7.1.1 Expectations
While over 1000 isolated neutron stars have now been discovered as radio pulsars, the total number in the Galaxy is much larger. Radio pulsars emit pulsations for∼107 yr and are visible due to radio beams that subtend 1–10% of the sky, so the total number of neutron stars just in the local region of the Galaxy (where radio pulsars are detectable) should be∼>106 (e.g., Lorimer 2003).
Are these objects truly invisible, or is there some chance of their being observed? For years astronomers have proposed that a large fraction of these objects would be visible through one of two mechanisms:
accretion or cooling. The first mechanism could revive old, dead pulsars, while the second would primarily work for younger sources but would not depend on the presence of radio pulsations. Both mechanisms, however, make the neutron stars visible in the soft X-ray regime, not in the radio regime that had dominated the study of neutron stars.
Accretion takes advantage of the gravitational potential wells of neutron stars (with radii of ≈3 times their gravitational radii). First proposed by Ostriker et al. (1970), the idea was revived (Treves & Colpi 1991; Blaes & Madau 1993) when it was realized that the ROSAT satellite might be able to discover as many as 5000 of these sources. In this scenario, neutron stars moving through the interstellar medium (ISM) would accrete and material and shine due to the release of potential energy.
However, the estimates of these populations were very uncertain, as they depended critically on the (relatively unknown) velocity, spin, and magnetic field distributions of the sources as well as the distribution of the accreting matter. This is because the accretion rate scales asv−3 (in the nonmagnetized, spherical, Bondi-Hoyle limit, which is only approximate; Bondi & Hoyle 1944; Bondi 1952) and also depends critically
75
on the strength and rotation rate of the magnetic field (e.g., Illarionov & Sunyaev 1975; Alpar 2001;
Toropina et al. 2003; Perna et al. 2003).
Cooling takes advantage of the initially very hot (∼ 1011 K) temperatures of newly-formed neutron stars to radiate primarily neutrinos but more importantly for observers X-rays as well for about 106 yr (e.g., Tsuruta & Cameron 1965; Tsuruta et al. 1972). After this point the neutron stars cools into the ultraviolet band, where interstellar absorption and theT4 dependence of the flux render it invisible. While the basic formulation of neutron star cooling has been known for decades, the details are still elusive (e.g., Tsuruta et al. 2002; Yakovlev et al. 2002a; Yakovlev et al. 2003; Page et al. 2004), as uncertainties in the neutron star’s structure, envelope, and magnetic field can all have significant effects.
These isolated neutron stars should have been identifiable based on the following criteria (Treves &
Colpi 1991):
1. Largely thermal emission peaking in the soft X-ray or far-UV band, requiring small hydrogen column densities to remain visible
2. The absence of bright optical counterparts 3. Significant (∼>0.1 arcsec yr−1) proper motions 4. Preferred locations in the Galactic plane
The first two criteria relate to the spectra of the neutron stars, and serve to rule out the active galaxies and stars that dominate X-ray surveys (Hertz & Grindlay 1988). The third criterion reflects the proximity of the sources (with maximum distances of∼1 kpc) and the large space velocities of known neutron stars (presumably due to supernova kicks). The final criterion comes from the Galactic nature of the sources, and is similar to the distribution of radio pulsars. As we shall see, while most of the original predictions were wrong, the first three criteria have been borne out observationally and the fourth may also be true.
The second criterion relates to many classes of neutron stars, not just the accreting/cooling sources discussed here. In fact, due to their small sizes and hot temperatures, neutron stars that are detectable in bands outside the radio regime generally have very high ratios of X-ray to optical flux. For thermal sources, this is approximately
LX
Lopt ∼105.5+3 log(kT /100 eV) (7.1)
(Treves et al. 2000; Rutledge et al. 2003). This compares to stars values of 10−3–10−2 for stars (Katsova
& Cherepashchuk 2000) and 0.1–10 for active galaxies (Brandt et al. 2001). Only white dwarfs and X-ray binaries (compact objects, like neutron stars) can come close, with ratios of 10–1000 (Hertz & Grindlay 1988). For a more general discussion of this, see Hulleman et al. (2000) or Kaplan et al. (2004).
7.1.2 The Legacy of ROSAT
Instead of the anticipated 5,000 objects, ROSAT discovered only half a dozen nearby cooling neutron stars (see reviews by Motch 2001; Haberl 2004; Tab. 7.1). Much of the difference can be ascribed to poor assumptions regarding the velocity distribution of pulsars (Colpi et al. 1998; Neuh¨auser & Tr¨umper 1999; Treves et al. 2000) and the effects of magnetic fields (Illarionov & Sunyaev 1975; Perna et al. 2003).
However, they are all the more valuable because of their rarity.
The first such source to be discovered was RX J1856.5−3754. It was originally identified serendipitously as a soft, bright X-ray source with no obvious optical counterpart (Walter et al. 1996). Its location in front of the R CrA molecular cloud meant that it had to be nearby (∼<200 pc)—otherwise the X-ray emission would have been absorbed. Confirmation of its nature came with the discovery of a very faint (B ≈25.8 mag), blue optical counterpart (Walter & Matthews 1997).
7.1 Introduction 77
Table 7.1. The Nearby Isolated Neutron Stars Detected By ROSAT
RX J PSPC kT Eabsa P B Optical Bcycc BHd de
(ct/s) (eV) (eV) (s) (mag) Excessb (×1013G) (pc)
1856.5−3754 3.64 60 · · · · · · 25.8 6 · · · · · · 175
0720.4−3125 1.64 85 271 8.39 26.5 6 5.6 1.6 290
1605.3+3249 0.90 95 450 · · · 26.9 9 9.4 14.3 370
0806.4−4123 0.38 96 460 11.37 >25.5 · · · 9.6 15.8 >190
1308.6+2127 0.29 90 <300 10.31 28.5 6 6.2 2.5 740
2143.0+0654 0.18 92 · · · · · · f ∼>22 · · · · · · · · · >38
0420.0−5022 0.14 45 329 3.45 26.6 13 6.8 3.6 220
aCentral energy of the best-fit Gaussian absorption feature.
bExtrapolation of X-ray blackbody into the optical band, divided by the optical flux.
cMagnetic field assuming that the absorption feature is due to the fundamental proton cy- clotron line: Bcyc= 1.6×1014EkeV(1 +z) G. See Figure 7.7.
dMagnetic field assuming that the absorption feature is due to the bound-free transition of neutral hydrogen at an observed energy of E ≈ 0.31(log(B/B0))2/(1 +z) keV, where B0 = 2.35×109 G; (Potekhin 1998; Ho et al. 2003). See Figure 7.7.
eAll distances are scaled from the distance and optical emission of RX J1856.5−3754: d = 175 pcp
kT /60 eV10(B−25.8)/5 (cf. Kaplan et al. 2002c).
fHas not been deeply searched for periodicities.
Note. — We assume a gravitational redshiftz= 0.3.
References. — Walter et al. (1996); Walter & Matthews (1997); Haberl et al. (1997); Kulkarni
& van Kerkwijk (1998); Zampieri et al. (2001); van Kerkwijk & Kulkarni (2001b); Kaplan et al.
(2002c); Kaplan et al. (2002a); Ransom et al. (2002); Burwitz et al. (2003); Kaplan et al. (2003a);
Kaplan et al. (2003b); Haberl et al. (2003a); van Kerkwijk et al. (2004); Haberl et al. (2003b);
Haberl et al. (2004)
Since then, six other similar sources have been identified through the efforts of the group at MPE (Haberl et al. 1997, 1998; Schwope et al. 1999; Motch et al. 1999; Haberl et al. 1999; Zampieri et al. 2001).
We summarize the properties of the sources in Table 7.1. Identification of additional sources that may still be present (Rutledge et al. 2003) in theROSAT Bright Sources Catalog (containing ≈18000 sources with
>0.05 counts s−1in the Position-Sensitive Proportional Counter, or PSPC; Voges et al. 1996) is extremely difficult given the poor positional accuracy of the PSPC (Fox 2004).
Right away with the discoveries of the first two sources (RX J1856.5−3754 and RX J0720.4−3125), astronomers had a puzzle: the first source did not pulsate at all, while the second pulsated with a period of 8.4 s. These were both far different from the known population of radio pulsars and led to a number of models being proposed for these sources, known as the isolated neutron stars (INSs):1 accreting neutron stars with conventional magnetic fields spun down to long equilibrium spin periods (Konenkov & Popov 1997; Wang 1997; Alpar 2001); cooling middle-aged pulsars with ∼ 1012-G magnetic fields whose radio beams are directed away from the Earth (Kulkarni & van Kerkwijk 1998); cooling off-beam pulsars with high (∼1013 G) magnetic fields (HBPSRs); or old magnetars (Duncan & Thompson 1992)—neutron stars with magnetic fields > 1014 G—that are kept warm by the decay of their strong magnetic field (Heyl &
Hernquist 1998b; Heyl & Kulkarni 1998).
In what follows we will discuss the observation of the INSs (§7.2). We will then apply these observations to the models discussed above, try to distinguish between them (§7.3), and place the INSs in the context of the greater pulsar population (§7.3.3). Finally, we will discuss how the INSs can be be used to constrain basic fundamental physics (§ 7.4).