IB PHYSICS WELCOME TO ASTROPHYSICS CLASS

The Universe (A good video to watch) http://www.youtube.com/watch?v=-QGU0m7T9Q4

Solar system Solar system has 8 planets (earlier 9 planets including Pluto) Planets move around in elliptical orbits The elliptical orbits are characterized by their eccentricities Ellipse with ‘e’ close to 1 are more flatter Near circular orbits have ‘e’ close to 0 Inner planets are planets closest to Sun – Mercury, Venus, Earth and Mars Outer planet are Jupiter, Saturn, Uranus, Neptune

Eccentricity of an elliptical orbit Eccentricity is the ratio between the distance between the two foci of the ellipse and the length of the major axis of the ellipse (e=0 is perfect circle and e=1 is straight line)

Status of Pluto Pluto first discovered in 1930 by Clyde W. Tombaugh A full-fledged planet is an object that orbits the sun and is large enough to have become round due to the force of its own gravity. In addition, a planet has to dominate the neighborhood around its orbit. Pluto has been demoted to be a “Dwarf planet” (2006) because it does not dominate its neighborhood. Charon, its large “moon,” is only about half the size of Pluto, while all the true planets are far larger than their moons. Tyche  tenth planet???

Solar system (Sidereal period is the Time required for a celestial body in the solar system to complete one revolution with respect to the fixed stars) Aspects Mercury Venus Earth Mars Jupiter Saturn Uranus Neptune Pluto Mean Distance from the Sun (AU) 0.3871 0.7233 1 1.524 5.203 9.539 19.19 30.06 39.48 Orbital period (years) 0.24 0.62 1.88 11.86 29.46 84.01 164.79 248.54 Mean Orbital Velocity (km/sec) 47.89 35.04 29.79 24.14 13.06 9.64 6.81 5.43 4.74 Orbital  Eccentricity 0.206 0.007 0.017 0.093 0.048 0.056 0.046 0.010 0.248 Body rotation period (hours) 1408 5832 23.93 24.62 9.92 10.66 17.24 16.11 153.3 Number of observed satellites 2 >28 30 24 8  

Asteroid belt Asteroid Belt is the region between the inner planets and outer plants where thousands of asteroids are found orbiting around the Sun Asteroids are chunks of rock and metal that orbit around the Sun The largest known asteroid is CERES

Beyond solar system – Other stars Other stars – There millions and millions of stars other than sun in the universe - Nearest star system is Alpha Centauri consists of 3 stars - Proxima Centauri at 4.22 light years and Alpha Centauri A, B (binary stars) at 4.35 light years Stars are of different types – Giants, Super Giants, Red Giants, Neutron Star, White Dwarfs, Main Sequence Stars, Black Holes - all names based on their different stages of evolution

Beyond solar system – Stellar clusters Stellar clusters are groups of stars that are gravitational bound Two types of stellar clusters Globular cluster – tight groups of hundreds of thousands of very old stars Open cluster - contain less than a few hundred members, and are often very young - may eventually become disrupted over time and no longer gravitational bound – move in broadly same direction in space – referred to as stellar association or moving group

Beyond solar system - Galaxies We belong to the Milky Way galaxy – spiral galaxy – 1000,000 light years wide – 10,000 light years thick at the centre – has three distinct spiral arms - Sun is positioned in one of these arms about two-thirds of the way from the galactic center, at a distance of about 30,000 light-years The Andromeda Galaxy, M31, is the nearest major galaxy to our own Milky Way. It is about 3 million light years away

Clusters Group of galaxies form a cluster Milky Way belongs to “The Local Group” cluster that consists of over 30 galaxies Local Group is held together by the gravitational attraction between its members, and does not expand with the expanding universe Its two largest galaxies are the Milky Way and the Andromeda galaxy - most of the others are small and faint.

Super-clusters Groups of clusters and smaller galaxy groups Not bound by gravity Take part in expansion of universe Largest known structure of cosmos Our local cluster belongs to the local super cluster, also known as the virgo super-cluster

Map of Super-clusters

So where are we? Universe Local (virgo) super-cluster Local cluster Milky way Solar system Inner planets Earth Asia India My school

Beyond solar system - Nebula Nebula is a huge, diffuse cloud of gas and dust in intergalactic space. The gas in nebulae (the plural of nebula) is mostly hydrogen gas (H2). THEY ARE THE BIRTH PLACE OF STARS

The Celestial Sphere

The Celestial Sphere Zenith = Point on the celestial sphere directly overhead Nadir = Point on the c.s. directly underneath (not visible!) Celestial equator = projection of Earth’s equator onto the c. s. North celestial pole = projection of Earth’s north pole onto the c. s.

Different sets of constellations are visible in northern and southern skies.

Apparent Motion of The Celestial Sphere

Apparent Motion of The Celestial Sphere (2)

Constellation A constellation is a group of stars that, when seen from Earth, form a pattern The stars in the sky are divided into 88 constellations (12 based on zodiac signs) The brightest constellation is Crux (the Southern Cross) The constellation with the greatest number of visible stars in it is Centaurus (the Centaur - with 101 stars) The largest constellation is Hydra (The Water Snake) which extends over 3.158% of the sky. One of the most popular constellation is the Orion

What we see… The stars of a constellation only appear to be close to one another Usually, this is only a projection effect. The stars of a constellation may be located at very different distances from us.

Seasonal Changes in the Sky The night-time constellations change with the seasons. This is due to the Earth’s orbit around the Sun.

The Sun and Its Motions (2) Due to Earth’s revolution around the sun, the sun appears to move through the zodiacal constellations. The Sun’s apparent path on the sky is called the Ecliptic. Equivalent: The Ecliptic is the projection of Earth’s orbit onto the celestial sphere.

January  Caelum, Dorado, Mensa, Orion, Reticulum, Taurus February  Auriga, Camelopardalis, Canis Major, Columba, Gemini, Lepus, Monoceros, Pictor March  Cancer, Canis, Minor, Carina, Lynx, Puppis, Pyxis, Vela, Volans April  Antlia, Chamaeleon, Crater, Hydra, Leo, Leo Minor, Sextans, Ursa Major May  Canes Venatici, Centaurus, Coma Berenices, Corvus, Crux, Musca, Virgo June  Boötes, Circinus, Libra, Lupus, Ursa Minor July  Apus, Ara, Corona Borealis, Draco, Hercules, Norma, Ophiuchus, Scorpius, Serpens, Triangulum Australe August  Corona Austrina, Lyra, Sagittarius, Scutum, Telescopium September  Aquila, Capricornus, Cygnus, Delphinus, Equuleus, Indus, Microscopium, Pavo, Sagitta, Vulpecula October  Aquarius, Cepheus, Grus, Lacerta, Octans, Pegasus, Piscis Austrinus November  Andromeda, Cassiopeia, Phoenix, Pisces, Sculptor, Tucana December  Aries, Cetus, Eridanus, Fornax, Horologium, Hydrus, Perseus, Triangulum

Source of stellar energy P-P Chain 109years H1 H1 He3 H1 1 sec He4 H1 106year H1 H1 H1 Gamma ray H1

P-P Chain The net result is 4H1 --> He4 + energy + 2 neutrinos where the released energy is in the form of gamma rays and visible light.

Hydrostatic equilibrium

Luminosity and Apparent Brightness * Luminosity is the total light energy emitted per second. * Apparent brightness is the light received per unit area per second at the earth’s surface.

Black body A black body is a good emitter of radiation as well as a good absorber of radiation

Black body radiation lmax T = constant (2.9 x 10-3 mK) The intensity of light emitted by a black body is distributed over a range of wavelength. The maximum intensity is radiated at a particular wavelength designated as lmax The value of lmax decreases with increasing temperature as per the Wien’s Displacement given by lmax T = constant (2.9 x 10-3 mK) The area under each curve gives the total energy radiated by the black body (luminosity) per second at that temperature and is governed by the Stefan-Boltzmann law, which is L = sAT4 where A is the surface area of the black body and s is the known as the Stefan constant (5.67 x 10-8 Wm-2K-4)

LIGHT SPECTRA

Stellar Spectra Absorption Lines and Classifications

Spectral Classification of Stars Spectral Class Summary

Spectral Classification of Stars Spectral Class Summary Oh Be A Fine Girl/Guy Kiss Me Oh Only Boy, Bad An Astronomers F Forget Grade Generally Kills Known Me Mnemonics Mnemonics to remember the spectral sequence:

Organizing the Family of Stars: The Hertzsprung-Russell Diagram We know: Stars have different temperatures, different luminosities, and different sizes. To bring some order into that zoo of different types of stars: organize them in a diagram of Luminosity versus Temperature (or spectral type) Absolute mag. Hertzsprung-Russell Diagram Luminosity or Temperature Spectral type: O B A F G K M

Hertzsprung-Russell Diagram Betelgeuse Rigel Absolute magnitude Sirius B Color index, or spectral class

Figure 8.6: We could analyze automobiles by plotting their horsepower versus their weight and thus reveal relationships between various models. Most would lie somewhere along the main sequence of “normal” cars.

Stars in the vicinity of the Sun

90% of the stars are on the Main Sequence!

Specific segments of the main sequence are occupied by stars of a specific mass Majority of stars are here

H R Diagram

H R Diagram- Hertzsprung – Russel diagram luminosity Lower right – coolest stars reddish color. Further up towards left we find hotter and more luminous stars – yellow and white in color. Still further up we find more luminous blue stars. The mass of a star increases moving up the main sequence. Because the gravitational pressure increases with mass, favoring the fusion reaction. Red giants and super giants are more luminous but the temperature is less. White dwarfs are hot and not luminous – because of their less surface area.

H R Diagram To learn more visit, http://aspire.cosmic-ray.org/labs/star_life/starlife_main.html

Binary stars – Visual binary stars Visual binary star can be distinguished as two stars using a telescope

Binary stars – Spectroscopic binary stars Spectroscopic binary is a system of two stars orbiting around a common centre of mass. They are identified by a the periodic shift or splitting infrequency. The shift is caused because of Doppler effect

Binary stars – Eclipsing binary stars Eclipsing binary star shows a periodic drop in the brightness of the light from the ‘star’

Cepheid variable Cepheids, also called Cepheid Variables, are stars which brighten and dim periodically. The time period of variation is proportional to the Luminosity of the star.

Distance measurement Trigonometric parallax method Distance is given by the expression, d=1/p (p expressed in seconds of arc) Distance is measured in “parsec” abbreviated as “pc” 1 pc is the distance is the distance of a star that has a parallax angle of one arc second using a baseline of 1 astronomical unit. 1pc = 206,265 astronomical units = 3.08 x 1016m This method is suitable up to a distance of 100pc (25pc for ground based measurements)

Problems The distance to Sun and Moon are about 1.5 x 1011 m and 3.8 x 108 m respectively. Both subtend an angle of about 0.5o from earth. Use this information to estimate their radii. (6.8 x 108 m, 1.7 x 106 m) Barnard’s star has a trigonometric parallax of 0.55 seconds of an arc. How far is it from earth? (3.1 x 1015m)

Apparent magnitude (m) It is a measure of how bright a star appears as seen from the earth The brightness is rated from a scale of 1 to 6 The classification scheme was proposed and used by Greek Astronomer about 2000 years ago Stars numbered 1 are the brightest and those numbered 6 are very dim Now stars have been discovered with magnitude values outside the range from 1 to 6.

Apparent magnitude (m) The ratio of the apparent brightness of star with m=1 to that of a star with m=6 is The ratio of the apparent brightness of stars with apparent magnitude values differing by 1 is In general, the ratio of apparent brightness of stars with apparent magnitudes m1 and m2 is

Absolute magnitude (M) Absolute magnitude is the apparent magnitude of a star at a distance of 10 pc from Earth (or) it is a measure of how bright a star would appear if it were at a distance of 10 pc from Earth The relation between apparent magnitude and absolute magnitude is ‘d’ is to be taken in pc. 3. The ratio of the luminosities of two stars is given by

The period of a cepheid variable is 10 days and its brightness 1 x 10 -10 w/m2. How far is it from the Earth?

Distance measurement – Spectroscopic parallax method (up to 10 Mpc) Step1 – Observe the star’s spectrum (with instruments) and identify its spectral type Step2 – Get the luminosity (L) of the star from the HR diagram Step3 – Measure (with instruments) the star’s apparent brightness (b) Step4 – Calculate the distance using the formula

Distance measurement - Cepheid variables method (suitable up to 4Mpc using terrestrial telescopes and up to about 40 Mpc using Hubble Space Telescope) Cepheid Variables are those whose absolute Magnitude (or luminosity) varies periodically The period of variation is related to their absolute magnitude (or luminosity) Distance measurement method Measure apparent magnitude of the star (m) Measure period (T) Use period-luminosity law to find M Use the equation below and find distance

Newton’s model of Universe Universe is infinite (in space and time) It is uniform and static Newton’s model leads to Olber’s paradox

Olber’s paradox If the universe extends infinitely, then eventually if we look out into the night sky, we should be able to see a star in any direction, even if the star is really far away. Since the universe was infinitely old, the light from stars at extremely far distances would have already reached us, even if they were 40 billion light years away. Then according to Steady State Theory we should be able to see a star anywhere in the night sky, and so the sky should have the same brightness everywhere. But as you all know, if you look at the sky at night, it's dark and speckled with bright points of light called stars! How can this be explained? Something seemed to be amiss….

Olber’s paradox

Olber’s paradox

Olbers’ Paradox in another way There will be a tree at every line of direction if the forest is sufficiently large

Possible Explanations There's too much dust to see the distant stars. The Universe has only a finite number of stars. The distribution of stars is not uniform.  So, for example, there could be an infinity of stars, but they hide behind one another so that only a finite angular area is subtended by them. The Universe is expanding, so distant stars are red-shifted into obscurity (Doppler effect). The Universe is young.  Distant light hasn't even reached us yet.

Correct Answer(s) The Universe is expanding The Universe is young

The Universe is young We live inside a spherical shell of "Observable Universe" which has radius equal to the lifetime of the Universe.  Objects more than about 13.7 thousand million years old (the latest figure) are too far away for their light ever to reach us. Redshift effect certainly contributes.  But the finite age of the Universe is the most important effect.

Big Bang Model Light from galaxies show red shift This indicates that the universe is expanding Working backward, it is predicted that the universe should have started with a tiny volume of extremely dense matter Big Bang – NOT AN EXPLOSION – just an expansion of the Universe from an extremely tiny and dense state to what it is today Space and time started with Big Bang Before Big Bang, nothing existed ! Universe does not expand into a VOID

Cosmic Microwave Background (CMB) In 1964, Penzias and Wilson discover Cosmic Microwave Background (CMB) radiation CMB comes from outside our galaxy and is remarkably uniform The CMB corresponds to a temperature of 2.725K and a wavelength of a few cms (microwave region). CMB is considered as the remnant of the radiation from the Big Bang CMB supports the Big Bang theory that the universe must have started with extremely high temperature and high density and has cooled by expansion to what is it now

Fate of the Universe The future of the universe depends on the density of universe Open universe - density (r) of universe is less than critical density (ro) Closed Universe - density of universe (r) more than critical density (ro) Flat universe - density of the universe (r) is equal to critical universe (ro)

Space-time curvature For open universe: W < 1 and space-time has a negative curvature For closed universe: W > 1 and space-time has a positive curvature For flat universe: W = 1 and space-time no curvature

Dark Matter, MACHO and WIMP There does not appear to be enough visible matter to account for the mass that is required to gravitationally bind the universe together. There could be some matter which is not visible There could invisible matter such a Dark Matter, Massive Compact Halo Objects (MACHO) and Weakly Interactive Massive Particles (WIMP)