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Transcript of Scuola Nazionale di Dottorato Cagliari, May 25 2007 Proprietà Osservative delle Binarie X...
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
Scuola Nazionale di DottoratoCagliari, May 25 2007
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
Scuola Nazionale di DottoratoCagliari, May 25 2007
X-ray Binaries Classification• High magnetic field neutron stars in X-ray binaries
• Black Hole Candidates in X-ray binaries
Scuola Nazionale di DottoratoCagliari, May 25 2007
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
Scuola Nazionale di DottoratoCagliari, May 25 2007
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:
Scuola Nazionale di DottoratoCagliari, May 25 2007
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)
Scuola Nazionale di DottoratoCagliari, May 25 2007
Mass Transfer in LMXBs: Roche Lobe Overflow
Potenziale di Roche
Scuola Nazionale di DottoratoCagliari, May 25 2007
X-ray pulsars
Scuola Nazionale di DottoratoCagliari, May 25 2007
BB
Fe Lines
PL ~
Ecyc
Wien Hump
Dal Fiume et al. 1998
Scuola Nazionale di DottoratoCagliari, May 25 2007
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
Scuola Nazionale di DottoratoCagliari, May 25 2007
cos2ln8
2mc
kTcd
Meszaros 1992
Coburn et al. 2002
Orlandini & Dal Fiume 2001
Santangelo et al. 2003
Scuola Nazionale di DottoratoCagliari, May 25 2007
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….
Scuola Nazionale di DottoratoCagliari, May 25 2007
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).
Scuola Nazionale di DottoratoCagliari, May 25 2007
Low Mass X-ray Binaries
Companion star: M < 1 MSUN
Accretion disk
Compact object:NS with B < 1010 G
Close X-ray binaries:
Scuola Nazionale di DottoratoCagliari, May 25 2007
Low Mass X-ray Binaries
Companion star: M < 1 MSUN
Accretion disk
Compact object:NS with B < 1010 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.
Scuola Nazionale di DottoratoCagliari, May 25 2007
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.
Scuola Nazionale di DottoratoCagliari, May 25 2007
Low Mass X-ray Binaries
Companion star: M < 1 MSUN
Accretion disk
Compact object:NS with B < 1010 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 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.
Scuola Nazionale di DottoratoCagliari, May 25 2007
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
.
Scuola Nazionale di DottoratoCagliari, May 25 2007
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
Scuola Nazionale di DottoratoCagliari, May 25 2007
Scuola Nazionale di DottoratoCagliari, May 25 2007
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)
Scuola Nazionale di DottoratoCagliari, May 25 2007
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)
Scuola Nazionale di DottoratoCagliari, May 25 2007
Spin Frequencies of AMSPs
All the spin frequencies are in the rather narrow range between 200 and 600 Hz.
(From Wijnands,2005)
Scuola Nazionale di DottoratoCagliari, May 25 2007
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)
Scuola Nazionale di DottoratoCagliari, May 25 2007
Disc Pressureproportional to M
Magnetic PressureProportional to B2
Disc – Magnetic Field Interaction
.
Rm = 10 B84/7 dotM-8
-2/7 m1/7 km
Scuola Nazionale di DottoratoCagliari, May 25 2007
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
Scuola Nazionale di DottoratoCagliari, May 25 2007
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
Scuola Nazionale di DottoratoCagliari, May 25 2007
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
Scuola Nazionale di DottoratoCagliari, May 25 2007
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
Scuola Nazionale di DottoratoCagliari, May 25 2007
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)
Scuola Nazionale di DottoratoCagliari, May 25 2007
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.
Scuola Nazionale di DottoratoCagliari, May 25 2007
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
Scuola Nazionale di DottoratoCagliari, May 25 2007
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.
Scuola Nazionale di DottoratoCagliari, May 25 2007
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)
Scuola Nazionale di DottoratoCagliari, May 25 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 J1807-294: Ps=5.2ms, Porb=40m SPIN UP
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
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 J1807-294: Ps=5.2ms, Porb=40m SPIN UP
XTE J0929-314: Ps=5.4ms, Porb=43.6m SPIN DOWN
These exclude GR as a limiting spin period mechanism
Scuola Nazionale di DottoratoCagliari, May 25 2007
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.
Scuola Nazionale di DottoratoCagliari, May 25 2007
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.
Scuola Nazionale di DottoratoCagliari, May 25 2007
Spettri dei BHXB
Stati molto alti
Stati high o soft
Stati intermedi
Stati low o hard
Stati di quiescenza
Scuola Nazionale di DottoratoCagliari, May 25 2007
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
Scuola Nazionale di DottoratoCagliari, May 25 2007
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.
Scuola Nazionale di DottoratoCagliari, May 25 2007
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.
Scuola Nazionale di DottoratoCagliari, May 25 2007
Self consistent models of Compton reflection and associated iron line
Reflection fromionized matter
Reflection fromNeutral matter
narrow
smeared
Scuola Nazionale di DottoratoCagliari, May 25 2007
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)
Scuola Nazionale di DottoratoCagliari, May 25 2007
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.
Scuola Nazionale di DottoratoCagliari, May 25 2007
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
Scuola Nazionale di DottoratoCagliari, May 25 2007
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
Scuola Nazionale di DottoratoCagliari, May 25 2007
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).
Scuola Nazionale di DottoratoCagliari, May 25 2007
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
Scuola Nazionale di DottoratoCagliari, May 25 2007
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
Scuola Nazionale di DottoratoCagliari, May 25 2007
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
Scuola Nazionale di DottoratoCagliari, May 25 2007
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
Scuola Nazionale di DottoratoCagliari, May 25 2007
INTEGRAL/RXTE Observations of Sco X-1
Di Salvo et al. (2005, ApJL)
Soft Comptonization
Hard power law
PI = 2.7kT > 290 keVFlux (40 – 200 keV) = 0.48 10-9 ergs/cm2/s
Lowest dotM
Scuola Nazionale di DottoratoCagliari, May 25 2007
Di Salvo et al. (2005, ApJL)
PI = 2.7 (fixed)
Flux (40 – 200 keV) = 0.06 10-9 ergs/cm2/s
INTEGRAL/RXTE Observations of Sco X-1
Highest dotM
Scuola Nazionale di DottoratoCagliari, May 25 2007
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 !
Scuola Nazionale di DottoratoCagliari, May 25 2007
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
Scuola Nazionale di DottoratoCagliari, May 25 2007
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
Scuola Nazionale di DottoratoCagliari, May 25 2007
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
Scuola Nazionale di DottoratoCagliari, May 25 2007
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
Scuola Nazionale di DottoratoCagliari, May 25 2007
The end
Thank you very much!
Scuola Nazionale di DottoratoCagliari, May 25 2007
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)
Scuola Nazionale di DottoratoCagliari, May 25 2007
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!
Scuola Nazionale di DottoratoCagliari, May 25 2007
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
Scuola Nazionale di DottoratoCagliari, May 25 2007
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..
Scuola Nazionale di DottoratoCagliari, May 25 2007
The Strange case of XTE J1807
The outburst of February 2003(Riggio et al. 2007, in preparation)
Scuola Nazionale di DottoratoCagliari, May 25 2007
But… There is order beyond the chaos!
The key idea:Harmonic decomposition of the pulse profile
Scuola Nazionale di DottoratoCagliari, May 25 2007
Timing of the second harmonic
Scuola Nazionale di DottoratoCagliari, May 25 2007
Back to the fundamental
Scuola Nazionale di DottoratoCagliari, May 25 2007
Positional Uncertainties of XTE J1807 (0.6’’)
Scuola Nazionale di DottoratoCagliari, May 25 2007
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
Scuola Nazionale di DottoratoCagliari, May 25 2007
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
Scuola Nazionale di DottoratoCagliari, May 25 2007
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.
Scuola Nazionale di DottoratoCagliari, May 25 2007
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.
Scuola Nazionale di DottoratoCagliari, May 25 2007
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)
Scuola Nazionale di DottoratoCagliari, May 25 2007
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)
Scuola Nazionale di DottoratoCagliari, May 25 2007
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
Scuola Nazionale di DottoratoCagliari, May 25 2007
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
Scuola Nazionale di DottoratoCagliari, May 25 2007
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)
Scuola Nazionale di DottoratoCagliari, May 25 2007
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.
Scuola Nazionale di DottoratoCagliari, May 25 2007
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.