AS 4024 InclinationsRadial velocities give minimum masses149need inclinations150 orbits150eclipsing binaries150apsidal motion 333 AS 4024 Binary Stars and Accretion Disks Astrometric Orbit ID: 295448
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AS 4024 Binary Stars and Accretion Disks InclinationsRadial velocities give minimum massesneed inclinations orbitseclipsing binariesapsidal 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 eclipsessizes, shapes of stars, inclination,temperatures, limb darkening, apsidal motion4 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=-==±=ºRR 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 Pulsarsbinary system where one star is a pulsaremits pulses of radiationaccurate timing possible (accurate clocks)need narrow pulsesradio signals from neutron starssolitary pulsarif at 0 velocity relative to ustime between pulses, dt = constant (unless being spunup/down)if at Vrel relative velocity = constant x pulse numberif pulsar spins up, dt decreases with pulse numberconcave curveif pulsar spins down, dt increases with pulse numberconvex 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 PulsarsIn binary system, time between pulses affected byorbital motionsdue 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 residualsTime 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 pulsara: from systematic velocityb: from Keplerian velocityfor 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 determinationsvisible companion starO-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 shiftsBinary orbit also affects pulsar frequencyradio pulsars , very narrow pulse widthspulse frequency affected by orbital velocityDoppler shift:gives a phase lag of: () ûùêëé-»=f&&00 f AS 4024 Binary Stars and Accretion Disks Pulsar Phase lagCombined phase lag isfrom light travel time due to orbitand from Doppler shiftbut measurable in radio pulsars LDffffffffûùêëé--ûùêëéûùêëé= )( 00000&&