1. 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. X-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 stars
Cyclotron lines

3. X-ray Binaries Classification
High magnetic field neutron stars in X-ray binaries
Black Hole Candidates in X-ray binaries

4. 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. 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:

6. Caratteristiche generali
Range tipico di emissione
Modalità 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

7. Mass Transfer in LMXBs: Roche Lobe Overflow
Potenziale di Roche

8. X-ray pulsars

9. BB
Fe Lines
PL a~1
Ecyc
Wien Hump
Dal Fiume et al. 1998

10. Cyclotron lines
Meszaros, 1992

11. Coburn et al. 2002
Meszaros 1992
Orlandini & Dal Fiume 2001
Santangelo et al. 2003

12. Multiple 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-3
4U1907
4U (?)
VELA X-1 (?)
There are however some “extraordinary” observations….

13. The case of X0115+63 Similar asymmetric variations
The EW of harmonics were found to be larger than the fundamental
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).
Deep 2nd harmonic
keV
keV
keV
Santangelo et al. 1999

14. Low Mass X-ray Binaries
Close X-ray binaries:
Companion star:
M < 1 MSUN
Compact object:
NS with B < 1010 G
Accretion
disk

15. Low 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 MSUN
Compact object:
NS with B < 1010 G
Accretion
disk

16. kHz QPOs
Possibly related to Keplerian frequencies at the inner edge of the disk.
Sco X-1
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)
4U 1608

17. Low 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 MSUN
Compact object:
NS with B < 1010 G
Accretion
disk

18. The energy lost in electromagnetic radiation and relativistic particle beam comes from the rotational energy of the pulsar, which slows down.
Radio Pulsars
Measuring P and P . .
allows to derive m:
B ~ 108 Gauss for MSPs

19. The “classical” recycling scenario
Low mass X-ray
Binaries
B ~ 108 – 109 G
Low mass companion
(M ~ 1 Msun)
Progenitors (Pspin >> 1ms)
Accretion of mass from the companion causes spin-up
Millisecond radio
Pulsars
B ~ 108 – 109 G
Low mass companion
(M ~ 0.1 Msun)
End products (Pspin ~ 1ms)

21. 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)

22. 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 msec), working in the X-ray range (2-60 keV)

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

24. Light 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)

25. Disc – Magnetic Field Interaction
Disc Pressure
proportional to M .
Magnetic Pressure
Proportional to B2
Rm = 10 B84/7 dotM-8-2/7 m1/7 km

26. R(m) < R(cor) < R(lc)
Accretion conditions
(Illarionov & Sunyaev 1975)
Rco = 15 P–32/3 m1/3 km
RLC = 47.7 P–3 km
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

27. Pulsars 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)1/2 2
The process goes on until the pulsar reaches the keplerian velocity at Racc (equilibrium period); Pmin when Racc = Rns
Pmin << 1 ms
for most EoS
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

28. R(cor) < R(m) < R(lc)
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 Rm
accretion onto Rm: lower gravitational energy released
energy release L = e GM(dM/dt)/R*, e = R*/2 Rm

29. Rotating magnetic dipole phase.
Radio Pulsar regime
Rm > 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 / P)4

30. 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)

31. 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
Matter 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

32. IGR J00291: the fastest accreting MSP
IGR J00291: the fastest accreting MSP
Porb = 2.5 h
ns = 600 Hz
outburst of 2004 8
dotn = 8.5(1.1) x Hz/s (c2/dof = 106/77)
(Burderi et al. 2007, ApJ; Falanga et al. 2005, A&A)

33. Conclusions: 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.

34. Spin down in the case of XTE J0929-314
Porb = 44 min
ns = 185 Hz
Spin 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/s
Estimated magnetic field: B = 5 x 108 Gauss
(Di Salvo et al. 2007)

35. These exclude GR as a limiting spin period mechanism
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
These exclude GR as a limiting spin period mechanism

36. Spettri dei Black Holes Candidates in X-ray Binaries
Stati hard o low
Sono fittati da:
Legge di potenza
G = 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.

37. 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:
G = 2 – 3
alle alte energie senza evidenza di cutoff fino a energie dell’ordine di circa 511KeV
Luminosità > LEDD.

38. Spettri dei BHXB Stati molto alti Stati high o soft Stati intermedi
Stati low o hard
Stati di quiescenza

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

40. 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.

41. Fe 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.
HPGSPC
Iron line
profile E E0

42. Self consistent models of Compton reflection and associated iron line
narrow
Reflection from
ionized matter
Reflection from
Neutral matter
smeared

43. High 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 than
6 G M / C2.
Spinning black hole? (a > 0.93)
Fabian et al. 2002)

44. 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. 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. 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. X-ray energy spectra up to ~20 keV
X-ray energy spectra of Z sources up to ~20 keV
X-ray energy spectra 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. 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. 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, 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 keV
EW = 170 eV

50. 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)
TE Mode 25 ks
Hints of a double-peaked line profile

51. Hard X-ray Emission in LMXBs: INTEGRAL/RXTE Observations of Sco X-1
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/cm2/s
Flux (40 – 200 keV) = ergs/cm2/s
ISGRI
SPI
Di Salvo et al. (2005, ApJL)

52. INTEGRAL/RXTE Observations of Sco X-1
Lowest dotM
Hard power law
Soft Comptonization
PI = 2.7
kT > 290 keV
Flux (40 – 200 keV) =
ergs/cm2/s
Di Salvo et al. (2005, ApJL)

53. INTEGRAL/RXTE Observations of Sco X-1
Highest dotM
PI = 2.7 (fixed)
Flux (40 – 200 keV) =
ergs/cm2/s
Di Salvo et al. (2005, ApJL)

54. NS 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 MeV
Similar 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 !

55. Geometry and Models for hard tails in NS binaries
Origine della legge di potenza negli stati soft di BHXB e LMXBs:
Temperature altissime
Ipotesi I: comptonizzazione termica
Ipotesi II: (comptonizzazione non termica) caduta radiale della materia in corrispondenza di LSO.
Non può spiegare l’hard tail nelle NS LMXB
Distribuzione 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 relativistici
Molto probabile

56. Geometry and Models for hard tails in NS binaries
- 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
Jet: hard tail ?
Disk: soft X-rays
Comptonising
corona: hard tail ?

57. 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
Transient BHCs ~15/35
NS Z-sources /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. 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. The end Thank you very much!

60. Threaded disc model Bz
Dragging of the field line: a Bf component is generated
Bz = h m2 / R3 ,
<= 1 screening factor
Bf is amplificated by differential rotation up to:
Bf = g / a [(W - WK)/WK]/Bz
(a = SS viscosity, g >= 1) Bf W
Where the amplification is limited by turbulent diffusion
(Wang 1995)

61. 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):
tmag = m2 / 9 Rco3
A self consistent solution of the Threaded Disc is required!

62. Results for IGR J
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 days
Assuming 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/yr
Measured dotn–13= 11.7, gives a lower limit of dotM = (7+/-1) 10-9 Msun/yr, corresponding to Lbol = 7 x 1037 ergs/s

63. 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 !)
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

64. The Strange case of XTE J1807
The outburst of February 2003
(Riggio et al. 2007, in preparation)

65. But… There is order beyond the chaos!
The key idea:
Harmonic decomposition of the pulse profile

66. Timing of the second harmonic

67. Back to the fundamental

68. Positional Uncertainties of XTE J1807 (0.6’’)

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

70. 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. 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.

72. 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 days
derived 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)2
where 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.

73. Discussion of the results for SAX J1808
Spin up: dotn0 = Hz/s corresponding to a mass accretion rate of dotM = Msun/yr
Spin-down: dotn0 = 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: 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)

74. Timing of XTE J1751
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 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 min
ns = 435 Hz

75. Spin down in the case of XTE J1814
Papitto et al. 2007, MNRAS
Phase Delays of
The Fundamental
Phase Delays of
The First Harmonic
Spin-down:
dotn = Hz/s
Pspin = 3.5 msec, Porb = 4.3 h

76. Phase 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 changes
Post fit residuals of the Fundamental
Post fit residuals of the harmonic
Estimated magnetic field:
B = 8 x 108 Gauss

77. 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
nspin-up << -nspin-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 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)

78. Conclusions: Spin-up
XTE 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.

79. Conclusions: 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.