planet s orbit. Its amplitude tells you the mass of the planet. Doppler shift in spectrum of star 51 Pegasi - shows presence of large planet with orbital period of about 4 days.
27 Determining Planet Mass and Orbit Animation
28 Remember - Doppler shift only tells us radial motion. If plane of orbit perpendicular to our line of sight - no shift seen. If we view it from edge on, maximum Doppler shift seen. Orbit generally tilted at some angle - star s full speed not measured. So mass derived from Doppler technique is minimum possible. If changing velocity and varying position in sky measured (as in one case - Gliese 876) orbital tilt can be determined and mass measured accurately. Gliese 876 is only about 15 LY away.
29 Planetary Transit The Doppler technique yields only planet masses and orbits. Planet must eclipse or transit the star in order to measure its radius. Size of the planet is estimated from the amount of starlight it blocks. We must view along the plane of the planet s orbit for a transit to occur. transits are relatively rare They allow us to calculate the density of the planet. Initially, all the extrasolar planets detected had Jovian-like densities. Since then, because of the Kepler spacecraft, we have detected a number of rocky planets. Method used by Kepler spacecraft Planetary Transit Animation
30 Planets Discovered by Kepler Spacecraft The Kepler Mission was specifically designed to survey a portion of our region of the Milky Way galaxy to discover dozens of Earth-size planets in or near the habitable zone and determine how many of the billions of stars in our galaxy have such planets. - uses transit method - Launched March confirmed planets! 364 Earth sized (< 1.25 R E ) " R E < R < 2 R E! 297 within habitable zone - On November 4, 2013, astronomers reported, based on Kepler space mission data, that there could be as many as 40 billion Earth-size planets orbiting in the habitable zones of sun-like stars and red dwarf stars within the Milky Way Galaxy. 11 billion of these estimated planets may be orbiting sun-like stars. The nearest such planet may be 12 light-years away.
31 Kepler Mission Confirmed Planets: 2330 Planet Candidates: 4746 The first page of the Kepler catalog
32 Confirmed planet statistics
35 Potentially Habitable Exoplanets Habitable Size Habitable Orbit M (M E ) R (R E ) d (AU) T eq (K) S (S o ) P (days) Min inner max outer Subterran (Mars-size) Terran Superterran(Super-Earth) Total
36 If you look at the habitable planet archives, you will note that the equilibrium temperature of the Earth is listed as about 255K instead of the 279K in my calculations last class period. This is because I chose to ignore albedo in the calculation to simplify them. Albedo is the reflctivity of an object. 0 is all light absorbed (black body) and 1 is all light reflected. The Earth s albedo is about 0.3. So the calculations using albedo are: P E = L S πr E 2 /r 2 4π (1 a) L S πr E 2 /r 2 4π ( 4πR 2 4 S σt ) πr E S 4π P E = L E (1 a) = 4πR E 2 σt E 4 2 /r 2 (1 a) = 4πR E 2 σt E 4 T E = 5780 K T E = R S 2r 4 1 a m 2( m) T S = 255 K
38 List of exoplanets more likely to have a rocky composition and maintain surface liquid water (i.e. 0.5 < Planet Radius 1.5 Earth radii or 0.1 < Planet Minimum Mass 5 Earth masses, and the planet is orbiting within the conservative habitable zone).
39 Earth Similarity Index (ESI) ESI = n i=1 1 x x i io x i + x io where x i is a planetary property (e.g. surface temperature), x io is the corresponding terrestrial reference value (e.g. 255 K), w i is a weight exponent, n is the number of planetary properties, and ESI is the similarity measure. The weighting exponents are used to adjust the sensitivity of the scale and equalize its meaning between different properties. Earth-like planets can be defined as any planetary body with a similar terrestrial composition and a temperate atmosphere. As a general rule, any planetary body with an ESI value over 0.8 can be considered an Earth-like planet. This means that the planet is rocky in composition (silicates) and could have an atmosphere suitable for most terrestrial vegetation including complex life. Planetary Property Reference Value Weight Exponent Mean Radius 1.0 Eu 0.57 Bulk Density 1.0 Eu 1.07 Escape velocity 1.0 Eu 0.70 Surface Temperature 288 K 5.58 w i n
42 A potentially habitable world orbiting Proxima Centauri, closest star to Earth, was discovered this year using using the radial velocity method Proxima Centauri is a cool red-dwarf slightly older than the Sun Proxima b minimum mass 1.3 times that of Earth suggests a rocky composition radius between 0.8 and 1.4 Earth radii 11.2-day orbit receives 70% the energy Earth receives from the Sun equilibrium temperature 227 K ESI of 0.87 Probably tidally locked illuminated side might be too hot - dark side too cold for liquid water or life thick atmosphere or a large ocean, though, could regulate the temperatures across the planet Most red dwarfs are very active strong magnetic fields, flares, and high UV and X-ray fluxes may lead to the atmospheric and water loss, high radiation magnetic field could potentially provide a shield! Either a lucky find or these worlds are more common than previously thought! Close enough to Earth for detailed studies in the next years! Perhaps a goal for projects like StarShot