NextPaper(s)•  ModellingthebehaviourofaccretionflowsinX-ray

binariesEverythingyoualwayswantedtoknowaboutaccretionbutwereafraidtoaskDone,Gierlinski&Kubota2007A&ARv..15....1D

•  Sec1and2ONLY-ORSec7onlythisisaverylongarticle!•  ----------------------------------------------------------------------------------------•  2014MNRAS.437.1698X-rayemissionfromstar-forminggalaxies-III.

CalibrationoftheLX-SFRrelationuptoredshiftz≈1.3Mineo,S.;Gilfanov,M.;Lehmer,B.D

PeriodandMagneticField

A. Harding 2013

accreting sources

Population•  Themost'common'

observationalpopulationarenon-accretingpulsars

•  Periodsfrom..0.001-100secs

•  22ordersofmagnituderangeindP/dt

•  dipolemagneticBs~1019(P/dP/dt)1/2wherePisinseconds,Bingauss

•  ‘Millisecondpulsars’arerotation-powered,buthavedifferentevolutionaryhistories,involvinglong-livedbinarysystemsanda‘recyclingaccretionepisodewhichspun-uptheneutronstarandquencheditsmagneticfield

•  Wewillnotdiscuss–  Xray-DimIsolatedNSs(XDINSs),CentralCompactObject(CCOs)RotatingRadioTransients(RRATs),AXPSandMagnetars...

Longair13.5.3-13.5.5Open circles are in binaries

The diversity of non-accreting NSs

DegenerateCompactObjects-SeeLongairpg394-398•  Thedeterminationoftheinternalstructuresofwhitedwarfsand

neutronstarsdependsupondetailedknowledgeoftheequationofstateofthedegenerateelectronandneutrongases

•  Intheseobjectsdegeneracypressureismainforcebalancinggravity•  pressureisindependentofthetemperaturefordegeneratestars,

onlyneedthefirsttwoequationsofstellarstructure(2.6)tocarryouttheanalysis,

•  dp/dr��� �ρ/r2;dM/dr����ρ����•  Ineqs13.16-13.24theeqsforawhitedwarfarederived

•  M=5.836/μ2eM¤.μe=2forwhitedwarfanthusthe

ChandrasekarmassforawhitedwarfMCh=1.46M!(eq.13.24)•  ForNSgeneralrelativityisimportant..

WhiteDwarfs…CourtesyofC.Reynolds

•  Size,andpressure

Mass of particle producing degeneracy pressure

Number of nucleons per degenerate particle

•  So,anapproximateexpressionforradiusofwhitedwarfis:

•  Exactcalculationgives

DegneracyandAllThat-Longairpg395sec13.2.1-2.•  Inwhitedwarfs,internalpressuresupportisprovidedbyelectron

degeneracypressureandtheirmassesareroughly<1M¤•  thedensityatwhichdegeneracyoccursinthenon-relativisticlimitis

proportionaltoT3/2

•  Thisisaquantumeffect:Heisenberguncertaintysaysthat δpδx>h/2π–  Thuswhenthingsaresqueezedtogetherandδxgetssmallerthemomentum, p,increases,particlesmovefasterandthushavemorepressure

•  Considerabox-withanumberdensity,n,ofparticlesarehittingthewall;thenumberofparticleshittingthewallperunittimeandareais1/2nv(visvelocity)–  themomentumperunittimeandunitarea(Pressure)transferredtothewallis2nvp;P~nv p=(n/m) p2(mismassofparticle)

InotherwordsHeisenberguncertaintyprinciple,ΔxΔp≥�

whereΔxistheuncertaintyofthepositionmeasurements,Δpistheuncertaintyofthemomentummeasurements,andħish/2π.•  Aspressureincreases,systemwillbemorecompactand,for

electronswithinit,theirdelocalization,Δx,willdecrease.•  Thus,theuncertaintyinthemomentaoftheelectrons,Δp,willgrow.

nomatterhowlowthetemperaturedrops,theelectronsmustbetravellingatlargervelocities,contributingtothepressure

•  Whenthistermexceedsthatofthepressurefromthethermalmotionsoftheelectrons,theelectronsarereferredtoasdegenerate,andthematerialistermeddegeneratematter.–  Thisanalysisistrueevenatalmostzerotemperature.

Degeneracy-continued•  Theaveragedistancebetweenparticlesisthecuberootofthe

numberdensityandifthemomentumiscalculatedfromtheUncertaintyprinciple p~h/(2πδx)~hn1/3

•  andthusP=h2n5/3/m-ifwedefinematterdensityasρ=[n/m]then•  P~ρ5/3independentoftemperatureρ ismassdensity•  DimensionalanalysisgivesthecentralpressureasP~GM2/r4

•  Ifweequatethesewegetr~M-1/3e.qadegeneratestargetssmallerasitgetsmoremassive

•  Athigherdensitiesthematerialgets'relativistic'e.g.thevelocitiesfromtheuncertaintyrelationgetclosetothespeedoflight-thischangesthingsandP~ρ4/3;

•  thisisimportantbecausewhenweuseP~GM2/r4wefindthatthepressuredoesnotdependonradiusandjustgetanexpressionthatdependsonmass-thisistheChandrasekarmass.(see13.2.2inLongair)

WhenDoesRelativityBecomeImportant•  Particles are moving at relativistic speeds when density

satisfies:

MaximumMassofaCompactObject-Longair13.2.2•  The Chandrasekar limit (maximum mass of a white dwarf) is when it costs

less energy for a electron to fuse with a proton to form a neutron then to climb higher in the Fermi sea.– Above this limit the compact object becomes all neutrons (a neutron star)

An alternative way of looking at this is to calculate the equation of state(EOS) of degenerate matter and use hydrostatic equilibrium.

– Pe=(1/20)(3/π)2/3(h2/me) (ρ/μemp)5/3 ----ρ is the total mass density and μemp is the mass per electron (composition of the material) - or more simply

– Pe~ρ5/3 - non relativistic•  for relativistic matter Pe=(1/8)(3/π)1/3ch(ρ/μemp)4/3 - notice the appearance of the

speed of light– Pe~ρ4/3

•  in hydrostatic equilibrium (remember dP(r)/dr=GM(r)ρ(r)/r2 ; P~GM2/R4

•  Setting the 2 pressures equal produces the Chandrasekhar limit at which awhite dwarf collapses to a neutron star M~1.46M� (but depends on its composition μe, eg an iron core??))

ChandrasekarLimiteqs13.15-13.25•  ElectrondegeneracyisresponsibleforbalancinggravityinWhite

Dwarfs

gravity

Pressure gradient = weight

NeutronStarSizeCourtesyofC.Reynolds

•  So,wecantrytoestimateradiusofneutronstargivenwhatweknowaboutwhitedwarfs

– Weknowthat

–  Soweexpect

•  Byanalogytowhitedwarfs,neutronstarshave(toacrudeapproximation)…

•  Where…

–  I.e.,degenerateparticleshavemassmn,andµ=1

InsideaNeutronStar?

see fig 13.13 in Longair

Lots more going on... a lot is uncertain Lattimer and Prakash 2004

RadiusofNS•  Usethe'known'densityofnuclearmatter(ρNeutron~1.2x1014g/cm3)andtheChandrasekarmassgivesaradius•  RNS~(3MChandra/4πρNeutron)1/3~10kmconsistencybetweentheobservedspinperiods,andneutronstars

Cen X-3 Schreier et al 1971

EOSofNeutronStar-Size/MassRelation•  RatherComplex

–HavetouseGeneralRelativisticformofhydrostaticequilibriumequation–Neutronsdonʼtbehavelikeanidealdegenerategas…•  strongforceinteractions

arecrucial–Thereremainuncertaintiesaboutthe“equationofstate”ofneutronstars

FundamentalPhysics:TheNeutronStarEquationofState(EOS)

dP/dr = -ρ G M(r) / r2

•  High mass limit sets highest possible density achievable in neutron stars (thus, in nature, �the MOST dense�).

•  Radius is prop. to P1/4 at nuclear saturation density. Directly related to symmetry energy of nuclear interaction

•  Other issues: have to use general relativistic eq for hydrostatic equil

•  Maximum mass measurements, limits softening of EOS from hyperons, quarks, other �exotica�.

Li

FunFactfortheFamily•  oneteaspoonofaneutronstarhasa

massof~5x1012kilograms.•  http://videos.howstuffworks.com/

nasa/13498-chandra-neutron-stars-video.htm

C. Miller

AQuickTour•  Somepropertiesofthevarious

'types'ofneutronstars....•  IsolatedNeutronStars

–  cooling–  spinning(radiopulsars)–  magnetars

•  accretingneutronstars

IsolatedNeutronStars-NonAccreting•  Theseobjectsarecooling

fromtheinitialhightemperatureofthesupernovaexplosion

•  Recentresultsshowthattheyhaveanalmostpureblackbodyspectrum-

Burwitz et al 2001

•  AfterNeutronstariscreatedinasupernova,ifitisisolateditcools

•  Therateatwhichitcoolsdependsontheconductivityandheatcapacitywhichdependsonwhatitismadeofandadditionalphysicsnotwellunderstood.

(L.Cominsky)

NeutronStarContinuumSpectroscopyandCooling

Prakash and Lattimer

CoolingObservationalestimatesofneutronstartemperaturesandagestogetherwiththeoreticalcoolingsimulationsforM=1.4M�.•  Lattimerand

Prakash2004

InterestingPhysics-WillNotDiscussFurther•  Thephysicsof

howneutronstarscooldependcriticallyontheirexactcomposition

IsolatedNeutronStarsLongair13.5.1•  Mostisolatedneutronstarsthatare

radioandγ-raypulsars�–  rapidlyspinningneutronstarsthatemit

relativisticparticlesthatradiateinastrongmagneticfield

•  Thepulsesoriginatefrombeamsofradioemissionemittedalongthemagneticaxis-thepulsarlosesenergybyelectromagneticradiationwhichisextractedfromtherotationalenergyoftheneutronstar.

•  toproducepulsedradiationfromthemagneticpoles,themagneticdipolemustbeorientedatananglewithrespecttotherotationaxisandthenthemagneticdipoledisplaysavaryingdipolemoment

•  EnergylossgoesasΩ4B2•  Astheyradiatethestarspinsdown-

visiblefor~107yrshttp://www.jb.man.ac.uk/~pulsar/Education/Tutorial/tut/tut.html

Taylor 1991Proc. IEEE, 79, 1054

•  Theshortestperiod(orangularvelocityΩ)whichastarofmassMandradiusRcanhavewithoutbeingtornapartbycentrifugalforcesis(approximately)Ω2R~GM/R2

•  Withanaveragedensityoftheneutronstar ρ,Ω~(Gρ)1/2

–  ArotationperiodofP=2π/Ω~1secrequiresdensityof108gm/cm3

•  To'radiate'awaytherotationalenergyErot=1/2IΩ2~2x1046I45P-2ergs–  τloss~Erot/L~60I45P-2L37-1yr(I=2/5MR2)–  WherethemomentofinertiaIisinunitsof1045gmcm2

•  IfthestarisspinningdownataratedΩ/dtitsrotationalenergyischangingatarateErot~IΩ(dΩ/dt)+1/2(dI/dt)Ω2~4x1032I45P-3dP/dtergs/sec

•  Howeveronlyatinyfractionofthespindownenergygoesintoradiopulses-amajorrecentdiscoveryisthatmostofitgoesintoparticlesandγ-rays.

RadiationMechanism+MagneticField−dE/dt~µ0Ω4p2m0/6πc3.eq13.33Wherepisthemagneticmoment•  Thismagneticdipoleradiationextractsrotationalenergyfromthe

neutronstar.–  Iisthemomentofinertiaoftheneutronstar,

•  -d[1/2IΩ2]/dt=-IΩdΩ/dt=Ω4p2m0/6πc3andsodΩ/dt�Ω3

•  TheageofthepulsarcanbeestimatedifitisassumedthatitsdecelerationcanbedescribedbyalawdΩ/dt�Ωnifnisconstantthroughoutitslifetime

•  Usingtherelationτ=P/(2dP/dt),thetypicallifetimefornormalpulsarsisabout105−108years.

•  Ifthelossofrotationalenergyisduetomagneticbreaking(seederivationinLongair13.40-13.42)B~���x������/d�/dt ��������

RadiationMechanism•  Itisconventionaltosetn=3toderivetheageofpulsarsandsoτ=P/(2dP/dt)(seederivationinLongair13.35-13.37).•  Usingthisrelationthetypicallifetimefornormalpulsarsisabout

105−108years.•  extractingrotationalenergy-dErot/dt=-IΩ(dΩ/dt)=-4πI(dP/dt)P-3

Longair13.39•  InmoreuseableunitsarotatingdipolehasaPoyntingfluxof

(Harding2013

in units of 1012 Gauss

•  WhereradiopulsarslieintheP,dP/dtplot.–  thelinescorrespondtoconstantmagneticfieldandconstantage.

•  Ifmagneticbrakingmechanismslows-downtheneutronstarthen(seeeqs13.40-13.42)

•  Bs≈3x1015(P/{dP/dt})1/2TBisinteslas

•  Theradiopulsationsmakeup~10−4orlessofthespin-downpower

•  Thepulsedradiation<10%ofthetotalspin-downpower.

•  Mostofthepowerinpulsedemissionisin γraysaroundaGeV

•  γ-raypeaksarenotinphasewiththeradiopulses,buttypicallyarrivelaterinphase,

Comparison of Spin Down Energy and γ-ray Luminosity of Pulsars

L γ-ray= spindown energy

L γ-rayα√ (spindown energy)

Caraveo 2010

Magnetars13.5.5TheirdefiningpropertiesoccasionalhugeoutburstsofX-raysandsoft-gammarays,aswellasluminositiesinquiescencethataregenerallyordersofmagnitudegreaterthantheirspin-downluminosities.•  Theiraretwoclasses:the‘anomalousX-raypulsars’(AXPs)andthe

‘softgammarepeaters’(SGRs)Magnetarsarethoughttobeyoung,isolatedneutronstarspoweredbythedecayofaverylargemagneticfield.Theirintensemagneticfield,inferredviaspin-downtobe•  intherange1014-1015Gisclosetothe‘quantumcriticalfield’

BQED≡m2ec3/αhq=4.4×1013G.,q=charge,αisthefinestructure

•  wheretheLandaulevelseparationconstantexceedstherestmassenergyofanelectron,mec2=511keV.

Intheirmostluminousoutburstmagnetarscanbrieflyout-shineallothercosmicsoft-gamma-raysourcescombined[Kaspi2010]

S.Mereghetti-Madrid4-6June2007

Properties?1) �Persistent�X-rayemissionLx~1035erg/s;kT~0.5keV+hardpowerlawP~5-12shighspin-down10-11–10-13s/s;dEROT/dt<<Lx2)Short(<1s),super-EddingtonburstskT~30keV3)GiantFlares-rareevents!L~1044–>1046ergs

9 AXPs + 4 SGRs in our Galaxy and in Magellic. Clouds

What is a Magnetar ? Isolated neutron star powered by magnetic energy B~1014-1015 Gauss-the origin of strong magnetism in neutron stars is not well understood

SGR 1806-20 - INTEGRAL – Dec. 27, 2004 Giant Flare

E > 80 keV

Mereghetti et al. 2005, ApJ 624, L105

S.Mereghetti-Madrid4-6June2007

Mereghetti et al. 2005, ApJ 624, L105 2.8 light seconds

Initial giant pulse backscattered by the Moon

Peak affected by instrument saturation

SGR 1806-20 Giant Flare 2004 Dec 2004

AccretingNeutronStars:Longair13.5.2-AlsoCh14•  Thesearethebrightest

x-raysourcesintheskyandwerethefirstx-raysourcesdiscovered

•  Theyhaveawiderangeofproperties(spectralandtemporal)andshowanalmostbewilderingarrayofbehaviors

•  Theirluminositiesrangeover6ordersofmagnitudeandarehighlyvariable