# The Neutron Star Zoo

Alice K. Harding<EMAIL_ADDRESS>Astrophysics Science Division
NASA Goddard Space Flight Center
Greenbelt, MD 20771

###### Abstract

Neutron stars are a very diverse population, both in their observational and
their physical properties. They prefer to radiate most of their energy at
X-ray and gamma-ray wavelengths. But whether their emission is powered by
rotation, accretion, heat, magnetic fields or nuclear reactions, they are all
different species of the same animal whose magnetic field evolution and
interior composition remain a mystery. This article will broadly review the
properties of inhabitants of the neutron star zoo, with emphasis on their
high-energy emission.

Stars: Neutron stars, Pulsars, Binary stars

###### pacs:

97.60.Jd,97.60.Gb

###### Contents

  1. I Introduction
  2. II Rotation-Powered Pulsars
  3. III Magnetars
  4. IV Compact Central Objects
  5. V Isolated Neutron Stars
  6. VI Accreting Neutron Stars
    1. VI.1 Low-Mass X-Ray Binaries
    2. VI.2 Intermediate- and High-Mass X-Ray Binaries
    3. VI.3 Microquasars and Gamma-Ray Binaries
  7. VII Summary

##  I Introduction

Neutron stars are the remnants of massive stars whose cores collapse during
the supernova explosions at the end of their nuclear fusion lifetimes.
Conservation of both the angular momentum and the magnetic flux of the
progenitor star during the collapse gives the neutron star an extremely high
spin rate and magnetic field. The collapse ends when the degeneracy pressure
of neutrons balances the gravitational forces of the matter. At that point the
core radius is about 10 km and with a mass $\sim 1.4M_{\odot}$ the center of
the star has already reached nuclear densities. Neutron stars thus possess the
highest spin frequencies, magnetic fields and densities of any known objects
in the Universe. Since their theoretical conception by Baade1934  they have
been fascinating celestial objects, both for study of their exotic interiors
and environments and for their important place in stellar evolution.

Figure 1: Schematic diagram of neutron star populations with respect to their
periods and derived surface magnetic field strengths.

Neutron stars (NSs) all typically have detectable pulsations, since they are
rapidly spinning and their emission patterns are highly anisotropic. This may
be one of the few observational properties that they have in common, because
they otherwise show an amazing variety of pulsating and bursting behaviors.
Neutron star types are classified according to the primary power source for
their emission and spin evolution. Rotation-powered pulsars (RPP) derive their
energy primarily from the rotation of the NS, magnetars from magnetic field
energy, isolated NSs (INS) from the latent heat of the NS matter, and
accretion-powered NSs from the energy released by matter accreting onto the NS
from a binary companion. A subclass of accreting NSs are X-ray bursters whose
bursts are powered by thermo-nuclear explosions. An additional class, Central
Compact Objects (CCO), are seen as soft X-ray point sources inside supernova
remnants and seem to be quiet at all other wavelengths. Figure 1 shows where
these different NS types roughly fall in period and surface magnetic field
space. Although period is a measured quantity, surface magnetic field is
derived in different ways for the various NS types. Magnetic fields in RPPs,
magnetars, INS and CCO are derived from measured period derivatives,
$\dot{P}$, assuming magnetic dipole radiation spin down, although in magnetars
this can only give an approximate value since their spin behavior is
complicated by magnetically-driven NS heating and bursting. The surface dipole
field at the pole determined assuming the observed $\dot{P}$ is from magnetic
dipole radiation is

$B_{d}=\left({\frac{{3Ic^{3}P\dot{P}}}{{2\pi^{2}R^{6}}}}\right)^{1/2}\simeq
2\times 10^{12}{\rm G}\,(P\dot{P}_{15})^{1/2},$ (1)

where $\dot{P}_{15}\equiv\dot{P}/(10^{-15}\,\rm s\,s^{-1})$, $P$ is in units
of seconds, and $I$ ($\simeq 10^{45}$ g cm2) and $R$ ($\simeq 10^{6}$ cm) are
the neutron star moment of inertia and radius. Magnetic fields of accretion-
powered NSs cannot be measured from their $\dot{P}$ since their spin evolution
is governed by accretion torques. For accreting X-ray pulsars, the cyclotron
lines seen in their spectra give good estimates of surface field strength:

$B_{\rm cyc}\simeq\left({E_{c}\over 11.6{\rm keV}}\right)\,10^{12}\,{\rm G}$
(2)

where $E_{c}$ is the cyclotron line energy. For low-mass X-ray binaries (LMXB)
and bursting sources, the Alfven radius where the NS magnetic pressure
balances that of the accretion flow gives an estimate of the surface magnetic
field strength:

$B_{\rm A}\sim 10^{12}\,{\rm G}\,P_{\rm eq}\,\left({\dot{M}\over
10^{-9}M_{\odot}\,{\rm yr^{-1}}}\right)^{1/2}$ (3)

Ghosh1979  where $P_{\rm eq}$ (in seconds) is the equilibrium spin period of
the NS and $\dot{M}$ is the mass accretion rate. The NS types generally occupy
different areas of $P-B$ space, although there is a good deal of overlap. The
LMXB population, being progenitors of rotation-powered MSPs, overlap the MSP
population. CCOs lie at the lower end of the RPPs, coinciding with some of the
MSP population. The lower end of the magnetar population overlaps the upper
end of the RPPs, and the INS overlaps both. The accreting X-ray pulsars have
magnetic fields and periods similar to some of the older RPPs. The magnetars
have the highest surface magnetic fields, while the rotation-powered
millisecond pulsars and LMXBs have very low surface fields but the shortest
periods.

Figure 2: Plot of period vs. period derivative for the presently known
rotation-powered pulsars, Isolated Neutron Stars (INS), Compact Central
Objects (CCO), Rotating Radio Transients (RRATs) and magnetars (from
http://www.atnf.csiro.au/people/pulsar/psrcat/). Lines of constant
characteristic age, $P/2\dot{P}$, and dipole spin-down luminosity,
$\dot{E}_{d}$, are superposed.

Figure 2 shows the distribution of non-accreting NS in measured period and
period derivative. The radio pulsars occupy the largest region of this phase
space with their population extending from the very short period, low
$\dot{P}$ MSPs up to the high $\dot{P}$, high magnetic field pulsars that
border the magnetar range. The magnetars have the highest $\dot{P}$ and some
of the longest periods in the NS zoo. with some having $P\sim 11$ s (the
longest period of a radio pulsar is about 8 s). The INS have periods very
similar to those of magnetars, also reaching up to 11 s, but with $\dot{P}$
and magnetic fields about a factor of ten lower than those of the lower field
magnetars. The CCOs have very low $\dot{P}$, almost as low as the MSPs, but
their spin periods are more like those of young RPPs. High energy pulsars
(RPPs with X-ray or gamma-ray pulsations) typically have the highest spin-down
power (see Eq [4]) but are not necessarily the youngest, as many of the very
old MSPs are efficient X-ray and gamma-ray pulsars.

##  II Rotation-Powered Pulsars

Figure 3: Skymap in Galactic coordinates showing the gamma-ray pulsars of
different types detected by Fermi: Blue squares: radio quiet pulsars. Red
triangles: millisecond gamma-ray pulsars. Green circles: radio loud gamma-ray
pulsars. Black dots: Gamma-rays were phase-folded using a rotation ephemeris.
Gray dots: Pulsars for which no rotation ephemeris was available. From
Abdo2013 .

Neutron stars that are spinning down as a result of torques from magnetic
dipole radiation and particle emission are known as rotation-powered pulsars
(RPP). The energy from their spin down appears as broad-band pulsations from
radio to gamma-ray wavelengths and as a wind of energetic particles flowing
into their surrounding pulsar wind nebulae. Since the discovery of RPP through
their radio pulsations in 1967 Hewish1968 , more than 2000 radio pulsars are
now known with periods ranging from a few ms to several seconds Manchester2005
, http://www.atnf.csiro.au/people/pulsar/psrcat/). X-ray, gamma-ray and
optical pulsations were soon discovered in a few of these pulsars by folding
the time series obtained at these wavelengths at the radio periods. At
present, there are over 100 RPP detected at X-ray energies and over 130 gamma-
ray pulsars Abdo2013 ; most were discovered using known radio ephemerides, but
many were also discovered through their X-ray or gamma-ray pulsations and are
radio quiet. The spin down of RPPs is typically smooth and predictable, but
they have occasionally been observed to undergo sudden changes in spin called
‘glitches’, where the period decreases and then recovers back to its normal
spin-down rate on a timescale of days to weeks.

There are two main populations of RPPs: normal pulsars having characteristic
ages $\tau=P/2\dot{P}$ $<$ 100 Myr, and millisecond pulsars (MSP) with
$\tau\mathrel{\mathchoice{\lower
2.0pt\vbox{\halign{$\m@th\displaystyle\hfil#\hfil$\cr>\crcr\sim\crcr}}}{\lower
2.0pt\vbox{\halign{$\m@th\textstyle\hfil#\hfil$\cr>\crcr\sim\crcr}}}{\lower
2.0pt\vbox{\halign{$\m@th\scriptstyle\hfil#\hfil$\cr>\crcr\sim\crcr}}}{\lower
2.0pt\vbox{\halign{$\m@th\scriptscriptstyle\hfil#\hfil$\cr>\crcr\sim\crcr}}}}100$
Myr. The periods of the normal pulsars are thought to have increased at a
steady rate from their birth periods at the time of supernova core collapse.
The birth periods of RPPs are not well known, and inferences of the period
range from tens of ms to hundreds of seconds Kaspi2005 Gotthelf2010 . MSPs are
thought to have originally been members of the normal RPP population, spun
down for tens of Myr and then spun up by accretion from a binary companion
Alpar1982 . MSPs make up about 10% of the RPP population and about 80% of them
are in binary systems. A large number of new MSPs have recently been found
through radio searches at positions of Fermi unidentified gamma-ray sources
(e.g. Ransom2011 ), doubling the known numbers of radio MSPs in the Galactic
disk. Their radio ephemerides can then be used to find the gamma-ray
pulsations. They are extremely good clocks since they rarely glitch, they have
very little of the timing noise seen in young RPPs, and their spin down is
very stable. These characteristics make them potentially valuable sources for
use in celestial navigation Coll2009  and gravitational wave detection
Hobbs2010 .

Figure 4: Gamma-ray (black) and radio (red) pulse profiles for a selection of
pulsars detected by Fermi, from Abdo2013 .

The rotating dipole model that seems to well describe RPPs gives estimates of
their main electrodynamic properties. The Poynting flux of a rotating dipole
in vacuum gives an estimate of the spin-down power:

$\dot{E}_{d}={4\pi^{2}I\dot{P}\over P^{3}}={2B_{0}^{2}\Omega^{4}\over
3R^{6}c^{5}}=10^{31}\,{\rm erg\,s^{-1}}\,B_{12}^{2}\,P^{-4}$ (4)

where $\Omega=2\pi/P$ is the spin angular velocity, $R$ the NS radius, $B_{0}$
is the surface magnetic field and $B_{12}\equiv B_{0}/10^{12}$ G. The rotating
dipole induces strong electric fields, ${\bf E=\Omega\times r\times B}$ that
in vacuum are orders of magnitude larger than the gravitational force, pulling
charges out of the NS surface to fill the magnetosphere GJ1969 . The maximum
charge density, which screens the electric field along magnetic field lines,
is

$\rho_{\rm GJ}\simeq-{{\bf\Omega\cdot B}\over 2\pi c}$ (5)

which gives a scale for the current density flowing along the open field
lines, $J_{\rm GJ}=\rho_{\rm GJ}c$. The particles and magnetic field corotate
with the NS out to the light cylinder radius, $R_{\rm LC}=c/\Omega$, where the
corotation velocity reaches the speed of light. The magnetosphere is divided
into regions of open field lines that cross $R_{\rm LC}$ and regions of field
lines that close within $R_{\rm LC}$. The footpoints on the NS surface of the
open/closed boundary define the polar caps. The induced potential drop in
vacuum across the open field lines is

$V_{\rm pc}\simeq{1\over 2}\left({2\pi\over cP}\right)^{2}\,B_{0}R^{3}=6\times
10^{12}\,{\rm Volts}\,B_{12}\,P^{-2}$ (6)

The open field lines and the particles that flow along them become the pulsar
wind, which carries the bulk of the Poynting flux beyond $R_{\rm LC}$.

The pulsed radiation of RPPs carries less than about 10% of the total spin-
down power. Most of the power in pulsed emission is in gamma rays around a GeV
for all but a few RPPs, notably the Crab pulsar whose pulsed emission power
peaks in hard X rays. The radio pulsations make up typically only $10^{-4}$ or
less of the spin-down power, but are easier to detect since the photon flux is
much higher. Since the gamma-ray pulsations typically carry the highest
percentage of $\dot{E}_{d}$, they can reveal the most information about the
particle acceleration in pulsar magnetospheres. The discovery of gamma-ray
pulsations from over 130 RPPs by the Fermi Gamma-Ray Space Telescope Abdo2010
; Abdo2013 , where there were only seven known previously Thompson2001 , has
thus revolutionized the study of this type of NS (see Figure 3). Two new
populations of gamma-ray pulsars have been established with Fermi: radio quiet
pulsars discovered through blind searches for gamma-ray pulsations Abdo2009b ;
Pletsch2012 , and gamma-ray MSPs whose pulsations are found using radio
ephemerides Abdo2009c . These are presently equal in number to the radio-loud
gamma-ray pulsars. The gamma-ray pulse profiles show recurring patterns of two
narrow peaks separated by phase intervals of 0.1 - 0.5, with occasional single
peaks. The most striking pattern is that the gamma-ray peaks are not in phase
with the radio pulses, but typically arrive later in phase, with a lag that is
correlated with the gamma-ray peak separation (smaller lags for larger peak
separation, see Figure 4). The pulsed gamma-ray spectra are power laws with
high-energy exponential cutoffs in the range 1 - 10 GeV. The pulsed gamma-ray
emission of RPPs results from radiation of particles accelerated to energies
of order 10 TeV by electric fields parallel to the magnetic fields in the open
magnetosphere. Acceleration could take place near the polar caps Arons1979 ,
in the outer magnetosphere near the light cylinder Cheng1986  in slot gaps
along the last open field lines Arons1983 ; MH2004  or from reconnection in
the striped wind outside the light cylinder Petri2005 . The Fermi measurement
of an exponential shape for the spectral cutoff of the Vela pulsar Abdo2009a
ruled out emission in the intense magnetic field near the polar caps, whose
spectra would have much sharper, super-exponential cutoffs DH1996 , as being
the primary source of the observed gamma-rays. Instead, the softer cutoffs as
well as the observed profile shapes and peak separation vs. radio phase-lag
correlation Abdo2010  predicted by outer magnetosphere models Romani1995 ,
strongly suggest that the gamma-ray emission comes from high altitudes up to
and possibly beyond the light cylinder. In these models, the narrow gamma-ray
peaks are caustics formed by phase bunching of the emission along the open
field boundary through aberration and light travel time effects Dyks2004 ;
Harding2005 . The main radiation mechanism at GeV energies is thought to be
curvature radiation by the primary particles that have been accelerated to 10
TeV energies, but inverse-Compton emission may also contribute radiation at
the higher energies (up to 400 GeV) seen from the Crab pulsar Aliu2011 .

Many RPPs (over 100 at present) also show X-ray emission, with pulsations
detected in many of these. This emission is usually made up of two components:
non-thermal emission that is probably magnetospheric, and 0.05 - 0.1 keV
thermal emission from surface cooling or heated polar caps (see Kaspi2005  for
a detailed review). Some, like the Crab pulsar, show only non-thermal X-ray
emission, but in these cases the thermal components are probably buried under
the strong non-thermal emission. Others, like MSP J2124-3358, show only
thermal components with statistically insignificant non-thermal emission. The
thermal and non-thermal peaks in the pulse profiles are usually not in phase,
but the non-thermal peaks are sometimes in phase with one or two gamma-ray
peaks. In the youngest RPPs, emission from cooling of the NS surface is
thought to dominate the thermal radiation. In contrast, middle-aged RPPs like
Vela, Geminga and PSR J0659+1414 show a two-component thermal spectrum from
both heating and cooling, and a non-thermal power-law component. MSPs show all
of this behavior but, since these sources are too old to have detectable
emission from cooling, the thermal components, some of which are multiple
blackbodies, must be due to polar cap heating. The non-thermal emission is in
most models due to synchrotron radiation from electron-positron pairs, either
from the polar cap or the outer gap, emitting at high altitude Hirotani2006 ;
Harding2008 . The non-cooling thermal emission could come from polar caps
heated by high-energy particles flowing toward the NS from the polar cap
HM2001  or outer gap Halpern1993  accelerators.

There is an unusual and growing subpopulation of RPPs known as Rotating Radio
Transients (RRATS) (see Keane2011 , for review). They were discovered only
very recently McLaughlin2006 , through detections of their single, isolated
radio pulses. They show a variety of transient radio behavior, ranging from
nulling (or turning off for up to $\sim 10^{4}$ s) for long time periods to
steady pulsations that are highly modulated. While nulling behavior in normal
radio pulsars has been known for many years, the nulling of RRATS is extreme.
Over 70 RRATS have been identified and $\dot{P}$s have been measured for about
20 of these sources. Their $P$ and $\dot{P}$ are scattered throughout the
normal RPP population (see Figure 2), but they tend to be older
($\tau\mathrel{\mathchoice{\lower
2.0pt\vbox{\halign{$\m@th\displaystyle\hfil#\hfil$\cr>\crcr\sim\crcr}}}{\lower
2.0pt\vbox{\halign{$\m@th\textstyle\hfil#\hfil$\cr>\crcr\sim\crcr}}}{\lower
2.0pt\vbox{\halign{$\m@th\scriptstyle\hfil#\hfil$\cr>\crcr\sim\crcr}}}{\lower
2.0pt\vbox{\halign{$\m@th\scriptscriptstyle\hfil#\hfil$\cr>\crcr\sim\crcr}}}}10^{5}$
yr) and a number of them have higher than average surface magnetic fields.
X-ray pulsations have been detected from one RRAT, PSR J1819-1458
McLaughlin2007 , revealing a thermal spectrum and an absorption line at 0.5
keV, possibly due to proton cyclotron resonant scattering in a field of
$2\times 10^{14}$ G. The causes of such radio transient behavior is unknown,
but global changes in the currents or charge density in the pulsar
magnetosphere has been suggested Kala2012 ; Li2012 . It is not yet clear how
RRATS fit into the normal RPP population. They share some similar properties
with INS (see Section V), but if they are a separate evolutionary group they
would significantly raise the birthrate of NSs in the Galaxy Keane2008 .

In addition to pulsed emission, broadband, un-pulsed emission from radio to
high-energy (TeV) gamma-rays is detected from the pulsar wind nebulae (PWNe)
associated with RPPs. The PWN is a repository of high-energy particles and
fields from the RPP, accumulated over the pulsar’s lifetime and trapped by the
surrounding supernova shell that is moving more slowly than the relativistic
pulsar wind, or by the bow shock driven by the supersonic motion of the pulsar
through the interstellar medium. The particles are mostly electron-positron
pairs from the pair cascades DH1982  that occur in the magnetosphere, but
there could be some protons or positively-charged ions as well. Most of the
Poynting flux of the RPP must at some point, either in the wind or at the wind
termination shock, be transferred to the particles. In the Crab nebula, the
highest energy particles receive nearly the entire open-field voltage, as
deduced from the $\sim 100$ MeV cutoff in the synchrotron spectrum DJH1992 ;
Arons2011 . Many PWNe are detected at energies up to several or even tens of
TeV deJager2005 . This VHE emission is thought to be inverse-Compton emission
from the nebular particles, scattering either their own synchrotron radiation
as in the Crab PWN or, in most cases, the microwave and infrared background
radiation. Powerful gamma-ray flares from the Crab nebula that appear only in
the synchrotron emission component have recently been observed by Fermi
Abdo2011a  and AGILE Tavani2011 . Their short timescales of hours to days
indicate that they are coming from a very small region ($<1$ arcsec) and their
energies of up to several GeV challenge traditional models of acceleration in
pulsar wind nebulae Buehler2012 .

##  III Magnetars

NSs whose primary power source is the tapping of energy stored in their
magnetic fields are known as magnetars (see Woods2006 , for review). There are
two sub-classes of magnetars, Anomalous X-Ray Pulsars (AXPs) and Soft Gamma-
Ray Repeaters (SGRs), that were thought for many years to be separate and
unrelated objects. Today, we know that SGRs and AXPs are both NSs possessing
magnetic fields of unprecedented strength of $10^{14}-10^{16}$ G, and that
show both steady X-ray pulsations as well as soft $\gamma$-ray bursts. Their
inferred steady X-ray luminosities are about one hundred times higher than
their spin-down luminosities, requiring a source of power way beyond the
magnetic dipole spin-down that powers RPPs. New high-energy components
discovered in the spectra of a number of AXPs and SGRs require non-thermal
particle acceleration and look very similar to high-energy spectral components
of young rotation-powered pulsars denHartog2008  (see Figure 6).

Figure 5: Light curve of the 2005 superburst from SGR 1806-20, seen by the
Burst Alert Telescope on Swift. Strong pulsations are seen in the decaying
tail of the burst. (from Palmer2005 )

SGRs were first detected around 1979 as $\gamma$-ray transients and were
thought to be a type of classical $\gamma$-ray burst. They undergo repeated
bursts with several tenths of second duration and average energy
$10^{40}-10^{41}\,\rm erg$, and their bursting often occurs in episodes spaced
years apart. They more rarely undergo giant superflares of total energy
$10^{45}-10^{47}\,\rm erg$, consisting of an initial spike of duration several
hundred ms followed by a longer decay of duration several hundred seconds
showing pulsations (Figure 5). Such superflares have been observed in three
SGR sources, SGR0526-66 (the famous 5th March 1979 event) Cline1980 ,
SGR1900+14 Hurley1999  and SGR1806-20 Palmer2005 . In 1998, SGR1806-20 was
discovered to have 7.47 s pulsations in its quiescent X-ray emission
Kouveliotou1998  and a large $\dot{P}$ that implies a huge surface magnetic
field of $\simeq 10^{15}$ G if due to dipole spin-down. Quiescent
periodicities of 8 s and 5.16 s and large $\dot{P}$ were subsequently detected
in SGR0526-66 and SGR1900+14, implying similarly high surface magnetic fields.
In all three sources, the quiescent periods are the same periods seen in the
decay phases of their superflares. The quiescent pulse profiles are very broad
and undergo dramatic changes just before and after superflares. The profiles
are often more complex, with multiple peaks before flares, changing to more
simple single peaked profiles following the flares. Since the modulation is
thought to result from beaming along magnetic field lines, the profile changes
signal a re-arrangement of the magnetic field structure during the flares. All
of the SGRs lie near the Galactic plane and are thought to have distances
around 10-15 kpc (except for SGR0526-66, which is in the LMC). Recently, a
transient SGR was discovered with an apparent surface magnetic field strength
$<7.5\times 10^{12}$ G Rea2010 . This could be an aging magnetar that has
experienced significant field decay over its lifetime.

The first AXPs were discovered as pulsating X-ray sources in the early 1980s
by EXOSAT and were thought to be a strange (anomalous) type of accreting X-ray
pulsar. They are bright X-ray sources possessing luminosities (in their
highest states) of $L_{X}\sim 10^{35}\,\rm erg\;s^{-1}$, but show no sign of
any companion or accretion disks that would be required to support the
accretion hypothesis. The AXPs have pulsation periods in a relatively narrow
range of 5 - 11 s and are observed to be spinning down with large period
derivatives Vasisht1997 . Their pulse profiles are broad and very similar to
those of SGR sources. The very high surface magnetic fields of
$10^{14}-10^{15}$ G implied by dipole spin-down were originally controversial,
but have come to be accepted after the quiescent periods were found in SGRs
and especially following the recent discovery of SGR-like bursts from several
AXPs Kaspi2003 . It is now believed that SGRs and AXPs are two varieties of
the same type of object, very strongly magnetized, isolated NSs possibly
powered by magnetic field decay. In both sources, the high-state quiescent
luminosities of $L_{X}\sim 10^{35}\,\rm erg\;s^{-1}$ are much higher than
their spin-down luminosities of $\dot{E}_{d}\sim 2-6\times 10^{33}\,\rm
erg\;s^{-1}$, demanding an alternative power source.

Figure 6: Magnetar spectral components. Left: quiescent phase-averaged
spectrum of AXP 4U 0142+61 showing lower energy thermal and power law
components below 10 keV and high-energy component above 10 keV (from
denHartog2008 ). Right: typical burst spectra from AXP/SGR, compared with
burst spectra from X-ray and gamma-ray bursts (from Woods2006 ).

The quiescent spectra of AXPs and SGRs (see Figure 6) consist of a thermal
component fit by $\sim$ 0.5-1 keV blackbodies and one or more non-thermal
components. Until recently, non-thermal spectra were seen only below 10 keV
and were fit with steep power laws having photon indices $\sim 3-4$. When
INTEGRAL and RXTE recently measured the spectra above 10 keV for the first
time hard, non-thermal components were discovered in three AXPs, and also SGR
1806-20. In two of the AXPs, the differential spectra between 10 keV and 50
keV are extremely flat: 1E 1841-045 Kuiper2004  has a power-law photon index
of $s=0.94$ and 4U 0142+61 denHartog2004  displays a photon index of $s=0.45$,
both much flatter than the steep non-thermal components in the classic X-ray
band. RXS J1708-40 possesses a slightly steeper continuum with $s=1.18$. The
non-thermal tail of quiescent emission in SGR 1806-20 is similarly pronounced
Mereghetti2005 ; Molkov2005 , but somewhat steeper, with a photon index of
$s=1.6-1.9$ extending to 100 keV. Such hard non-thermal components require
continuous particle acceleration during the quiescent state. Transient, highly
variable radio emission has been detected from several magnetars Camilo2006 ;
Camilo2007  and may be correlated with their X-ray luminosity and
outburstsRea2012 .

It was proposed early on Ramaty1980 ; Katz1982  that SGRs were NSs with strong
magnetic fields in the range $10^{11}-10^{13}$ G to confine the super-
Eddington burst radiation. That SGRs and AXPs had much higher magnetic fields
above $10^{14}$ G was proposed by Duncan & Thompson [DT] Duncan1992  before
their existence was observationally verified. In this model, some NSs generate
huge magnetic fields by dynamo action soon after their birth in supernova
explosions. Such high fields have several properties that can cause the NSs to
behave differently from NS with lower fields. These fields can decay on much
shorter timescales, due to ambipolar diffusion Heyl1998 .

$t_{amb}\cong 10^{5}yr\left({\frac{{B_{core}}}{{10^{15}G}}}\right)^{-2}$ (7)

Diffusion of magnetic flux out of the NS core on these timescales provides the
power to magnetars in the DT model. Magnetar-strength fields also apply higher
stresses to the stellar crust, so that the yield strain can exceed the crustal
strength. This property is responsible for the small SGR and AXP bursts in the
DT model Thompson1996 . If a toroidal component of the field
$B_{core}>10^{15}$ G develops in the interior of the star, it can twist the
external field Duncan2001 . Such action can cause the superflares if the
twisted field lines reconnect. Finally, due to the much faster heat transport
in very strong magnetic fields, there is a greater heat flux through the crust
Heyl1998 . Such a property may explain the much hotter surface temperatures of
magnetars and the high quiescent X-ray emission.

Magnetar fields also produce a variety of different behavior of radiative
processes (see Duncan2000  and Harding&Lai2006  for reviews). In general, in
magnetic fields approaching and exceeding the quantum critical field $B_{\rm
cr}=4.4\times 10^{13}$ G, for radiative processes such as Compton scattering,
cyclotron and synchrotron emission and absorption, and pair production and
annihilation, classical descriptions are largely inaccurate and QED
descriptions must be used. In addition, new processes become possible in
strong fields, such as one-photon pair production and annihilation, vacuum
polarization and photon splitting, that cannot take place in field-free
environments. These processes, in particular vacuum polarization Lai2005 ,
strongly influence the propagation of photons in the NS atmosphere and the
spectrum of the emergent radiation.

According to the DT model Thompson1995 , the magnetar superflares result from
reconnection of sheared or twisted external field lines, leading to particle
acceleration and radiation of hard emission. The estimated luminosity of such
events,

$\frac{{B_{core}^{2}}}{{8\pi}}R^{3}\approx 4\times 10^{46}{\rm
erg}\left({\frac{{B_{core}}}{{10^{15}G}}}\right)^{2},$ (8)

is similar to observed luminosities of superflares. The smaller bursts result
from cracking of the crust, which is continually overstressed by diffusion of
magnetic flux from the NS interior. The shaking of magnetic footpoints then
excites Alfven waves that accelerate particles. The energy radiated in such
events would be

$E_{SGR}\cong 10^{41}{\rm
erg}\left({\frac{{B_{0}}}{{10^{15}G}}}\right)^{-2}\left({\frac{l}{{\rm
1km}}}\right)^{2}\left({\frac{{\theta_{\max}}}{{10^{-3}}}}\right)^{2},$ (9)

where $l$ is the length scale of the displacements, $B_{0}$ is the crustal
field and $\theta_{\max}$ is the yield strain of the crust. The quiescent
emission in the DT model is powered by magnetic field decay through conduction
of heat from the core. The NS crust is heated to a temperature of

$T_{crust}\cong 1.3\times
10^{6}K\left({\frac{{T_{core}}}{{10^{8}K}}}\right)^{5/9}$ (10)

where $T_{core}$ is the core temperature, and luminosity

$L_{\rm{x}}\cong 6\times 10^{35}{\rm
ergs^{-1}}\left({\frac{{B_{core}}}{{10^{16}G}}}\right)^{4.4}.$ (11)

Thompson2005  have proposed that the hard, non-thermal quiescent component is
due to the creation of a strong $E_{\parallel}$ induced by twisting of field
in the closed magnetosphere (see also Belo2009 ), producing synchrotron
radiation from electron acceleration at high altitude. An alternative model
for magnetar activity and emission has been discussed by Heyl2005 . The burst
and quiescent radiation are a result of shocks from fast-mode plasma waves and
the hard quiescent component is due to a pair-synchrotron cascade. On the
other hand, Baring Baring2004  and Baring & Harding Baring2007  propose that
resonant Compton upscattering of thermal X-rays by accelerated particles
produces the quiescent hard emission.

##  IV Compact Central Objects

Compact Central Objects (CCOs) are X-ray sources detected close to the centers
of young supernova remnants (SNRs) that have no apparent emission in other
wavebands and no binary companions. Although these sources have been known and
studied for several decades without much understanding of their nature,
exciting results over the past few years have brought them into the forefront
of NS studies. They have soft, exclusively thermal spectra in the few hundred
eV range and X-ray luminosities around $10^{33}-10^{34}\,{\rm erg\,s^{-1}}$.
About ten CCOs are presently known, including the central sources of CasA
(Figure 7), Puppis A and Kes 79 supernova remnants. Several, J1852+0040 in
Kes79 Gotthelf2010 , J0822.0-4300 in Puppis A Gotthelf2009  and 1E 1207.4
-5209 in PKS 1209-51/52 Zavlin2000  have detected pulsations in the hundreds
of ms range. J1852+0040 has a detected $\dot{P}$ Gotthelf2010 , indicating
that it is spinning down like a RPP. The measured $P$ and either measurements
or constraints on $\dot{P}$ indicate that these sources have very low magnetic
fields in the range $10^{10}-10^{11}$ G assuming magnetic dipole braking, so
that their birth periods were close to their present values. Since their SNRs
are all young, $\sim 10^{3}-10^{4}$ yr, they were probably born with unusually
low magnetic fields, which makes them ‘anti-magnetars’ Gotthelf2010 .

Figure 7: X-ray image of the supernova remnant Cassiopeia A taken with the
Chandra X-Ray Observatory, color coded for energy (Red: 0.5-1.5 keV; Green:
1.5-2.5 keV; Blue 4.0-6.0 keV). The CCO is the central white point source.
Credit: NASA/CXC/MIT/UMass Amherst/M.D.Stage et al.

The observed spectra are purely thermal, but some have multiple blackbody
components. The measured radii of the emitting areas, assuming blackbody
spectra or even H atmospheres, are less that 1 km, much smaller than a NS
radius. This is surprising if the emission is from cooling of the NS,
especially since the very low magnetic fields do not preferentially conduct
the cooling to small hotspots at the poles Zavlin1995 . Recently though, fits
of the spectrum of the CCO in CasA with C atmosphere models, that are harder
than those of H or He, give emitting radii that are consistent with a NS
radius of 10 - 12 km Ho2009 . This could be an indication of recent accretion
activity that would deposit some heavy elements on the NS surface. Even more
recently, the temperature of CasA is observed to be decreasing, by 4% in just
10 years Heinke2010 . If this is in fact the first measured cooling of a NS,
the rate of cooling is much more rapid than standard NS cooling models
predict. The measurements require proton or neutron superfluid models
Shternin2011  that predict sudden cooling at around the age of CasA (300 yr).
These measurements could thus also be the strongest evidence for superfluidity
in NS cores. Some CCOs show absorption lines in their spectra. 1E 1207.4 -5209
has 2-4 harmonically spaced lines at 0.7, 0.14, 0.21 and 0.28 keV Bignami2003
and the spectrum of J0822.0-4300 may have an absorption feature at 0.8 keV
Gotthelf2009 . These could be electron cyclotron lines in a field around
$8\times 10^{10}$ G.

Several mysteries surround these objects. Were they really born with such low
magnetic fields or were higher interior fields submerged by mass fallback
accretion to emerge later, enabling them to turn on as normal RPPs Ho2011 ?
This hypothesis would fit with the need for C atmospheres that make their
spectra consistent with full-surface NS cooling.

##  V Isolated Neutron Stars

Another class of NSs that appear to be thermally cooling with no emission
outside the soft X-ray band, except for faint optical/UV counterparts, are
known as Isolated Neutron Stars (INS) (see review by Kaplan2008 ). Although
these properties are similar to those of CCOs, they are a distinct class
because they lack any observable associated supernova remnant or nebula. There
are presently seven confirmed INS (sometimes referred to as The Magnificent
Seven), six of which have measured weakly modulated X-ray pulsations with
periods between 3 s and 11 s, much longer than those of CCOs. Two have high
measured $\dot{P}$ near $10^{-13}$, giving surface magnetic fields around
$10^{13}$ G, characteristic ages $\tau\sim 2$ Myr and spin-down luminosity
around $4\times 10^{30}\,{\rm erg\,s^{-1}}$ assuming dipole spindown. They
have significant proper motions, indicating distances of less than 500 pc. The
INS thus appear to be very nearby, cooling middle-aged NSs.

The X-ray spectra of INS are soft blackbodies with kT in the range 40 - 100
eV, and X-ray luminosities in the range $10^{30}-10^{32}\,{\rm erg\,s^{-1}}$,
with no measurable power law or non-thermal components. Four have observed
optical and/or UV counterparts that appear at first to be Rayleigh-Jeans
extensions of the X-ray blackbodies. However the optical spectra are about a
factor of 10 above the extrapolation of the X-ray blackbody. Alternatives to
simple blackbody fits have been explored, such as a thin magnetic, ionized H
atmosphere for the spectrum of J1856.5–3754, the original INS Ho2007 , or high
B-field atmospheres Potekhin2012 . Most INS show multiple or complex
absorption lines in their spectra at energy between 0.3 and 1 keV (e.g.
Kaplan2009 ). It is not clear what causes these features, but some
possibilities are proton cyclotron, and neutral or molecular H absorption. The
X-ray luminosities of several INS are larger than their spin down
luminosities, by a factor of 60 in the case of RX J0720, so that rotation
cannot power the observed X-ray emission. Furthermore, the temperatures and
thermal luminosities of INS are too high (by about a factor of 10) for
conventional cooling at their characteristic ages. This could imply that their
magnetic fields have not been constant since birth but have decayed Heyl1998 ,
providing another power source in addition to cooling and making them younger
than their spin-down ages.

It is not clear how INS are connected to the rest of the RPP population, other
than being NSs with thermal emission. Do they lack detectable radio emission
because our viewing angle does not cross the radio beam? A fit of the X-ray
profile of J1856.5–3754 Ho2007  constrains magnetic inclination and viewing
angles to be far apart. Or are they dead radio pulsars or extreme RRATS? They
do lie very near or beyond the empirical radio death line. But why do they not
have detectable non-thermal high energy emission? Other RPPs of similar ages
or older have detectable X-ray or gamma-ray pulsations. If their magnetic
fields are decaying or have decayed from magnetar-strength fields, then they
could be old magnetars Heyl1998  that wound up in the normal pulsar part of
$P$-$\dot{P}$ space Pons2009 . At the moment the population of INS is too
small to draw any firm conclusions about their nature and origin, but searches
for new INS are underway.

##  VI Accreting Neutron Stars

NSs in binary systems can accrete matter from the companion stars, either from
the stellar winds or from an accretion disk that forms if the companion
overflows its Roche Lobe. The gravitational energy from the infalling matter
provides at least part of the energy for the observed radiation and the
accretion torques dominate the spin evolution. Despite these common
properties, accreting NSs display a wide variety of behaviors, depending on
the NS magnetic field strength, mass of the companion and properties of the
accretion.

###  VI.1 Low-Mass X-Ray Binaries

LMXBs are binary systems in which one member is a NS or black hole and the
other star is a low-mass main sequence star, white dwarf or red giant that
fills its Roche Lobe, transferring matter onto the compact object through an
accretion disk. Almost all of the radiation is emitted as X rays with a very
small amount (about 1%) in optical light. The NS in LMXB are thought to be
old, have weak magnetic fields ($\sim 10^{8}$ G) and are being spun up by
torques from the accretion disk. One explanation for their very weak fields is
that the accretion has reduced or submerged the magnetic flux Romani1993 ;
Cumming2001 ; Ruderman2004 . Depending on the accretion rate $\dot{M}$, they
will reach an equilibrium where the pressure of the NS magnetic field balances
the pressure of the accretion flow after about 1 Myr, at which point the NS
period will have reached an equilibrium period $P_{\rm eq}$. The value of
$P_{\rm eq}$ depends on the NS field and $\dot{M}$ given by Eq (3). For
magnetic fields around $10^{8}$ G and $\dot{M}$ near the Eddington limit,
$P_{\rm eq}$ will reach millisecond periods. X-ray pulsations at millisecond
periods were in fact found in a number of LMXBs with the Rossi X-Ray Timing
Explorer (RXTE), the first being SAX J1808.4-3658 Wijnands1998 . Around 24 of
the more than 100 LMXB sources have shown ms X-ray pulsations, with
frequencies in the range 100 - 700 Hz (see review by Chak2005 ). Discovery of
these long-sought ms X-ray pulsations in LMXB finally established them as the
progenitors of the rotation-powered MSPs. The transition between an LMXB and a
MSP was actually observed when ms radio pulsations were discovered from the
source J102347.6+003841 which less than ten years earlier had shown optical
emission indicating an accretion disk Arch2009 .

Some LMXBs have steady X-ray emission, with occasional bursting behavior while
others are detectable only during their bursts. A good fraction are transient,
with outbursts on month to year timescales. The outbursts typically last weeks
to months. The X-ray bursts are thought to be thermonuclear explosions on the
NS surface, (see Strohmayer2004  for review) when the density and temperature
of the accreted material reach the critical point for igniting nuclear
reactions. The bursts have typical timescales of around 10 - 100 s and total
energy of $10^{39}-10^{40}\,{\rm erg\,s^{-1}}$. LMXBs also show kHz
quasiperiodic oscillations (QPO) in their X-ray emission (see vanderKlis2000
for review), thought to originate in the inner accretion disk flow. In most
models of QPO, the oscillation frequencies are the orbital frequencies of
accreting matter. Since these are stable orbits around a NS, they must be
outside the innermost stable circular orbit (ISCO) determined by General
Relativity, so their frequencies can be used to place limits on the NS mass
Miller1998 . Since the maximum measured QPO frequencies are about 1200 Hz,
using the ISCO of $6GM/c^{2}$ in the Schwarzschild metric gives the NS mass
$M<2M_{\odot}$ Zhang1997 .

Figure 8: X-ray burst oscillations in 4U 1702-43 (from Strohmayer1999 ). The
histogram shows the X-ray intensity of the X-ray burst. The contours show the
Fourier power level as a function of frequency and time, indicating a drifting
oscillation starting at 328 Hz (t = 7 s) and ending at 330.5 Hz.

A subset ($\sim 13$) of LMXB show ms pulsations in their persistent emission.
The rest (11) show the pulsations only during X-ray bursts Strohmayer1996 ;
Watts2012  or in QPO behavior. During the X-ray bursts, oscillations have been
observed, usually during the decay phase (see Fig 8), whose frequency rises to
an asymptotic limit as the intensity drops Strohmayer1999 . The interpretation
of this behavior is that the rotation of the NS is modulating the burst hot
spot which expands and rises in altitude, then drops back onto the surface.
The true rotation frequency of the NS is then the observed asymptotic
frequency. The NS spin frequency can also appear as the frequency difference
between pairs of QPO that move up and down in frequency together. Since the
difference in the frequencies of the QPO pair stays the same and is in the
range 200 - 400 Hz, it is thought to be the NS rotation frequency. In some
cases though, the frequency difference appears to be closer to 1/2 of the spin
frequency, and the relation between QPO and spin frequency has been questioned
Mendez2007 .

The distribution of NS spin frequencies from these various measurements cuts
off suddenly at a maximum frequency around 620 Hz Chak2005 , which is well
below the $\sim 1000$ Hz break-up frequency of a NS. This indicates that there
are some mechanisms that halt or counteract the spin up process. Several
possibilities have been suggested, including gravitational wave damping
Harding1983 ; Wagoner1984 , making these good sources of kHz gravitational
radiation for possible detection with Advanced LIGO.

###  VI.2 Intermediate- and High-Mass X-Ray Binaries

Binary systems consisting of a neutron star or black hole and high-mass O or B
star ($M\mathrel{\mathchoice{\lower
2.0pt\vbox{\halign{$\m@th\displaystyle\hfil#\hfil$\cr>\crcr\sim\crcr}}}{\lower
2.0pt\vbox{\halign{$\m@th\textstyle\hfil#\hfil$\cr>\crcr\sim\crcr}}}{\lower
2.0pt\vbox{\halign{$\m@th\scriptstyle\hfil#\hfil$\cr>\crcr\sim\crcr}}}{\lower
2.0pt\vbox{\halign{$\m@th\scriptscriptstyle\hfil#\hfil$\cr>\crcr\sim\crcr}}}}5M_{\odot}$
) are known as High-Mass X-Ray Binaries (HMXB), an example being Vela X-1. In
a large subclass of HMXBs, the NS orbits a Be star in a very eccentric orbit,
accreting material only occasionally in outbursts when the NS crosses a disk
of material surrounding the Be star. An example of a Be X-ray binary is
A0535+26. If the donor star is an intermediate-mass star
($1.0M_{\odot}\mathrel{\mathchoice{\lower
2.0pt\vbox{\halign{$\m@th\displaystyle\hfil#\hfil$\cr<\crcr\sim\crcr}}}{\lower
2.0pt\vbox{\halign{$\m@th\textstyle\hfil#\hfil$\cr<\crcr\sim\crcr}}}{\lower
2.0pt\vbox{\halign{$\m@th\scriptstyle\hfil#\hfil$\cr<\crcr\sim\crcr}}}{\lower
2.0pt\vbox{\halign{$\m@th\scriptscriptstyle\hfil#\hfil$\cr<\crcr\sim\crcr}}}}M\mathrel{\mathchoice{\lower
2.0pt\vbox{\halign{$\m@th\displaystyle\hfil#\hfil$\cr<\crcr\sim\crcr}}}{\lower
2.0pt\vbox{\halign{$\m@th\textstyle\hfil#\hfil$\cr<\crcr\sim\crcr}}}{\lower
2.0pt\vbox{\halign{$\m@th\scriptstyle\hfil#\hfil$\cr<\crcr\sim\crcr}}}{\lower
2.0pt\vbox{\halign{$\m@th\scriptscriptstyle\hfil#\hfil$\cr<\crcr\sim\crcr}}}}5M_{\odot}$),
the system is an intermediate-mass X-ray binary (IMXB) Pod2002 , a well-known
example being Her X-1. In HMXBs, the compact object accretes material from the
wind of the companion star or from a Be star disk, while in IMXBs the NS
accretes from a disk as in LMXBs. Both of these classes, numbering about
several hundred, are bright X-ray sources, and a large number show either
persistent or transient X-ray pulsations (in the case of Be star binaries). In
contrast to the ms pulsations of LMXBs, pulsation periods of HMXBs are much
longer, in the range 1 - 1000 s. The relation in Eq (3) then requires that the
NS magnetic field in these sources are near $10^{12}$ G. In fact, many X-ray
pulsars in IMXBs and HMXBs (about 20) show absorption features in their
spectra Heindl2004  that are almost certainly due to electron cyclotron
resonance scattering. The energies of these cyclotron resonant scattering
features (CRSF) are in the range 10 - 50 keV, also suggesting (Eq. [2]) that
the surface magnetic of the NSs are around $10^{12}-10^{13}$ G.

Because the NS magnetic fields are high in these systems, the Alfven radius

$r_{\rm A}=3\times 10^{8}\,{\rm cm}\,B_{12}^{4/7}\,\left({\dot{M}\over
10^{17}\,{\rm g\,s^{-1}}}\right)^{-2/7}\,\left({M/M_{\odot}}\right)^{-1/7},$
(12)

lies at a much larger distance from the NS than in LMXBs, and the accreting
material is strongly channeled via the magnetic field lines onto a small polar
cap. The infalling material then heats the NS atmosphere above the polar cap
to temperatures around $10^{8}$ K . The proposed mechanisms by which the
kinetic energy of the infalling material is decelerated and transferred to
heat depends on the mass accretion rate, which in turn determines its pressure
and the source luminosity $L_{\rm X}=GM\dot{M}$. If the accretion pressure
exceeds the radiation pressure, which is much higher than the spherical
Eddington limit due to the channeling of the flow, a radiative shock will form
at some distance above the NS surface Basko1976 . If the pressure of the
accretion flow does not exceed the radiation pressure, the atmosphere is
heated either by Coulomb collisions Pavlov1976  or a collisionless shock. In
the case where a stand-off shock forms, a slowly sinking accretion column
radiates mostly perpendicular to the magnetic axis in a fan beam Becker2005 ,
while in the Coulomb-heated case, the atmosphere is a thin slab at the NS
surface and radiates primarily along the magnetic axis Harding1984 . The
continuum spectrum of the X-ray pulsar radiation is thermal bremsstrahling and
Compton scattering emission (e.g. Becker2007 ). The CRSFs appear as absorption
lines and as many as four harmonics also appear in some X-ray pulsars such as
4U 0115+63 Heindl1999 . They are formed through resonant scattering of
continuum photons by electrons that have a thermal distribution of momenta
along the strong magnetic field lines (see Harding&Lai2006 , for a detailed
description of the physics of CRSFs). Since the resonant scattering cross
section has a strong dependence on angle, CRSFs can provide a good diagnostic
of the geometry and physical conditions of the emitting atmosphere Araya1999 ;
Schonherr2007 .

###  VI.3 Microquasars and Gamma-Ray Binaries

A subclass of accreting X-ray binaries are called microquasars since they
display properties similar to those of quasars, including rapid variability of
their X-ray emission and radio jets. Strong, broadband emission as well as
broad emission lines are also observed from their accretion disks. They
consist of a compact object, either neutron star or black hole, with a normal
companion. These sources undergo repeated and sometimes periodic radio,
optical and X-ray flaring with associated formation of relativistic jets.
Cygnus X-3 is a well-known microquasar that could be a black hole or neutron
star in a 4.8 hr orbit around a massive hot star. One of the strongest X-ray
sources in the sky, it is also detected from radio to GeV gamma-ray
wavelengths Abdo2009d .

The term gamma-ray binary has come to include binary systems that contain a
compact object and emit high energy gamma rays. Since several microquasars
have been detected in gamma rays, they are one of the gamma-ray binary source
types. The other gamma-ray binary source type is a system containing a RPP
orbiting a massive star. The prototype of this source class is PSR B1259-63,
which is a 48 ms radio pulsar in a 3.4 yr eccentric orbit around a Be star. It
appears as a normal radio pulsar at apastron, but at periastron the pulsar is
thought to make several crossings through the Be star disk, producing X-rays
and gamma-rays at GeV Abdo2011b  and TeV Ahar2005  energies. The X-ray
binaries LSI+61 303 and LS5039 have been detected by Fermi in high-energy
gamma rays Abdo2009e ; Abdo2009f , have characteristics similar to PSR
B1259-63 and are thought to contain undetected pulsars. The Fermi source 1FGL
J1018.6 5856 is the first Galactic binary system to have been discovered at
gamma-ray energies Abdo2012  but appears similar to LS5039, as both X-ray and
radio modulation at the orbital period were subsequently detected.

##  VII Summary

Neutron stars are found in a wide variety of sources, displaying an amazing
array of behavior. They can be isolated or in binary systems, accreting,
heating, cooling, spinning down, spinning up, pulsing, flaring and bursting.
The one property that seems to determine their behavior most strongly is their
magnetic field strength, structure and evolution. The hot polar caps, bursts
and flares of magnetars are likely due to the rapid decay and twisting of
their superstrong magnetic fields, whose very existence requires some kind of
early dynamo activity. The intermediate-strength magnetic fields of RPPs
determines their spin-down behavior and radiation properties. However, the
overlap of the magnetar and RPP populations is not understood at present. Why
don’t high-field RPPs burst or flare? Why don’t lower-field magnetars
sometimes behave more like RPPs? INS may be old magnetars whose high fields
have decayed, but they do not account for the existence of younger RPPs with
magnetar-strength fields. Not only the strength of the magnetic field but also
its configuration may be important in making a NS a magnetar or a RPP.
Magnetic field decay is a critical link between other NS populations as well.
“Decay” of the magnetic field is necessary for normal RPPs to evolve into MSPs
through accretion and spin up in LMXBs. Some kind of accretion-driven field
reduction is the most likely mechanism, but it is controversial since it is
not clear how effective it is or on what timescale a buried field might re-
emerge. One piece of evidence in favor of accretion-driven field reduction is
the fact that NSs in LMXBs, which are older systems ($>10^{8}$ yr), have
mostly low fields and NSs in HMXBs, which are younger systems ($10^{7}-10^{8}$
yr), have higher fields. This may be an indication that accretion-driven field
reduction or decay has not had enough time to operate in HMXBs but has in
LMXBs. However, there does not seem to be any evidence of decaying fields in
either the LMXB or HMXB populations; e.g. smaller magnetic fields in older
systems. On the other hand, CCOs are very young so if they acquired their low
fields through mass fallback accretion, the field submergence would have had
to operate on much faster timescales than it apparently does in LMXBs. But as
we continue to find new species in the NS zoo, one of these may someday be the
“Rosetta Stone” that will give us the clues for solving these puzzles.

I would like to thank Megan Decesar, Isabelle Grenier, Peter Meszaros, Tod
Strohmayer and Bing Zhang for providing helpful comments on the manuscript.

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