A100 Exploring the Universe: Stellar Remnants. Martin D. Weinberg UMass Astronomy

A100 Exploring the Universe: Stellar Remnants Martin D. Weinberg UMass Astronomy astron100-mdw@courses.umass.edu March 24, 2015 Read: S3, Chap 18 03/24/15 slide 1

Exam #2: March 31 One week from today! Covers Chaps: 14, 15, (16), 17, 18, (S3), (S4) ( ) means covered in part Read: S3, Chap 18 03/24/15 slide 2

Exam #2: March 31 One week from today! Covers Chaps: 14, 15, (16), 17, 18, (S3), (S4) ( ) means covered in part Today: Review: white dwarf Origin Features Read: S3, Chap 18 03/24/15 slide 2

Exam #2: March 31 One week from today! Covers Chaps: 14, 15, (16), 17, 18, (S3), (S4) ( ) means covered in part Today: Review: white dwarf Origin Features Questions? Read: S3, Chap 18 03/24/15 slide 2

After a star has burned out its fuel supply, its remnants can take one of three forms, depending on its initial mass 1. (which eventually become black dwarfs) 2. 3. Black holes Read: S3, Chap 18 03/24/15 slide 3

are the remaining cores of dead stars Electron degeneracy pressure supports them against gravity Read: S3, Chap 18 03/24/15 slide 4

are the remaining cores of dead stars Electron degeneracy pressure supports them against gravity Read: S3, Chap 18 03/24/15 slide 4

White dwarf cooling cool off and grow dimmer with time Eventually become too dim to observe = black dwarf Read: S3, Chap 18 03/24/15 slide 5

White dwarf cooling cool off and grow dimmer with time Eventually become too dim to observe = black dwarf Read: S3, Chap 18 03/24/15 slide 5

White dwarf size with same mass as Sun About same size as Earth (!) Higher mass white dwarfs are smaller (why?) Read: S3, Chap 18 03/24/15 slide 6

White dwarf limit Quantum mechanics says that electrons must move faster as they are squeezed into a very small space As a white dwarf s mass approaches 1.4M Sun, its electrons must move at nearly the speed of light Because nothing can move faster than light, a white dwarf cannot be more massive than 1.4M Sun, the white dwarf limit (or Chandrasekhar limit) Read: S3, Chap 18 03/24/15 slide 7

White dwarf limit Quantum mechanics says that electrons must move faster as they are squeezed into a very small space As a white dwarf s mass approaches 1.4M Sun, its electrons must move at nearly the speed of light Because nothing can move faster than light, a white dwarf cannot be more massive than 1.4M Sun, the white dwarf limit (or Chandrasekhar limit) Mass distribution for common white dwarf type Peak: 0.56 M sun Read: S3, Chap 18 03/24/15 slide 7

White dwarf binary Star that started with less mass gains mass from its companion Eventually the mass-losing star will become a white dwarf Next the companion star evolves, transferring mass to the white dwarf What happens next? Read: S3, Chap 18 03/24/15 slide 8

White dwarf binary Star that started with less mass gains mass from its companion Eventually the mass-losing star will become a white dwarf Next the companion star evolves, transferring mass to the white dwarf What happens next? Read: S3, Chap 18 03/24/15 slide 8

White dwarf binary Star that started with less mass gains mass from its companion Eventually the mass-losing star will become a white dwarf Next the companion star evolves, transferring mass to the white dwarf What happens next? Read: S3, Chap 18 03/24/15 slide 8

Accretion disks Mass falling toward a white dwarf from its close binary companion has some angular momentum Spin increases as it falls (i.e. figure skater) The matter therefore orbits the white dwarf in an accretion disk Read: S3, Chap 18 03/24/15 slide 9

Accretion disks Friction between orbiting rings of matter in the disk transfers angular momentum outward and causes the disk to heat up and glow Read: S3, Chap 18 03/24/15 slide 9

The temperature of accreted matter eventually becomes hot enough for hydrogen fusion Fusion begins suddenly and explosively, causing a nova Read: S3, Chap 18 03/24/15 slide 10

The nova star system temporarily appears much brighter The explosion drives accreted matter out into space Read: S3, Chap 18 03/24/15 slide 11

Two types of supernova Massive star supernova Iron core of massive star reaches white dwarf limit and collapses into a neutron star, causing explosion White dwarf supernova Carbon fusion suddenly begins as white dwarf in close binary system reaches white dwarf limit, causing total explosion Read: S3, Chap 18 03/24/15 slide 12

Two types of supernova Light curves differ (how luminosity changes with time) Spectra differ (exploding white dwarfs don t have hydrogen absorption lines) Read: S3, Chap 18 03/24/15 slide 13

or supernova? Supernovae are MUCH MUCH more luminous!!! (about 10 thousand times) : H to He fusion of a layer of accreted matter, white dwarf left intact Supernova: complete explosion of white dwarf, nothing left behind Read: S3, Chap 18 03/24/15 slide 14

Supernova as standard candles Standard candle: an object whose luminosity is known and reveals its distance by a brightness measurement Data suggests that white-dwarf light curves are always similar Possibly a consequence of Chandrasekhar mass limit?! Good standard candles Another rung on the distance ladder... Read: S3, Chap 18 03/24/15 slide 15

What is a neutron star? A neutron star is the ball of neutrons left behind by a massivestar supernova Degeneracy pressure of neutrons supports a neutron star against gravity Read: S3, Chap 18 03/24/15 slide 16

What is a neutron star? Electron degeneracy pressure goes away because electrons combine with protons, making neutrons and neutrinos Roughly 10 57 neutrinos created in the iron core as protons are converted to neutrons Neutrons collapse to the center, forming a neutron star Approx. 10 km in radius (size of Amherst!) Strong magnetic fields Read: S3, Chap 18 03/24/15 slide 17

of neutron stars Using a radio telescope in 1967, Jocelyn Bell noticed very regular pulses of radio emission coming from a single part of the sky The pulses were coming from a spinning neutron star a pulsar Read: S3, Chap 18 03/24/15 slide 18

Read: S3, Chap 18 03/24/15 slide 19

Observable in X-ray R = 10 km = 0.000014 R T = 10 6 K = 170 T Wien s law x-ray Read: S3, Chap 18 03/24/15 slide 20

Observable in X-ray R = 10 km = 0.000014 R T = 10 6 K = 170 T Wien s law x-ray How much luminosity? L n /L = (R n /R ) 2 (T n /T ) 4 = 0.2 Read: S3, Chap 18 03/24/15 slide 20

A pulsar is a neutron star that beams radiation along a magnetic axis that is not aligned with the rotation axis The radiation beams sweep through space like lighthouse beams as the neutron star rotates Read: S3, Chap 18 03/24/15 slide 21

Magnetic fields in neutron stars Circulating electic currents in the Earth s molten metalic core generate a magnetic field Current loop Similar in Sun Read: S3, Chap 18 03/24/15 slide 22

Magnetic fields in neutron stars Rapidly rotating: Frequency: 1000 rotations/second (1 rotation/month for the Sun) Due to conservation of ang mom (recall skater) Read: S3, Chap 18 03/24/15 slide 23

Magnetic fields in neutron stars Rapidly rotating: Frequency: 1000 rotations/second (1 rotation/month for the Sun) Due to conservation of ang mom (recall skater) Strongly magnetized: 10 12 Gauss (1 and 0.5 Gauss for the Sun & Earth) Why? Magnetic field lines are conserved and compressed as star collapses. Read: S3, Chap 18 03/24/15 slide 23

Magnetic fields in neutron stars Rapidly rotating: Frequency: 1000 rotations/second (1 rotation/month for the Sun) Due to conservation of ang mom (recall skater) Strongly magnetized: 10 12 Gauss (1 and 0.5 Gauss for the Sun & Earth) Why? Magnetic field lines are conserved and compressed as star collapses. Very hot: 10 6 K at surface after collapse (5800 K for Sun) Read: S3, Chap 18 03/24/15 slide 23

Magnetic fields in neutron stars Read: S3, Chap 18 03/24/15 slide 24

Why pulsars must be neutron stars Circumference of NS = 2π(radius) 60 km Spin Rate of Fast 1000 cycles per second Surface Rotation Velocity 60,000 km/s 20% speed of light escape velocity from NS! Read: S3, Chap 18 03/24/15 slide 25

Why pulsars must be neutron stars Circumference of NS = 2π(radius) 60 km Spin Rate of Fast 1000 cycles per second Surface Rotation Velocity 60,000 km/s 20% speed of light escape velocity from NS! Read: S3, Chap 18 03/24/15 slide 25

Why pulsars must be neutron stars Circumference of NS = 2π(radius) 60 km Spin Rate of Fast 1000 cycles per second Surface Rotation Velocity 60,000 km/s 20% speed of light escape velocity from NS! Read: S3, Chap 18 03/24/15 slide 25

Why pulsars must be neutron stars Circumference of NS = 2π(radius) 60 km Spin Rate of Fast 1000 cycles per second Surface Rotation Velocity 60,000 km/s 20% speed of light escape velocity from NS! Anything else would be torn to pieces! Read: S3, Chap 18 03/24/15 slide 25

Quantum mechanics says that neutrons in the same place cannot be in the same state Neutron degeneracy pressure can no longer support a neutron star against gravity if its mass exceeds about 3 M Sun Beyond the neutron star limit, no known force can resist the force of gravity Gravity crushes all the matter into a single point known as a singularity Read: S3, Chap 18 03/24/15 slide 26

Stellar evolution Black Holes A star with M > 18M Sun would leave behind an iron core more massive than 2-3 M Sun Neutron degeneracy pressure would fail with nothing to stop its gravitational collapse Core would collapse into a singularity! Gravity becomes so strong that nothing, not even light, can escape Infalling matter is shredded by powerful tides Black hole! Black because they neither emit nor reflect light Hole because nothing entering can ever escape Read: S3, Chap 18 03/24/15 slide 27

Stellar evolution Black Holes A star with M > 18M Sun would leave behind an iron core more massive than 2-3 M Sun Neutron degeneracy pressure would fail with nothing to stop its gravitational collapse Core would collapse into a singularity! Gravity becomes so strong that nothing, not even light, can escape Infalling matter is shredded by powerful tides Black hole! Black because they neither emit nor reflect light Hole because nothing entering can ever escape Read: S3, Chap 18 03/24/15 slide 27

Stellar evolution Black Holes A star with M > 18M Sun would leave behind an iron core more massive than 2-3 M Sun Neutron degeneracy pressure would fail with nothing to stop its gravitational collapse Core would collapse into a singularity! Gravity becomes so strong that nothing, not even light, can escape Infalling matter is shredded by powerful tides Black hole! Black because they neither emit nor reflect light Hole because nothing entering can ever escape Read: S3, Chap 18 03/24/15 slide 27

Stellar evolution Black Holes A star with M > 18M Sun would leave behind an iron core more massive than 2-3 M Sun Neutron degeneracy pressure would fail with nothing to stop its gravitational collapse Core would collapse into a singularity! Gravity becomes so strong that nothing, not even light, can escape Infalling matter is shredded by powerful tides Black hole! Black because they neither emit nor reflect light Hole because nothing entering can ever escape Read: S3, Chap 18 03/24/15 slide 27

is conserved: a quick review Definition: is the capacity of a physical system to do work Definition: Work is application of force over a distance Read: S3, Chap 18 03/24/15 slide 28

Kinetic energy Example: kinetic energy from accelerating an object m v=0 d d m v=v f Push an object with a constant force over a distance d: final velocity v f Average velocity: v = v f 2 = d t Force required: F = ma = m v f t Work done (energy): E = Fd = mv fd t = 1 2 mv2 f Read: S3, Chap 18 03/24/15 slide 29

Potential energy Example: potential energy is energy that can be converted to kinetic energy by moving in a force field v=0 v=vf Ground level Potential energy is positive to start Kinetic energy is gained as ball rolls down hill Potential energy is zero at bottom of hill Read: S3, Chap 18 03/24/15 slide 30

Potential energy Example: potential energy is energy that can be converted to kinetic energy by moving in a force field v=0 Ground level v=vf v=vf v=0 Potential energy is zero at top of well Kinetic energy is gained as ball rolls into well Potential energy is negative at bottom of well Total energy (kinetic plus potential) is conserved Read: S3, Chap 18 03/24/15 slide 30

Need a critical value of velocity to escape the surface of a gravitating body To escape the gravitational pull of a planet, need an initial velocity that will make your total mechanical energy be unbound Total mechanical energy of a blob the energy of motion added to the energy given up by falling in: E = KE +PE = 1 2 mv2 GMm R Read: S3, Chap 18 03/24/15 slide 31

must be greater than zero to be unbound: 0 = 1 2 mv2 GMm R 2GM v esc = R [Just like ball rolling in the potential well] Examples: Earth: v esc = 11.2 km/s Moon: v esc = 2.4 km/s Read: S3, Chap 18 03/24/15 slide 32

must be greater than zero to be unbound: 0 = 1 2 mv2 GMm R 2GM v esc = R [Just like ball rolling in the potential well] Examples: Earth: v esc = 11.2 km/s Moon: v esc = 2.4 km/s Neutron star: v esc = 160,000 km/s = 0.53 c! Read: S3, Chap 18 03/24/15 slide 32

Radius For a given escape velocity and mass, we can compute the radius we need to just escape: R = 2GM v 2 esc Read: S3, Chap 18 03/24/15 slide 33

Radius For a given escape velocity and mass, we can compute the radius we need to just escape: R = 2GM v 2 esc Nothing moves faster than the speed of light... Read: S3, Chap 18 03/24/15 slide 33

Radius For a given escape velocity and mass, we can compute the radius we need to just escape: R = 2GM v 2 esc Nothing moves faster than the speed of light... Light cannot escape from a Black Hole if it comes from a radius closer than the Radius, R s : R s = 2GM c 2 where M is the mass of the hole. Read: S3, Chap 18 03/24/15 slide 33

Sizes of black holes Comparison: R s = 2GM c 2 0.6 M Sun White Dwarf: radius of 1 R earth = 6370 km 1.4 M Sun Neutron Star: radius of 10 km A black hole with a mass of 1 M Sun has R s =3 km Read: S3, Chap 18 03/24/15 slide 34