neutron-stars - ‘ 'r r-'.:: a n ounceme‘fi‘ . due...

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Unformatted text preview: ‘ 'r r-'.:: a n ounceme‘fi‘ . due Thurs. Mar. i S on April 5, 2011 ill be the same as the first exam I'.’ entrate on the material since the last exam (including res on the Sun). _ 0rk #6 solutions will be posted electronically just after on Fir. xam Extra Credit #2 assigned (due in class on the day of the exam) NASA, NOAO, ESAand The Hubble Heritage Team (STSCI/ AURA) Neutron Stars/Pulsars/Black Holes (Kulner, Ch. 11) AST 203 (Spring 2011) Neutron Stars Neutron stars can show a wide variety of activity that make it possible to determine information about them. They can exhibit thermonuclear explosions of material dumped onto their surface from a binary companion, They can act as pulsars. Pulsars: rapidly spinning neutron stars that emit electromagnetic radiation at their magnetic poles. As they spin around, they act as lighthouses, with their beam briefly entering and exiting our line of sight. AST 203 (Spring 2011) Neutron Stars Neutron stars are one of the end states of massive star evolution. We know of a number of supernova remnants and sometimes we see a neutron star. The gas surrounding the neutron star is the outer layers that were mWNW/EurekaWMMMWL ejected during the explosion. Chandra image of the supernova remnant G11 .2—03. This star exploded in 386 AD. The white dot in the center is a neutron star. (http://chandra.harvard.edu/photo/2007/g1 1/) AST 203 (Spring 2011) Supernova Remnants Crab nebula—remnant creme Museum of a core-collapse supernova (1054). X-rays (blue/purple) optical (green) infrared (red) Bright point at center: rapidly spinning ,. III II’,//L:llANLmA HANVARLLLlJLl Credit: NASA- X-my: CXC, J.Hester (ASU) et al.; Optical: ESA, J.Hesler and A.L0|| (ASU); Infrared: JPL—Caltech. R.Gehrz (U. Minn) AST 203 (Spring 2011) Supernova Remnants Supernova remnants have strong Mayne“: magnetic fields. Produce radiation from electrons interacting with magnetic fields. A charged particle in a magnetic field will experience a force proportional to ’9; my": 6 X B‘ (Gemini) Electrons will spiral around the magnetic field lines. Accelerating changes radiate—synchrotron radiation. AST 203 (Spring 2011) Supernova Remnants Synchrotron radiation non-thermal—spectrum not a blackbody. Furthermore, the radiation is polarized. Most of the radiation is in long wavelengths, and the intensity falls off as wavelength raised to some power—a power law. Spiraling electrons radiate energy—they must be slowing down. For the Crab nebula, the radiation is still strong 1000 years after the explosion—something continues to energize the remnant... AST 203 (Spring 2011) Spinning Neutron Stars How fast do neutron stars spin? Consider collapsing the Sun's down to the size of a neutron star, conserving angular momentum. The angular momentum of an object can be written as J = Iw where w is the angular speed (# of rotations/second) and I is the moment of inertia. For a uniform sphere, the moment of inertia is 2 I : —MR2 5 AST 203 (Spring 2011) Spinning Neutron Stars Shrink Sun down to neutron star size, conserving angular momentum: 2 2 wQRG = szRNS (w) : (&)2_ (7_><10106m)2_2x109 019 RNS 1.5 X 106 cm The rotation period of the Sun is 30 days (2.6 x 106 s), and P N 1/u) 30 So our neutron star period is PNS ~ 1.3 X 10—3 s A neutron star could be rotating 1000 times per second! AST 203 (Spring 2011) Neutron Star Magnetic Fields Magnetic flux conservation: Magnetic flux is the number of field lines x the surface area that they pass through. The number of field lines isjust another way of measuring the magnetic field strength. Flux conservation tells us that B®R2 = BNSRfis 30 Magnetic fields in neutron stars can be enormous. AST 203 (Spring 2011) Pulsars Antony Hewish and Jocelyn Bell Burnell found a rapidly varying radio source (1967). Signal was composed of pulses, with a very regular period. Eventually more such sources were found. A. G. Lyne and F. G. Smith. PulsarAstronomy. Cambridge Univelsity Press, 1990.; http://www.atnf.csir0.au/reseaIch/pulsar/Tutorial/tut/node3html These sources were named g. l 1 l l l l l l l l pulsars. E l l l l UW Olllléllll‘llolllI‘IISIIII2IO (from Bennett et al.) time (seconds) AST 203 (Spring 2011) Mllky Way 101 halo: spherically symmetric distribution of older stars. Density falls off with distance from galactiy center disk: distribution of stars orbiting the galactic center in the thin plane“”" b U I g e : dISk $m‘slloca1ion 1.000 lighl-years < ._ I » 3/ Spherical distribution surrounding the galactic center. _ 100.000 light-years (from Bennett et al.) Wigwam mmnmw WW "gamwww AST 203 (Spring 2011) Pulsars The distribution of known pulsars shows that they are concentrated in the disk of the galaxy—they are in our galaxy. If they were outside of our galaxy, we would expect to see them uniformly distributed in the sky. :H :0: :N: :U‘: 530 TAYLOR, MANCHESTER, & LYNE Vol. 88 b=90. =-90' F IG, l.-—Distribu1i0n ofSSS pulsars in Galactic coordinates, using the Hammer-Aitolf equal-area projection The Galactic center is in the middle othc As figure, and longitude increases toward the left. Pulsars o A wide range of periods ‘ 7 are observed in pulsars— from milliseconds to a , second. 2 ‘8 m These may have been 7 ’ “spun-up" via accretion. C, : Silt: Efgii‘iiiil‘ude {\2 + Swmburne Mullibcam * ‘ A RRATS ‘i‘r AXPs ' other pulsars 7 3 7 2 7 l 0 l R. N. Manchester, CSIROIATNF Aglpggm‘uhfiérgdfiifo.aulnewslnewsletterljunOG/RRATs.htm 1 0g [P am 0d (5)] What Are Pulsars? Signals from ET? Physical explanations: pulsation orbital motion rotation AST 203 (Spring 2011) What Are Pulsars? Pulsation timescale is t N (Gle/Q The densities needed to explain the observed periods is higher than a WD but lower than we get in a neutron star. Pulsation of a stellar object can be rejected. AST 203 (Spring 2011) What Are Pulsars? Orbital motion: the period/separation of a binary system is 47TZR3 G P = 1 5 implies R ~ 2000 km, P = 0.1 s, R ~ 100 km. These R < radius of a normal star or white dwarf. 2 (m1 + mg)P2 Two neutron stars could work though. Pulsar radiates —> orbital E decreases —> system more bound (smaller R). Decrease in R —> decrease in P (GR also says that this system emits gravitational radiation). Observations of pulsars show that the periods increase slowly with time, not decrease—orbital motion cannot explain pulsars. AST 203 (Spring 2011) What Are Pulsars? The final mechanism to consider is rotation. To stay intact: gravitational force on the outer layers > centripetal force resulting from the rotation. GMm mt)2 R2>R Now, 1] : 27rR/P, so 479133 G This eliminates normal stars and white dwarfs, but leaves neutron stars as a viable option. <MP2 AST 203 (Spring 2011) Pulsars Pulsar: beamed emission from the magnetic poles of a neutron star, rotating in and out of our view. (Vlnkipedia/UserMysid, UsenJm smils) The period is related to the rotation rate of the neutron star—we are directly measuring the spin rate of the neutron star. AST 203 (Spring 2011) Pulsars Details of the emission are not fully understood. Strong, rotating magnetic field = electric field Charged particles come off NS surface at high speed Emission mechanism due to relativistic energies. (Vlnkipedia/UserMysid, UsenJm smils) Misalignment of the rotation and magnetic poles (like on Earth) mean that the magnetic poles come into and out of view. AST 203 (Spring 2011) Crab Nebula CRFIB NEBLILFI The Crab nebula contains a pulsar Neutron stars are the underlying engine. Pulsars are associated with stellar death. The Crab nebula is radiating away energy—the pulsar is energizing it. H| l F,:"./'CHANURA.HANVARLI.I;UU Credit: X-ray: NASA/CXC/ASU/JHester at al.; Optical: NASA/ESA/ASU/JHester Ii A.L0||; Infrared: NASA/JPL- Canaan/Univ. Minn./R.Gehr AST 203 (Spring 2011) Crab Nebula http://www.noao.edulimage_galleiylhlmllim0565.hlml . .Sh Nvo/AURNNSF AST 203 (Spring 20% am] Crab Nebula Close up of the Crab pulsar showing activity surrounding the neutron star. X-ray (blue) and optical (red) are shown. Time-lapse movie of rings moving around the crab pulsar, taken by HST and Chandra. http:/Ichandra.haward.edu/photo/2002/0052/movies.hlml (NASNCXC/ASU/J. Hester et al.; http:/thbblesiteorg/newsoenter/arohivelreleaseleOOZ/ZNimage/a) AST 203 (Spring 2011) Pulsars I... Q _ J 1 ‘l' - _1_T + Pulsars slow down—periods increase. 3 \\ . E \. The faster the pulsar, In general, the ‘~ \ faster it is slowing down. Faster pulsars = youngest. E3 ‘ Pulsar period increase = slower m “m aim m m Period :hangesl‘ormaCnbpulsanThegeneral sluwriown is :lunGlitches.brivef period increasestare indicated ‘ by the locations of the an‘cvws.{fllchatl KramerILyne 8; Smith Pulsar Astronomy. 1nd edn. CUP] urom nuIner) Pulsar lifetime can be estimated spin down rate t ~ 104 yr See your text for the derivation. AST 203 (Spring 2011) Pulsars The rate at which the Crab pulsar is losing energy balances the rate at which the Crab nebula is losing energy by synchrotron radiation The pulsar that powers the nebula. Magnetic field couples pulsar and nebula AST 203 (Spring 2011) Pulsars d I. 2501 L fififr Some pulsars also show period g f" glitches—sudden changes likely due + f to sudden changes in the neutron 3 star radius—star q ua kes. " “Timid” 23m :6”: 2422365? 53.20“ — {lg-4+ r: 445? E as mi — f”. _ E a” Hf Si Fig. 16 + nfizmu - +4} ‘F Jr .. 5:242”; " €91 f 1 89 2725 i I"- “wt-l- uff f“ 1 W W timetable,52:22:55" 1“ AST 203 (Spring 2011 ) Fig. I. Plan ar the pulsar period dctcnnmpd daily about the time at occurrence at each oflhe LIII'BC periodjumps. (MECulloch, P. M. at all 1937,Aust.l Phys 40, 725) Binary Pulsars Some pulsars have been found in binary systems l U1 companion often a white dwarf or neutron star I ._| O orbit decays due to gravitational radiation | |_l U'I important test of GR Double pulsars exist. I N U1 Cumulative period shift (5) J; L O O I LU ()1 —40 1975 1980 1985 1990 1995 2000 2005 Year binary star system PSR B1913+16 (\Mkipedia I InductiveLoad) AST 203 (Spring 2011) Stellar Black Holes As we saw, above 1.4 MG, electron degeneracy pressure can not support the mass of a white dwarf, and it collapses. When it approaches nuclear densities, neutron degeneracy pressure (and more exotic interactions from nuclear forces) support the neutron star. This can work up to ~ 3 MO. Beyond this, the neutron star is also not stable, and it will collapse. The star will become a black hole. AST 203 (Spring 2011) Some neutron star masses have been found by observi AST 203 (Spring 2011) A very massive compact object will have an escape velocity > c Maximum Neutron Star Mass ng binary systems. 66 IBM in NGC 644! I—‘—.‘—l HH in use 5752 I 5 i-oi i—o——im n ' "F3? (Lattimer) 0.5 1.0 L5 2.0 Neutron stor moss (Me) What is a black hole? (Bennett et al. Ch. 18) Light cannot escape Event horizon: boundary beyond which light cannot escape Nothing that enters inside the event horizon can escape General relativity: massive objects distort spacetime. Gravity is represented by curvature in spacetime. AST 203 (Spring 2i 3 A tworzlimenyonal representation ot’ “flat” h A mass affects the ruboer sheet Similarly spacetime :ach pair oi axles is separated 3y to the may gravlty curves spacetime The the same radial crstance, Circles Deco we more Widely separated i ll1dlCa’tll’lg greater curvature 7 as We move closer to .l'ie mass. cowrtriom venison 2mm“ in: oublishmg ;; Piano” Addison Wailsy event ll'Jl mil :2 The curvature of spacetime becomes greater and greater as we aoproach a black he 6, and a black hole itself 3 a bottomless pit lrl spacetime, (from Bennett et al.) taunted in November‘ zoio iJ—‘o-i—ll pha— K»ro O ticul _. [2/5 a double _ t : I neu rpn s or ‘fluhI—Ynylu pulsar banI’IES - I a p, :15" ms binaries I—o—Ii'ri M 5 in Mac 6M0 n—o—i $ngng $rrorie5| What is a black hole? A black hole is really a singularity—gravity wins, and collapses the mass into a point. Schwarzschild radius is the radius of the event horizon This is a measure of the circumference of the event horizon RSch : C2 Our laws of physics are insufficient to tell us about the singularity. Quantum mechanics and General Relativity disagree here. AST 203 (Spring 2011) ...
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This note was uploaded on 05/04/2011 for the course AST 203 taught by Professor Simon,m during the Spring '08 term at SUNY Stony Brook.

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