Astrophysics and Cosmology Chapter 33 Astrophysics and Cosmology © 2006, B.J. Lieb Some figures electronically reproduced by permission of Pearson Education, Inc., Upper Saddle River, New Jersey Giancoli, PHYSICS,6/E © 2004. Ch 33

Stars and Galaxies Our sun is a very average star Energy of sun is from fusion in center Sun is located in Milky Way Galaxy Milky Way has about 100 billion stars About 100 billion galaxies in universe Ch 33

Stars and Galaxies Ch 33

General Theory of Relativity concerned with accelerated reference frames Principle of Equivalence: No observer can determine whether he or she is accelerating or is in a gravitational field. Ch 33

Inertial and Gravitational Mass Inertial Mass: resistance to force Gravitational mass: gravitational force of attraction depends on the products of the two masses Throughout this course we have assumed that these two “masses” are equal, but are they? Experiments with an accuracy of a few parts in 1012 show no difference between inertial and gravitational mass. Principle of Equivalence says they are equal. Ch 33

Light beam in constantly moving elevator moves directly across because of special nature of light In accelerated elevator, light beam is bent because of increasing velocity of elevator Principle of Equivalence says that there is no difference between accelerated frame and frame in gravitational field Ch 33

Bending Light Rays passing near the Sun Consider three stars in the sky. If the light from one of these stars passes very near the Sun, whose gravity bends the rays, the star will appear higher than it actually is. Ch 33

Curved Space Light beam must travel by the shortest, most direct path Can explain bending of light ray by assuming space is curved. In Euclidian geometry, the sum of the angles in a triangle must be 1800 if sum >180 0 space is positively curved If sum < 1800 space is negatively curved Ch 33

Black Hole Black Hole is a massive collapsed star. Gravity is so strong that photons can’t escape from its surface. Can see X-Rays from matter being pulled into it. Ch 33

Expanding Universe Hubble measured the distance to galaxies by measuring the brightness of certain stars whose intrinsic brightness was known the velocity of galaxies was determined by the Doppler effect all galaxies showed a redshift (spectral lines were shifted toward lower frequency indicating they moved away from the earth.) doesn’t mean we are at center of universe Ch 33

Hubble’s Law Hubble found a linear relationship between the velocity ( v ) of galaxies away from us and the distance to the galaxy ( d ). The slope of the line is H, called the Hubble Constant. Ch 33

So the light left the galaxy 1.4 billion years ago. Example 33-1 If a galaxy is traveling away from us at 10.0% of the speed of light, roughly how far away is it? So the light left the galaxy 1.4 billion years ago. Ch 33

Hubble’s Law We can use this to estimate the age of the universe: Assume that the universe a galaxy at distance d from has been moving away from us since the start of the universe and calculate how long that has been. Ch 33

four forces unified, theory ≈ ??? Big Bang 0→10-43seconds four forces unified, theory ≈ ??? 10-43→10-35sec. Grand Unified Theory Era gravity was a separate force no distinction between quarks and leptons Ch 33

strong force is separate force 10-35 →10-4 seconds Hadron Era strong force is separate force slight excess of quarks over anti-quarks results in excess of nucleons over anti-nucleons 10-4→ 10 seconds Lepton Era slight excess of electrons over positrons results in only electrons after annihilation Ch 33

radiation dominates (photons and neutrinos) 10-4→ 300,000 year Radiation Era radiation dominates (photons and neutrinos) 300,000 year → now Matter Dominated Era atoms formed stars and galaxies formed Universe is matter dominated Ch 33

Future of Universe Can the gravitational force reverse expansion of the universe? Answer depends on average density critical density c = 10-26 kg / m3 ( a few nucleons per m3)  < c curvature is negatively curved and universe expands forever  > c curvature is positive and universe expansion is reversed . Ch 33

Big Surprise!! Recent evidence suggests that the universe is expanding at an accelerating rate. . Ch 33

Dark Energy There is now evidence that the expansion of the universe is accelerating This would imply the existence of an unknown force which has been given the name “Dark Energy”. Dark implies that astronomers can’t see it. It is interesting that Einstein had included a fudge factor in the General Theory of Relativity called the “Cosmological Constant” that explained the stability of the universe. When it was discovered that the universe is expanding then the Cosmological Constant was not necessary so Einstein considered it his biggest mistake. Now we find that the Cosmological Constant may explain the acceleration that has been recently observed.  . Ch 33

Best Estimate of Mass-Energy in the Universe 73 % dark energy 27% subject to the known gravitational force 23% is dark matter (matter that astronomers can’t detect) 4% is baryons and leptons Ch 33