Proprietà Osservative delle Binarie X Contenenti Stelle di Neutroni

Scuola Nazionale di DottoratoCagliari, May 25 2007

Proprietà Osservative delle Binarie X Contenenti Stelle di Neutroni

Tiziana Di Salvo

Dipartimento di Scienze Fisiche ed Astronomiche, Università di PalermoVia Archirafi 36- 90123 Palermo Italy


X-ray Binaries Classification

Gauss) 12

10 of(unit 6.11 12BE c

Cyclotron lines

• High Mass X-ray Binaries: Young objects with a high mass companion star (> 10 Msun) and (usually) High magnetic field (about 1012 Gauss) neutron stars


X-ray Binaries Classification• High magnetic field neutron stars in X-ray binaries

• Black Hole Candidates in X-ray binaries


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


Caratteristiche generali dell’accrescimento

• Energia liberata:

• Luminosità:– Valore massimo dato

dalla luminosità di Eddington

• Efficienza:

– Valore tipico per una NS:

– Valore tipico per la fusione nucleare:


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)


Mass Transfer in LMXBs: Roche Lobe Overflow

Potenziale di Roche


X-ray pulsars


BB

Fe Lines

PL ~

Ecyc

Wien Hump

Dal Fiume et al. 1998


Gauss) 12

10 of(unit 6.11 12BE c

cos2ln8

2mc

kTcd

Meszaros, 1992

Cyclotron lines

θsin

1θsinωn2mcmcω

;ωnω; γmc

eBω

2

2c

22

n

cnc


cos2ln8

2mc

kTcd

Meszaros 1992

Coburn et al. 2002

Orlandini & Dal Fiume 2001

Santangelo et al. 2003


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

4U1626-67 (?)

VELA X-1 (?)

Multiple Harmonics?

There are however some “extraordinary” observations….


Deep 2nd harmonic

E1cyc 12.74 E2

cyc 24.16 keV

E3cyc 35.74 E4

cyc 49.5 keV

E5cyc 60. keV

The EW of harmonics were found to be larger than the fundamental

The case of X0115+63

Santangelo et al. 1999

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 RNS) of the dipolar magnetic field with respect to the neutron star center. Offsets are also suggested by an analysis of pulse profiles (Leahy 1991).


Low Mass X-ray Binaries

Companion star: M < 1 MSUN

Accretion disk

Compact object:NS with B < 1010 G

Close X-ray binaries:




Accretion disk



• 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.


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.




Accretion disk



• 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 300-600 Hz (probably the NS spin frequency).

• Some are transient, with quiescent luminosities of 1032-1033 erg/s and outburst luminosities of 1036-1038 erg/s.


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 ~ 108 Gauss for MSPs

.


Millisecond radioPulsars

B ~ 108 – 10

9 G

Low mass companion(M ~ 0.1 Msun)

Low mass X-rayBinaries

B ~ 108 – 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



Confirmed by 7 (transient) LMXBs which show X-ray millisecond coherent

pulsations

Confirmed by 7 (transient) LMXBs which show X-ray millisecond coherent

pulsationsKnown accreting millisecond pulsars (in order of increasing spin period):

IGR J00291+5934: Ps=1.7ms, Porb=2.5hr (Galloway et al. 2005)XTE J1751-306: Ps=2.3ms, Porb=42m (Markwardt et al.

2002)

SAX J1808.4-3658: Ps=2.5ms, Porb=2hr (Wijnands & van der Klis 1998)HETE J1900.1-2455: Ps=2.7ms, Porb=1.4hr (Kaaret et al. 2005)

XTE J1814-338: Ps=3.2ms, Porb=4hr (Markwardt et al. 2003)XTE J1807-294: Ps=5.2ms, Porb=40m (Markwardt et al. 2003)XTE J0929-314: Ps=5.4ms, Porb=43.6m (Galloway et al. 2002)

Known accreting millisecond pulsars (in order of increasing spin period):

IGR J00291+5934: Ps=1.7ms, Porb=2.5hr (Galloway et al. 2005)XTE J1751-306: Ps=2.3ms, Porb=42m (Markwardt et al.

2002)

SAX J1808.4-3658: Ps=2.5ms, Porb=2hr (Wijnands & van der Klis 1998)HETE J1900.1-2455: Ps=2.7ms, Porb=1.4hr (Kaaret et al. 2005)

XTE J1814-338: Ps=3.2ms, Porb=4hr (Markwardt et al. 2003)XTE J1807-294: Ps=5.2ms, Porb=40m (Markwardt et al. 2003)XTE J0929-314: Ps=5.4ms, Porb=43.6m (Galloway et al. 2002)


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 cm2 and very good time resolution (up to 1 sec), working in the X-ray range (2-60 keV)


Spin Frequencies of AMSPs

All the spin frequencies are in the rather narrow range between 200 and 600 Hz.

(From Wijnands,2005)


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)


Disc Pressureproportional to M

Magnetic PressureProportional to B2

Disc – Magnetic Field Interaction

.

Rm = 10 B84/7 dotM-8

-2/7 m1/7 km


Accretion conditions(Illarionov & Sunyaev 1975)

Accretion regimeR(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

Rco = 15 P–32/3 m1/3 km

RLC = 47.7 P–3 km


Pulsars spin up

The accreting matter transfers its specific angular momentum (the Keplerian AM at the accretion radius) to the neutron star:

L=(GMRacc)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


Propeller phase

M.

Propeller regimeR(cor) < R(m) <

R(lc)

• centrifugal barrier closes (B-field drag stronger than gravity)• matter accumulates or is ejected from Rm • accretion onto Rm: lower gravitational energy released

• energy release L = GM(dM/dt)/R*, = R*/2 Rm


Rotating magnetic dipole phase

M. Radio Pulsar

regimeRm > RLC

• no accretion, radio pulsar emission• disk matter swept away by pulsar wind and pressure• Energy release given by the Larmor formula:

L = 2 R6/3c3 B2 (2 / P)4


Timing Technique • Correct 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 frequency

• Main overall delays caused by spin period correction (linear term) and spin period derivative (quadratic term)


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 Rm 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 Rco3

Matter transfers to the neutron star its specific angular momentum l = (GM Rm)1/2 at Rm, causing a torque = l dotM.


IGR J00291: the fastest accreting MSP

dot = 8.5(1.1) x 10-13 Hz/s 2/dof = 106/77

(Burderi et al. 2007, ApJ; Falanga et al. 2005, A&A)

Porb = 2.5 hs = 600 Hz

0 8


Conclusions: Spin-up in IGR J00291

IGR J00291+5934 shows a strong spin-up: dot = 1.2 x 10-12 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.


Spin down in the case of XTE J0929-314

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 = -5.5 10-14 Hz/sEstimated magnetic field: B = 5 x 108 Gauss

Porb = 44 mins = 185 Hz

(Di Salvo et al. 2007)


Results for 6 of the 7 known LMXBs which show X-ray millisecond coherent

pulsations

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 J00291+5934: Ps=1.7ms, Porb=2.5hr SPIN UP

XTE J1751-306: Ps=2.3ms, Porb=42m SPIN UP

SAX J1808.4-3658: Ps=2.5ms, Porb=2hr SPIN UP (SPIN DOWN)

HETE J1900.1-2455: Ps=2.7ms, Porb=1.4hr ??

XTE J1814-338: Ps=3.2ms, Porb=4hr SPIN DOWN


XTE J0929-314: Ps=5.4ms, Porb=43.6m SPIN DOWN

Results for accreting millisecond pulsars (in order of increasing spin period):

IGR J00291+5934: Ps=1.7ms, Porb=2.5hr SPIN UP


SAX J1808.4-3658: Ps=2.5ms, Porb=2hr SPIN UP (SPIN DOWN)

HETE J1900.1-2455: Ps=2.7ms, Porb=1.4hr ??

XTE J1814-338: Ps=3.2ms, Porb=4hr SPIN DOWN


XTE J0929-314: Ps=5.4ms, Porb=43.6m SPIN DOWN

These exclude GR as a limiting spin period mechanism


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 LEDD.


Spettri 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:

= 2 – 3

alle alte energie senza evidenza di cutoff fino a energie dell’ordine di circa 511KeV

•Luminosità > 0.2-0.3LEDD.


Spettri dei BHXB

Stati molto alti

Stati high o soft

Stati intermedi

Stati low o hard

Stati di quiescenza


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


Spettri 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.


Fe K-shell Line and Reflection

HPGSPC

Iron lineprofile

EE0

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.


Self consistent models of Compton reflection and associated iron line

Reflection fromionized matter

Reflection fromNeutral matter

narrow

smeared


High resolution spectroscopy of massive BHs: MCG-6-30-15

XMM observation of the iron line region in MCG-6-30-15 taken in 2001. The red wing extends to less than 4 keV, indicating an inner radius of less than 6 G M / C2.

Spinning black hole? (a > 0.93)

Fabian et al. 2002)


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.


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 ~ 0.01-0.1 L(Edd) type I X-ray bursts some transients

Z-sources: Lx ~ 0.1-1.0 L(Edd) all persistent


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


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).


Fe K-shell Line in Neutron Star Low Mass X-ray binaries

Chandra observation of the LMXB/atoll source 4U 1705-44 (Di Salvo et al. 2005, ApJ Letters)

TE Mode 25 ksCC Mode 5 ks


Fe K-shell Line in NS LMXBsTE Mode 25 ks

Soft Comptonization model for the X-ray continuum plus 3 narrow lines and a broad Fe line:

• E1 = 1.476 keV, 1 = 17 eV (ID: Mg XII Ly-, 1.473 keV)

• E2 = 2.03 keV, 2 = 28 eV (ID: Si XIV Ly-, 2.006 keV)

• E3 = 2.64 keV, 3 = 40 eV (ID: S XVI Ly-, 2.6223 keV)

• E_Fe = 6.54 keV, Fe = 0.51 keV EW = 170 eV


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


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 = 2.3kT > 200 keV

Flux (20 – 40 keV) = 5.9 10-9 ergs/cm2/sFlux (40 – 200 keV) = 0.33 10-9 ergs/cm2/s


INTEGRAL/RXTE Observations of Sco X-1


Soft Comptonization

Hard power law

PI = 2.7kT > 290 keVFlux (40 – 200 keV) = 0.48 10-9 ergs/cm2/s

Lowest dotM



PI = 2.7 (fixed)

Flux (40 – 200 keV) = 0.06 10-9 ergs/cm2/s

INTEGRAL/RXTE Observations of Sco X-1

Highest dotM


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 !


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 l’hard 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


Geometry and Models for hard tails in NS binaries

Jet: hard tail ?

Disk: soft X-rays

Comptonisingcorona: 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


The radio connection: other NS binaries

- Radio jets: likely a common phenomenon also in X-ray binaries

Class Fraction as radio sources

Persistent BHCs 4/4Transient BHCs ~15/35

NS Z-sources 6/6NS 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


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


The end

Thank you very much!


Threaded disc model

Bz

B

Dragging of the field line: a B component is generated

Bz = 2 / R3 ,<= 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)


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 Rco3

A self consistent solution of the Threaded Disc A self consistent solution of the Threaded Disc is required!is required!


Results for IGR J00291+5934

In 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;

= 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-T0) – ½ dot0 (t – T0)2 [1 – (2-) (t-T0)/6TB]

Measured dot–13= 11.7, gives a lower limit of dotM = (7+/-1) 10-9 Msun/yr, corresponding to Lbol = 7 x 1037 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, I45 = 1.29)

dotM = 5.9 10-10 dot–13 I45 m-2/3 Msun/yr


Distance to IGR J00291+5934

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..


The Strange case of XTE J1807

The outburst of February 2003(Riggio et al. 2007, in preparation)


But… There is order beyond the chaos!

The key idea:Harmonic decomposition of the pulse profile


Timing of the second harmonic


Back to the fundamental


Positional Uncertainties of XTE J1807 (0.6’’)


SAX J1808: the outburst of 2002

Phase Delays ofThe Fundamental

Phase Delays ofThe First Harmonic

Spin-down at the end of the outburst:

dot = -7.6 10-14 Hz/s

(Burderi et al. 2006, ApJ Letters)

Porb = 2 h= 401 Hz

Spin-up:

dot = 4.4 10-13 Hz/s


SAX J1808.4-3658: 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


SAX 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.


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) = 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:

= - 0 – (t-T0) – C exp[(t-T0)/TB] + ½ dot0 (t – T0)2

where B = 0 + C/TB and C = 1.067 10-4 I45-1 P-3

1/3 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.


Discussion of the results for SAX J1808

Spin up: dot0 = 4.4 10-13 Hz/s corresponding to a mass accretion rate of dotM = 1.8 10-9 Msun/yr

Spin-down: dot0 = -7.6 10-14 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 Rco3 = 2 I dotsd from where we evaluate the NS magnetic field: B = (3.5 +/- 0.5) 108 Gauss: (in agrement with previous results, B = 1-5 108

Gauss, Di Salvo & Burderi 2003)


Timing of XTE J1751

Porb = 42 mins = 435 Hz

As 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 = 2/7, and gives dot0 = 6.3 10-13 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 7-8.5 kpc using the same arguments used for IGR J00291).

(Papitto et al. 2007, in preparation)


Spin down in the case of XTE J1814

Phase Delays ofThe Fundamental

Phase Delays ofThe First Harmonic

Papitto et al. 2007, MNRAS

Spin-down:dot = -6.7 10-14 Hz/s


Phase residuals anticorrelated to flux changes in XTE J1814-

338Modulations 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 Fundamental

Post fit residuals of the harmonic

Estimated magnetic field:B = 8 x 108 Gauss


XTE 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 assume

spin-up << -spin-down = 5.5 x 10-14 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 10-11 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)


Conclusions: Spin-up

XTE J1751-306 shows a strong spin-up: dot = 6.3 x 10-13 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.

XTE J1807-294 shows a noisy fundamental and a clear spin-up in the second harmonic: dot = (1 – 3.5) 10-14 Hz/s. No clear diagnostic is possible, spin-up and spin-down may be both present.


Conclusions: Spin-down

XTE J1814-338 shows noisy fundamental and harmonic phase delays, and a strong spin-down: dot = -6.7 x 10-14 Hz/s, which indicates a quite large magnetic field of B = 8 108 Gauss.

XTE J0929-314 shows a clear spin-down of dot = -5.5 x 10-14 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.

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Proprietà Osservative delle Binarie X Contenenti Stelle di Neutroni