Presentation on theme: "Proprietà Osservative delle Binarie X Contenenti Stelle di Neutroni"— Presentation transcript:
1Proprietà Osservative delle Binarie X Contenenti Stelle di Neutroni Tiziana Di Salvo Dipartimento di Scienze Fisiche ed Astronomiche, Università di PalermoVia Archirafi Palermo Italy
2X-ray Binaries Classification High Mass X-ray Binaries: Young objects with a high mass companion star (> 10 Msun) and (usually) High magnetic field (about 1012 Gauss) neutron starsCyclotron lines
3X-ray Binaries Classification High magnetic field neutron stars in X-ray binariesBlack Hole Candidates in X-ray binaries
4X-ray Binaries Classification High magnetic field neutron stars in X-ray binariesBlack Hole Candidates in X-ray binariesLow magnetic field neutronstars in X-ray binaries:temporal and spectralanalysis
5Caratteristiche generali dell’accrescimento Energia liberata:Luminosità:Valore massimo dato dalla luminosità di EddingtonEfficienza:Valore tipico per una NS:Valore tipico per la fusione nucleare:
6Caratteristiche generali Range tipico di emissioneModalità di accrescimento:Accrescimento tramite venti stellari.(Binarie X di alta massa)Accrescimento tramite tracimazione dal lobo di Roche.(Binarie X di bassa massa)Emissione X e γ
7Mass Transfer in LMXBs: Roche Lobe Overflow Potenziale di Roche
11Coburn et al. 2002Meszaros 1992Orlandini & Dal Fiume 2001Santangelo et al. 2003
12Multiple Harmonics?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-34U19074U (?)VELA X-1 (?)There are however some “extraordinary” observations….
13The case of X0115+63 Similar asymmetric variations The EW of harmonics were found to be larger than the fundamentalSimilar asymmetric variationsof the cyclotron line energy(up to 8 keV) were observedin Cen X-3 (Burderi et al.2000). These variations of thecyclotron line energy could beexplained by assuming anoffset (~ 0.1 RNS) of thedipolar magnetic field withrespect to the neutron starcenter. Offsets are alsosuggested by an analysis ofpulse profiles (Leahy 1991).Deep 2nd harmonickeVkeVkeVSantangelo et al. 1999
14Low Mass X-ray Binaries Close X-ray binaries:Companion star:M < 1 MSUNCompact object:NS with B < 1010 GAccretiondisk
15Low Mass X-ray Binaries 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.Companion star:M < 1 MSUNCompact object:NS with B < 1010 GAccretiondisk
16kHz QPOsPossibly related to Keplerian frequencies at the inner edge of the disk.Sco X-1Two 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)4U 1608
17Low Mass X-ray Binaries 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.Companion star:M < 1 MSUNCompact object:NS with B < 1010 GAccretiondisk
18The energy lost in electromagnetic radiation and relativistic particle beam comes from the rotational energy of the pulsar, which slows down.Radio PulsarsMeasuring P and P..allows to derive m:B ~ 108 Gauss for MSPs
19The “classical” recycling scenario Low mass X-rayBinariesB ~ 108 – 109 GLow mass companion(M ~ 1 Msun)Progenitors (Pspin >> 1ms)Accretion of mass from the companion causes spin-upMillisecond radioPulsarsB ~ 108 – 109 GLow mass companion(M ~ 0.1 Msun)End products (Pspin ~ 1ms)
21Confirmed 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)
22Rossi 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 cm2 and very good time resolution (up to 1 msec), working in the X-ray range (2-60 keV)
23Spin Frequencies of AMSPs All the spin frequencies are in the rather narrow range between 200 and 600 Hz.(From Wijnands,2005)
24Light Curves of AMSPs(X-ray Outburst of 2002)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)
25Disc – Magnetic Field Interaction Disc Pressureproportional to M.Magnetic PressureProportional to B2Rm = 10 B84/7 dotM-8-2/7 m1/7 km
26R(m) < R(cor) < R(lc) Accretion conditions(Illarionov & Sunyaev 1975)Rco = 15 P–32/3 m1/3 kmRLC = 47.7 P–3 kmAccretion regimeR(m) < R(cor) < R(lc)Pulsar spin-upaccretion of matter onto NS (magnetic poles)energy release L = dotM G M/R*Accretion of angular momentum dL/dt = l dotMwhere l = (G M Rm)1/2 is the specific angular momentum at Rm
27Pulsars spin up L=(GMRacc)1/2 The accreting matter transfers its specific angular momentum (the Keplerian AM at the accretion radius) to the neutron star:L=(GMRacc)1/22The process goes on until the pulsar reaches the keplerian velocity at Racc (equilibrium period); Pmin when Racc = RnsPmin << 1 msfor most EoSThe 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
28R(cor) < R(m) < R(lc) Propeller phaseM.Propeller regimeR(cor) < R(m) < R(lc)centrifugal barrier closes (B-field drag stronger than gravity)matter accumulates or is ejected from Rmaccretion onto Rm: lower gravitational energy releasedenergy release L = e GM(dM/dt)/R*, e = R*/2 Rm
29Rotating magnetic dipole phase .Radio Pulsar regimeRm > RLCno accretion, radio pulsaremissiondisk matter swept awayby pulsar wind and pressureEnergy release given by theLarmor formula:L = 2 R6/3c3 B2 (2 p / P)4
30Timing TechniqueCorrect time for orbital motion delays: t tarr – x sin 2/PORB (tarr –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 frequencyMain overall delays caused by spin period correction (linear term) and spin period derivative (quadratic term)
31Accretion 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 radiusMatter accretes through a Keplerian disk truncated at magnetospheric radius Rm dotM-. In standard disk accretion =2/7Matter transfers to the neutron star its specific angular momentum l = (GM Rm)1/2 at Rm, causing a torque = l dotM.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: t = dotM l – m2 / 9 Rco3
32IGR J00291: the fastest accreting MSP IGR J00291: the fastest accreting MSPPorb = 2.5 hns = 600 Hzoutburst of 20048dotn = 8.5(1.1) x Hz/s (c2/dof = 106/77)(Burderi et al. 2007, ApJ; Falanga et al. 2005, A&A)
33Conclusions: Spin-up in IGR J00291 IGR J shows a strong spin-up: ndot = 1.2 x Hz/s, which indicates a mass accretion rate of dotM = 7 10-9 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.Stronger spin up for the fastest pulsar, less spin up or spin down for the slowest ones. In the case of SAX J1808, at day 14 from the beginning of the outburst we observe a steepening of the flux decay, a shift in the pulse phase delays and possibly a change from spin-up to spin-down. These are in agreement with a scenario in which a sort of ejection mechanism becomes important when the mass accretion rate decreases explaining the steeepness in the decrease of the flux and the change from spin-up to spin.down, and this may be responsible of movements of the magnetic footpoints and of the change of the shape of the pulse profile, which probably cause the phase shift of the fundamental.
34Spin down in the case of XTE J0929-314 Porb = 44 minns = 185 HzSpin down in XTE J0929, the slowest among accreting MSPs.During the only outburst of this source observed by RXTE.Measured spin-down rate:dotn = Hz/sEstimated magnetic field: B = 5 x 108 Gauss(Di Salvo et al. 2007)
35These exclude GR as a limiting spin period mechanism Results for 6 of the 7 known LMXBs which show X-ray millisecond coherent pulsationsResults for accreting millisecond pulsars (in order of increasing spin period):IGR J : Ps=1.7ms, Porb=2.5hr SPIN UPXTE J : Ps=2.3ms, Porb=42m SPIN UPSAX 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 DOWNXTE J : Ps=5.2ms, Porb=40m SPIN UPXTE J : Ps=5.4ms, Porb=43.6m SPIN DOWNThese exclude GR as a limiting spin period mechanism
36Spettri dei Black Holes Candidates in X-ray Binaries Stati hard o lowSono fittati da:Legge di potenzaG = 1.4 – 1.9alle alte energie, con cutoff a circa 100 KeV.Corpo nero alle basse energie (circa 0.1 keV)Luminosità < 0.1 LEDD.
37Spettri dei BHXB Stati soft o high Sono fittati da: Corpo nero alle basse energie (temp. kT circa 0.5-1KeV) dominante rispetto alla legge di potenza.Legge di potenza:G = 2 – 3alle alte energie senza evidenza di cutoff fino a energie dell’ordine di circa 511KeVLuminosità > LEDD.
38Spettri dei BHXB Stati molto alti Stati high o soft Stati intermedi Stati low o hardStati di quiescenza
39Fe K-shell Line and Reflection Cygnus X-1: BeppoSAX Broad Band (0.1 – 200 keV) SpectrumSchema della regione di emissioneDi Salvo et al. (2001)HPGSPCMECSMECS
40Spettri dei BHXB: Componente di riflessione Compton Componente di riflessione è dovuta all’incidenza 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.
41Fe K-shell Line and Reflection 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.HPGSPCIron lineprofileEE0
42Self consistent models of Compton reflection and associated iron line narrowReflection fromionized matterReflection fromNeutral mattersmeared
43High resolution spectroscopy of massive BHs: MCG-6-30-15 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 than6 G M / C2.Spinning black hole? (a > 0.93)Fabian et al. 2002)
44Spettri 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.
45Neutron 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 sourcesAtoll sources:Lx ~ L(Edd)type I X-ray burstssome transientsZ-sources:Lx ~ L(Edd)all persistent
46Atoll sources: energy spectra - Soft component (few keV)(blackbody or disk-blackbody model)- Power law with exponentialcutoff (5-20 keV): ThermalComptonization.- Soft and hard states:in the hard state the cutoff shiftsto higher energies (up to > 200 keV)- Iron emission (fluorescence) lineat ~6.4 keV- Evidence for a reflection component
47X-ray energy spectra up to ~20 keV X-ray energy spectra of Z sources up to ~20 keVX-ray energy spectra up to ~20 keVTwo components needed (at least):- Eastern model (Mitsuda et al. 1984):multitemperature-blackbody + blackbody spectra(disk emission with kT = a R-3/4, and NS surfacecomptonized emission)- Western model (White et al. 1986):blackbody + Comptonized blackbody spectra(NS or disk emission, and disk emission modified byComptonization in a hotter region).
48Fe 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 ksCC Mode 5 ks
49Fe K-shell Line in NS LMXBs TE Mode 25 ksSoft Comptonization model for the X-ray continuum plus 3 narrow lines and a broad Fe line:E1 = keV, s1 = 17 eV(ID: Mg XII Ly-a, keV)E2 = 2.03 keV, s2 = 28 eV(ID: Si XIV Ly-a, keV)E3 = 2.64 keV, s3 = 40 eV(ID: S XVI Ly-a, keV)E_Fe = 6.54 keV, sFe = 0.51 keVEW = 170 eV
50Fe 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 keVRin = 7-11 Rg (15-23 km)Inclination = 55 – 84 degAlternatively, Compton broadening in the external parts of the Comptonizing corona (s = 0.5 impliest = 1.4 for kT = 2 keV)TE Mode 25 ksHints of a double-peaked line profile
52INTEGRAL/RXTE Observations of Sco X-1 Lowest dotMHard power lawSoft ComptonizationPI = 2.7kT > 290 keVFlux (40 – 200 keV) =ergs/cm2/sDi Salvo et al. (2005, ApJL)
53INTEGRAL/RXTE Observations of Sco X-1 Highest dotMPI = 2.7 (fixed)Flux (40 – 200 keV) =ergs/cm2/sDi Salvo et al. (2005, ApJL)
54NS hard tails: analogy with BHCs (Grove et al. 1998)- 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 MeVSimilar to Z-sources in HB-NB- BHCs in HS: very soft thermal component.Similar to Z-sources in NB-FB.Hard X-ray NS/BHC indicators are uncertain at least !
55Geometry and Models for hard tails in NS binaries Origine della legge di potenza negli stati soft di BHXB e LMXBs:Temperature altissimeIpotesi I: comptonizzazione termicaIpotesi II: (comptonizzazione non termica) caduta radiale della materia in corrispondenza di LSO.Non può spiegare l’hard tail nelle NS LMXBDistribuzione a legge di potenza.Evidenze radio in BH e NS.Intensità radio maggiore più è intensa la componente hard.Ipotesi III: (comptonizzazione non termica) Jet relativisticiMolto probabile
56Geometry and Models for hard tails in NS binaries - Bulk motion Comptonisation convergingradial or disk inflow (Titarchuk & Zannias1998; Luarent & Titarchuk 1999;Psaltis 2001)Inflow in Z-sources is strongly affected byradiation from the NS- Comptonisation by thermal e- in a coronapredicts high energy cutoff- Comptonisation (or synchrotronradiation) 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 veryhigh energiesJet: hard tail ?Disk: soft X-raysComptonisingcorona: hard tail ?
57The radio connection: other NS binaries - Radio jets: likely a common phenomenon also in X-ray binariesClass Fraction as radio sourcesPersistent BHCs /4Transient BHCs ~15/35NS Z-sources /6NS Atoll sources ~5/100(Fender 2001)- In Z sources (e.g. GX 17+2) radio flaring in the HB (i.e. low accretionrates)- Fewer searches (and detections) in Atoll sources
58The 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
60Threaded disc modelBzDragging of the field line: a Bf component is generatedBz = h m2 / R3 ,<= 1 screening factorBf is amplificated by differential rotation up to:Bf = g / a [(W - WK)/WK]/Bz(a = SS viscosity, g >= 1)BfWWhere the amplification is limited by turbulent diffusion(Wang 1995)
61Threaded disc modelYet, 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):tmag = m2 / 9 Rco3A self consistent solution of the Threaded Disc is required!
62Results for IGR JIn a good approximation the X-ray flux is observed to linearly decrease with time during the outburst:dotM(t) = dotM0 [1-(t – T0)/TB], where TB = 8.4 daysAssuming Rm dotM-. ( = 2/7 for standard accretion disks; a = 0 for a constant accretion radius equal to Rc; a = 2 for a simple parabolic function), we calculate the expected phase delays vs. time:f = - f0 – Dn0 (t-T0) – ½ dotn0 (t – T0)2 [1 – (2-a) (t-T0)/6TB]We have calculated a lower limit to the mass accretion rate (obtained for the case a = 0 and no negative threading (m = 1.4, I45 = 1.29)dotM = dotn–13 I45 m-2/3 Msun/yrMeasured dotn–13= 11.7, gives a lower limit of dotM = (7+/-1) 10-9 Msun/yr, corresponding to Lbol = 7 x 1037 ergs/s
63Distance to IGR JThe 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 !)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..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
64The Strange case of XTE J1807 The outburst of February 2003(Riggio et al. 2007, in preparation)
65But… There is order beyond the chaos! The key idea:Harmonic decomposition of the pulse profile
69(Burderi et al. 2006, ApJ Letters) SAX J1808: the outburst of 2002(Burderi et al. 2006, ApJ Letters)Phase Delays ofThe First HarmonicPhase Delays ofThe FundamentalSpin-up:dotn = Hz/sPorb = 2 hn = 401 HzSpin-down at the end of the outburst:dotn = Hz/s
70SAX J : Pulse ProfilesFolded 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
71SAX J1808.4-3658: 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.
72Discussion 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) = dotM0 exp[(t – T0)/TB], where TB = 9.3 daysderived from a fit of the first 14 days of the light curve.Assuming Rm dotM-. (with = 0 for a constant accretion radius equal to Rco), we calculate the expected phase delays vs. time:f = - f0 – B (t-T0) – C exp[(t-T0)/TB] + ½ dotn0 (t – T0)2where B = Dn0 + C/TB and C = I45-1 P-31/3 m2/3 TB2 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.
73Discussion of the results for SAX J1808 Spin up: dotn0 = Hz/s corresponding to a mass accretion rate of dotM = Msun/yrSpin-down: dotn0 = Hz/sIn 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: m2 / 9 Rco3 = 2 p I dotnsd from where we evaluate the NS magnetic field: B = (3.5 +/- 0.5) 108 Gauss: (in agrement with previous results, B = Gauss, Di Salvo & Burderi 2003)
74Timing of XTE J1751As in the case of SAX J1808, the X-ray flux of XTE J1751 decreases exponentially with time (TB = 7.2 days).The best fit of the phase delays corresponds to Rm dotM-.wth a = 2/7, and gives dotn0 = Hz/s and dotM0 = (3.4 – 8.7) 10-9 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)Porb = 42 minns = 435 Hz
75Spin down in the case of XTE J1814 Papitto et al. 2007, MNRASPhase Delays ofThe FundamentalPhase Delays ofThe First HarmonicSpin-down:dotn = Hz/sPspin = 3.5 msec, Porb = 4.3 h
76Phase residuals anticorrelated to flux changes in XTE J1814-338 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 changesPost fit residuals of the FundamentalPost fit residuals of the harmonicEstimated magnetic field:B = 8 x 108 Gauss
77XTE J0929-314: 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 assumenspin-up << -nspin-down = 5.5 x Hz /sAssuming 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 1035 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)
78Conclusions: Spin-upXTE J shows a noisy fundamental and a clear spin-up in the second harmonic: ndot = (1 – 3.5) Hz/s. No clear diagnostic is possible, spin-up and spin-down may be both present.XTE J shows a strong spin-up: ndot = 6.3 x Hz/s, which indicates a mass accretion rate of dotM = (3.4 – 8.7) 10-9 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.Stronger spin up for the fastest pulsar, less spin up or spin down for the slowest ones. In the case of SAX J1808, at day 14 from the beginning of the outburst we observe a steepening of the flux decay, a shift in the pulse phase delays and possibly a change from spin-up to spin-down. These are in agreement with a scenario in which a sort of ejection mechanism becomes important when the mass accretion rate decreases explaining the steeepness in the decrease of the flux and the change from spin-up to spin.down, and this may be responsible of movements of the magnetic footpoints and of the change of the shape of the pulse profile, which probably cause the phase shift of the fundamental.
79Conclusions: Spin-down XTE J shows noisy fundamental and harmonic phase delays, and a strong spin-down: ndot = -6.7 x Hz/s, which indicates a quite large magnetic field of B = 8 108 Gauss.XTE J shows a clear spin-down of ndot = -5.5 x Hz/s, which indicates a magnetic field of B = 4-5 108 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.