Presentation for perspective graduate students 2006

Astronomy 1 Fall 2014 Lecture 14; November 25, 2014

1Previously on Astro 1Late evolution and death of intermediate-mass stars (about 0.4 M to about 4 M): red giant when shell hydrogen fusion begins, a horizontal-branch star when core helium fusion beginsasymptotic giant branch star when the no more helium core fusion and shell helium fusion begins.Then alf of the mass of the star is ejected exposing the CO core of the star. The core is a white dwarf the envelope a planetary nebula. Late Evolution and death of High-Mass Star (>4 M) Can undergo carbon fusion, neon fusion, oxygen fusion, and silicon fusion, etcThe highest mass stars eventually find themselves with a iron-rich core surrounded by burning shells (>8 M). The star dies in a violent cataclysm in which its core collapses and most of its matter is ejected into space: a supernova!! 99% of the energy can come out in neutrinos!

Midterm 2 [U: ch 10, 16-20]Key TopicsTidal Forces [10]Origin of Moon [10]H Fusion & Lifetime of Sun [16]Stellar Parallax as a distance measure[17]Luminosity Mass Relation of stars [17]Kelvin-Helmholtz Contraction [18]Mass lifetime relation for stars [19]Cepheid Period Luminosity Relationas a distance indicator [19]Type Ia Supernova as distance indicators [20]Nucleosynthesis of the elements [19,20]Formation of white dwarfs, neutron stars, and black holes [19,20]Evolutionary path of the Sun in the HR diagram [19,20]

Today on Astro-1Introduction to special relativityIntroduction to general relativityIntroduction to black holes stellar mass black holes [U: 21]Supermassive black holes [see also U: 24]

Introduction to special relativity

The speed you measure for ordinary objects depends on how you are moving.6Figure 22-1 The Speed of Light Is the Same to All Observers (a) The speed you measure for ordinary objects depends on how you are moving. Thus, thebatter sees the ball moving at 30 m/s, but the outfielder sees it movingat 40 m/s relative to her.

7Figure 22-1 The Speed of Light Is the Same to All Observers (a) The speed you measure for ordinary objects depends on how you are moving. Thus, thebatter sees the ball moving at 30 m/s, but the outfielder sees it movingat 40 m/s relative to her.

No matter what your constant velocity, the laws of physics are the same.Einsteinsspecial theoryof relativity (1905)

Einstein in 19058How Can You Tell If This Airplane is Moving?

You are on a windowless airplane and cannot see outside. The ride is extremely smooth. Is it possible to make a measurement inside the airplane to determine whether you are moving or are stationary? Yes. Drop an object and see if it falls vertically or is deflected backward. Yes. Shine a light forward up the aisle and backward down the aisle and measure the difference in their speeds. Yes. Throw one ball forward down the aisle and throw a second ball backward down the aisle. Then determine which one went further. No. There is no experiment that you can do inside the train to determine whether the train is moving at constant speed or is stationary. Q21.3You are on a windowless airplane and cannot see outside. The ride is extremely smooth. Is it possible to make a measurement inside the airplane to determine whether you are moving or are stationary? Yes. Drop an object and see if it falls vertically or is deflected backward. Yes. Shine a light forward up the aisle and backward down the aisle and measure the difference in their speeds. Yes. Throw one ball forward down the aisle and throw a second ball backward down the aisle. Then determine which one went further. No. There is no experiment that you can do inside the train to determine whether the train is moving at constant speed or is stationary. Q21.3No matter what your constant velocity, the laws of physics are the same.No matter what your constant velocity, the speed of light in a vacuum is the sameEinsteinsspecial theoryof relativity (1905)

Einstein in 190512

What speed of light does each astronaut measure?13Figure 22-1 The Speed of Light Is the Same to All Observers (b) Einstein showed that this commonsenseprinciple does not apply to light. No matter how fast or in what directionthe astronaut in the spaceship is moving, she and the astronaut holdingthe flashlight will always measure light to have the same speed.

Spacetime = 3 spatial dimensions + time14Figure 22-1 The Speed of Light Is the Same to All Observers (b) Einstein showed that this commonsenseprinciple does not apply to light. No matter how fast or in what directionthe astronaut in the spaceship is moving, she and the astronaut holdingthe flashlight will always measure light to have the same speed.

Space and time are intertwined in SR

An Interesting Consquence of All Observers Measuring the Same Speed of Light!15A friend takes a ride on a spaceship to a distant star and returns to Earth. You and your friend were the same age when your friend left on the spaceship. When your friend returns shewill be the same age as you. will be younger than you. will be older than you.will be two times older than you. could be older or younger than you depending on the speed during the journey. Q21.4A friend takes a ride on a spaceship to a distant star and returns to Earth. You and your friend were the same age when your friend left on the spaceship. When your friend returns shewill be the same age as you. will be younger than you. will be older than you.will be two times older than you. could be older or younger than you depending on the speed during the journey. Q21.4Consequence: TIME DILATION

T = time interval measured by an observer moving relative to the phenomenon

T0 = time interval measured by an observer not moving relative to the phenomenon (proper time)

v = speed of the moving observer relative to the phenomenon

c = speed of light18

19Question (iclickers!)Suppose you are in a spaceship traveling toward Earth at 95% of the speed of light. Compared to when your ship was at rest on Mars, you measure the length of your ship to be:A) The same as when it was on MarsB) Longer than when it was on MarsC) You cant tell. Your life processes have slowed down too much for you to measure the lengthD) Shorter than when it was on Mars

Question (iclickers!)Suppose you are in a spaceship traveling toward Earth at 95% of the speed of light. Compared to when your ship was at rest on Mars, you measure the length of your ship to be:A) The same as when it was on MarsB) Longer than when it was on MarsC) You cant tell. Your life processes have slowed down too much for you to measure the lengthD) Shorter than when it was on Mars

Consequence: LENGTH CONTRACTIONL = length measured (along the direction of motion) by an observer moving relative to the phenomenon

L0 = length measured by an observer not moving relative to the phenomenon (proper length)

v = speed of the moving observer relative to the phenomenon

c = speed of light

22Example of Special Relativity: Muon Decay in Earths AtmosphereAn unstable particle called a muon is produced when fast moving protons from interstellar space collide with atoms in Earths upper atmosphere.The muons move at speeds close to the speed of light.Special relativity helps us understand the high flux of muons that reach Earths surface.An unstable particle called a muon is produced when fast moving protons from interstellar space collide with atoms in Earths upper atmosphere.

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An unstable particle called a muon is produced when fast moving protons from interstellar space collide with atoms in Earths upper atmosphere.

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An unstable particle called a muon is produced when fast moving protons from interstellar space collide with atoms in Earths upper atmosphere.

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An unstable particle called a muon is produced when fast moving protons from interstellar space collide with atoms in Earths upper atmosphere.

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An unstable particle called a muon is produced when fast moving protons from interstellar space collide with atoms in Earths upper atmosphere.

27Introduction to general relativity

(Includes Gravity)The downward pull of gravity can be accurately and completely duplicated by an upward acceleration of the observer.

Gravity can be described as a property of spacetime!The Equivalence Principle (1915)29EP allowed Einstein focus on motion instead of force in discussing gravity.

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31Note that photons can be affected by gravity now!

GR Predicts the Deflection of Light32Eclipse of 1919

Explains the Precession of Mercurys Orbit33Most of Mercurys precession is caused by the gravitaitonal pull of the other planets.

There remained an excess rotation of 43 per century.A prediction ofEinsteins general theory of relativity:Gravitational time dilation

34Another prediction: Gravitational Waves (Ripples in Spacetime)

Question (iclickers!)Suppose you are far from a planet that has a very strong gravitational field, and you are watching a clock on the surface of the planet. During the time in which your own clock ticks out a time of 1 hour, how much time does the clock on the planet tick out?A) More than 1 hourB) No time at allC) Exactly 1 hour, the same as your clockD) Less than 1 hour

Question (iclickers!)Suppose you are far from a planet that has a very strong gravitational field, and you are watching a clock on the surface of the planet. During the time in which your own clock ticks out a time of 1 hour, how much time does the clock on the planet tick out?A) More than 1 hourB) No time at allC) Exactly 1 hour, the same as your clockD) Less than 1 hour

General Relativity Predicts Black Holes

Do They Really Exist?

39Structure of a black holeSchwarzschild radius RSch = 2GM/c2

The event horizon is the point where the escape velocity equals the speed of light. It is the point of no return.

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Schwarzschild radiusof a 1-solar-massblack hole= 3 kilometers 42Stellar Mass Black Holes

44Figure 20-14 A Core-Collapse Supernova This series of illustrations depicts ourunderstanding of the last day in the life of a star of more than about8 M. (Illustration by Don Dixon, adapted from Wolfgang Hillebrandt,Hans-Thomas Janka, and Ewald Mller, How to Blow Up a Star, ScientificAmerican, October 2006)

45Figure 20-26 A Summary of Stellar Evolution (a) The evolution of an isolated star (one that is not part of a close multiple-starsystem) depends on the stars mass. The more massive the star, the morerapid its evolution. The scale on the left gives the mass of the star whenit is on the main sequence, and the scale at the right shows the mass ofthe resulting stellar corpse. If the stars initial mass is less than about0.4 M , it evolves slowly over the eons into an inert ball of helium. If theinitial mass is in the range from about 0.4 M to about 8 M , it ejectsenough mass over its lifetime so that what remains is a white dwarf witha mass less than the Chandrasekhar limit of 1.4 M . If the stars initialmass is more than about 8 M it ends as a core-collapse supernova,leaving behind a neutron star or black hole.

The larger member of the Cygnus X-1 system is a B0 supergiant of about 30 M. The other, unseen member of the system has a mass of at least 7 M and is probably a black hole. 46Figure 22-11 The Cygnus X-1 System (a) The larger member of theCygnus X-1 system is a B0 supergiant of about 30 M. Theother, unseen member of the system has a mass of at least 7 M and isprobably a black hole. (b) This illustration shows how the Cygnus X-1system might look at close range. (The illustration that opens thischapter depicts a similar system.) At even closer range, the black holeand its immediate surroundings might appear as shown in Figure 22-12.(Courtesy of D. Norton, Science Graphics)

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50Supermassive black holes

52Figure 22-12 The Environment of an Accreting Black Hole If a black hole is rotating, it can generate strong electric and magnetic fields in itsimmediate vicinity. These fields draw material from the accretion diskaround the black hole and accelerate it into oppositely directed jets alongthe black holes rotation axis. This illustration also shows other featuresof the material surrounding such a black hole. (CXC/M. Weiss)

Galactic Center (Ghez Group/UCLA)iClicker QuestionCalculate the Schwarzschild radius (RS = 2GM/c2) of the 4 million solar mass black hole at the center of the Milky Way Galaxy.[Hint: G = 6.67E-11 m2/kg2)1.2 X 1010 m (or 17 R0)1.2 cm10 kpc (the size of the galaxy)10-10 m (the size of an atom)1.2 Mpc (the distance to Andromeda Galaxy)iClicker QuestionCalculate the Schwarzschild radius (RS = 2GM/c2) of the 4 million solar mass black hole at the center of the Milky Way Galaxy.[Hint: G = 6.67E-11 m2/kg2)1.2 X 1010 m (or 17 R0)1.2 cm10 kpc (the size of the galaxy)10-10 m (the size of an atom)1.2 Mpc (the distance to Andromeda Galaxy)

Gravitational energy is extracted from matter falling into the black hole~0.1 mc2 compared to 0.007 mc2 from fusion. 1 marshmallow = Hiroshima56Figure 22-16 A Supermassive Black Hole The galaxy NGC 4261 lies some 30 million pc (100 million ly)from Earth in the constellation Virgo. (a) This compositeview superimposes a visible-light image of the galaxy(white) with a radio image of the galaxys immense jets(orange). (b) This Hubble Space Telescope image shows adisk of gas and dust about 250 pc (800 ly) across at thecenter of NGC 4261. Observations indicate that asupermassive black hole is at the center of the disk.(NASA, ESA)

57Black holes can be detected by the X rays they emit. How are these X rays produced?Black holes are very hot and radiate X rays from within their event horizon. In the accretion disk around the black hole, matter is moving rapidly enough that any light emitted is blueshifted to the X-ray range. Friction within the accretion disk heats up matter to temperatures high enough that the matter radiates in the X-ray range. The intense gravitational field causes electromagnetic frequencies to increase, shifting them into the X-ray range. Q21.8Black holes can be detected by the X rays they emit. How are these X rays produced?Black holes are very hot and radiate X rays from within their event horizon. In the accretion disk around the black hole, matter is moving rapidly enough that any light emitted is blueshifted to the X-ray range. Friction within the accretion disk heats up matter to temperatures high enough that the matter radiates in the X-ray range. The intense gravitational field causes electromagnetic frequencies to increase, shifting them into the X-ray range. A21.8iClicker QuestionThe Galactic Center is 8 kpc from the Sun. What is the angular size (radius) of the event horizon of the black hole at the center of the Milky Way galaxy? [Recall: RS=17 R0 = 1.2E10 m and D = a()d/206265]Half a degree (similar to the full moon)About 1 arcminuteAbout 1 arcsecondAbout 1 milli-arcsecondAbout 10 micro-arcsecondsiClicker QuestionThe Galactic Center is 8 kpc from the Sun. What is the angular size (radius) of the event horizon of the black hole at the center of the Milky Way galaxy? [Recall: RS=17 R0 = 1.2E10 m and D = a()d/206265]Half a degree (similar to the full moon)About 1 arcminuteAbout 1 arcsecondAbout 1 milli-arcsecondAbout 10 micro-arcsecondsiClicker QuestionHow large a telescope would you need to resolve the shadow of the event horizon of the black hole at the center of the Milky Way galaxy? Assume you observe at a wavelength of 1.3mm to see through the dust. [Hint: Angular radius of 10 micro-arcseconds and diffraction limit is q = 2.5E5 l/D)Diameter of 3 X 107 m (earth size)Diameter of the size of the galaxyDiameter of 10-10 m (the size of an atom)Diameter of 10 m (like the Keck telescopes)The size of the solar system.iClicker QuestionHow large a telescope would you need to resolve the shadow of the event horizon of the black hole at the center of the Milky Way galaxy? Assume you observe at a wavelength of 1.3mm to see through the dust. [Hint: Angular radius of 10 micro-arcseconds and diffraction limit is q = 2.5E5 l/D)Diameter of 3 X 107 m (earth size)Diameter of the size of the galaxyDiameter of 10-10 m (the size of an atom)Diameter of 10 m (like the Keck telescopes)The size of the solar system.Event Horizon Telescope

Simulation: Event Horizon Telescope Picture of Sagittarius A*

More Properties of Black Holes

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71SummaryThe Special Theory of Relativity:The laws of physics are the same in any (intertial) reference frameThe speed of light is the same to all observersAn observer will note a slowing of clocks and a shortening of rulers that are moving with respect to them. Space and time are aspects of a single entity called spacetime. The General Theory of Relativity: Inertial mass and gravitational mass are the sameGravity = accelerationGravity is nothing but the distortion of spacetime by massPredicts bending of light by gravity, gravitational redshift and gravitational wavesBlack Holes: A stellar corpse with mass greater than 3 ~M, will collapse under gravity. Will be so dense that not even light can escape.Homework (Due Friday 12/04)Do all review questions from ch. 21 on your own.For TAs, do 21.34. 21.36, 21.47, 21.50According to general relativity, a beam of light bends as it passes close to a massive object becausethe massive object exerts an electromagnetic force on the photons. the photons exert an electromagnetic force on the massive object. it follows the curvature of the space around the massive object. the speed of light increases.the speed of light decreases.Q21.6According to general relativity, a beam of light bends as it passes close to a massive object becausethe massive object exerts an electromagnetic force on the photons. the photons exert an electromagnetic force on the massive object. it follows the curvature of the space around the massive object. the speed of light increases.the speed of light decreases.A21.6