PHYS 3380 Astronomy The first exam will be

PHYS 3380 - Astronomy The first exam will be Tuesday (9/29/20). It will cover everything I have covered in class up to and including Tuesday, 9/15/20, i. e. , up to but not including Light. The exam will be conducted asynchronously, i. e. , at a time of your choosing, between 10: 00 AM and 10: 00 PM Tuesday. You will not be able to take the exam after 10: 00 PM on Tuesday. It will be given through our class page on e. Learning. You will go to the class homepage and click on the “Quizzes and Exams” link on the left. You will then click on the “Physics 3380 Exam 1” link. When you are ready, click begin. You will have 1 hour and 15 minutes to complete the exam. Once you start, you cannot pause the exam. It will consist of ~45 multiple choice, T/F, and matching questions.

PHYS 3380 - Astronomy Homework Set #6 9/23/20 Due 10/6/20 Chapter 6 Review questions 3 and 6 Problems 4 and 13 Extra Problems 1. At a temperature of 5800 K, hydrogen atoms have typical random speeds of about 12 km/s. Assuming that spectral line broadening is simply the result of atoms moving away or towards us at this random speed, estimate thermal width (in nanometers) of the 656. 3 -nm H line. 2. Vulcan has an escape velocity 1. 4 times that of Earth. It radius and density are, respectively, 1. 2 and 1. 5 times that of earth. It’s surface temperature is 298 K. What is it’s ESI? 3. Venus can be as bright as apparent magnitude -4. 7 when at a distance of about 1 AU. How many times fainter would Venus from a distance of 1 pc? What would its apparent magnitude be? Assume Venus has the same illumination phase from your new vantage point. 4. Light travels from air into an optical fiber with an index of refraction of 1. 44. (a) In which direction does the light bend? (b) If the angle of incidence on the end of the fiber is 22 o, what is the angle of refraction inside the fiber? © Sketch the path of light as it changes media.

PHYS 3380 - Astronomy 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: - 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 ~0. 001 - 0. 00001 nm

PHYS 3380 - Astronomy Spectral Line Broadening - Zeeman effect -the splitting of a spectral line into several components in the presence of a static magnetic field. -attributed to the interaction between the magnetic field and the magnetic dipole moment associated with the orbital angular momentum. - 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

PHYS 3380 - Astronomy 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 434. 0 nm line (H ) from two A 1 stars (same temperature) - differences in width due to differences in density of gas

PHYS 3380 - Astronomy 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

PHYS 3380 - Astronomy 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.

PHYS 3380 - Astronomy 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 1995. – A planet was discovered in orbit around the star 51 Pegasi. • To date: – 4055 Confirmed Planets around 3014 Stars – 667 Systems with Multiple Planets – 4717 Kepler Candidates and Confirmed planets FYI: Most of the information I give here came from the NASA Exoplanet Archive (http: //exoplanetarchive. ipac. caltech. edu) and the Kepler spacecraft website (https: //exoplanets. nasa. gov/)There is a lot more information on those sites (and others) if you are interested

PHYS 3380 - Astronomy 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.

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.

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.

PHYS 3380 - Astronomy Atacama Large Millimeter/submillimeter Array (ALMA) images of circumstellar disks.

PHYS 3380 - Astronomy

PHYS 3380 - Astronomy Radial Velocity Doppler shift allows detection of slight motion of star caused by orbiting planet

PHYS 3380 - Astronomy Determining Star’s Velocity Animation

PHYS 3380 - Astronomy 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.

PHYS 3380 - Astronomy Determining Planet Mass and Orbit Animation

PHYS 3380 - Astronomy 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.

PHYS 3380 - Astronomy 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

PHYS 3380 - Astronomy 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 2009 • 2392 confirmed planets Ø 400 Earth sized (< 1. 25 RE) § 847 - 1. 25 RE < R < 2 RE Ø 361 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 only 4 light-years away.

Kepler Mission Confirmed Planets: 2392 Planet Candidates: 4760 The first page of the Kepler catalog

PHYS 3380 - Astronomy Confirmed planet statistics

PHYS 3380 - Astronomy

PHYS 3380 - Astronomy

PHYS 3380 - Astronomy Potentially Habitable Exoplanets Habitable Size M (ME) R (RE) Min 0. 1 0. 5 max 10 2. 5 Habitable Orbit d (AU) Teq (K) S (So) P (days) inner 0. 75 294 1. 78 237 outer 1. 84 187 0. 29 910 Subterran (Mars-size) Terran Superterran (Super-Earth) Total 1 20 34 55 subterran = 0. 1 — 0. 5 ME or 0. 4 — 0. 8 RE, terran = 0. 5 — 5 ME or 0. 8 — 1. 5 RE, superterran = 5 — 10 ME or 1. 5 — 2. 5 RE http: //phl. upr. edu/projects/habitable-exoplanets-catalog/

PHYS 3380 - Astronomy If you look at the habitable planet archives, you will note that the equilibrium temperature of the Earth is listed as about 255 K (288 K with greenhouse effect) instead of the 279 K in my calculations last class period. This is because I chose to ignore albedo in the calculation to simplify them. Albedo is the reflectivity 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:

PHYS 3380 - Astronomy

PHYS 3380 - Astronomy 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).

Earth Similarity Index (ESI) where xi is a planetary property (e. g. surface temperature), xio is the corresponding terrestrial reference value (e. g. 255 K), wi 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

PHYS 3380 - Astronomy

PHYS 3380 - Astronomy A potentially habitable world orbiting Proxima Centauri, closest star to Earth, was discovered in 2016 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 Ø Either a lucky find or these worlds are more common than previously thought Ø Close enough to Earth for detailed studies in the next years Ø Perhaps a goal for projects like Star. Shot

PHYS 3380 - Astronomy In 2013, Kepler lost the second of its four reaction wheels, rendering it incapable of maintaining precision pointing in three dimensions. Engineers devised a remarkable solution: using the pressure of sunlight to stabilize the spacecraft so it could continue to do science. The K 2 mission began in Mar 2014 The K 2 Mission

PHYS 3380 - Astronomy The Transiting Exoplanet Survey Satellite (TESS) • Launched on April 18, 2018, aboard a Space. X Falcon 9 rocket. • Searching for exoplanets using the transit method like Kepler. • Will survey 200, 000 of the brightest stars near the sun to search for transiting exoplanets. • Will survey the entire sky over the course of two years by breaking it up into 26 different sectors, each 24 degrees by 96 degrees across. • The stars TESS will study are 30 to 100 times brighter than those the Kepler mission and K 2 follow-up surveyed, which will enable far easier follow-up observations with both ground-based and space-based telescopes. • will also cover a sky area 400 times larger than that monitored by Kepler. • So far has found 2240 candidates and 68 confirmed exoplanets