I I I

Fig. 14.7 Observations of surface temperatures and upper bounds for several isolated neutron stars. The solid line is the basic theoretical cooling curve of a nonsuperfluid neutron star with M = 1.3 [email protected] [112]. The upper limit on the temperature of the old pulsar PSR 1929+10 was added [8]

B1055-52 [78,79], and a few other sources. ROSAT also discovered seven neutron stars showing pure thermal emission in X-rays (see next paragraph). More sources and many more details on spectra and time variability were obtained more recently with Chandra and XMM-Newton [9]. Figure 14.7 shows a comparison of observed neutron star temperatures as a function of age compared with the results of standard cooling theory as summarized by Yakovlev and Pethick [112]. This comprehensive article also contains more detailed comparisons of observations and predictions from a variety of cooling models.

Addressing cooling neutron stars it might be worth to closer consider the group of isolated radio-quiet neutron stars. ROSAT observations revealed the existence of a group of seven of these bright and soft X-ray sources [44, 73, 97]. The X-ray spectra of the "magnificent seven," as they are sometimes called, are purely thermal and blackbody-like. Derived blackbody temperatures are in the range of (0.5—1.2) x 106 K. They do not show hard spectral components or radio emission (with maybe the exception of RBS 1223) making them the best candidates for "genuine" isolated neutron stars with the least disturbed view to their stellar surface. With the known distance to RX J1856.5—3754 an X-ray luminosity of <1031 erg s—1 is inferred. Because of this intrinsically faint emission, the ROSAT-discovered isolated neutron stars are also called X-ray dim isolated neutron stars.

Table 14.4 X-ray and optical properties of nearby radio-quiet isolated neutron stars

Object

T

Flux(3)

Period

PfW

Optical

PM

(106 K)

(erg cm—2 s—1)

(s)

(%)

(mag)

(mas yr—-1)

RXJ0420.0—5022

0.51

3.3 >

< 10—13

3.45

13

B = 26.6

RX J0720.4—3125

0.99-1.10

9.7 >

10—12

8.39

8-15

B = 26.6

97

RX J0806.4—4123

1.11

2.4 x

10—12

11.37

6

B >24

RXS J1308.8+2127(1)

1.00

3.2x

10—12

10.31

18

m50ccd = 28.6

RX J1605.3+3249

1.11

6.1 x

10—12

B = 27.2

145

RX J1856.5—3754

0.73

1.3 x

< 10—11

7.06

1.5

V = 25.7

332

RXS J2143.0+0654(2)

1.17

2.8 x

10—12

9.44

4

R >23

(1) = RBS 1223; (2) = RBS 1774; (3) X-ray flux in the 0.1— 2.4keV band, (4) pulsed fraction

(1) = RBS 1223; (2) = RBS 1774; (3) X-ray flux in the 0.1— 2.4keV band, (4) pulsed fraction

For six objects a periodic modulation was discovered in the X-ray flux, which indicates the rotation of the neutron star. Spin periods in the range of 3.4 —11.4 s are longer than found for the bulk of radio pulsars, although also a few radio pulsars are known with similar pulse periods. The pulsed fraction in the X-ray flux varies from a few percent up to 18% in the case of RBS 1223. Table 14.4 summarizes X-ray and optical properties of the seven known radio-quiet isolated neutron stars. New X-ray observations with Chandra and XMM-Newton and deep optical imaging revealed new interesting and unexpected results that are described in the following.

Low interstellar absorption columns of these objects and high proper motions for the three brightest ones indicate that they represent a local population at distances up to a few hundred parsec, which is supported by the parallax of 120 pc observed for the brightest member of the class, RX J1856.5—3754. The high proper motions make accretion from the interstellar medium inefficient and favor the picture of neutron star cooling. Tracing back the apparent sky trajectories inferred from the proper motion measurements of RX J1856.5—3754, RX J1605.3+3249 and possibly also RX J0720.4—3125 points into the direction of the nearby OB association Sco OB2 [72]. The time it took for the neutron stars to move from this potential birth place to their current position is consistent with ages of around 106 years (RX J1856.5—3754: 0.5 x 106). Such an age is expected from their current temperature under the assumption of standard neutron star cooling scenarios. The Sco OB2 complex is the closest OB association and part of the Gould Belt. Population synthesis studies [88] for isolated neutron stars support the idea that the "magnificent seven" are of local origin dominated by the production of the Sco OB2 association.

The X-ray spectra obtained with the ROSAT PSPC were compatible with black-body radiation (e.g., RX J0720.4—3125 [45]), only modified by moderate photoelectric absorption by the interstellar medium. From high-resolution observations with the grating spectrometers on board of Chandra and XMM-Newton, it was expected to see spectral features originating in the atmospheres of the neutron stars. However, the first Chandra observations of RXJ1856.5—3754, collecting more than 5 days of LETGS high-resolution data, showed a featureless spectrum best represented by a blackbody model. Moreover, after the first optical identifications, it became immediately clear that the radio-quiet isolated neutron stars are optically brighter by typically a factor of 5-10 than expected from the extrapolation of their X-ray spectrum using the blackbody model. Hydrogen or Helium atmosphere models on the other hand produce a spectrum with Planckian shape in the X-ray band and reproduce the observed spectrum but predict a far too high optical flux. To reduce this discrepancy in the optical brightness heavy elements would be required which, on the other hand, produce features not observed in the X-ray spectra [85].

The problems to explain the overall energy distribution from optical to X-rays wavelengths with neutron star atmosphere or blackbody models led to the suggestion of a nonuniform temperature distribution on the stellar surface. Hot spots at the magnetic poles would account for the X-ray spectrum, while the cooler and larger part of the emitting surface could explain the optical emission. They also can explain the observed low amplitude smooth X-ray pulsations. Such hot spots could arise from anisotropic heat transport from the neutron star interior through the crust in a strong magnetic field or by polar cap heating by bombardment of particles from the magnetosphere.

These isolated neutron stars must have very strong magnetic fields, based on a number of arguments: From period measurements distributed over more than 10 years by ROSAT, XMM-Newton, and Chandra, the first accurate value for the spin period change was obtained for RX J0720.4-3125 [57]. Under the assumption of the magnetic dipole model this allows an estimate for the magnetic field strength of 2.4x 1013 G. This model can also be used to estimate the magnetic field of RX J1856.5-3754, using the observed period and the age of the star (see earlier). This results in B = 3x 1013 G. For such strong magnetic fields cyclotron absorption lines from protons or heavier nuclei are expected in the 0.1-1.2 keV band. Indeed strong evidence for a broad absorption line was first found for RBS 1223 [46] and later detected in other sources (cf. Table 14.5 and for an example see Fig. 14.8). For the two pulsars RBS 1223 and RX J0720.4-3125 the depth of the absorption line was found to vary with pulse phase [46,47].

Table 14.5 Magnetic field estimates

(eV)

Bdb (1013 G)

Bcyc (1013 G)

RX J0420.0— 5022

<92

-330?

<18

6.6?

RX J0720.4—3125

0.698(2)

260

2.4

5.2

RX J0806.4—4123

<18

400-450?

<14

8.0-9.1

RBS 1223

1.120(3)

100-300

3.4

2-6

RX J1605.3+3249

450-480

9.1-9.7

RX J1856.5—3754

<19

4.2«

RBS 1774

700?

14

« based on P = 7.06 s and an age of —5 x 105 years

« based on P = 7.06 s and an age of —5 x 105 years

Fig. 14.8 RGS spectrum of RXJ1605.3+3249 (reproduced from [58]). The upper histograms show blackbody continua

Fig. 14.8 RGS spectrum of RXJ1605.3+3249 (reproduced from [58]). The upper histograms show blackbody continua

For a line centered at the energy E caused by proton cyclotron absorption, the magnetic field strength is given by B = 1.6x 1011 E(eV)/(1-2GM/c2R)1/2 G. For a standard neutron star with M = 1.4M© and R = 10 km, the corresponding magnetic field strengths are listed in Table 14.5. If the line were produced by heavier nuclei, the magnetic field would be larger by a factor A/Z—2. Also given are the magnetic field strengths Bdb of RX J0720.4-3125 and RBS 1223 inferred from the spin down measurements. These values are probably more uncertain as they depend on how close the model assumption of a vacuum magnetic dipole is to the real situation. Upper limits for the period derivative from two other objects only allow restrictions on Bdb to smaller than —2 x 1014 G.

The brightest object among the magnificent seven, RX J1856.5-3754, is unique in many respects. Apart from the featureless spectrum and the small amplitude (—1.5%) of periodic modulation in the X-ray flux (with P=7.06s [96]), it possesses an emission nebula with cometary-like morphology. The nebula was discovered on Ha images [59] with an apex approximately 1" ahead of the neutron star and aligned with the direction of the proper motion of the star. Under the assumption that the age of the star is —5 x 105 yrs (consistent with a likely birthplace in the Sco OB2 association) and using a period of 7.06 s the magnetic dipole braking model allows an estimate for the magnetic field strength of —4.1 x 1013 G. We conclude that there

10.0

0.01

10.0

0.01

RXJ0720.4 3125 13 05 2000 06 11 2002 08 11 2002 22 05 2004 28 04 2005

12 11 2005

Channel Energy (keV)

RXJ0720.4 3125 13 05 2000 06 11 2002 08 11 2002 22 05 2004 28 04 2005

12 11 2005

Channel Energy (keV)

10.0

0.01

10.0

0.01

RXJ1856.5 3745 08 04 2002 24 09 2004

23 03 2005

24 09 2005 26 03 2006

Channel Energy (keV)

RXJ1856.5 3745 08 04 2002 24 09 2004

23 03 2005

24 09 2005 26 03 2006

Channel Energy (keV)

Fig. 14.9 EPIC-pn spectra of RXJ0720.4-3125 and RXJ1856.5-3754 modeled with blackbody continuum and in the case of RX J0720.4—3125 an additional broad absorption line with Gaussian shape is strong evidence that the magnetic fields of the magnificent seven are of the order of a few times 1013 G.

The discovery of spectral changes from RXJ0720.4-3125 on time scales of years was a big surprise. For no other cooling neutron star detected in X-rays such a behavior is known. The object was frequently observed as calibration target for XMM-Newton to monitor the low-energy response of the EPIC instruments. Readout modes and filters were alternated for the EPIC cameras and a spectral hardening was first noticed in the RGS spectra [24]. Figure 14.9 shows the spectral evolution of RX J0720.4-3125 as measured by EPIC-pn from observations with the same instrumental setup. For comparison, five spectra obtained from RX J1856.5-3754 are fully consistent with each other, demonstrating the stability of both source and instrument.

Simultaneously with the spectral change observed from RX J0720.4-3125 the pulsed fraction as measured by EPIC increased from about 8% to 15%. Already from the first XMM-Newton observation in May 2000 it was found that the hardness-ratio4 is modulated with the spin period of the neutron star. However, the hardness-ratio pulse profile is shifted with respect to the intensity pulse profile, showing that the spectrum is hardest just before intensity minimum and softest before intensity maximum. In October 2003, this phase offset has reversed, the hardness ratio pulse profile then lagging the full intensity pulse profile.

The analysis of the spectra from different epochs has shown that the blackbody temperature increased from 1.0 x 106 K in May 2000 to 1.1 x 106 K in May 2004. Simultaneously the equivalent width (a measure of the depth of the absorption line with respect to the continuum) of the absorption line increased by a factor of nearly 10 from <6 to 50 eV. It was suggested that the behavior of RX J0720.4-3125 is caused by precession of the neutron star and that we saw more directly onto the hot spot at the magnetic pole in 2004. However, in this case it is puzzling that the

4 The hardness ratio is calculated as ratio of count rates in two different energy bands and can be used as measure for spectral changes.

derived size of the emitting area decreased from 2002 to 2004. Further monitoring of this interesting object with Chandra and XMM-Newton is in progress and should reveal if the spectral changes are periodic.

14.3.2.1 The Radius of RX J1856.5-3754 and the Equation of State at Supernuclear Densities

Neutron stars are giant atomic nuclei of stellar dimensions, bound by gravity. Because of the effects of gravity, the density of matter in the cores of neutron stars must be larger than that of atomic nuclei, but the composition and equation of state (EOS) of matter at supernuclear densities is still poorly understood, largely due to the fact that these conditions cannot be tested directly by colliding beam experiments at high energies. The equations under discussion show a dispersion of a factor of six or more of the pressure at a given density (e.g., [19,62]). Therefore, observations of neutron stars constraining the nuclear physics parameters are very important. Since a given EOS leads to a specific mass-radius relationship, the relevant prime observables are the mass and the radius of a neutron star. Unluckily, there is not a single neutron star for which both the mass and the radius have been determined yet. While masses can be directly determined for neutron stars in binary systems, and have reached a high accuracy in the case of binary neutron stars, estimates of neutron star radii have been based on more indirect and model dependent methods:

1. Luminosities of X-ray bursts, assuming that they are close to the Eddington limit (e.g. [102])

2. Frequency of quasi-periodic oscillations, assuming that they reflect the Kepler frequency of accreted matter close to the neutron star (e.g. [69])

3. Limit of rotational stability of neutron stars by observing coherent high frequency oscillations in X-ray bursts (e.g. [27])

4. Measuring the light curve of coherent X-ray burst oscillations (e.g. [4])

5. "Radiation radii" of neutron stars using their thermal emission (e.g. [98])

Another method implies the measurement of the gravitational redshift of atomic lines in neutron stars with low magnetic fields (<1010 G) where magnetic shifts are not important. Several papers have claimed the detection of lines in X-ray bursts (e.g., [31,74]). Unfortunately, the real existence of these features has remained in doubt because they were not confirmed by later observations. But this method is very promising, because in principle it allows to determine three key parameters simultaneously: mass, radius, and distance of the neutron star [80].

In the following, we will concentrate on method No. 5 and its application to RX J1856.5-3754. To derive a radiation radius from observed thermal spectra, one needs to know the radiative properties of the atmosphere and the distance to the source. In the case of RX J1856.5-3754 an astrometric distance has been derived from HST observations, yielding 117 ± 12 pc [104] or more recently 140 ± 40 pc [51]. The X-ray spectrum of the neutron star measured with high resolution and large photon statistics with the Chandra LETG can be very well fitted by a blackbody with kT=0.63 ± 0.2 keV, devoid of any spectral features [23]; the optical/UV-spectrum measured by HST and VLT shows an v2 dependence typical for a Rayleigh-Jeans spectrum. However, its intensity is a factor —5 higher than the extrapolation of the X-ray blackbody, indicating that the latter comes from a small hot spot (with a radius of 4.4 ± 0.1 km x d/117pc) [23], while the optical/UV is emitted by the bulk surface. A double component fit to the overall spectrum yields a blackbody radius R^=16.5 km, while a fit with a continuous temperature distribution across the stellar surface gives Rbb=16.8 km, both for a distance of 117 pc. It has been argued that these figures represent lower limits to the real radiation radius using the argument that a blackbody is the most efficient radiator for a given temperature distribution [22,98]. Thus, we conclude that the radiation radius is R > 16.5 km. A model involving a thin (1 g cm-2), magnetic (3 - 4 x 1012 G), partially ionized hydrogen atmosphere on top of a condensed matter surface gives a radiation radius of 17km assuming a distance of 140pc [51]. However, this model is not fully self-consistent and assumes a magnetic field that is one order of magnitude below the one estimated from observations (cf. Table 14.5).

From the radiation radius R (seen by an observer at infinity) the true stellar radius Ro can be calculated using the relation R = Ro( 1 - Rs/Ro)-1/2, where Rs = 2GM/c2 is the Schwarzschild radius of the neutron star. The resulting lower limit to Ro as a function of mass is shown in Fig. 14.10, using the lower limit for Ro of 16.5 km. This implies a rather stiff EOS and is inconsistent with RX J1856.5-3754 being a quark star.

Fig. 14.10 Constraints provided by neutron star observations for the mass-radius relation: The numbers attached to the different curves refer to the methods 1-5 mentioned in the text. The massradius relations for various equations of state for nucleon/hyperon stars (left) and for kaon condensates/strange quark matter (right) are taken from [62]

Fig. 14.10 Constraints provided by neutron star observations for the mass-radius relation: The numbers attached to the different curves refer to the methods 1-5 mentioned in the text. The massradius relations for various equations of state for nucleon/hyperon stars (left) and for kaon condensates/strange quark matter (right) are taken from [62]

14.3.3 Millisecond Pulsars

In the P-P parameter space, millisecond pulsars (ms-pulsars) are distinguished from the majority of ordinary-field pulsars by their short spin periods of <20 ms and small period derivatives of «10-18 - 10-21. In the frame of the magnetic braking model this corresponds to very old spin-down ages of typically 109 - 1010 yrs and low magnetic field strengths of -108 - 1010 G (cf. Fig. 14.1). More than -75% of the known disk ms-pulsars are in binaries, usually with a low-mass white dwarf companion, compared to = 1% binaries among the ordinary pulsars. This gives support to the idea that these neutron stars have been spun-up by angular momentum transfer during a past mass accretion phase [1,5,18]. Further evidence for this came from the discovery of seven accreting ms-pulsars, which seem to confirm this scenario (see [105] for a review). Presumably, these pulsars were originally among ordinary pulsars that would have turned off because of the loss of their rotational energy if they were not in close binaries (cf. Fig. 14.11). Millisecond pulsars are, therefore, often called "recycled" pulsars to better distinguish them from fast spinning pulsars seen in young supernova remnants.

By the end of 2006, about 10% of the 1 765 known radio pulsars fall into the category of ms-pulsars, i.e., are recycled [66]. The majority of them (almost 130) are located in 24 globular clusters [26], which apparently provide a favorable environment for the recycling scenario. Of these globular cluster ms-pulsars 54 (41%) are solitary, the others are in binaries. Interestingly, the ratio of solitary to binary ms-pulsars is almost identical to the 40% observed in the population of galactic disk ms-pulsars. The formation of solitary recycled pulsars is not well-understood, but it is widely believed that either the pulsar's companion was evaporated (a process that is believed to be at work in the PSR 1957+20 ms-pulsar/binary system) or the system was tidally disrupted after the formation of the ms-pulsar.

Recycled pulsars had been studied exclusively in the radio domain until the 1990s, when ROSAT, ASCA, EUVE, RXTE, and BeppoSAX were launched. The first millisecond pulsar discovered as pulsating X-ray source was PSR J0437-4715 [14], a nearby 5.75 ms pulsar that is in a binary orbit with a low-mass white dwarf companion. Further detections followed, which, by the end of 2006 sum up to -40% of all X-ray detected rotation-powered pulsars (cf. [21] and references therein).

The data quality available from them, though, is far from being homogenous. While from several ms-pulsars high quality spectral, temporal and spatial information is available, many others, especially those on globular clusters, are just detected with a handful of events. Nevertheless, the improvements in sensitivity by Chandra and XMM-Newton provided a step forward in classifying the ms-pulsars' X-ray emission properties, indicating that there is a dichotomy between thermal and non-thermal dominated emitters, similar to what is observed from nonrecycled pulsars.

X-ray emission observed from ms-pulsars, which have a spin-down energy of E > 1035ergs-1, i.e., PSR J0218+4232, PSR B1821-24, and PSR B1937+21, is caused by nonthermal radiation processes [9,61,76]. This is confirmed from their power law spectra (photon-index a in the range 1.5-2) and pulse profiles that show

Fig. 14.11 Weakly-magnetized neutron stars that accrete matter from low-mass companion stars form the —150 currently known low-mass X-ray binaries. These systems are believed to be the progenitors of "recycled" pulsars. Along with the accretion of matter angular momentum transfer from the companion star takes place which spins-up the neutron star to millisecond periods. As the companion star evolves a solitary ms-pulsar or a ms-pulsar binary system is left

Fig. 14.11 Weakly-magnetized neutron stars that accrete matter from low-mass companion stars form the —150 currently known low-mass X-ray binaries. These systems are believed to be the progenitors of "recycled" pulsars. Along with the accretion of matter angular momentum transfer from the companion star takes place which spins-up the neutron star to millisecond periods. As the companion star evolves a solitary ms-pulsar or a ms-pulsar binary system is left narrow peaks and have pulsed fractions of up to —90-100% (cf. Fig. 14.12). In common to these pulsars is that all show relatively hard X-ray emission, which made it possible to study some of them already with ASCA, BeppoSAX, and RXTE. For example, emission from PSR B1821—24 is detected by RXTE up to —20keV [70] and PSR J0218+4232 is a candidate for a gamma-ray pulsar [61].

For the remaining ms-pulsars (P > 4 ms, E — 1033—34ergs—1), the X-ray emission is found to be much softer. Their X-ray spectra can be described by compound models consisting of a blackbody plus a power law component. The latter is required to describe the emission beyond 2-3 keV. For PSR J0437—4715 that is the brightest ms-pulsar detected in X-rays and thus is the one for which the best photon statistics is available, a three component spectral model is required consisting of a

PSR 1821-24

2.0-10 keV

PSR 1821-24

2.0-10 keV

PSR 1937+21

2.0-10 keV

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 l.B 2.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 Pulse Phase

PSR J2124-3358

PSR J2124-3358

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 Pulse Phase

Fig. 14.12 X-ray and radio pulse profiles for the six brightest ms-pulsars. Two full pulse cycles are shown for clarity. The relative phase between the radio and X-ray pulses is only known for PSR 1821—24, B1937+21, 0218+4232, and PSR J0437-4715 with sufficient accuracy. The phase alignment in all other cases is arbitrary

Fig. 14.13 X-ray spectrum of PSR J0437-4715. The solid curves show the best fitting model that is the sum of a power law (PL) and a two temperature blackbody model labeled as core and rim

Fig. 14.13 X-ray spectrum of PSR J0437-4715. The solid curves show the best fitting model that is the sum of a power law (PL) and a two temperature blackbody model labeled as core and rim two temperature blackbody plus a power law model. The X-ray spectrum of PSR J0437-4715 as detected with XMM-Newton is shown in Fig. 14.13.

The relatively small blackbody radii found by these spectral fits suggest that the thermal emission is coming from one or two heated polar-caps whereas the power law component describes the nonthermal radiation emitted from accelerated particles in the corotating magnetosphere. The prototypical ms-pulsar of this group, which is still the one for which the best data are available, is the nearest and brightest millisecond pulsar PSR J0437-4715. It was already evident in the ROSAT and ASCA data that its X-ray emission consists of at least two different spectral components [12-14]. Chandra and XMM-Newton data have further constrained its emission properties [21,115]. The two thermal components are interpreted as emission from a hot polar cap, having a nonuniform temperature distribution with a hot core (Tcore = 1.4 x 106 K, Rcore = 0.4km) and a cooler rim (Trim = 0.5 x 106 K, Rrim < 2.6 km). The power law component yields a photon index of a < 2.0. The size of the polar cap is found to be roughly in agreement with the theoretical predictions. Defined as the area of open field lines in which the bombardment by rela-tivistic particles is expected, it is Rpc = R(RQ/c)1/2. Assuming R = 10km for the neutron star radius and taking Q = 1.09 x 103 for the pulsars angular frequency yields Rpc = 1.9 km for a polar cap radius of PSR J0437-4715.

Interaction between relativistic pulsar winds (which carry away the rotational energy of pulsars) and the surrounding interstellar medium is expected to create detectable diffuse emission. If the physical conditions are appropriate this emission takes the form of a pulsar bow-shock nebula (cf. Fig. 14.14).

By now, such diffuse emission is seen in Ha from the black widow pulsar PSR B1957+20 [52,91], from PSR J0437-4715 [15], and from PSR J2124-3358 [35]. Diffuse X-ray emission associated with these bow-shock nebulae could only be detected from PSR B1957+20 [15,91] and from the solitary ms-pulsar PSR J2124-3358 [55]. For the latter the emission extends from the pulsar to the northwest by —0.5arcmin (cf. Fig. 14.14). Adopting the pulsar distance of —250pc, the tail has a length of —1.1 x 1017 cm. The spectrum of this nebular emission can be modeled with a power-law of photon index 2.2 ± 0.3, in line with the emission originating from accelerated particles in the post shock flow. Comparable deep observations to those of PSR J2124-3358 and PSR B1957+20 have been performed by XMM-Newton in previous years on almost all X-ray bright ms-pulsars. For PSR J0437-4715, PSR J0030+0451, and PSR J1024-0719, which all have spin parameters similar to that of PSR J2124-3358, no diffuse emission was detected down to a 3 - a limiting flux of —4 - 7 x 10-15 erg s-1 cm-2 [55], suggesting that the formation of bow-shocks depends not on the pulsars spin-parameters but might be a function of the ISM density and pulsar proper motion only.

The majority of the detected ms-pulsars resides in globular clusters. The first millisecond pulsar discovered in a globular cluster was PSR B1821-24 in M28 [65]. Its inferred pulsar parameters make it the youngest (P/2P = 3.0 x 107 yrs) and most powerful (E = 2.24 x 1036/45 erg s-1) pulsar among all known MSPs. Since the

Chandra

0.3 - 8 keV

ACIS

-

\

b

45.0 21:24:44.0 43.0 Right ascesion (J2000)

45.0 21:24:44.0 43.0 Right ascesion (J2000)

Fig. 14.14 (a) The bow-shock around PSR J0437-4715 as visible in Ha. (b) Chandra image of PSR J2124-3358 and its diffuse, arc-like X-ray emission associated with the pulsar's bow-shock. The pulsars proper motion directions are indicated

Einstein era, it has been clear that globular clusters contain various populations of X-ray sources of very different luminosities [49]. The stronger sources (Lx « 1036 -1038 ergs-1) were seen to exhibit X-ray bursts, which led to their identification as low-mass X-ray binaries (LMXBs). The nature of the weaker sources, with Lx < 3 x 1034 ergs-1, however, was more open to discussion [30,56]. Although many weak X-ray sources were detected in globulars by ROSAT [56,103], their identification has been difficult because of low photon statistics and strong source confusion in the crowded globular cluster fields, except for a few cases. Of particular interest are the results obtained from Chandra observations of PSR B1821-24 in M28 [9] and on 47 Tuc = NGC 104. From the latter, Grindlay [42] reported the detection of 108 sources within a region corresponding to about five times the 47 Tuc core radius. Nineteen of the soft/faint sources were found to be coincident with radio-detected millisecond pulsars (MSPs), and Grindlay [41,42] concluded that more than 50% of all the unidentified sources in 47 Tuc are MSPs. This conclusion is in line with theoretical estimates on the formation scenarios of short-period (binary) pulsars in globular clusters [89]. The application of the Chandra X-Ray Observatory sub-arcsecond angular resolution along with the temporal resolution provided by its HRC-S detector allowed to detect X-ray pulsations at a —4 a level from four of these sources in a recent 830ks deep observation [25].

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