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Scuola Nazionale di Dottorato Cagliari, May 25 2007 Proprietà Osservative delle Binarie X Contenenti Stelle di Neutroni Tiziana Di Salvo Dipartimento di.

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Presentation on theme: "Scuola Nazionale di Dottorato Cagliari, May 25 2007 Proprietà Osservative delle Binarie X Contenenti Stelle di Neutroni Tiziana Di Salvo Dipartimento di."— Presentation transcript:

1 Scuola Nazionale di Dottorato Cagliari, May Proprietà Osservative delle Binarie X Contenenti Stelle di Neutroni Tiziana Di Salvo Dipartimento di Scienze Fisiche ed Astronomiche, Università di Palermo Via Archirafi Palermo Italy

2 Scuola Nazionale di Dottorato Cagliari, May X-ray Binaries Classification Cyclotron lines High Mass X-ray Binaries: Young objects with a high mass companion star (> 10 Msun) and (usually) High magnetic field (about Gauss) neutron stars

3 Scuola Nazionale di Dottorato Cagliari, May X-ray Binaries Classification High magnetic field neutron stars in X-ray binaries Black Hole Candidates in X-ray binaries

4 Scuola Nazionale di Dottorato Cagliari, May X-ray Binaries Classification High magnetic field neutron stars in X-ray binaries Black Hole Candidates in X-ray binaries Low magnetic field neutron stars in X-ray binaries: temporal and spectral analysis

5 Scuola Nazionale di Dottorato Cagliari, May Caratteristiche generali dellaccrescimento Energia liberata: Luminosità: –Valore massimo dato dalla luminosità di Eddington Efficienza: –Valore tipico per una NS: –Valore tipico per la fusione nucleare:

6 Scuola Nazionale di Dottorato Cagliari, May Caratteristiche generali Range tipico di emissione Emissione X e γ Modalità di accrescimento: –Accrescimento tramite venti stellari.(Binarie X di alta massa) –Accrescimento tramite tracimazione dal lobo di Roche.(Binarie X di bassa massa)

7 Scuola Nazionale di Dottorato Cagliari, May Mass Transfer in LMXBs: Roche Lobe Overflow Potenziale di Roche

8 Scuola Nazionale di Dottorato Cagliari, May X-ray pulsars

9 Scuola Nazionale di Dottorato Cagliari, May BB Fe Lines PL ~ Ecyc Wien Hump Dal Fiume et al. 1998

10 Scuola Nazionale di Dottorato Cagliari, May Meszaros, 1992 Cyclotron lines

11 Scuola Nazionale di Dottorato Cagliari, May Meszaros 1992 Coburn et al Orlandini & Dal Fiume 2001 Santangelo et al. 2003

12 Scuola Nazionale di Dottorato Cagliari, May BeppoSAX has discovered or has evidence of multiple harmonics in some of the sources, therefore establishing the presence of second harmonic as a rather common feature! CEN X-3 4U1907 4U (?) VELA X-1 (?) Multiple Harmonics? There are however some extraordinary observations….

13 Scuola Nazionale di Dottorato Cagliari, May Deep 2nd harmonic E 1 cyc E 2 cyc keV E 3 cyc E 4 cyc 49.5 keV E 5 cyc 60. keV The EW of harmonics were found to be larger than the fundamental The case of X Santangelo et al Similar asymmetric variations of the cyclotron line energy (up to 8 keV) were observed in Cen X-3 (Burderi et al. 2000). These variations of the cyclotron line energy could be explained by assuming an offset (~ 0.1 R NS ) of the dipolar magnetic field with respect to the neutron star center. Offsets are also suggested by an analysis of pulse profiles (Leahy 1991).

14 Scuola Nazionale di Dottorato Cagliari, May Low Mass X-ray Binaries Companion star: M < 1 M SUN Accretion disk Compact object: NS with B < G Close X-ray binaries:

15 Scuola Nazionale di Dottorato Cagliari, May Low Mass X-ray Binaries Companion star: M < 1 M SUN Accretion disk Compact object: NS with B < G Close X-ray binaries: Rich time variability, such as twin QPOs at kHz frequencies (from 400 to 1300 Hz, increasing with increasing mass accretion rate); kHz QPOs are thought to reflect Keplerian frequencies at the inner accretion disk.

16 Scuola Nazionale di Dottorato Cagliari, May kHz QPOs Sco X-1 4U 1608 Two peaks are usually present, whose frequency increses when the mass accretion rate increases, with almost constant separation. The peak separation is almost equal to the NS spin frequency (if known from pulsations or burst oscillations) Possibly related to Keplerian frequencies at the inner edge of the disk.

17 Scuola Nazionale di Dottorato Cagliari, May Low Mass X-ray Binaries Companion star: M < 1 M SUN Accretion disk Compact object: NS with B < G Close X-ray binaries: Rich time variability, such as twin QPOs at kHz frequencies (from 400 to 1300 Hz, increasing with increasing mass accretion rate); kHz QPOs are thought to reflect Keplerian frequencies at the inner accretion disk. Type-I X-ray bursts, with nearly coherent oscillations in the range Hz (probably the NS spin frequency). Some are transient, with quiescent luminosities of erg/s and outburst luminosities of erg/s.

18 Scuola Nazionale di Dottorato Cagliari, May Radio Pulsars The energy lost in electromagnetic radiation and relativistic particle beam comes from the rotational energy of the pulsar, which slows down. Measuring P and P. allows to derive B ~ 10 8 Gauss for MSPs.

19 Scuola Nazionale di Dottorato Cagliari, May Millisecond radio Pulsars B ~ 10 8 – 10 9 G Low mass companion (M ~ 0.1 Msun) Low mass X-ray Binaries B ~ 10 8 – 10 9 G Low mass companion (M ~ 1 Msun) Progenitors (Pspin >> 1ms) End products (Pspin ~ 1ms) Accretion of mass from the companion causes spin-up The classical recycling scenario

20 Scuola Nazionale di Dottorato Cagliari, May

21 Scuola Nazionale di Dottorato Cagliari, May Confirmed by 7 (transient) LMXBs which show X-ray millisecond coherent pulsations Known accreting millisecond pulsars (in order of increasing spin period): IGR J : Ps=1.7ms, Porb=2.5hr (Galloway et al. 2005) XTE J : Ps=2.3ms, Porb=42m (Markwardt et al. 2002) SAX J : Ps=2.5ms, Porb=2hr (Wijnands & van der Klis 1998) HETE J : Ps=2.7ms, Porb=1.4hr (Kaaret et al. 2005) XTE J : Ps=3.2ms, Porb=4hr (Markwardt et al. 2003) XTE J : Ps=5.2ms, Porb=40m (Markwardt et al. 2003) XTE J : Ps=5.4ms, Porb=43.6m (Galloway et al. 2002) Known accreting millisecond pulsars (in order of increasing spin period): IGR J : Ps=1.7ms, Porb=2.5hr (Galloway et al. 2005) XTE J : Ps=2.3ms, Porb=42m (Markwardt et al. 2002) SAX J : Ps=2.5ms, Porb=2hr (Wijnands & van der Klis 1998) HETE J : Ps=2.7ms, Porb=1.4hr (Kaaret et al. 2005) XTE J : Ps=3.2ms, Porb=4hr (Markwardt et al. 2003) XTE J : Ps=5.2ms, Porb=40m (Markwardt et al. 2003) XTE J : Ps=5.4ms, Porb=43.6m (Galloway et al. 2002)

22 Scuola Nazionale di Dottorato Cagliari, May Rossi X-ray Timing Explorer RXTE carries 5 Proportional Counter Units, which constitues the Proportional Counter Array (PCA), with a large effective area of about 6000 cm 2 and very good time resolution (up to 1 sec), working in the X-ray range (2-60 keV)

23 Scuola Nazionale di Dottorato Cagliari, May Spin Frequencies of AMSPs All the spin frequencies are in the rather narrow range between 200 and 600 Hz. (From Wijnands, 2005)

24 Scuola Nazionale di Dottorato Cagliari, May Light Curves of AMSPs All the 7 known accreting MSPs are transients, showing X-ray outbursts lasting a few tens of days. Typical light curves are from Wijnands (2005) (X-ray Outburst of 2002)

25 Scuola Nazionale di Dottorato Cagliari, May Disc Pressure proportional to M Magnetic Pressure Proportional to B 2 Disc – Magnetic Field Interaction. R m = 10 B 8 4/7 dotM -8 -2/7 m 1/7 km

26 Scuola Nazionale di Dottorato Cagliari, May Accretion conditions (Illarionov & Sunyaev 1975) Accretion regime R(m) < R(cor) < R(lc) Pulsar spin-up accretion of matter onto NS (magnetic poles) energy release L = dotM G M/R* Accretion of angular momentum dL/dt = l dotM where l = (G M Rm) 1/2 is the specific angular momentum at Rm R co = 15 P –3 2/3 m 1/3 km R LC = 47.7 P –3 km

27 Scuola Nazionale di Dottorato Cagliari, May Pulsars spin up The accreting matter transfers its specific angular momentum (the Keplerian AM at the accretion radius) to the neutron star: L=(GMR acc ) 1/2 The process goes on until the pulsar reaches the keplerian velocity at Racc (equilibrium period); Pmin when Racc = Rns The conservation of AM tells us how much mass is necessary to reach Pmin starting from a non-rotating NS. Simulations give ~0.3Msun (e.g. Lavagetto et al. 2004) During the LMXB phase ~1 Msun is lost by the companion Pmin << 1 ms for most EoS 2

28 Scuola Nazionale di Dottorato Cagliari, May Propeller phase M. Propeller regime R(cor) < R(m) < R(lc) centrifugal barrier closes (B-field drag stronger than gravity) matter accumulates or is ejected from R m accretion onto R m : lower gravitational energy released energy release L = GM(dM/dt)/R*, = R*/2 R m

29 Scuola Nazionale di Dottorato Cagliari, May Rotating magnetic dipole phase M. Radio Pulsar regime R m > R LC no accretion, radio pulsar emission disk matter swept away by pulsar wind and pressure Energy release given by the Larmor formula: L = 2 R 6 /3c 3 B 2 (2 / P) 4

30 Scuola Nazionale di Dottorato Cagliari, May Timing Technique Correct time for orbital motion delays: t t arr – x sin 2 /P ORB (t arr –T*) where x = a sini/c is the projected semimajor axis in light-s and T* is the time of ascending node passage. Compute phase delays of the pulses ( -> folding pulse profiles) with respect to constant frequency Main overall delays caused by spin period correction (linear term) and spin period derivative (quadratic term)

31 Scuola Nazionale di Dottorato Cagliari, May Accretion Torque modelling Bolometric luminosity L is observed to vary with time during an outburst. Assume it to be a good tracer of dotM: L= (GM/R)dotM with 1, G gravitational constant, M and R neutron star mass and radius Matter accretes through a Keplerian disk truncated at magnetospheric radius R m dotM -. In standard disk accretion =2/7 Possible threading of the accretion disk by the pulsar magnetic field is modelled here as in Rappaport et al. (2004), which gives the total accretion torque: = dotM l – 2 / 9 Rco 3 Matter transfers to the neutron star its specific angular momentum l = (GM R m ) 1/2 at R m, causing a torque = l dotM.

32 Scuola Nazionale di Dottorato Cagliari, May IGR J00291: the fastest accreting MSP dot = 8.5(1.1) x Hz/s 2 /dof = 106/77 (Burderi et al. 2007, ApJ; Falanga et al. 2005, A&A) Porb = 2.5 h s = 600 Hz 0 8

33 Scuola Nazionale di Dottorato Cagliari, May Conclusions: Spin-up in IGR J00291 IGR J shows a strong spin-up: dot = 1.2 x Hz/s, which indicates a mass accretion rate of dotM = M yr -1. Comparing the bolometric luminosity of the source as derived from the X-ray spectrum with the mass accretion rate of the source as derived from the timing, we find a good agreement if we place the source at a quite large distance between 7 and 10 kpc.

34 Scuola Nazionale di Dottorato Cagliari, May Spin down in the case of XTE J Spin down in XTE J0929, the slowest among accreting MSPs. During the only outburst of this source observed by RXTE. Measured spin-down rate: dot = Hz/s Estimated magnetic field: B = 5 x 10 8 Gauss Porb = 44 min s = 185 Hz (Di Salvo et al. 2007)

35 Scuola Nazionale di Dottorato Cagliari, May Results for 6 of the 7 known LMXBs which show X-ray millisecond coherent pulsations Results for accreting millisecond pulsars (in order of increasing spin period): IGR J : Ps=1.7ms, Porb=2.5hr SPIN UP XTE J : Ps=2.3ms, Porb=42m SPIN UP SAX J : Ps=2.5ms, Porb=2hr SPIN UP (SPIN DOWN) HETE J : Ps=2.7ms, Porb=1.4hr ?? XTE J : Ps=3.2ms, Porb=4hr SPIN DOWN XTE J : Ps=5.2ms, Porb=40m SPIN UP XTE J : Ps=5.4ms, Porb=43.6m SPIN DOWN Results for accreting millisecond pulsars (in order of increasing spin period): IGR J : Ps=1.7ms, Porb=2.5hr SPIN UP XTE J : Ps=2.3ms, Porb=42m SPIN UP SAX J : Ps=2.5ms, Porb=2hr SPIN UP (SPIN DOWN) HETE J : Ps=2.7ms, Porb=1.4hr ?? XTE J : Ps=3.2ms, Porb=4hr SPIN DOWN XTE J : Ps=5.2ms, Porb=40m SPIN UP XTE J : Ps=5.4ms, Porb=43.6m SPIN DOWN These exclude GR as a limiting spin period mechanism

36 Scuola Nazionale di Dottorato Cagliari, May Spettri dei Black Holes Candidates in X-ray Binaries Stati hard o low Sono fittati da: Legge di potenza = 1.4 – 1.9 alle alte energie, con cutoff a circa 100 KeV. Corpo nero alle basse energie (circa 0.1 keV) Luminosità < 0.1 L EDD.

37 Scuola Nazionale di Dottorato Cagliari, May Spettri dei BHXB Stati soft o high Sono fittati da: Corpo nero alle basse energie (temp. kT circa KeV) dominante rispetto alla legge di potenza. Legge di potenza: = 2 – 3 alle alte energie senza evidenza di cutoff fino a energie dellordine di circa 511KeV Luminosità > L EDD.

38 Scuola Nazionale di Dottorato Cagliari, May Spettri dei BHXB Stati molto alti Stati high o soft Stati intermedi Stati low o hard Stati di quiescenza

39 Scuola Nazionale di Dottorato Cagliari, May Fe K-shell Line and Reflection MECS Cygnus X-1: BeppoSAX Broad Band (0.1 – 200 keV) Spectrum HPGSPC Di Salvo et al. (2001) MECS Schema della regione di emissione

40 Scuola Nazionale di Dottorato Cagliari, May Spettri dei BHXB: Componente di riflessione Compton Componente di riflessione è dovuta allincidenza della componente hard di Comptonizzazione sul disco di accrescimento. –Energia dei fotoni incidenti inferiore a circa 15 KeV: predomina il fotoassorbimento righe di emissione e bordi di assorbimento (sprattutto relativi al Fe). –Energia dei fotoni incidenti maggiore di 15KeV: predomina la riflessione Compton larga gobba tra circa 10 e 50 KeV.

41 Scuola Nazionale di Dottorato Cagliari, May Fe K-shell Line and Reflection HPGSPC Iron line profile E E0E0 Important information can be obtained from the iron line profile. Doppler and relativistic effects due to the keplerian motion in the disk modify the profile (double peak, Doppler boositng, Gravitational redshift). From high resolution spectra we can obtain info on the inner disk radius and inclination of the disk.

42 Scuola Nazionale di Dottorato Cagliari, May Self consistent models of Compton reflection and associated iron line Reflection from ionized matter Reflection from Neutral matter narrow smeared

43 Scuola Nazionale di Dottorato Cagliari, May High resolution spectroscopy of massive BHs: MCG XMM observation of the iron line region in MCG taken in The red wing extends to less than 4 keV, indicating an inner radius of less than 6 G M / C 2. Spinning black hole? (a > 0.93) Fabian et al. 2002)

44 Scuola Nazionale di Dottorato Cagliari, May Spettri di LMXB contenenti NS Forti analogie con gli spettri di BHXBs:presenza di stati hard e soft. Differenza nella temperatura della nube comptonizzante. Raffreddamento extra dovuto alla superficie della NS.

45 Scuola Nazionale di Dottorato Cagliari, May Neutron star low mass x-ray binaries classification - Late type mass donor (usually K-M star) or white dwarf - Accreting NS primary: fast spinning (2-3 ms), weakly magnetic - Characteristic phenomena: type I X-ray bursts, fast (> 100 Hz) quasi periodic oscillations in the X-ray flux - Useful classification: Z-sources, Atoll sources Atoll sources: Lx ~ L(Edd) type I X-ray bursts some transients Z-sources: Lx ~ L(Edd) all persistent

46 Scuola Nazionale di Dottorato Cagliari, May Atoll sources: energy spectra - Soft component (few keV) (blackbody or disk-blackbody model) - Power law with exponential cutoff (5-20 keV): Thermal Comptonization. - Soft and hard states: in the hard state the cutoff shifts to higher energies (up to > 200 keV) - Iron emission (fluorescence) line at ~6.4 keV - Evidence for a reflection component

47 Scuola Nazionale di Dottorato Cagliari, May X-ray energy spectra up to ~20 keV X-ray energy spectra of Z sources up to ~20 keV Two components needed (at least): - Eastern model (Mitsuda et al. 1984): multitemperature-blackbody + blackbody spectra (disk emission with kT = a R -3/4, and NS surface comptonized emission) - Western model (White et al. 1986): blackbody + Comptonized blackbody spectra (NS or disk emission, and disk emission modified by Comptonization in a hotter region).

48 Scuola Nazionale di Dottorato Cagliari, May Fe K-shell Line in Neutron Star Low Mass X-ray binaries Chandra observation of the LMXB/atoll source 4U (Di Salvo et al. 2005, ApJ Letters) TE Mode 25 ks CC Mode 5 ks

49 Scuola Nazionale di Dottorato Cagliari, May Fe K-shell Line in NS LMXBs TE Mode 25 ks Soft Comptonization model for the X-ray continuum plus 3 narrow lines and a broad Fe line: E1 = keV, 1 = 17 eV (ID: Mg XII Ly-, keV) E2 = 2.03 keV, 2 = 28 eV (ID: Si XIV Ly-, keV) E3 = 2.64 keV, 3 = 40 eV (ID: S XVI Ly-, keV) E_Fe = 6.54 keV, Fe = 0.51 keV EW = 170 eV

50 Scuola Nazionale di Dottorato Cagliari, May Fe K-shell Line in Neutron Star Low Mass X-ray binaries Fitting the iron line profile with a disk (relativistic) line we find: E_Fe = 6.40 keV Rin = 7-11 Rg (15-23 km) Inclination = 55 – 84 deg Alternatively, Compton broadening in the external parts of the Comptonizing corona ( s = 0.5 implies t = 1.4 for kT = 2 keV) Hints of a double- peaked line profile TE Mode 25 ks

51 Scuola Nazionale di Dottorato Cagliari, May Hard X-ray Emission in LMXBs: INTEGRAL/RXTE Observations of Sco X-1 ISGRI SPI Di Salvo et al. (2005, ApJL) Soft Comptonization: kT (seed) = 1.3 keV (fixed) kTe = 4.7 keV t = 2.4 Hard Power law: PI = 2.3 kT > 200 keV Flux (20 – 40 keV) = ergs/cm 2 /s Flux (40 – 200 keV) = ergs/cm 2 /s

52 Scuola Nazionale di Dottorato Cagliari, May INTEGRAL/RXTE Observations of Sco X-1 Di Salvo et al. (2005, ApJL) Soft Comptonization Hard power law PI = 2.7 kT > 290 keV Flux (40 – 200 keV) = ergs/cm 2 /s Lowest dotM

53 Scuola Nazionale di Dottorato Cagliari, May Di Salvo et al. (2005, ApJL) PI = 2.7 (fixed) Flux (40 – 200 keV) = ergs/cm 2 /s INTEGRAL/RXTE Observations of Sco X-1 Highest dotM

54 Scuola Nazionale di Dottorato Cagliari, May NS hard tails: analogy with BHCs - BHCs in low state: extended power law with high energy cutoff (plus faint very soft and reflection components seen occasionally) Similar to hard state Atolls - BHCs in IS/VHS: very soft thermal component plus power law without high energy cutoff up to 1 MeV Similar to Z-sources in HB-NB - BHCs in HS: very soft thermal component. Similar to Z-sources in NB-FB. (Grove et al. 1998) Hard X-ray NS/BHC indicators are uncertain at least !

55 Scuola Nazionale di Dottorato Cagliari, May Geometry and Models for hard tails in NS binaries Origine della legge di potenza negli stati soft di BHXB e LMXBs: Ipotesi I: comptonizzazione termica Temperature altissime Ipotesi II: (comptonizzazione non termica) caduta radiale della materia in corrispondenza di LSO. Non può spiegare lhard tail nelle NS LMXB Ipotesi III: (comptonizzazione non termica) Jet relativistici Distribuzione a legge di potenza. Evidenze radio in BH e NS. Intensità radio maggiore più è intensa la componente hard. Molto probabile

56 Scuola Nazionale di Dottorato Cagliari, May Geometry and Models for hard tails in NS binaries Jet: hard tail ? Disk: soft X-rays Comptonising corona: hard tail ? - Bulk motion Comptonisation converging radial or disk inflow (Titarchuk & Zannias 1998; Luarent & Titarchuk 1999; Psaltis 2001) Inflow in Z-sources is strongly affected by radiation from the NS - Comptonisation by thermal e- in a corona predicts high energy cutoff - Comptonisation (or synchrotron radiation) by non-thermal e- in a (non-confined) corona or relativistic jets (Zdziarski 2000; Vadawale et al. 2001; Markoff et al. 2001) power law spectra can extend up to very high energies

57 Scuola Nazionale di Dottorato Cagliari, May The radio connection: other NS binaries - Radio jets: likely a common phenomenon also in X-ray binaries Class Fraction as radio sources Persistent BHCs 4/4 Transient BHCs ~15/35 NS Z-sources 6/6 NS Atoll sources ~5/100 (Fender 2001) - In Z sources (e.g. GX 17+2) radio flaring in the HB (i.e. low accretion rates) - Fewer searches (and detections) in Atoll sources

58 Scuola Nazionale di Dottorato Cagliari, May The radio jets and states of NS X-ray binaries (Fender 2001) - Radio emission (probably due to jets) is anti- correlated with the mass accretion rate -Similarity with the hard X-ray tails! More simultaneous hard X-ray / radio observations are needed

59 Scuola Nazionale di Dottorato Cagliari, May The end Thank you very much!

60 Scuola Nazionale di Dottorato Cagliari, May Threaded disc model Bz B Dragging of the field line: a B component is generated Bz = 2 / R 3, <= 1 screening factor B is amplificated by differential rotation up to: B = / [( - K )/ K ]/Bz ( = SS viscosity, >= 1) Where the amplification is limited by turbulent diffusion (Wang 1995)

61 Scuola Nazionale di Dottorato Cagliari, May Threaded disc model Yet, we do not have a self-consistent disc solution for this case of disk - magnetic field interaction. Possible threading of the accretion disk by the pulsar magnetic field gives a negative torque which is modelled here as in Rappaport et al. (2004): mag = 2 / 9 Rco 3 A self consistent solution of the Threaded Disc is required!

62 Scuola Nazionale di Dottorato Cagliari, May Results for IGR J In a good approximation the X-ray flux is observed to linearly decrease with time during the outburst: dotM(t) = dotM 0 [1-(t – T 0 )/T B ], where T B = 8.4 days Assuming R m dotM -. ( = 2/7 for standard accretion disks; = 0 for a constant accretion radius equal to Rc; = 2 for a simple parabolic function), we calculate the expected phase delays vs. time: = - 0 – 0 (t-T 0 ) – ½ dot 0 (t – T 0 ) 2 [1 – (2- ) (t-T 0 )/6T B ] Measured dot –13 = 11.7, gives a lower limit of dotM = (7+/-1) Msun/yr, corresponding to Lbol = 7 x ergs/s We have calculated a lower limit to the mass accretion rate (obtained for the case = 0 and no negative threading (m = 1.4, I 45 = 1.29) dotM = dot –13 I 45 m -2/3 Msun/yr

63 Scuola Nazionale di Dottorato Cagliari, May Distance to IGR J The timing-based calculation of the bolometric luminosity is one order of magnitude higher than the X-ray luminosity determined by the X- ray flux and assuming a distance of 5 kpc ! The X-ray luminosity is not a good tracer of dotM, or the distance to the source is quite large (15 kpc, beyond the Galaxy edge in the direction of IGR J00291 !) In this way we can reduce the discrepancy between the timing- determined mass accretion rate and observed X-ray flux by about a factor of 2, and we can put the source at a more reliable distance of 7.4 – 10.7 kpc We argue that, since the pulse profile is very sinusoidal, probaly we just see only one of the two polar caps, and possibly we are missing part of the X-ray flux..

64 Scuola Nazionale di Dottorato Cagliari, May The Strange case of XTE J1807 The outburst of February 2003 (Riggio et al. 2007, in preparation)

65 Scuola Nazionale di Dottorato Cagliari, May But… There is order beyond the chaos! The key idea: Harmonic decomposition of the pulse profile

66 Scuola Nazionale di Dottorato Cagliari, May Timing of the second harmonic

67 Scuola Nazionale di Dottorato Cagliari, May Back to the fundamental

68 Scuola Nazionale di Dottorato Cagliari, May Positional Uncertainties of XTE J1807 (0.6)

69 Scuola Nazionale di Dottorato Cagliari, May SAX J1808: the outburst of 2002 Phase Delays of The Fundamental Phase Delays of The First Harmonic Spin-down at the end of the outburst: dot = Hz/s (Burderi et al. 2006, ApJ Letters) Porb = 2 h = 401 Hz Spin-up: dot = Hz/s

70 Scuola Nazionale di Dottorato Cagliari, May SAX J : Pulse Profiles Folded light curves obtained from the 2002 outburst, on Oct 20 (before the phase shift of the fundamental) and on Nov 1-2 (after the phase shift), respectively

71 Scuola Nazionale di Dottorato Cagliari, May SAX J : phase shift and X-ray flux Phase shifts of the fundamental probably caused by a variation of the pulse shape in response to flux variations.

72 Scuola Nazionale di Dottorato Cagliari, May Discussion of the results for SAX J1808 In a good approximation the X-ray flux is observed to decrease exponentially with time during the outburst: dotM(t) = dotM 0 exp[(t – T 0 )/T B ], where T B = 9.3 days derived from a fit of the first 14 days of the light curve. Assuming R m dotM -. (with = 0 for a constant accretion radius equal to Rco), we calculate the expected phase delays vs. time: = - 0 – (t-T 0 ) – C exp[(t-T 0 )/T B ] + ½ dot 0 (t – T 0 ) 2 where B = 0 + C/T B and C = I P -3 1/3 m 2/3 T B 2 dotM -10 (the last term takes into account a possible spin-down term at the end of the outburst). We find that the best fit is constituted by a spin up at the beginning of the outburst plus a (barely significant) spin down term at the end of the outburst.

73 Scuola Nazionale di Dottorato Cagliari, May Discussion of the results for SAX J1808 Spin up: dot 0 = Hz/s corresponding to a mass accretion rate of dotM = Msun/yr Spin-down: dot 0 = Hz/s In the case of SAX J1808 the distance of 3.5 kpc (Galloway & Cumming 2006) is known with good accuracy; in this case the mass accretion rate inferred from timing is barely consistent with the measured X-ray luminosity (the discrepancy is only about a factor 2), Using the formula of Rappaport et al. (2004) for the spin-down at the end of the outburst, interpreted as a threading of the accretion disc, we find: 2 / 9 Rco 3 = 2 I dot sd from where we evaluate the NS magnetic field: B = (3.5 +/- 0.5) 10 8 Gauss : (in agrement with previous results, B = Gauss, Di Salvo & Burderi 2003)

74 Scuola Nazionale di Dottorato Cagliari, May Timing of XTE J1751 Porb = 42 min s = 435 Hz As in the case of SAX J1808, the X-ray flux of XTE J1751 decreases exponentially with time (T B = 7.2 days). The best fit of the phase delays corresponds to R m dotM -.wth = 2/7, and gives dot 0 = Hz/s and dotM 0 = (3.4 – 8.7) Msun/yr. Comparing this with the X-ray flux from the source, we obtain a distance of 9.7–15.8 kpc (or kpc using the same arguments used for IGR J00291). (Papitto et al. 2007, in preparation)

75 Scuola Nazionale di Dottorato Cagliari, May Spin down in the case of XTE J1814 Phase Delays of The Fundamental Phase Delays of The First Harmonic Papitto et al. 2007, MNRAS Spin-down: dot = Hz/s

76 Scuola Nazionale di Dottorato Cagliari, May Phase residuals anticorrelated to flux changes in XTE J Modulations of the phase residuals, anticorrelated with the X-ray flux, and possibly caused by movements of the footpoints of the magnetic field lines in response to flux changes Post fit residuals of the Fundamental Post fit residuals of the harmonic Estimated magnetic field: B = 8 x 10 8 Gauss

77 Scuola Nazionale di Dottorato Cagliari, May XTE J : the most puzzling AMSP The mass accretion rate is varying with time, while instead the phase delays clearly indicate a constant (or at most decreasing) spin-down rate of the source. We therefore assume spin-up << - spin-down = 5.5 x Hz /s Assuming that the spin-up is at least a factor of 5 less than the spin- down, we find a mass accretion rate at the beginning of the outburst of dotM < 6 x Msun/yr, which would correspond to the quite low X-ray luminosity of Lbol < 6 x ergs/s. Comparing this with the X-ray flux of the source we find an upper limit to the source distance of about 1.2 kpc (too small !! Although this is a high latitude source)

78 Scuola Nazionale di Dottorato Cagliari, May Conclusions: Spin-up XTE J shows a strong spin-up: dot = 6.3 x Hz/s, which indicates a mass accretion rate of dotM = (3.4 – 8.7) M yr -1. Comparing the bolometric luminosity of the source as derived from the X-ray spectrum with the mass accretion rate of the source as derived from the timing, we find a good agreement if we place the source at a quite large distance between 7 and 8.5 kpc. XTE J shows a noisy fundamental and a clear spin-up in the second harmonic: dot = (1 – 3.5) Hz/s. No clear diagnostic is possible, spin-up and spin-down may be both present.

79 Scuola Nazionale di Dottorato Cagliari, May Conclusions: Spin-down XTE J shows noisy fundamental and harmonic phase delays, and a strong spin-down: dot = -6.7 x Hz/s, which indicates a quite large magnetic field of B = Gauss. XTE J shows a clear spin-down of dot = -5.5 x Hz/s, which indicates a magnetic field of B = Gauss. Imposing that the spin-up contribution due to the mass accretion is negligible, we find however that the source is at the very close distance of about 1 kpc. Independent measures of the distance to this source will give important information on the torque acting on the NS and its response.


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