Slide 1WR104 - Looking Down the Barrel of a GRB system 8000 lt-years from usSlide 3Slide 4Slide 5Slide 6Slide 7Slide 8Slide 9Slide 10Slide 11Clicker Question:Slide 13Slide 14Slide 15Slide 16Slide 17Slide 18Slide 19Slide 20Slide 21Slide 22Slide 23Slide 24Slide 25Slide 26Slide 27Slide 28Slide 29Slide 30Slide 31Slide 32Slide 33Slide 34Slide 35Slide 36Slide 37Review for Test #3 April 13Topics:•Measuring the Stars•The Interstellar medium•Stellar Evolution and Stellar Death•Gamma Ray Bursts•Neutron stars, pulsars and magnetars•Black HolesMethods • Conceptual Review and Practice Problems Chapters 10 - 13• Review lectures (on-line) and know answers to clicker questions• Do Mastering Astronomy homework• Try practice quizzes on-line• Bring:• Two Number 2 pencils• Simple calculator (no electronic notes)Reminder: There are NO make-up tests for this classWR104 - Looking Down the Barrelof a GRB system 8000 lt-years from usBlack HolesA stellar mass black hole accreting material from a companion starBlack Holes and General RelativityThe Equivalence PrincipleLet's go through the following series of thought experiments and arguments:1) Imagine you are far from any source of gravity, in free space, weightless. If you shine a light or throw a ball, it will move in a straight line.General Relativity: Einstein's description of gravity (extension of Newton's). Published in 1915. It begins with:2. If you are in freefall, you are also weightless. Einstein says these are equivalent. So in freefall, the light and the ball also travel in straight lines. 3. Now imagine two people in freefall on Earth, passing a ball back and forth. From their perspective, they pass the ball in a straight line. From a stationary perspective, the ball follows a curved path. So will a flashlight beam, but curvature of light path is small because light is fast (but not infinitely so).The different perspectives are called frames of reference.4. Gravity and acceleration are equivalent. An apple falling in Earth's gravity is the same as one falling in an elevator accelerating upwards, in free space.5. All effects you would observe by being in an accelerated frame of reference you would also observe when under the influence of gravity.Examples:1) Bending of light. If light travels in straight lines in free space, then gravity causes light to follow curved paths.Observed! In 1919 eclipse.Gravitational lensing of a single background quasar into 4 objects1413+117 the“cloverleaf” quasarA ‘quad’ lensGravitational lensing. The gravity of a foreground cluster of galaxies distorts the images of background galaxies into arc shapes.Saturn-massblack holeClicker Question:Eddington and his team were able to see a star appear from behind the sun sooner than expected during the 1919 solar eclipse due to:A: bending of the light by heat waves from the sunB: bending of the light due to the mass of the sunC: acceleration of the light to higher speeds by the sunD: bending of the light by strong magnetic fieldsClicker Question:Einstein’s equivalence principle states that:A: Mass and Energy are relatedB: All clocks appear to record time at the same rate regardless of how fast they move.C: Time and Money are relatedD: An observer cannot distinguish between an accelerating frame due to motion or due to gravity.2. Gravitational RedshiftConsider accelerating elevator in free space (no gravity).time zero, speed=0later, speed > 0light received when elevator receding at some speed.light emitted when elevator at rest.Received light has longer wavelength (or shorter frequency) because of Doppler Shift ("redshift"). Gravity must have same effect! Verified in Pound-Rebka experiment.3. Gravitational Time DilationA photon moving upwards in gravity is redshifted. Since 1Tthe photon's period gets longer. Observer 1 will measure a longer period than Observer 2. So they disagree on time intervals. Observer 1 would say that Observer 2's clock runs slow!12All these effects are unnoticeable in our daily experience!They are tiny in Earth’s gravity, but large in a black hole’s.Escape VelocityVelocity needed to escape the gravitational pull of an object.vesc =2GM REscape velocity from Earth's surface is 11 km/sec.If Earth were crushed down to 1 cm size, escape velocity would be speed of light. Then nothing, including light, could escape Earth.This special radius, for a particular object, is called the Schwarzschild Radius, RS. RS  M.Black HolesIf core with about 3 MSun or more collapses, not even neutron pressure can stop it (total mass of star about 25 MSun).Core collapses to a point, a "singularity".Gravity is so strong that nothing can escape, not even light => black hole.Schwarzschild radius for Earth is 1 cm. For a 3 MSun object, it’s 9 km.Clicker Question:X-rays coming from the surface of a neutron star observed at Earth are shifted to:A: lower energies. B: higher energies.C: the energy doesn’t change.D: lower speeds.Clicker Question:Suppose we start with two atomic clocks and take one up a high mountain for a week. Which is true? A: The two clocks will show the same amount of time has passed.B: The mountain clock will be slightly ahead (fast)C: The mountain clock will be slightly behind (slow)Event horizon: imaginary sphere around object with radius equal to Schwarzschild radius.Event horizonSchwarzschild RadiusAnything crossing over to inside the event horizon, including light, is trapped. We can know nothing more about it after it does so.Like a rubber sheet, but in three dimensions, curvature dictates how all objects, including light, move when close to a mass.Black hole achieves this by severely curving space. According to Einstein's General Relativity, all masses curve space. Gravity and space curvature are equivalent.Curvature at event horizon is so great that space "folds in on itself", i.e. anything crossing it is trapped.Approaching a Black Hole:QuickTime™ and aYUV420 codec decompressorare needed to see this picture.Circling a Black Hole at the Photon Sphere:QuickTime™ and aYUV420 codec decompressorare needed to see this picture.Effects around Black Holes1) Enormous tidal forces.2) Gravitational redshift. Example, blue light emitted just outside event horizon may appear red to distant observer.3) Time dilation. Clock just outside event horizon appears to run slow to a distant observer. At event horizon, clock appears to stop.Black Holes