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Binary Stars and Accretion Disks Binary Stars and Accretion Disks

Binary Stars and Accretion Disks - PDF document

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Binary Stars and Accretion Disks - PPT Presentation

AS 4024 InclinationsRadial velocities give minimum masses149need inclinations150 orbits150eclipsing binaries150apsidal motion 333 AS 4024 Binary Stars and Accretion Disks Astrometric Orbit ID: 295448

4024 InclinationsRadial velocities give minimum

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AS 4024 Binary Stars and Accretion Disks InclinationsRadial velocities give minimum masses•need inclinations– orbits–eclipsing binaries–apsidal motion 333 AS 4024 Binary Stars and Accretion Disks Astrometric Orbits Get inclination,hence massesInterferrometrymeasures therelative orbit(Fit ellipticalorbit model tox(t) and y(t). AS 4024 Binary Stars and Accretion Disks Polarimetry Get inclination,hence massesScattered light is polarised (e.g. our sky) AS 4024 Binary Stars and Accretion Disks Eclipsing Binaries •Binary properties from eclipses–sizes, shapes of stars, inclination,–temperatures, limb darkening, apsidal motion–4 contact phases:– 1 2– 3 4– primary eclipse secondary eclipse AS 4024 Binary Stars and Accretion Disks Partial Eclipse AS 4024 Binary Stars and Accretion Disks Eclipses 2sin 2sin sin :contact 4on -2112122121qqqqf=-==±=º�RR 1R= AS 4024 Binary Stars and Accretion Disks Eclipses 1212102143212222221 : partial : total mid 4 4 coscos :contact 4 RRRRRR--=+=+=±fffffqqq cos 1R AS 4024 Binary Stars and Accretion Disks redder �Colour changes -- T, L AS 4024 Binary Stars and Accretion Disks Application to Binary Pulsars•binary system where one star is a pulsar–emits ‘pulses’ of radiation–accurate timing possible (accurate clocks)–need narrow pulses–radio signals from neutron stars•solitary pulsar–if at 0 velocity relative to us–time between pulses, dt = constant (unless being spunup/down)if at Vrel relative velocity– = constant x pulse number–if pulsar spins up, dt decreases with pulse number–concave curve–if pulsar spins down, dt increases with pulse number–convex curve AS 4024 Binary Stars and Accretion Disks Timing Residuals O - C Correct period Period too longPeriod too short Cycle numberO-C = observed timeminus calculated time O - C Period constantPeriod increasingPeriod decreasingCycle number AS 4024 Binary Stars and Accretion Disks Binary Pulsars•In binary system, time between pulses affected byorbital motions–due to light travel time (distance) changing along orbit �Observer-- AS 4024 Binary Stars and Accretion Disks Light travel time () øöçèæ=+++=+=++=(sin orbitcircular cos : timevellight tra sinsin : of line along distance cos :pulsar 022eczepppppppq AS 4024 Binary Stars and Accretion Disks light travel time AS 4024 Binary Stars and Accretion Disks Binary Pulsar timing residuals•Time difference between predicted , j tt, and actual(binary) pulse arrival times, tn is– P is the orbital period, T0 is a reference time– a,b are determined by the velocity of the pulsar–a: from systematic velocity–b: from Keplerian velocity–for circular orbits: b = (a/c) sini ûùêëé+=-=ttn( AS 4024 Binary Stars and Accretion Disks Binary Pulsar Orbits timingradial velocity AS 4024 Binary Stars and Accretion Disks Mass determinations•visible companion star–O-B star in High-Mass X-ray Binaries (HMXB)–A-K star in Low-Mass X-ray Binaries (LMXB) mass functionmass ratio, q,–If inclination, i, can be found, then masses follow immpcpcsin 2( 22223322=-==-=pp AS 4024 Binary Stars and Accretion Disks Frequency shifts•Binary orbit also affects pulsar frequency–radio pulsars , very narrow pulse widths–pulse frequency affected by orbital velocity–Doppler shift:–gives a phase lag of: () ûùêëé-»=f&&00 f AS 4024 Binary Stars and Accretion Disks Pulsar Phase lag•Combined phase lag is–from light travel time due to orbit–and from Doppler shift–but measurable in radio pulsars LDffffffffûùêëé--ûùêëéûùêëé= )( 00000&&