11institutetext: Arash Bahramian 22institutetext: International Centre for
Radio Astronomy Research – Curtin University, GPO Box U1987, Perth, WA 6845,
Australia, 22email<EMAIL_ADDRESS>33institutetext: Nathalie
Degenaar 44institutetext: Anton Pannekoek Institute for Astronomy, University
of Amsterdam, Postbus 94249, NL-1090 GE Amsterdam, the Netherlands, 44email:
<EMAIL_ADDRESS>
# Low-Mass X-ray Binaries

Arash Bahramian and Nathalie Degenaar corresponding author

###### Abstract

A large fraction of X-ray sources in our Galaxy are low-mass X-ray binaries,
containing a black hole or a neutron star accreting from a gravitationally
bound low-mass ($\buildrel<\over{\sim}$1 M⊙) companion star. These systems are
among the older population of stars and accreting systems in the Galaxy, and
typically have long accretion histories. Low-mass X-ray binaries are
categorized into various sub-classes based on their observed properties such
as X-ray variability and brightness, nature of the companion star and/or the
compact object, and binary configuration. In this Chapter, we review the
phenomenology of sub-classes of these systems and summarize observational
finding regarding their characteristics, populations, and their distribution
in the Galaxy.

## Keywords

Accretion Discs; Black Holes; Neutron Stars; X-ray Binaries.

###### Contents

  1. 1 Introduction
  2. 2 The nature of the compact primary in LMXBs
  3. 3 Donors and accretion phenomenology in LMXBs
    1. 3.1 Canonical Roche-lobe overflow with main sequence or giant stars
    2. 3.2 Ultra-compact X-ray binaries
    3. 3.3 Eclipsing LMXBs
    4. 3.4 Wind-fed accretion in LMXBs: Symbiotic X-ray binaries
    5. 3.5 Magnetically-channeled accretion in LMXBs: X-ray pulsars
  4. 4 Variability and transient outbursts in LMXBs
    1. 4.1 Long-term X-ray behavior: Transient and persistent LMXBs
    2. 4.2 Short-term X-ray behavior and sub-classes of NS LMXBs
    3. 4.3 Classification based on X-ray luminosity: Two extreme ends
  5. 5 Distribution and demographics of LMXBs in the Galaxy
    1. 5.1 Galactic center and bulge
    2. 5.2 Galactic plane and outer parts
    3. 5.3 Globular clusters
    4. 5.4 Orbital period distribution
  6. 6 Summary and prospects for future observatories and surveys
  7. 7 Cross-References

##  1 Introduction

In this Chapter we introduce and review basic properties of the low-mass X-ray
binaries (LMXBs): binary star systems comprised of a compact object, either a
black hole (BH) or neutron star (NS), that accretes gas from a companion star
less massive than the compact primary (typically $\lesssim$ 1 M⊙).111X-ray
binaries with massive companion stars (typically $\gtrsim$ 10 M⊙) are called
high-mass X-ray binaries (HMXBs). The focus of this Chapter is on the
demographics of LMXBs (e.g., binary configurations and formation, companion
and compact object types, Galactic numbers and distribution), as well as their
phenomenological behavior, particularly in the X-ray band (e.g., luminosity
and variability).222Other Chapters in this book delve into the physics of
accretion and compact objects. See Section 7 for a list of these chapters.

LMXBs are among the brightest X-ray point sources in the sky when they are
actively accreting. This is therefore how they are typically discovered and
identified. However, most LMXBs are not continuously accreting and are
classified as transients, showing X-ray outbursts with high levels of
accretion onto the compact object that typically only last for weeks to
months. These accretion outbursts are separated by long intervals of
quiescence, lasting months to tens of years, during which little or no
accretion occurs. This transient behavior is commonly explained in terms of
thermal-viscous instabilities in the accretion disk, the so-called Disk
Instability Model (DIM; Smak1983 ; Lasota2000 ; hameury2020 ).333See also
chapter “Formation and Evolution of Accreting Compact Objects” by Belloni et
al. Despite their generally low duty cycles, enhancements in the sensitivity
and monitoring capabilities of X-ray instruments have led to a steady increase
in the discovery of transient LMXBs (see Figure 1).

To date, there are $\sim$200 confirmed and candidate LMXBs identified in our
Galaxy, through their X-ray properties (e.g., Liu2007, ; Tetarenko2016a, ;
CorralSantana16, ). For many LMXBs the nature of the compact primary remains
to be identified, yet for several tens of systems we know whether these
contain BHs or NSs. Observationally, known NS-LMXB outnumber BH-LMXBs by a
factor of $\sim$2, and this is consistent with theoretical predictions based
on formation history of NSs and BHs (Kalogera98, ). It is also worth noting
that accreting BHs have been found more frequently in LMXBs, as opposed to
HMXBs. This could either be a result of binary evolution belczynski2009 , or
of observational biases casares2014_BeXRB .

Around one fifth of the current observed NS-LMXBs sample is made up of
accreting millisecond X-ray pulsars (AMXPs) and transitional Millisecond Radio
Pulsars (tMSRPs). In these systems, the accretion flow near the NS is shaped
by the magnetic field of the NS and is directed towards the magnetic poles,
producing X-ray pulsations Bildsten1997 ; Wijnands1998 . AMXPs and tMSRPs are
considered evolutionary links between (some) NS-LMXBs and recycled Millisecond
Radio Pulsars (MSRPs).

In a large fraction of LMXBs, the compact object is accreting from a main
sequence, sub-giant or red giant star that is filling its Roche lobe, and thus
mass transfer towards the compact object is primarily through Roche lobe
overflow. However, other types of LMXBs, for example, consisting of a compact
object accreting from a stripped remnant “core” of a star, or winds of a low-
mass giant that is not filling its Roche lobe (i.e., wind accretion) have also
been observed.

In this Chapter we briefly go into common methods to determine the nature of
the compact object in LMXBs (Section 2), after which we explore the dichotomy
of LMXBs based on their companion type and accretion mechanism (Section 3),
X-ray luminosity and (long-term) X-ray variability (Section 4), and their
distribution throughout our Galaxy (Section 5). We close the Chapter with a
brief summary and prospects offered by future observatories and surveys
(Section 6).

Figure 1: Growing population of BH LMXBs over the lifetime of X-ray
observatories. Enhancements in observatories, and analysis has increased the
rate at which transient X-ray binaries have been discovered/confirmed. This
figure was created in December 2021 by the BlackCAT team, based on the
continuously updated and publicly available data from BlackCAT
(CorralSantana16, , https://www.astro.puc.cl/BlackCAT).

##  2 The nature of the compact primary in LMXBs

Determining the nature of the compact object in a LMXB is generally an
observationally challenging task. While there are phenomenological features in
LMXB outbursts (either spectral or temporal) that sometimes allow
distinguishing between NS- or BH-LMXB candidates (e.g., Belloni05, ; Lin2007,
), these features are not sufficient to prove the nature of the compact
object. Here we review some of the more widely used methods to determine the
nature of the compact object in LMXBs.

Bursts and Pulsations \- The most robust method for confirming the presence of
a NS in a LMXB is the detection of events that require a solid surface, like
thermonuclear X-ray bursts (also called type-I X-ray bursts and arising from
rapid runway fusion of accreted matter on the surface of the NS; Lewin1993, ;
Strohmayer2006, ), or coherent (X-ray) pulsations (caused by surface hotspots
and modulated by the rotation of the NS; Alpar1982, ; Bildsten1997, ). NSs can
be sub-classified based on their magnetic field. In LMXBs we find primarily
weakly magnetic NSs with $B\lesssim 10^{8}$ G, though a handful of systems
contain NSs with stronger magnetic fields of $B\lesssim 10^{11-13}$ G
Patruno2012a . However, NSs with strong magnetic fields are more commonly
found in HMXBs Bildsten1997 . It is important to emphasize that the absence of
coherent pulsations or thermonuclear X-ray bursts does not rule out a NS
accretor in a LMXB, but there are other methods to investigate the nature of
the compact primary.

Radial velocity and estimation of the mass function \- One of the most robust
methods for verifying BHs in LMXBs (and estimating their mass) is generally
through radial velocity studies via optical or near-infrared spectroscopy -
relying on Doppler displacement of spectral features that are confidently
associated with the companion. While such radial velocity studies (and
inferred mass estimates) have a strong dependence on systems’ inclination
angle - a parameter difficult to constrain observationally, a lower limit of
$\geq 3$ M⊙, unambiguously identifies the compact object as a BH, since
degeneracy pressure would not be able to prevent a star of such mass from
collapsing (vanParadijs1995, ; Casares2014, ).

Disk-Jet coupling \- Another diagnostic method assisting in determining the
compact object in LMXBs is based on the observed coupling between jet outflow
(observed in the radio bands) and accretion rate (associated with the X-ray
luminosity). While both NS- and BH-LMXBs show evidence for jets, when at
similar X-ray luminosity, BHs tend to be brighter in the radio than NSs by a
factor of $\sim$5 to 20 (Fender2003, ; Migliari2006, ; Tudor2017, ; Gallo2018,
). This correlation has shown to be promising in identifying candidates, but
the scatter and overlap of NS and BH systems in this correlation is
significant and thus it is not sufficient for confirming nature of the compact
object. Two notable examples of this scatter are IGR J17591$-$2342, a NS-LMXB
that due to its bright radio emission was initially thought to harbor a BH
(Russell2018, ; Gusinskaia2020, ), and the dynamically confirmed BH-LMXB Swift
J1357.2$-$0933, for which its low radio luminosity initially led to
speculations on the NS nature for the compact object (Sivakoff2011ATel, ;
MataSanchez2015, ).

Quiescent X-ray properties \- The fact that NSs have a solid surface that, for
typical temperatures of $\sim 10^{6}$ K, should give rise to a black-body like
thermal emission component in the quiescent X-ray spectrum of the LMXB. This
diagnostic has often been used, for example, to identify NS-LMXBs in globular
clusters (see Section 5.3). However, if the NS is very cold (causing its
thermal emission peak to move out of the X-ray band), if residual accretion or
magnetospheric processes play a role (giving rise to a bright, harder X-ray
emission component), or if the extinction along the line of sight is very high
(causing the soft thermal X-rays to be absorbed), this method may break down
(Wijnands2005, ; Heinke2009, ; Degenaar2012a, ). In other words, the absence
of a thermal emission component in quiescent LMXBs is not evidence for a BH
accretor.

Other methods \- Apart from the detection of surface phenomena, dynamical mass
measurements, radio/X-ray luminosity ratio, or quiescent properties, other
methods used to gauge the nature of the compact object in LMXBs include the
ratio of their optical/infrared over X-ray fluxes Russell2006 ; Russell2007 ,
approximation of mass ratio via properties of the hydrogen Hα emission line
(Casares2016, ), or their X-ray spectral-timing behavior wijnands1999 ;
vanderKlis2006 ; Wijnands2015 .

In exploring the nature of a compact object in a LMXB, it is important to note
that detection of bursts or pulsations, and radial velocity studies generally
lead to relatively robust classification of the compact object, while methods
relying on luminosity ratios, emission features, and quiescent properties
generally provide valuable circumstantial evidence regarding the nature of the
compact object, particularly when the former methods are unfeasible.

##  3 Donors and accretion phenomenology in LMXBs

Many physical and observational characteristics of LMXBs such as mass transfer
rate, accretion mechanism, luminosity and outburst duty cycle are largely -
but not exclusively, linked with the binary configuration properties like
binary separation/period, eccentricity, and nature of the donor star, and, to
a lesser extent, the nature of the compact object. For instance, all these
factors play a role in the X-ray emission produced by a LMXB. The intrinsic
brightness of a LMXB scales with the rate at which mass is accreted. There is
a physical limit for the rate at which mass can be accreted hence on the
brightness of LMXBs. This limit is the Eddington luminosity (above which
radiation pressure prevents further accretion), which scales with the mass of
the compact object as $L_{\mathrm{Edd}}\approx
10^{38}\left(M/M_{\odot}\right)$ erg s-1. It is often useful to express the
brightness of LMXBs as a fraction of this Eddington luminosity.

In this section, we discuss various sub-classes of LMXBs based on binary
configuration as determined through observations, and their accretion
properties. Figure 2 shows graphical impressions of some of the different
types of LMXB systems discussed in the next sections.

Figure 2: Illustration of LMXBs in various configurations. Top-left: a
transient eclipsing LMXB during outburst (e.g., GRS 1747$-$312), top-right: a
persistent ultra-compact X-ray binary with a low inclination angle (e.g., 2S
0918$-$549,Zhong2011 ), middle-left: V404 Cyg during an outburst (as a well
known transient BH-LMXB), middle-right: Scorpius X-1 (as a well known
persistent NS-LMXB), bottom-left: GC 1+4 (as a symbiotic X-ray binary),
bottom-right: IGR J17062–6143 (as a very faint X-ray binary). These
visualisations were produced using the publicly available binsim code
(Hynes2002, , http://www.phys.lsu.edu/~rih/binsim/). Input for binsim includes
parameters describing binary configuration (e.g., separation, inclination),
companion properties (e.g., mass, Roche-lobe overflow fraction, temperature),
accretion flow and disk characteristic (disk inner and outer radii,
temperature gradient), jet angle and brightness, among other parameters. These
visualizations prioritize simplification for clarity of impression over
scientific accuracy. our aim here is to demonstrate relative size and
brightness of some of the main components of LMXBs. Note that scales are not
the same across the panels and vary from $\sim 10^{-2}$ AU (e.g., for an
ultra-compact X-ray binary) to $\sim$ a few AU (e.g., for a Symbiotic X-ray
binary).

###  3.1 Canonical Roche-lobe overflow with main sequence or giant stars

A large fraction of LMXBs consist of main sequence, sub-giant or red giant
branch stars filling their Roche lobe in a binary with a BH or a NS. Mass
transfer from the companion then occurs through Roche-lobe overflow onto an
accretion disk. The orbital period in these systems is typically of order of
hours for systems with a main sequence star and order of days/weeks for
systems with giants (Liu2007, ; CorralSantana16, ). Figure 2 shows schematic
impressions of different Roche-lobe overflow LMXBs (all but the bottom left
image).

Most of these canonical LMXBs are transient systems, identified in the X-rays
by their outbursts that typically reach $0.01-0.5L_{\mathrm{Edd}}$ while in
quiescence their X-ray luminosity is $\leq 10^{-5}L_{\mathrm{Edd}}$. When
actively accreting, the emission of LMXBs at all wavelengths is typically
dominated by that of the accretion flow and associated outflows. Direct and
detailed studies of the donor star are therefore generally not possible when
active accretion is occurring (i.e., in outbursting transients or persistent
LMXBs).

In quiescence, optical and infrared emission from LMXBs harboring main
sequence stars and hydrogen-rich giants is generally dominated by the
companion star, showing stellar atmospheric features like TiO features in the
optical or CO bandheads in the near-infrared. These features are crucial for
radial velocity measurements and thus dynamical mass measurements for compact
objects in these systems. In addition to stellar features many of these
systems show strong hydrogen emission lines (hydrogen H-$\alpha$ in the
optical, or Bracket-$\gamma$ in the near-infrared), associated with the
accretion disk. As these systems enter outburst, typically the optical and
infrared emission gets dominated by the accretion disk continuum emission,
sometimes with numerous hydrogen and helium emission features. The profile and
strength of accretion emission lines H-$\alpha$ or Bracket-$\gamma$ (in
quiescent and/or outburst) are among key indirect indicators for accretion
geometry (Steeghs2004, ) and potential nature of the compact object
(Casares2016, ).

###  3.2 Ultra-compact X-ray binaries

Ultra-compact X-ray binaries (UCXBs) are primarily defined (and identified) by
their very short orbital period of ${\lower
3.44444pt\hbox{$\buildrel<\over{\sim}$}}80$ minutes. At these orbital periods,
only helium burning sub-dwarf stars or white dwarfs are small enough to fit
into the orbit and fill their Roche lobe (Paczynski81, ; Rappaport1982, ;
Savonije1986, ). We tabulate a list of currently known UCXBs and candidates in
Table 1. A schematic impression of an UCXB is shown in Figure 2 (top right and
bottom right).

Observationally, confirming the UCXB nature of a LMXB binary requires
measurement of the orbital period. Thus, so far, only a few dozen UCXBs have
been confirmed (e.g., Cartwright2013, ). While direct observation of orbital
modulation has been the prime method for identifying UCXBs (e.g., Stella1987,
; Zurek2009, ; Galloway2010, ; Zhong2011, ), in a significant fraction of
these systems, discovery of an accreting millisecond X-ray pulsar (AMXP) has
allowed estimation of orbital period through accurate timing of the X-ray
pulsations (e.g., Wijnands1998, ; Chakrabarty1998_sax, ; Altamirano2010, ;
Sanna2016, ; Strohmayer2018, ). In addition to confirmed UCXBs, there are also
candidate systems that are identified as such based on the X-ray evolution of
their accretion outbursts (Heinke2015, ; Stoop2021, ), or their optical and
X-ray spectral properties (Bassa2006, ; ArmasPadilla2020, ; CotiZelati2021, ).
Furthermore, LMXBs that persistently accrete at very low rates are suspected
to have small disks (since these are easier kept photo-ionized sustaining
active accretion) and are hence considered good candidate UCXBs intZand2005a ;
intZand2007 .

While most UCXBs discovered to date have been found to be persistently bright
in the X-rays with the X-ray luminosity varying typically at $L_{X}>10^{36}$
erg s-1, a subset of UCXBs are transient systems, showing quiescent periods
with $L_{X}<10^{32}$ erg s-1 interspersed by outbursts. Additionally, some
UCXBs are classified as very faint X-ray binaries (see Section 4.3), showing
very faint (transient) accretion emission of $L_{X}\simeq 10^{34}-10^{36}$ erg
s-1(vanHaaften2012, ; Cartwright2013, ).

Given the natures of both accretor and companion in UCXBs, these systems are
extremely hydrogen deficient and abundance of elements is particularly
unusual, typically dominated by He, C, O, Ne (or less likely, by heavier
elements). Thus the spectral continuum (particularly in the optical band) in
these systems is generally void of stellar absorption features or any hydrogen
emission or absorption lines. Instead, emission lines from He, N, C, O are
prevalent in the optical (Nelemans2004, ; Nelemans2006, ), ultra-violet
(Homer2002, ) and X-rays (Juett2001, ; Juett2003, ; Madej2010, ).

To date, there have been no BHs confirmed in any UCXB system. However
candidates have been identified based on X-ray and radio properties
(Bahramian2016, ), X-ray outburst properties along with radio and X-ray
properties (Stoop2021, ), or X-ray luminosity and optical spectroscopy (in an
extragalactic system, Dage2019, ). There might be an observational bias
against detecting BH-UCXB systems in the X-rays because the radiative
efficiency and duration of the outbursts of BH LMXBs may drop sharply towards
shorter orbital periods Knevitt2014 . Furthermore, confirming the presence of
a BH in a UCXB system dynamically is particularly challenging, as traditional
methods, like radial velocity measurements based on spectral features
associated with the surface of the donor, are unfeasible.

Galactic compact binaries like UCXBs are expected to be among the main sources
of gravitational wave emission to be detected by future facilities like the
Laser Interferometer Space Antenna (LISA) and TianQin (AmaroSeoane2017, ;
Luo2016, ). This includes the “dual-line” signal from the combination of NS
spin and system orbit, and the “chirp” signal from those of these systems that
eventually go through coalescence (Nelemans2001, ; Tauris18, ; chen2021, ;
Suvorov21, ). Therefore, it is highly desired to search for and find more
UCXBs.

System | Distance | $P_{\textrm{orb}}$ | T/P | NS/BH | Reference
---|---|---|---|---|---
| (kpc) | (min) |  |  |
Confirmed UCXBs
4U 1820$-$303 | 8.0 | 11 | P | NS | Stella1987
4U 0513$-$40 | 11.9 | 17 | P | NS | Zurek2009
2S 0918$-$549 | 5.4 | 17.4 | P | NS | Zhong2011
4U 1543$-$624 | $\sim 6$ | 18.2 | P | NS | Wang2004 ; Wang2015
4U 1850$-$087 | 7.38 | 20.6 | P | NS | Homer1996
M15 X-2 | 10.7 | 22.6 | P | NS | Dieball2005
47Tuc X-9 | 4.5 | 28 | P | BH? | Bahramian2017
IGR J17062$-$6143 | $\sim 7.3$ | 38 | T | NS | Strohmayer2018
XTE J1807$-$294 | $\sim 8$ | 40.1 | T | NS | Markwardt2003
XTE J1751$-$305 | $\sim 8$ | 42 | T | NS | Markwardt2002
4U 1626$-$67 | $\sim 8$ | 42 | P | NS | Chakrabarty1998
XTE J0929$-$314 | $\sim 8$ | 43.6 | T | NS | Galloway2002
MAXI J0911$-$655 | 10 | 44.3 | T | NS | Sanna2017
IGR J16597$-$3704 | 7.2 | 46.0 | T | NS | Sanna2018
4U 1916$-$053 | $\sim 9.3$ | 50 | P | NS | Walter1982
Swift J1756.9$-$2508 | $\sim 8$ | 54.7 | T | NS | Krimm2007
NGC 6440 X-2 | 8.2 | 57.3 | T | NS | Altamirano2010
IGR J17494$-$3030 | ? | 75 | T | NS | Ng2021
2FGL J1653.6$-$0159 | $\sim 1$ | 75 | Qa | NS | Kong2014 ; Romani2014
Candidate UCXBs
4U 1728$-$34 | 5.2 | 10.8b | P | NS | Galloway2010
4U 0614+091 | 3.2 | 51c | P | NS | Shahbaz2008
1A 1246$-$588 | 4.3 | ? | P | NS | intZand2008
4U 1812$-$12 | $\sim 4$ | ? | P | NS | Bassa2006 ; ArmasPadilla2020
XMMU J181227.8$-$181234 | $\sim 14$ | ? | T | NS | Goodwin2019
1RXS J180408.9$-$342058 | $<5.8$ | ?d | T | NS | Baglio2016
IGR J17285$-$2922 | ? | ? | T | BH? | Stoop2021
Swift J0840.7$-$3516 | ? | ? | T | ? | CotiZelati2021
4U 1857+01 | ? | ? | T | NS | Jonker2006
SAX J1712.6$-$3739 | $\sim 7$ | ? | T | NS | intZand2007
1RXS J170854.4$-$321857 | $\sim 13$ | ? | P | NS | intZand2007 ; ArmasPadilla2019
1RXS J171824.2$-$402934 | ? | ? | P | NS | intZand2009
4U 1722$-$30 | 7.7 | ? | P | NS | intZand2007
1RXS J172525.2$-$325717 | ? | ? | P | NS | intZand2007
SLX 1735-269 | $\sim 6$ | ? | P | NS | intZand2007
SLX 1737-282 | 7.3 | ? | P | NS | intZand2007
SLX 1744-299 | ? | ? | P | NS | intZand2007
XMMU J174716.1-281048 | $\leq 8.4$ | ? | P | NS | degenaar2011burst
Table 1: A catalog of known Galactic UCXBs and candidates. Table partially
based on intZand2007  and Cartwright2013 . “T/P” indicates whether the source
is transient (T) or persistent (P). “NS/BH” indicates nature of the compact
object (e.g., determined via detection of Type I X-ray bursts or pulsations).
Currently, there are no confirmed BH-UCXB systems identified. Candidate UCXBs
are generally identified based on their characteristics suc as signatures of
hydrogen deficiency (e.g., long Type I X-ray bursts, featureless optical
spectrum, or prominence of neon, carbon or oxygen features). a- 2FGL
J1653.6$-$0159 was identified as a Gamma ray millisecond pulsar with a
quiescent (L${}_{X}\sim 10^{31}$ erg s-1) X-ray counterpart. b- Galloway2010
identify a suggestive periodic signal at 10.8 min, however we note that
Vincentelli2020  recently suggest that the orbital period is unlikely to be
shorter than 66 min and thus the system is not a confirmed UCXB. c- An orbital
period of $\sim 50$ has been suggested by Shahbaz2008 ; Baglio2014  suggest
that the orbital period may be $>1$ hour. However, the authors note that the
companion still appears to be hydrogen-deficient (thus still likely to be a
UCXB). d- An orbital period of 40 minutes is indirectly inferred by Baglio2016
based on evolutionary tracks of a presumed He donor. However, this periodicity
is not yet observationally confirmed, specially as Marino2019  note possible
presence of H/He in the accreted material.

###  3.3 Eclipsing LMXBs

Eclipsing LMXBs are not a characteristically separate class of LMXBs, as the
eclipses are merely a result of high inclination angle ($i\sim 90^{\circ}$) of
the binary orbital plane from our point of view (see Figure 2). However, our
observational perspective of eclipsing binaries provides a unique direct
method to study properties of accretion disk via eclipse mapping
(Baptista2001, ), and evolution of orbital period in LMXBs on timescales of
years/decades (e.g., Chou2014, ). It has also been suggested that study of
eclipses in accreting systems in the radio band can prove powerful in
understanding jet physics (maccarone2020_eclipse, ).

Broadly speaking, the orbital period in X-ray binaries is expected to decay,
as momentum is lost in accretion processes, outflows, gravitational radiation,
and magnetic breaking (e.g., Paczynski1967, ; Verbunt1981, ; Tavani1991, ).
Studying the evolution of orbital period on timescale of years/decades in
HMXBs has shown that such a decay is indeed present and can be generally
described by a smooth linear or quadratic ephemeris model (e.g., Falanga2015,
). However, observations of LMXBs indicate while many of them show orbital
decay, the changes in the orbital decay in some cases cannot be well described
by linear or quadratic ephemeris models (Jain2011, ; Wolff2009, ; Iaria2018, ;
Ponti2017, ), and many of these systems exhibit multiple “epochs” of orbital
decay with highly variable rates (Figure 3), sometimes accompanied by period
“jitters”. These anomalies demonstrate that evolution of orbital period in
LMXBs on short timescales (years) is not fully understood.

Currently there are $\sim$a dozen eclipsing Galactic LMXBs identified (Table
2). Almost all of these systems have been identified as eclipsing LMXBs during
bright outbursts. However, a select few have been identified in quiescence in
deep observations (e.g., X5 in globular cluster 47 Tuc, which has been
observed substantially by the Chandra X-ray observatory). In addition to the
sources cataloged in Table 2, there are a handful of other eclipsing systems
that either show only partial eclipses (e.g., see Chou2014, , and references
therein), or while eclipses have been observed period or nature of the system
are uncertain (e.g., Maeda2013, ).

System | $P_{\textrm{orb}}$ | $\dot{P}_{\textrm{orb}}$ | NS/BH | Reference
---|---|---|---|---
| (hour) | ($10^{-12}$ s s-1) |  |
XTE J1710$-$281a | 3.281063218(7) | $-1.6\leq\dot{P}_{\textrm{orb}}\leq 0.2$ | NS | (Jain2011, )
EXO 0748$-$676b | 3.824088(1) | - | NS | (Wolff2009, )
4U 2129+47c | 5.238220(2) | $103(\pm 13)$ | NS | (Bozzo2007, )
IGR J17451$-$3022 | 6.2834(5) | - | ? | (Bozzo2016, )
H 1658$-$298d | 7.1161099(3) | $-8.5(\pm 1.2)$ | NS | (Wachter2000, ; Iaria2018, )
CXOGC J174540.0$-$290031 | 7.767(2) | - | ? | (Muno2005a, ; porquet2005, )
AX J1745.6$-$2901 | 8.3510081(2) | $-40.3(\pm 2.7)$ | ? | (Ponti2017, )
47 Tuc X5 | 8.67(1) | - | NS | (Heinke2003, )
3FGL J0427.9$-$6704 | 8.80128(2) | - | NS | (Strader2016, )
Swift J1749.4$-$2807 | 8.816866(2) | - | NS | (Markwardt2010, )
GRS J1747$-$312 | 12.3595273(2) | - | NS | (intZand2003, )
Swift J1858.6$-$0814 | 21.3448(4) | - | NS | Buisson2021
Her X-1e | 40.80402216(5) | $-48.5(\pm 1.3)$ | NS | (Staubert2009, )
Table 2: A catalog of known Galactic LMXBs exhibiting clear total eclipses
(for the purpose of this catalog we omit LMXBs with suggestive or partial
eclipses). “NS/BH” indicates nature of the compact object (via detection of
Type I X-ray bursts or pulsations, or deep X-ray spectroscopy in case of
quiescent systems like 47 Tuc X5). No eclipsing BH-LMXB has been confirmed as
of this writing. a\- (Jain2011, ) demonstrate that XTE J1710-281 shows
irregular variations, and find the best-fit ephemeris solution is a piece-wise
linear model. b\- EXO 0748-676 shows strong variations in ephemeris and
(Wolff2009, ) indicate no simple linear or quadratic solution describes all
data. c\- (Bozzo2007, ) speculate that the ephemeris of 4U 2129+47 indicates
that it could be in fact part of a hierarchical triplet system. d\- The best-
fit ephemeris solution suggested by (Iaria2018, ) contained linear, quadratic
and a sinusoidal term with a period of 2.31 yr. The authors suggest such a
modulation could be produced by the gravitation coupling of the orbit with
changes in the shape of the magnetically active companion star. e\- We note
that Her X-1 is not strictly a LMXB as the companion is estimated to be $\sim
2$M⊙. Figure 3: Evolution of orbital period in EXO 0748-676 (based on
(Wolff2009, )). The change in orbital period does not follow a single pattern
and appears to show epochs, with different rates of change. EXO 0748-676 is
among the best documented cases of such anomalous orbital changes in LMXBs,
however it is not the only eclipsing LMXB exhibiting irregular variations in
orbital period evolution.

###  3.4 Wind-fed accretion in LMXBs: Symbiotic X-ray binaries

In contrast with other classes of LMXBs, symbiotic X-ray binaries (SyXBs)
stand out by the absence of Roche-lobe overflow. These systems consist of a
compact object (BH or NS) accreting from the winds of a low-mass late-type
giant. It is important to clarify that we define symbiotic X-ray binaries
distinctly from “symbiotic stars” (or symbiotic binaries), which are defined
by a white dwarf accreting from winds of a late-type giant.444In
classification of symbiotic stars and systems based on their X-ray properties
(e.g., the groups labeled as $\alpha$, $\beta$, $\gamma$, $\delta$,
$\beta/\delta$), symbiotic X-ray binaries are generally classified as the
$\gamma$ group (Murset1997, ; Luna2013, ).

GX 1+4 is the only SyXBs identified so far that has been observed to be
persistently bright ($\geq 10^{36}$ erg s-1) in the X-rays (Lewin1971, ;
Serim2017, ; Ilkiewicz2017, ). However, most SyXBs show strong rapid
variability, with quiescence luminosity $L_{X}\leq 10^{33}$ erg s-1 and
outburst $L_{X}\geq 10^{34}$ erg s-1 within hours/days, and can decay as
quickly (e.g., Patel2007, ; Masetti2007, ; Heinke2009b, ). Additionally, SyXBs
tend to show rapid “faint” outbursts with peak luminosity $10^{34}$ erg s-1
$\leq L_{X}\leq 10^{36}$ erg s-1 (Masetti2006, ; Kaplan2007, ; Farrell2010, ;
Kuranov2015, ). The sporadic nature of their variability makes SyXBs
particularly difficult to detect and identify, thus characterizing their
population and behavior requires sensitive frequent monitoring (e.g., with
Swift/XRT or eROSITA; Bahramian2021, ).

To date, no BH SyXB system has been identified. In a large fraction of SyXBs,
discovery of spin periods (in the 100s to 1000s of seconds range) have led to
identification of the NS accretor (Patel2004, ; Bodaghee2006, ; Thompson2006,
; Corbel2008, , see also Table 3). Companion stars in SyXBs are typically K-M
III giants (Chakrabarty1997, ; Masetti2002, ; Bozzo2013, ; Bahramian2014a, ;
Shaw2020, ). However, in rare cases the companions have been identified as
carbon stars (Masetti2011, ; Hynes2014, ). Owing to the detached nature of
SyXBs and the size of the companion, these systems typically have long orbital
periods ranging from tens to thousands of days and in many cases difficult to
constrain with current available coverage of these systems (Hinkle2006, ;
Nespoli2010, ; Kuranov2015, ).

The spectrum of SyXBs in the optical and NIR regimes is typically dominated
(almost completely) by the companion star. In some cases, strong hydrogen
emission lines like H-$\alpha$ or Br-$\gamma$ (sometimes broad and/or double-
peaked) are also observed, particularly during enhanced X-ray activity
(Chakrabarty1997, ; Nespoli2010, ). Furthermore, during enhanced activity,
contribution from the accretion continuum can be noticed at shorter
wavelengths (Fig. 4; Bozzo2018, ).

Study of accretion and outflows in SyXBs in the radio frequencies is also
challenging due to their rapid variability. However, radio observations of GX
1+4 - the only persistent SyXB, has allowed study of these mechanisms in
SyXBs. While earlier radio observations of this system reported non-detections
or marginal detections (Seaquist1993, ; Fender1997, ; Marti1997, ), later
observations by the Karl G. Jansky Very Large Array showed significant
detection of emission, which perhaps could be caused by the outflow
(vandeneijnden2018b, ).

System | $P_{\textrm{spin}}$ | $P_{\textrm{orbit}}$ | Peak Lx | Distance | NS/BH | Reference
---|---|---|---|---|---|---
| s | d | erg s-1 | kpc |  |
GX 1+4 | 140 | 1161 | $10^{36}$ | 4.3 | NS | (Chakrabarty1997, ; Hinkle2006, ; Ferrigno2007, ; GonzalezGalan2012, )
Sct X-1 | 113 | ? | $2\times 10^{34}$ | $\geq 4$ | NS | Kaplan2007
3XMM J181923.7–170616 | 408 | ? | ? | ? | NS | (Qiu2017, )
IGR J16358$-$4726 | 5850 | ? | $3\times 10^{36}$ | 5–13 | NS | (Patel2004, ; Patel2007, ; Nespoli2010, ; Lutovinov2005, )
IGR J17329$-$2731 | 6680 | ? | $3\times 10^{35}$ | $\sim 2.7$ | NS | (Bozzo2018, )
CGCS 5926 | ? |  $\sim$151 | $3\times 10^{32}$ | $6(\pm 1)^{a}$ | ? | Masetti2011
4U 1700+24 | ? | 4391c | $10^{34}$ | 0.544 | NS | Masetti2002 ; Masetti2006 ; Hinkle2019
IGR J16194$-$2810 | ? | ? | $\leq 10^{35}$ | $2.1(\pm 0.2)^{a}$ | ? | Masetti2007
CXOGBS J173620.2$-$293338 | ? | ? | $10^{33}$ | $\sim 8^{a,b}$ | ? | (Hynes2014, )
XTE J1743$-$363 | ? | ? | ? | $\sim 8^{a,b}$ | ? | (Smith2012, ; Bozzo2013, )
IGR J17445$-$2747 | ? | ? | ? | 1.1–7.6 | NS | (Mereminskiy2017, ; Shaw2020, )
XMMU J174445.5$-$295044 | ? | ? | $10^{35}$ | 3.1 | ? | (Bahramian2014a, )
IGR J17197$-$3010 | ? | ? | $\leq 2\times 10^{35}$ | 6–17 | ? | (Masetti2012b, )
CXOGBS J174614.3$-$321949 | ? | ? | $10^{34}$ | $\sim 8^{a,b}$ | ? | (Wetuski2021, )
CXOGBS J173620.2$-$293338 | ? | ? | $\leq 10^{33}$ | $\sim 8^{a,b}$ | ? | (Wetuski2021, )
IGR J17597$-$2201 | ? | ? | ? |  $15$? | NS | (Chaty2008, ; Ratti2010, ; Zolotukhin2015, )
Swift J2037.2+4151 | ? | ? | $10^{36}$ | $\sim 10$ | ? | (Molina2021, )
Table 3: A catalog of identified Galactic SyXBs and SyXB candidates. Table
partially based on Yungelson2019 , see also Kuranov2015 ; Merc2019 . “NS/BH”
indicates nature of the compact object (via detection of Type I X-ray bursts
or pulsations). No Symbiotic BH-LMXB has been confirmed as of this writing. It
is worth noting that Peak LX is the _reported_ peak luminosity; SyXBs can have
short lived flares (minutes long) reaching higher luminosities that may have
been missed in pointed observations too short to be noticed in X-ray monitors.
SyXB candidates not listed in this table include 4U 1954+31 (proposed to be a
SyXB by Corbel2008 ; Masetti2006 , recent works indicate it is likely an HMXB
(Hinkle2020, )), IRXS J180431.1$-$273932 (suggested as SyXB by (Nucita2007, ),
disputed by (Masetti2012, )), IGR J16393$-$4643 (suggested as a SyXB by
(Nespoli2010, ), disputed by (Bodaghee2012b, )), 2XMM J174016.0$-$290337
(suggested as a SyXB by Farrell2010  and disputed by (Thorstensen2013, )),
Swift J175233.3$-$293944 (suggested as symbiotic by (Wevers2017, ), a white
dwarf compact object is favored by (Bahramian2021, )).
a \- indicates the distance (and luminosity) has been updated based on Gaia
EDR3 GaiaEDR3summary2021 . This includes applying parallax zero-point
correction based on (Lindegren2021, ) and considering a Galactic prior based
on distribution of LMXBs (Atri2019, ). b \- Indicates that while a parallax
value is reported EDR3 for the source, it is not significant and thus distance
estimation is dominated by prior assumptions. c\- An alternative period of 404
days is also discussed by (Galloway2002, ; Hinkle2019, ). Figure 4: Optical
spectrum of a typical Symbiotic X-ray binary (IGR J17329-2731) during an
outburst. While generally, the optical and infrared continua are dominated by
the companion, strong accretion features like broad or double-peaked
H-$\alpha$ lines can sometimes be visible. During outbursts, the continuum
emission from the accretion disk (i.e., multi-color blackbody) can also be
observed in some cases at shorter wavelengths. Figure based on (Bozzo2018, ).

###  3.5 Magnetically-channeled accretion in LMXBs: X-ray pulsars

In a sub-group of NS-LMXBs, material from the inner part of the accretion disk
is funneled along the magnetic field lines of the NS onto its magnetic poles.
This localized accretion causes hotspots that give rise to X-ray pulsations
modulated at the spin period of the NS Bildsten1997 ; Wijnands1998 . Roughly
20% of NS-LMXBs display rapid X-ray pulsations, in a range of $\sim$1–10 ms,
and are called Accreting Millisecond X-ray Pulsars (AMXPs; see campana2018
for an overview until 2018 and Sanna2018 ; Sanna2018b ; Ng2021  for 3 new
AMXPs discovered since). The NSs in AMXPs have relatively weak magnetic field
strengths of $B<10^{9}$ G Mukherjee2015 . Furthermore, these NSs are thought
to have acquired their rapid spin by angular momentum transfer in the
accretion process, and are likely the progenitors of millisecond radio pulsars
(MSRPs) Bhattacharya1991 ; Alpar1982 .

The connection between AMXPs and MSRPs seems to be supported by the discovery
of the so-called “transitional millisecond radio pulsars” (tMSRPs); these are
NSs in binary systems that are sometimes observable as regular millisecond
radio pulsars, but at other times look more like a LMXB with an accretion disk
present and no observable radio pulsations campana2018 . Currently, there are
3 systems showing clear evidence for switches between these two
manifestations, which occur on a timescale of years (IGR J18245–2452 in the
globular cluster M28, PSR J1023+0038 and XSS J12270–4859; Archibald2009 ;
Papitto2013 ; Bassa2014 ). Given the scientific interest of studying systems
that appear to bridge different NS populations, there has been much effort in
finding more tMSRPs. This has resulted in several good candidate systems (see
papitto2020  for a recent overview), but so far no new confirmed ones have
emerged yet.

The binary parameters of AMXPs (and tMSRPs) are well known through accurate
timing of their (X-ray) pulsations. In a handful of systems, for which the
orbital period is $\sim$2 hr, the companion is thought to be a brown dwarf.
The remaining AMXPs are split into roughly equal groups of systems with white
dwarf or helium donor stars in tight orbits ($\sim$0.25–1.25 hr, i.e., UCXBs),
and systems with main sequence donor stars and longer orbital periods (nearly
all $\sim$3–11 hr) campana2018 . The three confirmed tMSRPs all fall in the
latter group.

Apart from the rapidly spinning AMXPs, a very small subgroup ($\lesssim$10%)
of NS LMXBs displays much slower pulsations (seconds to hours). In addition to
slower spin, the NSs in these systems also have stronger magnetic fields
($B\sim 10^{10-12}$ G) than the rapidly spinning AMXPs. There are 4 slow
pulsars in Roche-lobe overflow LMXBs (2A 1822–371, 4U 1626–67, GRO 1744–28,
and Her X-1)555Her X-1 formally classifies as an intermediate-mass X-ray
binary (IMXB). and their spin periods are in the range of $\sim$0.1–2 s. In
addition, there are 5 slow pulsars found in the wind-fed SyXBs which have spin
periods of $\sim$10 min to $\sim$5 hr (see Table 3).

For the wind-accreting systems, the accretion efficiency is likely too low to
transfer significant amounts of angular momentum that spin up the NS. However,
for the slow pulsars in Roche-lobe overflow systems, it is not yet clear why
these NSs have not been spinned up. The explanation likely lies in the prior
evolution of the binary verbunt1990 ; Rappaport1997 ; vanparadijs1997 . In
terms of binary parameters, the slow LMXB pulsars are a heterogeneous group
with orbital periods from $<$1 hr to $>$11 days and white dwarf, main-sequence
or giant companions.

##  4 Variability and transient outbursts in LMXBs

In addition to the physical classification based on compact object type, donor
type and mode of mass transfer discussed in the previous sections, LMXBs can
be phenomenologically categorized based on their X-ray behavior. In the
following sections we provide an overview of classifications based on their
long-term X-ray variability (on $\sim$ months/year timescales), short-term
X-ray variability (on $\sim$ days/weeks timescales), and X-ray (peak)
luminosity. As we will see, the dynamic range in X-ray luminosity traced out
by the population of LMXBs as a whole covers many orders of magnitude; from
$L_{\mathrm{X}}\simeq 10^{39}$ erg s-1 for sources accreting around the
Eddington luminosity to $L_{\mathrm{X}}\simeq 10^{30}$ erg s-1 for quiescent
systems in which little or no accretion occurs.

It is important to remind the reader that with these various ways to
(physically or phenomenologically) classify LMXBs, there is overlap between
different categories. For instance, several AMXPs are UCXBs and the broad
distinctions of persistent and transient sources contain basically all other
sub-classes. Furthermore, NS-LMXBs can be divided into different categories
based on their X-ray properties (AMXPs, slow pulsars, non-pulsating systems,
atolls, Z-sources), as briefly discussed in Section 4.3.

###  4.1 Long-term X-ray behavior: Transient and persistent LMXBs

One of the primary classifications of LMXBs is based on their long-term X-ray
behavior, which separates the persistent systems from the transient ones.
Persistent LMXBs are always actively accreting, but can still show (in some
cases quite strong) X-ray variability (e.g. Figure 5 bottom). Transient LMXBs,
on the other hand, exhibit large swings in their X-ray luminosity that
separate outbursts of active accretion with periods of quiescence (an example
is shown in Figure 5 top).

Whereas there is no strict definition of what level of X-ray luminosity
variability defines a transient, generally LMXBs are considered transient if
their X-ray luminosity changes by a factor of $\gtrsim$1000\. The long-term
light curves shown in Figure 5 are examples of the differences in long-term
X-ray behavior observed among LMXBs. These light curves are based on publicly
available data from the all-sky X-ray monitoring of MAXI (2–20 keV;
Matsuoka2009 ).

#### Extended outbursts: Quasi-persistent LMXBs

Typically, the outbursts of transient LMXBs last for a few weeks up to $\sim$a
year, while their inactive quiescent phases may extend for many years or even
decades. A more detailed overview of this follows in Section 4.1, but here we
note that a small sub-class of LMXBs falls more or less in between the two
categories defined above: these systems are formally transient (i.e., clearly
switching between active and inactive periods), but exhibit extended outburst
episodes that last for years or even decades. An extreme example is the
(eclipsing) NS-LMXB EXO 0748–676, which exhibited an outburst of 24 years
between the early 80s and 2009 Degenaar2011 . Systems with extended outbursts
of $\gtrsim 1$ yr have been dubbed “quasi-persistent” LMXBs.

It is worth noting that the quasi-persistent LMXBs include a handful of
systems that were observed to switch on at some point in time, but have never
returned to quiescence since. Examples are the BH-LMXB GRS 1915+105, which has
been active since 1992 (e.g., Motta2021 ), and the NS system IGR J17062–6143,
which has been accreting actively since 2006 Hernandez2019 . On the other
hand, there are also LMXBs that were once thought to be persistent because
they continued to be detected for years following their original discovery,
but then suddenly dimmed into quiescence. One example is the NS-LMXB X1732–304
in the globular cluster Terzan 1, which was discovered in 1980 and suddenly
disappeared in the late 90s Guainazzi1999 . The cause of the extended
outbursts is not fully clear, but may lie in mass-transfer variations from the
donor star, e.g., due to irradiation or moving Sun spots King1998b ; Shaw2019
.666The standstill observed for Z Cam stars hameury2020  could be the white-
dwarf analogues of the extended outbursts of quasi-persistent LMXBs Shaw2019 .
Table 4 lists LMXBs known to display quasi-persistent outbursts.

System | current state | sub-class | Reference
---|---|---|---
GRS 1915+105 | activea | BH | Miller2020 ; Motta2021
Swift J1753.5–0127 | quiescent | BH | Zhang2019
IGR J17098–3628 | quiescent | BHC | Capitanio2009
IGR J17091-3624 | quiescent | BHC | Pereyra2020
EXO 0748–676 | quiescent | NS, eclipsing | Degenaar2011
MXB 1659–298 | quiescent | NS, eclipsing | Wijnands2003
KS 1731–260 | quiescent | NS | Wijnands2001
HETE J1900.1–2455 | quiescent | NS, AMXP | degenaar2017_hete
MAXI J0556–332c | quiescent | NS, transient Z-source | Homan2014
XTE J1701–462 | quiescent | NS, transient Z-source | Fridriksson2010
XTE J1701–407 | activeb | NS | degenaar2011_qp
IGR J17062–6143 | activeb | NS, VFXB, AMXP | Hernandez2019
Swift J0911.9–6452 (NGC 2808) | active | NS, AMXP, UCXB | Ng2021_0911 ; Sanna2017
Swift J1858.6–0814 | quiescent | NS, accreting near Eddington | Buisson2020 ; parikh2020_sw
1M 1716–315 | quiescent | NS | jonker2007qp
1H 1905+000 | quiescent | NS | Jonker2006
AX J1745.6–2901c (Galactic center) | active | NS, eclipsing | Degenaar2015GC
AX J1754.2–2754 | activeb | NS, VFXB | degenaar2012asca
XMMU J174716.1–281048 | quiescent | NS, VFXB | DelSanto2007
4U 2129+47 | quiescent | NS | Nowak2002
2S 1711–339 | quiescent | NS | Swank2001
XB 1733–30 (Terzan 1) | quiescent | NS | Guainazzi1999
Table 4: List of (confirmed) LMXBs that are quasi-persistent, i.e., transient
systems but exhibiting prolonged outbursts of $>$1 yr. Notes:
a The X-ray emission from GRS 1915+105 suddenly dropped in 2018 and has
remained low since, but this is likely caused by local obscuration and not by
ceasing accretion activity Motta2021 .
b These (NS) LMXBs accrete at relatively low X-ray luminosity and are
therefore not detected by all-sky X-ray monitors such as Swift/BAT and MAXI.
Therefore, the status of these sources can only be verified via pointed X-ray
observations (e.g., with Swift/XRT); since these generally do not occur
regularly, the status of these sources is not accurately known at present.
c These quasi-persistent LMXBs are known to also exhibit regular (i.e.,
shorter) outbursts. Figure 5: Light curves of LMXBs and their variability over
the past decade based on monitoring data from MAXI/GSC (Matsuoka2009, ). Top:
The transient black hole LMXB GX339-4, showing several distinct accretion
outbursts of different brightness. Bottom: The quasi-persistent black hole
LMXB GRS 1915+105, illustrating that large variations in brightness can also
occur in systems that are continuously active.

#### Outburst statistics of transient LMXBs

Systematically studying samples of transient LMXBs has provided insight into
their luminosity distribution, outburst duration and duty cycles Chen1997 ;
Yan2015 ; Lin2019 ; Tetarenko2016a . Many of these studies made use of RXTE,
which provided more regular and much denser coverage than any of the earlier
X-ray satellites, whilst providing a baseline longer than that of current
X-ray monitoring missions (15 years).

Yan & Yu 2015 Yan2015  performed a systematic analysis of 110 transient
outbursts from 36 sources, consisting of 22 (c)BHs and 14 NSs, observed with
RXTE between 1996 and 2011. This study was limited to fluxes above $\approx
2\times 10^{-9}$ erg s-1 cm-2 (2–12 keV), which translates into a luminosity
of $L_{\mathrm{X}}\approx 2\times 10^{37}$ ($D$/8 kpc)2 erg s-1 at the
distance of the Galactic center. The full range of (peak) X-ray luminosities
covered by this sample ranged from $L_{\mathrm{X}}\approx 2\times 10^{37}$ to
$3\times 10^{38}$ erg s-1, with an average peak luminosity of
$L_{\mathrm{X}}\approx 5\times 10^{37}$ erg s-1. This distribution is shown in
Figure 6. Furthermore, the range in outburst duration in this sample spanned
$\approx$2 weeks to 2 years, with an average duration of $\approx$50 days. The
sample under study showed that the duty cycle of transient LMXBs (i.e., the
ratio of the time spend in outburst versus that in quiescence) is generally
low: on average $\approx$2.5%, though with a wide spread of $\approx$1–50%.
Figure 7 shows the distribution of outburst duration (left) and duty cycle
(right) for this large sample of LMXBs studied with RXTE.

When comparing the BHs in the sample to the NSs, Yan & Yu 2015 Yan2015  found
that the BHs peak at higher X-ray luminosity than NSs in absolute numbers.
However, when scaled to the mass-dependent Eddington luminosity, the NS peak
at higher ratios (see Figures 6). Furthermore, it was found in this work that
the outbursts of BHs generally decay slower and last longer (88 days on
average) than for the NSs (39 days), while the NSs appear to have higher duty
cycles. This is shown in Figure 7). However, see below for an important caveat
about these average numbers.

A number of other, recent works performed similar systematic analyses of large
samples of LMXBs, but then focusing specifically on the BH systems. For
instance, Dunn et al. 2010 Dunn2010  studied the behavior of 25 BHs using 13
years of RXTE data, and Reynolds & Miller 2013 reynolds2013  studied 21 BH
LMXBs using 5 years of Swift/XRT data. Furthermore, Tetarenko et al. 2016
Tetarenko2016a  collected RXTE, MAXI and INTEGRAL data to study 132 outbursts
from 57 BH LMXBs (compiled in the WATCHDOG database).777A complementary BH
catalog, called BLACKCAT, has been drawn up by Corral Santana et al. 2016
CorralSantana16 . The average outburst stastics inferred from these BH-
targeted studies are broadly consistent with the NS/BH sample analyzed by Yan
& Yu 2015 Yan2015 .

Figure 6: Peak X-ray luminosity distribution of NS and BH LMXB outbursts
observed with RXTE between 1996 and 2011 (figure from Yan2015 ).

Figure 7: Distribution of the duty cycle (left) and duration (right) of
outbursts observed from transient NS and BH LMXBs with RXTE between 1996 and
2011 (figure from Yan2015 ).

It is important to note that the above discussed systematic studies do not
include i) LMXBs located within a few tens of arminutes (few tens of pc) of
the Galactic center, and ii) transient LMXBs with peak luminosities
$L_{\mathrm{X}}\lesssim 10^{37}~{}(D/8~{}\mathrm{kpc})^{2}$ erg s-1. This is
both because of the limitations in spatial resolution and sensitivity of the
instrument that accumulated the large amount of data used in these studies. It
is not a priory clear that LMXBs with fainter peak luminosities would behave
similar to the brighter systems. In Section 4.3 we discuss previous and
ongoing efforts to characterize the outburst properties of very faint LMXBs,
which have peak outburst luminosities as low as $L_{\mathrm{X}}\simeq
10^{34-36}~{}(D/8~{}\mathrm{kpc})^{2}$ erg s-1, including those located in
crowded regions like the Galactic center.

An important word of caution is that the above discussed outburst statistics
of LMXBs is typically driven by a small group of sources that have high
recurrence rates. For instance, in the work of Yan & Yu 2015 Yan2015  the
outburst statistics of the NS sample, containing 14 sources in total, is
largely driven by the behavior of the 3 most active systems that exhibit
outbursts every few ($<$5) years (Aql X-1, 4U 1608–52 and MXB 1730–33). For
reference, in the total sample of 36 sources studied by Yan2015 , $>50$%
exhibited only a single outburst.

#### The role of the orbital period in the long-term X-ray behavior

The distribution in observed (peak) luminosities among the LMXBs is in part
due to the range of orbital periods. Based on theoretical arguments, the peak
outburst luminosity is expected to scale with the size of the accretion disk,
hence the orbital period of the binary king1998a ; portegieszwart2004 ;
vanHaaften2012 . Although the number of LMXBs with known orbital periods is
modest, this theoretical expectation seems to be borne out by observations of
samples of NS and BH LMXBs shahbaz1998 ; wu2010 ; vanHaaften2012 . However, a
recent study foscussing only on BH LMXBs and applying rigorous statistical
tests, did not find a clear correlation between the peak X-ray luminosity and
orbital period Tetarenko2016a . Other factors that may play a role in setting
the outburst peak luminosity, reducing it from the value that could be
achieved based on the mass-transfer rate, are mass loss (e.g., via disk winds;
Tetarenko2018 ), and local obscuration (e.g., as for BH LMXB V404 Cyg;
koljonen2020 ).

Apart from the peak outburst luminosity, the recurrence time of LMXBs may also
depend on the orbital period. Mass transfer in LMXBs can be driven by
expansion of the donor star, which happens during different evolutionary
stages. Systems with long orbital periods ($\gtrsim$12 hr) harbor (sub)giant
donor stars that may drive larger mass-accretion rates than the main sequence
or evolved donor stars in short-period ($\lesssim$12 hr) LMXBs. This again
appears to be largely borne out by observations Lin2019 .

Finally, the orbital period of the binary also has impact on whether or not a
source is transient or persistent. This distinction depends on the mass-
accretion rate and size of the disk; i.e. whether the generated accretion
luminosity is sufficient to keep the entire disk ionized hence allowing for
continuous accretion Coriat2012 ; intZand2007 ; Tetarenko2016a .

###  4.2 Short-term X-ray behavior and sub-classes of NS LMXBs

In addition to long-term X-ray variations, both persistent and transient LMXBs
vary in X-rays on short timescales: from weeks to days, to second and even
sub-second variability. Such short-term variability in X-ray luminosity is
often associated with changes in the X-ray spectrum of LMXBs. This gives rise
to several distinct X-ray spectral-timing states, which are thought to be
related to changes in the accretion morphology Hasinger1989 ; Remillard2006 ;
Done2007

Among the NS LMXBs, several sub-groups with distinct short-term X-ray
variability have been defined. For instance, a small group of the brightest NS
LMXBs trace out a very distinct “Z”-shaped pattern when their intensity in
different energy bands is plotted in a so-called color-color diagram (CCD).
These Z-sources are thought to be accreting around $L_{\mathrm{X}}\simeq
L_{\mathrm{Edd}}$ (see Section 4.3). Other bright NSs, accreting at one to
several tens of percent of the Eddington limit, instead trace out an
“C”-shaped pattern in the CCD and are commonly referred to as atoll sources.

###  4.3 Classification based on X-ray luminosity: Two extreme ends

Wijnands et al. 2006 Wijnands2006  laid out a classification of LMXBs in terms
of their peak X-ray luminosity measured in the 2-10 keV band, making the
distinction between bright to very bright ($L_{\mathrm{X}}\sim 10^{37-39}$ erg
s-1), faint ($L_{\mathrm{X}}\sim 10^{36-37}$ erg s-1), and very faint
($L_{\mathrm{X}}\lesssim 10^{36}$ erg s-1) systems. This classification is
largely driven by the sensitivity limits of historic X-ray instruments and
does not necessarily reflect significant physical differences Wijnands2006 .
This is reinforced by the fact that many transient LMXBs display outbursts
with different peak luminosity that fall into different luminosity categories
Degenaar2010 ; Campana2013 ; Wijnands2013b .

Nevertheless, different sub-populations of LMXBs are more likely (or
exclusively) found in particular (2-10 keV) luminosity ranges. As already
touched upon in previous sections, the X-ray luminosity is expected to scale
with the system properties of the LMXB, such as the size of the accretion disk
(hence binary orbit) and mode of mass transfer. So there is a physical
motivation for a making a distinction based on the peak X-ray luminosity. To
illustrate this, we discuss in more detail the two extreme ends of the
luminosity classification of LMXBs: very-faint X-ray binaries (VFXBs) and
sources that accrete around the Eddington limit. In either of the luminosity
classes we find both persistent and transient systems.

#### Very-faint X-ray binaries

By definition, VFXBs have (peak) accretion luminosities of
$L_{\mathrm{X}}\lesssim 10^{36}$ erg s-1. Figure 8 shows an example of how the
outburst of a transient VFXB compares to that of a bright LMXB. For sources
located at distances of several kpc and beyond, historic X-ray missions and
current all-sky X-ray monitors like Swift/BAT and MAXI do not have the
required sensitivity to detect the accretion emission of VFXBs. This class of
LMXBs has therefore long remained hidden. Over the past two decades, however,
VFXBs have been found in increasing numbers by various means. At present, a
few tens of VFXBs have been identified in the Milky Way. Similar to the bright
LMXBs, the VFXBs can be either be classified as (quasi-)persistent or
transient based on their long-term X-ray behavior. In Table 5 we list
currently known VFXBs.

A significant number of VFXBs habor NSs and have been discovered through their
thermonuclear X-ray bursts, since this makes them shine close to the Eddington
limit for a brief moment of time. In particular, the BeppoSAX satellite picked
up a number of thermonuclear X-ray bursts without detecting any persistent
X-ray counterpart. These objects were hence dubbed “burst-only sources”
Cornelisse2002 ; Cornelisse2002a . We now know that these concern NSs that
accrete at very low X-ray luminosity, either persistently or transiently.
Other X-ray instruments such as INTEGRAL and Swift/BAT have also discovered
VFXBs through the detection (and follow-up) of thermonuclear X-ray bursts
Chelovekov2010 ; Degenaar2010burst ; Degenaar2012b .

The increased sensitivity and improved spatial resolution of X-ray instruments
has also allowed for the discovery of a growing number of VFXBs through X-ray
surveys, primarily of the Galactic center and bulge, with missions such as
ASCA, Chandra and XMM-Newton Sakano2005 ; Muno2005 ; Wijnands2006 ; Jonker2011
; Degenaar2012a . However, a detailed characterization of the outburst
properties of VFXBs, such as their outburst duration and recurrence time,
requires monitoring surveys in regular (at least weekly) visits with sensitive
X-ray instruments to be performed Degenaar2015GC ; Carbone2019 ; Bahramian2021
. Such programs have been carried out mostly with RXTE/PCA and Swift/XRT.

The RXTE/PCA bulge monitoring project ran between 1999 and 2011 Swank2001  and
pushed to a factor of a few lower X-ray luminositites than typical all-sky
X-ray monitors ($L_{\mathrm{X}}$ of a few times $10^{35}$ erg s-1). This
allowed to study the behavior of the brightest VFXBs and provided a first
picture of their outburst durations and recurrence times. In more recent
years, this has been complemented by monitoring campaigns that exploit the
flexibility of the Swift mission and push down a further order of magnitude
fainter X-ray luminosity Degenaar2015GC ; Bahramian2021 .

Statistics on the outburst properties of VFXBs has been steadily accumulated
through Swift’s Galactic Center monitoring program, which has provided nearly-
daily X-ray monitoring of about a dozen transient VFXBs since 2006 kennea2006
; Degenaar2015GC . Initial studies using the first few years of monitoring
data showed that the outbursts of the transient VFXBs are often short
($\lesssim$1 month), but that the outburst recurrence times are not very
different from that of bright LMXBs: typical duty cycles are $\simeq$1–30%
Degenaar2009 ; Degenaar2010 . As the Swift Galactic center monitoring program
is reaching a $\simeq$15 yr baseline, it is starting to provide similar
outburst statistics on transient VFXBs as has been available for bright
transient LMXBs.

Apart from providing valuable statistics on the X-ray outburst behavior,
determining the system parameters of VFXBs (i.e., donor types and orbital
periods) in the Galactic center is largely hampered by the very high
extinction and crowding. Based on what has been learned from the outburst
behavior of VFXBs in the Galactic center, a dedicated monitoring program was
therefore designed to effectively find such systems with Swift/XRT in less
obscured regions of the Galactic bulge Shaw2020 ; Bahramian2021 . This Swift
bulge survey is ongoing and are expected to provide more insight into the
(distribution of) system parameters of the faintest accreting LMXBs (see
Section 5.1).

Despite the observational challenges, system parameters are known for a number
of VFXBs. Nearly half of the VFXBs listed in Table 5 have NS primaries, as
evidenced by the detection of thermonuclear X-ray bursts or coherent X-ray
pulsations. In absence of such features it is often difficult to probe the
nature of the compact object. However, dynamical mass estimates reveal BHs in
Swift J1357.2–0933 CorralSantana2013  and XTE J1118+480 McClintock2001a ;
wagner2001 . Furthermore, the X-ray spectral properties of XTE J1728–295 point
to a BH accretor Sidoli2011 ; Stoop2021 , and the bright radio emission of the
Galactic center transient CXOGC J174540.0–290031 seem to argue in favor of a
BH as well Muno2005a ; porquet2005 . The latter is, however, a high-
inclination system that while appearing as a VFXB might be intrinsically
bright.

At present, the compact object has not yet been classified for nearly half of
VFXBs. The challenge arises from the fact that thermonuclear X-ray bursts are
rare at low accretion rates (i.e., it takes a long time to accumulate
sufficient fuel to ignite a burst; Degenaar2010burst ; degenaar2011burst ),
and X-ray pulsations are difficult to detect at low X-ray fluxes patruno2010b
; Strohmayer2017 ; vandeneijnden2018 ; bult2019 ; bult2021 . Furthermore, the
donor stars are often too faint or too highly absorbed for optical mass
measurements in quiescence Shaw2017 . Similarly, indirect methods such as
studying their rapid incoherent X-ray variability is hampered by their faint
emission armaspadilla2014 . Therefore, other methods have been explored to
classify VFXBs.

When the outburst of a transient VFXBs is densely monitored (e.g., using
Swift) or high-quality X-ray spectra are obtained (e.g., with XMM-Newton), a
tentative identification of the compact object may be made based on the
presence of a soft spectral component ArmasPadilla2011  (albeit see
ArmasPadilla2013  and ArmasPadilla2013a ), or the X-ray spectral evolution
along the decay of an accretion outburst Wijnands2015 . At least one transient
VFXB identified as NS based on this method (IGR J17494–3030; ArmasPadilla2013b
; Wijnands2015 ) was later found to be an AMXP Ng2021 . Spectral shape and its
evolution can thus be a diagnostic to identify the compact object in VFXBs
(though see parikh2017  for NSs with unusually hard spectra that do not
confirm the general trends).

For several VFXBs the detection of coherent (millisecond) X-ray pulsations has
allowed to measure orbital period through pulsar timing Sanna2018a ;
Strohmayer2018 , and for a handful of others such information is available
from X-ray or multi-wavelength studies Bahramian2014 ; Shaw2020 . This
suggests that VFXBs are an inhomogenous class in terms of donor stars and
mass-transfer mode. The population of VFXBs includes systems with evolved
dwarf donors in short orbits, main sequence and giant donors in wider orbits,
Roche-lobe overflow and wind-fed systems, as well as various sub-classes of
LMXBs such as UCXBs and tMSRPs.888We note that other classes of compact
objects such as HMXBs, magnetars and bright accreting white dwarfs
(cataclysmic variables) can show up as X-ray transients with similar
luminosities as that of transient VFXBs. The X-ray spectral-timing properties
of multi-wavelength properties of such objects would be different from LMXBs,
which are the focus here.

So far, many of the known VFXBs have (X-ray) characteristics consistent with
Roche-lobe overflow LMXBs, so this appears to the dominant sub-class. Since
the accretion luminosity of LMXBs scales (among other factors) with the
orbital period (see Section 5.4), it is not surprising that several VFXBs have
been found to have short orbital periods. For instance, the few BH systems
among the VFXBs all have orbital periods shorter than BHs in bright LMXBs (see
Section 5.4). Furthermore, several VFXBs have been identified as (candidate)
UCXBs (see Table 5). Binary evolution considerations predict that VFXBs should
present short-period systems with evolved donor stars King2006

There are also a few (transient or persistent) VFXBs that are SyXBs, e.g.,
accreting from the wind of a giant companion Shaw2020 ; Bahramian2021 . This
is also not unexpected based on binary evolution arguments Maccarone2013 .
Finally, we note that a number of VFXBs may be intrinsically bright LMXBs that
only appear sub-luminous because we are viewing the system at high
inclination. One example is the eclipsing Galactic center transient VFXB CXOGC
J174540.0–290031 Muno2005a ; porquet2005 . However, only a small fraction of
the full VFXB population is expected to appear faint due to such inclination
effects Wijnands2006 .

Summarizing, separating VFXBs as a class is mostly phenomenological, but there
might be actual physical differences with respect to brighter systems; e.g.,
they might be less X-ray luminous because their accretion disks are small
overall, or because their inner accretion disk is evaporated into a
radiatively-inefficient flow or pushed out by the NS magnetic field. Moreover,
at the low accretion rates associated with VFXBs, we can probe different
physics than with bright LMXBs in terms of accretion and outflows degenaar2017
; vandeneijnden2021 , NS physics wijnands2008 , thermonuclear burning
Cooper2007 ; Peng2007 , and binary evolution maccarone2015 .

Figure 8: Example lightcurves that illustrate the differences in outburst properties between VFXBs and bright LMXBs. Shown are two frequently two frequently active transient systems that both harbor a neutron star primary: the VFXB XMM J174457 and bright LMXB Aql X-1. For both sources, Swift/XRT data of outbursts occurring in 2016 were used. It is worth noting that while many transient VFXB outbursts are often short, as in this example, some can last for weeks/months.  System | T/P/QP | NS/BH | Comments | Reference
---|---|---|---|---
Persistent and quasi-persistent VFXBs
IGR J17254–3257 | P | NS | burster | chenevez2007 ; Ratti2010
1RXS J171824.2–402934 | P | NS | cUCXB, burster | intZand2005a ; intZand2009
1RXH J173523.7–354013 | P | NS | burster, H-rich donor | Degenaar2010burst
M15 X-3 | P | cNS | main-sequence donor | Heinke2009a ; Arnason2015
IGR J17062–6143 | QP | NS | UCXB, AMXP, buster | Strohmayer2018 ; Hernandez2019
AX J1754.2–2754 | QP | NS | cUCXB, burster | Chelovekov2007 ; Shaw2017a
XMMU J174716.1–281048 | QP | NS | cUCXB, burster | DelSanto2007 ; Kaur2017
SAX J1806.5–2215 | QP | NS | burster | Cornelisse2002 ; Shaw2017a
IGR J17597–2201 | QP | NS | buster, XTE J1759–220 | Brandt2007 ; Fortin2018
AX J1538.3–5541 | QP | ? | LMXB-like spectrum | Sugizaki2001 ; degenaar2012asca
XTE J1744–230 | QP | ? | RXTE bulge scan | Swank2001
Transient VFXBs
IGR J17379–3747a | T | NS | burster, AMXP | Chelovekov2010 ; Sanna2018b
IGR J17591–2342 | T | NS | burster, AMXP | Sanna2018a ; Kuiper2020
Swift J185003.2–005627 | T | NS | burster | Degenaar2012b
Swift J1734.5–3027 | T | NS | burster | Bozzo2015a
MAXI J1807+132 | T | NS | burster | Shidatsu2017 ; Jimenezibarra2019
MAXI J1957+032 | T | cNS |  | MataSanchez2017 ; Beri2019
IGR J17494–3030 | T | cNS |  | ArmasPadilla2013b ; Ng2021
XTE J1719–29 | T | cNS |  | ArmasPadilla2011
XTE J1118+480 | T | BH |  $P_{\mathrm{orb}}=$ 4.1 hr | wagner2001 ; McClintock2001a
Swift J1357.2–0933 | T | BH |  $P_{\mathrm{orb}}=$ 2.6 hr | 260; 246; 27
XTE J1728–295 | T | cBH | IGR J17285–2922 | Swank2001 ; Sidoli2011 ; Stoop2021
IGR J18175–1530 | T | ? | XTE J1817–155 | Markwardt2007b
XMMSL1 J171900.4–353217 | T | ? | XTE J1719–356 | Read2010a ; Markwardt2010b
XTE J1734–234 | T | ? |  | Swank2001
WGA J1715.3–2635 | T | ? |  | Swank2001
XTE J1637–498 | T | ? |  | Markwardt2008
Swift J175233.9–-290952 | T | ? |  | Shaw2020 ; Bahramian2021
Swift J174038.1–273712 | T | ? |  | Bahramian2021a ; RiveraSandoval2021
SRGt J071522.1–191609 | T | ? | Gokus2020 ; vandenEijnden2020_vfxt ; Bahramian2020a  |
IGR J17445$-$2747 | T | NS | SyXB | (Mereminskiy2017, ; Shaw2020, ; Bahramian2021, )
XMMU J174445.5$-$295044 | T | ? | SyXB | Heinke2009b ; Bahramian2014a
VFXBs covered by Swift’s Galactic Center monitoring campaign
XMM J174457–2850.3 | T | NS | burster | Sakano2005
Swift J174622.1–290634 | T | ? |  | Degenaar2009
Swift J174553.7–290347 | T | ? | CXOGC J174553.8–290346 | Degenaar2009
CXOGC J174540.0–290005 | T | ? |  | Muno2005 ; Degenaar2009 ; Koch2014 ; Heinke2015
CXOGC J174538.0–290022 | T | ? |  | Muno2005 ; Degenaar2015GC
CXOGC J174535.5–290124 | T | ? |  | Muno2005 ; Degenaar2009 ; Degenaar2010
CXOGC J174541.0–290014 | T | ? |  | Muno2005
CXOGC J174540.0–290031 | T | cBH |  $P_{\mathrm{orb}}=$7.9 hr, eclipser, obscured? | 241; 116; 117
CXOGCJ174554.3–285454 | T | ? | XMMU J174554.4–285456 | Muno2005
XMM J174544–2913.0 | T | ? |  | Sakano2005
Swift J174535.5–285921 | T | ? |  | Degenaar2015GC
Table 5: List of VFXBs in our Galaxy. The letters P, QP and T refer to
persistent, quasi-persistent and transient, respectively. cBH and cNS refer to
candidate BHs and candidate NSs, respectively. The indication “burster”
implies that the source displays thermonuclear X-ray bursts (hence must harbor
a NS). a = This is the same source as IGR J17364–2711, IGR J17380–3749 and XTE
J1737–376.

#### Accretion around the Eddington luminosity in LMXBs

At the other extreme end of VFXBs in terms of X-ray output, there are a modest
number of LMXBs that accrete around (slightly below and above) the Eddington
luminosity. Table 6 lists some of the basic characteristics of LMXBs that are
known to accrete at these high rates. Most of these harbor (confirmed or
expected) NS primaries; there are only two BH-LMXBs listed. These are the
well-known quasi-persistent BH GRS 1915+105 (see Figure 5 bottom), and the
transient system V404 Cyg (see Figure 2 middle left). The latter is not
observed to be particularly luminous, but is thought to be heavily obscured
and intrinsically accreting around the Eddington limit during (some of) its
outbursts Tetarenko2016a ; Motta2017 ; koljonen2020 .

The group of Eddington-accreting LMXBs includes the 6 persistent Z-sources
(see also Section 4.2), which have been known and extensively studied since
the dawn of X-ray astronomy Hasinger1989 . These sources are expected to
harbor NS primaries, although only GX 17+1 and Cyg X-2 show conclusive
evidence for this by the detection of thermonuclear bursts Kahn1984 .
Identifying the donor stars in the Z-sources is not straightforward, because
they are persistently accreting and their accretion disks and jets are so
bright that these contribute significantly to the optical/infrared emission
(Bandyopadhyay2003, ). A schematic impression from one of the Z-sources, Sco
X-1, is shown in Figure 2 (middle right). Furthermore, Cir X-1 and GX 13+1 are
two persistent sources that exhibit variations in their X-ray luminosity but
during some epochs behave similar to the Z-sources Oosterbroek1995 . Both Cir
X-1 and GX 13+1 are known to harbor a NS through the detection of
thermonuclear bursts Matsuba1995 ; Linares2010 . In case of Cir X-1, it is
debated whether it is a LMXB or a HMXB system Johnston2016 .

There are also 4 transient LMXBs, confirmed to harbor NSs through the
detection of thermonuclear bursts or quiescent thermal emission, that showed
similar behavior as the Z-sources during the peak of their outbursts (see
Table 6). These are, therefore, thought to have reach accretion rates around
the Eddington limit (despite their distances being poorly constrained in some
cases), and are referred to as transient Z-sources Wijnands1999a ;
altamirano2010_z ; Homan2010 ; Homan2014 . Furthermore, GRO J1744–28 is a
transient LMXB that harbors a slowly pulsating neutron star Finger1996
accretes around the Eddington limit at the peak of its outbursts Monkkonen2019
.

Finally, there are a handful of other LMXBs that, like V404 Cyg, are not
observed to be particularly luminous but are suspected to be intrinsically
accreting around the Eddington limit. Evidence pointing in this direction
comes e.g., from their orbital period evolution baknielsen2017 , or their
strong jets and disk winds panurach2021 . For these sources it appears that
the most luminous inner part of the binary is obscured, e.g., due to a high
inclination or because of strong disk winds.

As can be seen in Table 6, several of the high-accretion rate LMXBs have long
orbital periods and evolved donor stars. Indeed, their orbital periods are
typically too long for a main sequence star to fill its Roche lobe and drive
the observed high mass accretion rates. As discussed in Section 4.1, finding
that bright LMXBs have relatively long orbital periods is theoretically not
surprising. Indeed, it was already suggested early on that the mass donors in
Z-sources are evolved stars that are ascending on the giant branch and that
high mass-transfer rates could be driven by the associated expansion of the
donor star Taam1983 ; Webbink1983 ; Hasinger1989 . However, at least one
Z-source likely cannot harbor an evolved donor; the infrared counterpart of GX
17+1 is far too faint to allow a giant donor unless the source distance is
wrong jonker2000 ; Callanan2002 . It should also be noted that large orbital
period and evolved companion star do not necessarily imply that mass-accretion
can be driven up to the Eddington limit. For instance, 4U 1624–49 likely hosts
an evolved star and has an orbital period of $\approx$21 hr Jones1989 , but is
a luminous atoll instead of a Z-source.

We note that similarly high accretion rates as encountered in these LMXBs are
also reached in some HMXBs. Well-known examples are the (c)BH systems SS443,
V4641 Sgr, and Cyg X-3 koljonen2020 . Furthermore, (super-)Eddington accretion
rates are a defining property of the population of ultra-luminous X-ray
sources (ULXs). These are extra-Galactic BHs or NSs that appear to be
accreting at super-Eddington rates and of which there are many hundreds known
to date Walton2022 . However, a large fraction of ULXs may be HMXBs instead of
LMXBs (see Kuranov2021  and references therein).

System | T/P/QP | NS/BH |  $P_{\mathrm{orb}}$ (d) | Donor | Comments | Reference
---|---|---|---|---|---|---
Cyg X-2 | P | NS | 9.8 | A giant | Z-source | Cowley1979 ; Casares1998
GX 349+2 | P | NS | 0.9 | sub-giant? | Z-source | Wachter1996 ; Bandyopadhyay1999
Sco X-1 | P | NS | 0.8 | sub-giant (K or later) | Z-source | lasala1985 ; MataSanchez2015b
GX 5-1 | P | NS | ? | early-type giant? | Z-source | jonker2000 ; Bandyopadhyay2003
GX 17+1 | P | NS | ? | ? | Z-source | jonker2000 ; Callanan2002
GX 340+0 | P | NS | ? | ? | Z-source | vanderKlis2006
IGR J17480–2446 | T | NS | 0.9 | sub-giant | transient Z-source, AMXP | altamirano2010_z ; Patruno2012b
XTE J1701–462 | T | NS | ? | ? | transient Z-source | Homan2010
MAXI J0556–332 | T | NS | ? | ? | transient Z-source | Homan2014
2S 1803–245 | T | NS | ? | ? | transient Z-source | Wijnands1999a
GX 13+1 | P | NS | 24.5 | K giant | hybrid atoll/Z-source | Garcia1992
Cir X-1 | P | NS | 16.7 | debated | often in low-flux state | Shirey1999 ; Johnston2016
GRO J1744–28 | T | NS | 11.8 | G/K giant | slow pulsar | Finger1996 ; Gosling2007
GRS 1915+105 | QP | BH | 33.5 | K giant | sometimes obscured | Tetarenko2016a
V404 Cyg | T | BH | 6.5 | K subgiant | obscured | koljonen2020
2A 1822–371 | P | NS | 0.23 | main sequence | obscured, slow pulsar | Jonker2003b ; baknielsen2017
Swift J1858.6–0814 | T | NS | 0.9 | ? | obscured | Buisson2020 ; Buisson2021
AC 211 (X2127+119) | P | NS? | 0.7 | ? | obscured | vanZyl2004 ; panurach2021
Table 6: List of Galactic LMXBs accreting around the Eddington limit. The
letters P, QP and T refer to persistent, quasi-persistent and transient,
respectively. We note that in case of Cir X-1 it is debated whether the system
is a LMXB or a HMXB system Johnston2016 .

##  5 Distribution and demographics of LMXBs in the Galaxy

LMXBs are found all around us in the Galaxy (Figure 9), however their
formation channel, population density, and demographic varies depending on the
environment. Formation of the compact object in X-ray binaries inflicts a kick
on the binary. This kick adds a peculiar motion to the X-ray binary’s
Galactocentric orbit and can displace it substantially from where the binary
was formed. Despite this, given the large mass and short lifespan of the
companion, HMXBs are not generally expected to be displaced substantially from
their original birthplace. Observations indicating HMXBs trace star formation
and young star associations support these expectations (Grimm2003, ;
Bodaghee2012, ). In contrast, the low mass and long lifespan of companions in
LMXBs allows them to achieve significant displacement from their birthplace in
present day observations (e.g., Repetto2012, ) or be found in regions
associated with old star populations (e.g., Galactic center, Galactic bulge,
Globular clusters, e.g., Arnason2021, ).

Observed spatial distribution of LMXBs also shows a strong concentration of
these systems in the central 2 kpc of the Galaxy, with the overal population
showing a larger scale height compared to HMXBs (410 pc for LMXBs, compared to
150 pc for HMXBs Grimm2002, ). Consequently, Grimm2002  also note that around
$\sim 50\%$ of LMXBs are in the Galactic disk, compared to $\sim 25\%$ in the
Galactic bulge.

Over the past few decades monitoring and survey programs with various X-ray
observatories have provided a more complete picture of distribution of LMXBs
in our Galaxy. These include All-sky monitoring programs (e.g., with ROSAT,
Swift/BAT, MAXI, INTEGRAL, Voges1999, ; Baumgartner2013, ; Kawamuro2018, ;
Hori2018, ; Krivonos2013, ), and survey programs targeting the Galactic center
(Muno2006a, ; Heard2013, ; Degenaar2015GC, ; Sazonov2020, ), Galactic bulge
(Jonker2014, ; Kuulkers2007, ; Grebenev2015, ; Bahramian2021, ), Galactic
plane (Giacconi1971, ; Grindlay2003, ; Motch2010, ), and globular clusters
(Clark1975, ; Verbunt2001, ; Grindlay2001a, ; Pooley2003, ). These surveys
have substantially pushed our understanding of LMXB population and
distribution in the Galaxy. However, it is important to note that our current
view is still heavily impacted by selection effects caused by telescope
sensitivity and survey cadence limitations, interstellar absorption
(Jonker2021, ), among other effects such as uneven coverage. Current and
future survey efforts (e.g., e-ROSITA) will improve on some of these limits.
In the following sections, we briefly discuss a subset of surveys and
monitoring programs targeting different parts of the Galaxy in the context of
LMXBs.

Figure 9: Distribution of a subset of known LMXBs in the sky overlaid on the
Gaia all-sky image. Pink circles represent BH-LMXBs from (Tetarenko2016a, ),
and blue circles are all other LMXBs as cataloged by (Liu2007, ). Given
discovery of new LMXBs over the past decade and new revelations on
classification of some previously known LMXBs, this plot is not representing
the entire currently known sample of LMXBs and it serves only as an example
demonstrating the Galactic distribtuion of LMXBs. Background image from the
Gaia mission (A. Moitinho; ESA/Gaia/DPAC). Figure made using mw-plot
(https://pypi.org/project/mw-plot/).

###  5.1 Galactic center and bulge

The Galactic center has been heavily observed by various X-ray observatories
including Chandra, XMM-Newton, Swift, INTEGRAL. Using Chandra (Wang2002, ;
Muno2006a, ) reported and cataloged hundreds of X-ray sources in the central
part of the Galaxy, identifying numerous X-ray sources associated with old
stellar populations, thus classifying a large fraction of them as old
cataclysmic variables, and a smaller group ($\sim 10$) as likely LMXBs.
Swift/XRT has been observing the Galactic center on a $\sim$weekly basis since
2006. These observations have led to identification of multiple transient
LMXBs and outbursts within $25^{\prime}$ of the Galactic center Degenaar2015GC
. A large fraction of these transients were also identified as VFXBs, showing
outbursts with peak L${}_{X}<10^{36}$ erg s-1 (see Section 4.3).

Identification of dozens of faint and transient likely LMXBs (and hundreds of
other unclassified X-ray sources) in the Galactic center motivated theoretical
exploration of the origin and nature of these energetic systems in the region.
Population synthesis work by Liu2006  suggested that NS-LMXBs are likely to
dominate the population of X-ray sources in the Galactic center. However,
later work by Ruiter2006  suggested that a majority of these sources may be
intermediate polars (a subclass of cataclysmic variables) and that the
population of LMXBs is likely to be comparatively small ($\sim$dozens). This
was found to be consistent with further observations of the Galactic center by
Chandra Zhu2018  suggesting number of quiescent LMXBs in the Galactic center
cannot be substantially larger than $\sim 150$.

Muno2005  noted an overabundance of transients (particularly transient VFXBs)
in the central parsec of the Galaxy - suggesting these systems could be LMXBs
that have formed dynamically (similar to globular clusters; see Sec 5.3), or
alternatively HMXBs associated with the young star population in the central
region. However, this overabundance has not been observed in the Swift/XRT
monitoring of the Galactic center out to 25 pc (running since 2006;
Degenaar2015GC ).

Extending X-ray surveys to the Galactic bulge, the Chandra Galactic Bulge
Survey identified $\sim 170$ candidate cataclysmic variables and quiescent
LMXBs (Jonker2011, ; Jonker2014, ; Wevers2016, ; Wevers2017, ). Swift/XRT
monitoring of the Galactic bulge with, led to identification of $\sim$7 new
VXFBs, most of which appear to be symbiotic in nature (Shaw2020, ;
Bahramian2021, ); leading them to conclude that a large fraction of VFXBs are
perhaps SyXBs. At higher luminosities, INTEGRAL surveys of the Galactic bulge
have identified dozens of bright LMXB candidates (Kuulkers2007, ;
Grebenev2015, ). Exploring characteristics of the X-ray luminosity function of
persistent versus transient LMXBs detected by INTEGRAL Revnivtsev2008
concluded that the distribution of transient LMXBs is comparatively more
focused around the Galactic center.

###  5.2 Galactic plane and outer parts

Survey and monitoring coverage of the Galactic plane and halo in the X-rays is
substantially shallower and less complete than the Galactic center and bulge.
Nevertheless, surveys such as the XMM-Newton or Swift Galactic Plane surveys
(Motch2010, ; Gorgone2019, ) have discovered a handful of LMXBs and LMXB
candidates. However, the overwhelming majority of LMXBs identified in the
Galactic plane and halo are discovered while exhibiting bright outbursts
detected by all-sky monitors such as MAXI or Swift/BAT.

Most LMXBs (outside globular clusters) are expected to have formed in the
Galactic plane (e.g., following the mass distribution of low-mass stars in the
Galaxy Gilfanov2004 ). However, a small number of LMXBs are found at high
Galactic latitudes (e.g., see Jonker2004b, ; shaw2013, ; Arnason2021, ). While
it is possible that a non-zero fraction of LMXBs have formed in the halo, a
more likely explanation is receiving high natal kicks when the BH or NS is
formed through supernova. Given the relatively old age of LMXBs, a high binary
natal kick can displace the LMXB significantly from where the compact object
in the binary was originally formed999Assuming the binary is not disrupted as
a result of the supernova kick. Repetto2012 .

While both BH-LMXBs and NS-LMXBs have been found with high Galactic scale
heights, indicating evidence for large kicks in both classes (repetto2015, ),
NS-LMXBs are found to reach higher scale heights compared to BH-LMXBs with
similar binary natal kicks (repetto2017, ). Furthermore, comparing
observation-based distribution of binary natal kicks of BH-LMXBs and NS-LMXBS
indicates that the kick velocities are smaller for BH-LMXBs compared to NS-
LMXBs (Atri2019, ).

###  5.3 Globular clusters

Observationally, an overabundance of X-ray binaries in Milky Way globular
clusters was noticed soon after the emergence of X-ray astronomy (Clark1975,
). Globular clusters contain $\sim 10^{-4}$ fraction of Galactic mass, while
containing $\sim 10$–$20\%$ of the total population of Galactic LMXBs.

In the Galactic field, LMXBs are thought to have predominantly formed through
“primordial” binary evolution (e.g., Paczynski76, ; Tauris2003, ) (however,
challenges remain in explaining formation of LMXBs with heavy compact objects
- e.g., see (Podsiadlowski2003, )). In contrast, the high density of globular
clusters (which can reach up to $10^{6}$ times the Solar neighborhood), leads
to frequent encounters between members of the cluster. These encounters are
expected to open multiple channels for formation of LMXBs in globular
clusters, including collision of red giants with a compact object
(Sutantyo1975, ), tidal capture of a compact object by a companion star
(Fabian1975, ), or exchange encounters during which a compact object replaces
the lower mass member of an existing binary (Hills1976, ).

Observational evidence supporting this link was first discussed in
(Verbunt1987, ). Detailed follow up studies with the Chandra observatory
allowed high resolution imaging of faint X-ray sources and provided clear
evidence of this link in the Milky Way (Pooley2003, ; Heinke2003c, ) and other
galaxies (Sarazin2003, ; Kundu2007, ; Kundu2007a, ). Focused studies of
individual globular clusters over the past two decades have led to
identification and classification of dozens of X-ray binaries (e.g.,
Grindlay2001, ; Heinke2006a, ; Servillat2008, ; Maxwell2012, ), and X-ray
emission from radio millisecond pulsars (Bogdan2010, ; Bhattacharya2017, ).
Furthermore, a non-negligible fraction of transient and persistent LMXBs (with
peak L${}_{X}>10^{35}$erg s-1) discovered in the Milky Way have been localized
to globular clusters (see Table 7, Bahramian2014, ). A large fraction of these
systems have been determined to be NS-LMXBs based on detection of type I X-ray
bursts or of X-ray pulsations.

There are also numerous quiescent LMXBs identified in globular clusters which
have not exhibited bright outbursts yet. These systems are identified through
X-ray spectroscopy, generally showing a spectrum well described by NS
atmospheric models (e.g., Rutledge2002, ; Gendre2003a, ; Becker2003, ;
Heinke2006, ; Guillot2009, ; Walsh2015, ; Bahramian2015, ).

Quiescent and transient NS-LMXBs in globular clusters provide unique
opportunities for study of accretion and NS equation of state. These are
largely thanks to the independent constraints on distance that is achieved for
globular clusters (e.g., see (Harris1996, ) and references therein for
distance measurements) and in some cases existence of pre-outburst
observations of the LMXB as the globular cluster was targeted for other
studies. Observations of quiescent NS-LMXBs have allowed detailed study of the
equation of state in NSs based on constraints on mass and radius obtained via
X-ray spectral modeling of the NS atmosphere, which is the dominant emitting
region in the X-rays with little or no contamination from the accretion flow
in quiescence (Guillot2013, ; Heinke2014, ; Steiner2018, ). Detailed study of
transient systems during and after their outburst decay has provided insights
about thermal processes in the crust of NSs, for example showing that internal
heating of NSs occurs significantly closer to the surface than previously
thought (e.g., Degenaar2011b, ; Degenaar2012, ; wijnands2017, ; Vats2018, ).
Multi-wavelength observations of transient LMXBs in globular clusters during
their outbursts has led to the first confirmation of a transitional
millisecond pulsar (Papitto2013, ), and strong constraints on the disk-jet
coupling in NS-LMXBs (Tetarenko2016, ).

In contrast with the Galactic field, where there are dozens of strong BH-LMXB
candidates with $\sim$20 dynamically confirmed (Tetarenko2016a, ;
CorralSantana16, ), there are currently no dynamically confirmed BH-LMXBs
identified in globular clusters (Galactic or otherwise), and almost all
transient LMXBs in globular clusters so far have been identified to be NS-
LMXBs (Table 7, (Verbunt2006, )). Historically, it was thought that while
globular clusters produce thousands of BHs through their evolution, a large
fraction of these BHs decouple from the rest of the cluster in form of a
subcluster, segregate towards the cluster core and eventually get ejected from
the cluster (e.g. Sigurdsson1993, ). However, detection of strong BH-LMXB
candidates in Galactic (Strader2012, ; Chomiuk2013, ) and extra-galactic
clusters (Maccarone2007, ; Dage2020, ), along with identification of detached
dynamically confirmed BHs (Giesers2018, ; Giesers2019, ), changed these
assertions.

LMXB | globular cluster | State | Porb | nature | notes | accretor | references
---|---|---|---|---|---|---|---
Bright LMXBs (peak L$X\geq 10^{35}$ erg s-1)
4U 1820-30 | NGC 6624 | P | 11 min | U | X | NS | (Stella1987, )
4U 0513-40 | NGC 1851 | P | 17 min | U | UV | NS | (Zurek2009, )
X1850-087 | NGC 6712 | P | 20.6a min | U | UV | NS | (Homer1996, )
M15 X-2 | M 15 | P | 22.6 min | U | UV | NS | (Dieball2005, )
MAXI J0911-655 | NGC 2808 | T | 44.3 min | U | XP | NS | (Sanna2017, )
IGR J16597-3704 | NGC 6256 | T | 46.0 min | U | XP | NS | (Sanna2018, )
NGC 6440 X-2 | NGC 6440 | T | 57.3 min | U | XP | NS | (Altamirano2010, )
XB 1832-330 | NGC 6652 | P | 2.1 hrs | N | O | NS | (Engel2012, )
4U 1746-37 | NGC 6441 | P | 5.16 hrs | N | X | NS | (BalucinskaChurch2004, )
SAX J1748.9-2021 | NGC 6440 | T | 8.7 hrs | N | XP | NS | (Altamirano2008, )
IGR J18245-2452 | M28 | T | 11.0 hrs | N | XP | NS | (Papitto2013, )
GRS 1747-312 | Terzan 6 | T | 12.36 hrs | N | X | NS | (intZand2003, )
AC 211 | M 15 | P | 17.1 hrs | N | UV | NS? | (Ilovaisky1993, )
IGR J17480-2446 | Terzan 5 | T | 21.27 hrs | N | XP | NS | (Papitto2011, )
Rapid Burster | Liller 1 | T | ? | N | B | NS | (Galloway2008, )
EXO 1745-248 | Terzan 5 | T | ? | N | B | NS | (Galloway2008, )
Terzan 5 X-3 | Terzan 5 | T | ? | N | B | NS | (Bahramian2014, )
XB 1732-304 | Terzan 1 | T | ? | ? | ? | NS | (Guainazzi1999, )
4U 1722-30 | Terzan 2 | P | ? | U? | B | NS | (intZand2007, )
IGR J17361-4441 | NGC 6388 | T | ? | ? | ? | NS? | (Bozzo2011, )
CXOU J173324.6-332321 | Liller 1 | T | ? | ? | ? | NS? | (Homan2018, )
MAXI J1848-015 | GLIMPSE C01 | T | ? | ? | ? | ? | (Kennea2021, )
Faint LMXBs (peak L$X\leq 10^{35}$ erg s-1)
47 Tuc X9 | 47 Tuc | V | 28.2 min | U | X | BH? | (MillerJones2015, ; Bahramian2017, )
M15 X-3 | M 15 | T |  $\sim 240$ min | ? | AC | NS? | (Heinke2009a, ; Arnason2015, )
NGC 6652 B | NGC 6652 | V | ? | ? | ? | NS? | (Stacey2012, ; Paduano2021, )
Table 7: Galactic globular cluster LMXBs that are persistently bright or have
shown luminous outbursts (top) and faint LMXBs identified as LMXB candidates
through multi-wavelength or spectral studies (bottom). Table partially based
on (Bahramian2014, ) and updated. X-ray bursts have been detected from all the
bright LMXBs except for AC 211 in M15, IGR J17361-4441 in NGC 6388, CXOU
J173324.6-332321 in Liller 1, and MAXI J1848-015 in GLIMPSE C01. It is
important to note that there have been historical outbursts from the direction
of some of these globular clusters that have been attributed to a known
transient and absence of high-resolution follow up did not allow confirming
such association. State: P=persistent (or active for $>$30 years),
T=transient, V=variable (swinging between luminosity levels regularly).
Nature: U=ultra-compact, N=normal. Notes: X=period from X-ray photometry,
UV=period from UV photometry, XP=period from X-ray pulsations, O=period from
optical photometry, B=nature of donor inferred from properties of X-ray
bursts, H$\alpha$=hydrogen seen in optical counterpart spectrum. Notes
represent method of measuring Porb or determining donor natures. a\- Or the
alias period of 13 minutes.

###  5.4 Orbital period distribution

For a limited fraction of (transient and persistent) LMXBs, the orbital period
has been measured (via eclipses, radial velocity studies, pulsar timing).
There are $\sim$21 confirmed BH LMXBs with orbital periods measured, which
vary from a few hours to several weeks, see Figure 10. Almost all of these
systems show orbital periods of $<$1 week (with the exception of GRS
1915+105). Furthermore, there are currently no confirmed BH-LMXBs with orbital
period $<4$ hr101010While the ultracompact nature of 47Tuc X9 is clear (with
an orbital period of 28 minutes), BH nature of the compact object in this
system is not confirmed.. This suggests a notable paucity of BH-LMXBs with
orbital period $<4$ hr arur2018  compared to theoretical predictions
romani1992 ; portegieszwart1997 ; yungelson2006 ; repetto2015 .

While recent publications show the orbital period distribution of BHs, there
is no such recent overview for NSs. Therefore, we compiled an overview of
measured orbital periods in NS-LMXBs to compare them to the BH systems. The
presented sample of NS-LMXBs here contains 57 systems in which the nature of
the compact object was confirmed via detection of Type I X-ray bursts or
pulsations, ranging in orbital periods from 11 min (4U 1820$-$30) to 3.1 yr
(GX 1+4).

Figure 10 compares the known orbital periods of the NS- and BH- LMXB
populations. One aspect about the distribution that is highlighted by this
figure is that we know of many NSs with orbital periods $<4$ hr, while in the
BH population we know of very few of those systems Knevitt2014 ; arur2018 . It
is possible that this is due to selection effects. For example, it could be
that it is easier to find NSs with short orbital periods because the presence
of a solid surface (instead of an event horizon) causes the radiative
efficiency of NSs to be higher than that of BHs at low accretion rates
garcia2001 .

Figure 10: Top: orbital period for a subset of LMXBs. Periods for most BH-
LMXBs and candidates (green circles) are from (CorralSantana16, ) and
references therein. Measurements for NS-LMXBs (red triangles) and LMXBs with
unknown/uncertain compact objects (blue squares; denoted with “?-LMXBs”) are
from the literature, most of which are discussed in Sec. 3. Note that in
almost all cases uncertainties on orbital period are too small to be visible
on the plotted range. Bottom: comparison between cumulative distribution of
orbital periods in BH-LMXBs versus NS-LMXBs.

##  6 Summary and prospects for future observatories and surveys

In this Chapter, we reviewed observational characteristics of LMXBs linked
with the properties of the compact object (NS or BH), companion star (main
sequence, giant, or degenerate) in these systems, along with the binary
configuration (inclination angle, Roche-lobe overflow) and accretion status.
Multiple aspects of accretion and X-ray binaries from both theoretical and
observational perspectives are explored in further depth in other chapters of
this book. Namely, theoretical and observational details of accretion around
compact objects (Chapter by Davis et al. and Chapter by Qingcui Bu),
observational characteristics of black holes (Chapter by Kalemci et al. and
Chapter by Garcia), evolution of X-ray binaries (Chapter by Bellono et al.),
and Low magnetic field neutron stars (Chapter by Di Salvo et al.).

As indicated throughout the Chapter, the observational data is still
incomplete (or biased) on many fronts and thus limits our capacity to put
tight constraints on interpretations relating to population and evolution of
LMXBs. However, the growing multi-wavelength focus on study of LMXBs along
with the emergence of high-sensitivity wide-field astronomical surveys and
facilities (such as MeerKAT in the radio, Gaia mission in the optical regime,
and the eROSITA mission in the X-rays) already showcase significant
advancements. These advancements include expansion in the sample of known
LMXBs by dozens in the X-rays (e.g., by eROSITA, Doroshenko2014, ) or
identification of radio counterparts for many LMXBs (and candidates) and
numerous recycled pulsars (particularly in globular cluters) by MeerKAT.

Upcoming and future missions and observatories such as (but not limited to)
the next-generation VLA (ngVLA), Square-Kilometre Array (SKA) in the radio,
Vera Rubin Observatory (VRO) and James Webb Space Telescope (JWST) in the
infrared and optical, Imaging X-ray Polarimetry Explorer (IXPE), X-Ray Imaging
and Spectroscopy Mission (XRISM), enhanced X-ray Timing and Polarimetry
mission (eXTP) and Advanced Telescope for High Energy Astrophysics (ATHENA) in
the X-rays promise an exciting era in exploration of Low-mass X-ray Binaries.

## Acknowledgements

The authors thank J. C. A. Miller-Jones, J. M. Corral-Santana, T. J.
Maccarone, I. Mandel, J. A. Kennea, K. C. Dage, and K. Auchettl for helpful
comments and discussions.

AB is supported by the International Centre for Radio Astronomy Research, a
joint venture between Curtin University and the University of Western
Australia, funded by the state government of Western Australia and the joint
venture partners.

##  7 Cross-References

Below we list a selection of other chapters in this book and section that
provide more details on various aspects mentioned in this chapter.

  * •

Overall accretion disk theory
– Shane Davis

  * •

Overall binary evolution theory
– Diogo Belloni & Matthias Schreiber

  * •

Black holes: Accretion processes
– Qingcui Bu

  * •

Black holes: Timing and spectral properties and evolution
– Emrah Kalemci, John A. Tomsick, Erin Kara

  * •

Fundamental physics with black holes
– Javier Garcia

  * •

Low magnetic field Neutron Stars
Tiziana Di Salvo, Luciano Burderi, Rosario Iaria

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