#  _Gaia_ pulsars and where to find them

John Antoniadis1,2,3
1Max-Planck-Instutut für Radioastronomie, Auf dem Hügel 69, 53121, Bonn, DE
2Argelander Institut für Astronomie, Auf dem Hügel 71, 53121, Bonn, DE
3Institute of Astrophysics, FORTH, Dept. of Physics, University Campus,
GR-71003 Heraklion, Greece E-mail<EMAIL_ADDRESS>
###### Abstract

While the majority of massive stars have a stellar companion, most pulsars
appear to be isolated. Taken at face value, this suggests that most massive
binaries break apart due to strong natal kicks received in supernova
explosions. However, the observed binary fraction can still be subject to
strong selection effects, as monitoring of newly-discovered pulsars is rarely
carried out for long enough to conclusively rule out multiplicity. Here, we
use the second _Gaia_ Data Release (DR2) to search for companions to 1534
rotation-powered pulsars with positions known to better than
0$\aas@@fstack{\prime\prime}$5\. We find 22 matches to known pulsars,
including 1 not reported elsewhere, and 8 new possible companions to young
pulsars. We examine the photometric and kinematic properties of these systems
and provide empirical relations for identifying _Gaia_ sources with potential
millisecond pulsar companions. Our results confirm that the observed
multiplicity fraction is small. However, we show that the number of binaries
below the sensitivity of _Gaia_ and radio timing in our sample could still be
significantly higher. We constrain the binary fraction of young pulsars to be
$f_{\rm young}^{\rm true}\leq 5.3(8.3)\%$ under realistic(conservative)
assumptions for the binary properties and current sensitivity thresholds. For
massive stars ($\geq 10$ M⊙) in particular, we find $f_{\rm OB}^{\rm true}\leq
3.7\%$ which sets a firm independent upper limit on the galactic neutron-star
merger rate, $\leq 7.2\times 10^{-4}$ yr-1. Ongoing and future projects such
as the CHIME/pulsar program, MeerTime, HIRAX and ultimately the SKA, will
significantly improve these constraints in the future.

###### keywords:

stars: neutron — stars: pulsars – stars: massive – miscellaneous — catalogs —
surveys

††pubyear: 2020††pagerange: _Gaia_ pulsars and where to find them– _Gaia_
pulsars and where to find them

##  1 Introduction

Multiplicity plays a critical role in the evolution of massive stars:
interactions with a stellar companion can modify a star’s mass, composition
and angular momentum, thereby influencing the manner in which it dies, and the
type of remnant it produces. Studies of star-forming associations suggest that
most young massive stars ($\sim 100\%$) have a gravitationally-bound
companion, with the majority ($\sim 70$%) being close enough to eventually
interact via mass exchange (Sana et al., 2012). Such interactions can lead to
stellar mergers, X-ray binaries (XRBs), supernovae (SNe) and hyper-velocity
stars. Systems that survive these processes and remain bound ultimately become
compact-object binaries and gravitational wave (GW) sources.

Probing how the multiplicity fraction evolves as a stellar population ages is
crucial for understanding these astrophysical phenomena and the underlying
physical processes, including natal SN kicks (Bailes, 1989; Portegies Zwart &
Yungelson, 1999; Janka, 2013), the physics of common envelope (CE) evolution
(Ivanova et al., 2013), and the birth vs remnant mass relation (Antoniadis et
al., 2016; Tauris et al., 2017).

Theoretical models and predictions should confront to a number of
observational benchmarks, such as the distribution of pulsar velocities (Hobbs
et al., 2005), the number of XRBs and their relative distances from star-
forming regions (Walter et al., 2015; Tauris et al., 2017), the birth rates
and properties of double neutron star systems (Kalogera et al., 2004; Tauris
et al., 2017; Ferdman et al., 2020), and the observed GW merger rates (Abadie
et al., 2010; Abbott et al., 2017). One important independent constraint that
remains underutilized is the multiplicity fraction among young, non-recycled
pulsars (Bailes, 1989). The frequency of binary systems that survive SN
explosions is a sensitive probe of the SN kick magnitude distribution, which
remains one of the major theoretical uncertainties. There are only a handful
of known binaries hosting young radio pulsars, implying that most SNe result
in disruptions. However, the observed multiplicity fraction is likely subject
to significant selection effects as most new pulsar discoveries are typically
monitored only for up to a few months. Owing to the presence of timing noise
and the strong co-variances with the intrinsic spin-down, such observations
are not particularly sensitive to orbital acceleration caused by low-mass
companions and/or wide binary pairs. Indeed, even some of the few known
binaries have been discovered only by chance (Lyne et al., 2015; Kaplan et
al., 2016; Bassa et al., 2016).

In this work we revisit the constraints on pulsar multiplicity using the
second _Gaia_ data release (DR2; Gaia Collaboration et al., 2016; Lindegren et
al., 2018) which, for the first time, provides information on the distances
and kinematic properties of nearly two billion stars in the Galaxy and
Magellanic Clouds. In Section 2 we describe our sample and methodology, while
in Section 3 we present our results. In Section 4 we examine the influence of
various selection effects and current limitations, and derive a constraint on
the multiplicity fraction of young pulsars. We conclude with a discussion in
Section 5.

##  2 Methods

###  2.1 Sample

In what follows, we distinguish between different classes of rotation-powered
pulsars based on their inferred minimum dipole magnetic field strength,
$(B/{\rm G})\equiv 3.2\times 10^{19}(P\dot{P}s^{-1})^{1/2}$. More
specifically, sources with $(B/{\rm G})\leq 10^{9}$ are considered fully-
recycled millisecond pulsars (MSPs), the ones with $10^{9}<(B/{\rm G})\leq
10^{10}$ are mildly-recycled pulsars (henceforth mild MSPs), while those with
$(B/{\rm G})>10^{10}$ are referred to as young, non-recycled pulsars.

Our main goal is to identify possible companions to known rotation-powered
pulsars. There are currently 2492 pulsars outside of globular clusters listed
in the ATNF pulsar catalogue111http://www.atnf.csiro.au/research/pulsar/psrcat
accessed on Oct 20 2020 (PSRCat v1.63; Manchester et al., 2005). Since we are
primarily interested in finding close astrometric pairs, we only considered
those with positions known to better than 0$\aas@@fstack{\prime\prime}$5\.
This leaves 1534 objects (see Figure 1), a sample considerably larger than
those used in previous searches for _Gaia_ counterparts (65 MSPs in Mingarelli
et al. 2018, 155 binaries in Jennings et al. 2018 and 57 non-recycled pulsars
in Igoshev & Perets 2019). Of these, 107 are MSPs, 39 are mild MSPs and 1388
are young pulsars. The sample contains 145 known binaries (86 MSPs, 32 mild
MSPs and 27 young pulsars) and 11 extra-galactic sources.

Figure 1: P–$\dot{P}$ diagram of the pulsars contained in our sample.

###  2.2 Identification of Candidate Astrometric Pairs

We searched for possible pulsar companions among _Gaia_ DR2 objects (Lindegren
et al., 2018) located within 20″ of each pulsar. This search radius is
equivalent to the angular distance that would be covered by an object at 500
pc, moving with a transverse velocity of $v_{\rm tr}=1200$ km s-1 for 40 yr.
For each _Gaia_ entry, we used the available astrometry to propagate the
celestial coordinates and their uncertainties to the reference epoch of the
pulsar ephemeris (PosEpoch in PSRCat). This choice allowed us to utilize the
entire sample instead of only the subset of pulsars with timing proper
motions. For the few sources for which only a two-parameter astrometric
solution is available, we used directly their _Gaia_ epoch position (J2015.5).
Sources outside the 2$\sigma$ positional error circle of the pulsar were
dismissed as unrelated. For each possible astrometric pair, we inferred a
probability of chance coincidence using the average number density of stars
within 1′ of the pulsar (Antoniadis et al., 2011).

Given that many pulsar and _Gaia_ DR2 positions considered here are known to
$\ll 0\aas@@fstack{\prime\prime}5$ precision, their uncertainties are likely
dominated by systematics. One important source of potential errors is
rotations between the _Gaia_ reference frame — which is tied to the
International Celestial Reference Frame (ICRS, see Mignard et al., 2018) — and
the various incarnations of the Solar System ephemeris utilized in pulsar
timing. Co-variances between astrometric and other parameters in the pulsar
timing solution, red noise in the _Gaia_ astrometry and timing noise may play
a role as well. Here, we did not attempt to correct explicitly for these
effects. Instead, we compensated for them by adding
$0\aas@@fstack{\prime\prime}25$ in quadrature to the inferred position error.
This value was adopted solely based on empirical considerations. More
specifically, it corresponds to $\sim 1/2$ of the second largest separation
between a pulsar and its known optical counterpart (PSR J0045$-$7319; see
Table 1 and Section 3.2). This choice also made our search sensitive to nearby
astrometrically-resolved binaries that would have been missed otherwise
($0\aas@@fstack{\prime\prime}25$ is equivalent to a separation of $125$ AU at
500 pc, see Section 3.1). Increasing the systematic uncertainty beyond this
value — for instance, to include PSR J2129$-$0429 for which the inferred
separation is $\sim 1\aas@@fstack{\prime\prime}4$ — resulted in a very large
number of false positives.

###  2.3 Distances, Reddening and Kinematics

It is well known that obtaining distance estimates by directly inverting the
parallax measurement can lead to significant bias in the presence of noise.
Following previous work (Jennings et al., 2018) and recommendations (Bailer-
Jones, 2015; Astraatmadja & Bailer-Jones, 2016; Bailer-Jones et al., 2018;
Luri et al., 2018), we inferred probability density functions (PDFs) for the
distance to sources of interest using:

$P(d|\hat{\pi})\propto\frac{1}{2L^{3}}e^{-d/L}d^{2}e^{(-1/d-\hat{\pi})^{2}/2\sigma^{2}_{\hat{\pi}}},$
(1)

Here, we assume that the parallax measurement, $\hat{\pi}$ is normally
distributed about the true parallax, $1/d$, with a dispersion
$\sigma_{\hat{\pi}}$. The $e^{-d/L}d^{2}L^{-3}$ term accounts for a Lutz-
Kerker bias (Lutz & Kelker, 1973) with an exponentially-decreasing stellar
density (that is nearly constant for $d\ll L$). The former prior combined with
the condition $d>0$ has the advantage of making the distance PDF well-behaved
and normalisable so that statistical moments can be defined. For our purposes,
distances are not the primary quantity of interest and thus $L$ was simply
taken to be direction-independent and was set equal to 1.5 kpc (Bailer-Jones
et al., 2018). This should be adequate for the majority of sources with small
Galactic latitudes, but may overestimate the distances to sources with
imprecise parallaxes located outside the Galactic plane. For more detailed
models, see Jennings et al. (2018); Bailer-Jones (2015) and references
therein.

When applicable, we also made use of other available measurements that contain
distance information. More specifically, for certain pulsar/_Gaia_ cross-
matches we utilized timing and VLBI parallaxes (inverted using Eq. 1), and DM-
based distance estimates derived using the NE2001 model and assuming a 20%
uncertainty (Deller et al., 2019; Ding et al., 2020). For extra-galactic
sources we used the most recent distance estimates to the Large(Small)
Magellanic Cloud, $49.97\pm 1.13(62.1\pm 1.9)$ kpc (Pietrzyński et al., 2013;
Graczyk et al., 2013). For non-certain associations, we simply required the
distance be positive. In what follows we report median values as point
estimators together with 16% and 68% percentiles as uncertainties.

The interstellar reddening along each line of sight was traced using the
latest version of the 3D dust map of Green et al. (2019)
(Bayestar19222http://argonaut.skymaps.info/; see also Green et al., 2014;
Green, 2018). Finally we derived estimates for the reduced proper motion
(Luyten, 1922) using,

$H_{\rm g}=m_{\rm g}+5\log_{10}{\frac{\mu}{{\rm mas\,yr^{-1}}}}-10+A_{\rm g}$
(2)

where $m_{\rm g}$ and $A_{\rm g}(d)$ are the apparent magnitude and extinction
in the _Gaia_ band, and $\mu=\sqrt{\mu_{\alpha}^{2}+\mu_{\delta}^{2}}$ is the
magnitude of the proper motion. This quantity is analogous to the absolute
magnitude but sensitive to the source’s transverse velocity, $H_{\rm g}\equiv
M_{\rm g}+5\log_{10}(v_{\rm tr}/4.74057\,{\rm km}\,{\rm s}^{-1})$. This makes
it a useful quantity for distinguishing between different kinematic
populations, even in the absence of a precise parallax measurement.

##  3 Results

Our search identified 32 close astrometric pairs with a probability of chance
coincidence smaller than 10%. These sources include 22 known binaries, 8 new
candidate counterparts, the Crab pulsar (PSR B0531+21) and the pulsar wind
nebula of PSR B0540$-$69 in the LMC. For the majority of these sources, the
inferred probability of chance coincidence is $1-3\%$, implying that the
number of false positives in this sample is $\mathcal{O}(3)$ or smaller.

The properties these _Gaia_ sources are listed in Table 1, while Figure 2
shows their location on color–magnitude (henceforth HR) and color–Hg
(henceforth RPM) diagrams.

As can be seen, for most confirmed pulsars, the angular separation
$\hat{\theta}$ at PosEpoch is much smaller than the position error, which is
dominated by the systematics. Two notable exceptions are PSR J0045$-$7319, for
which the timing solution has not been updated for over 25 years (Kaspi et
al., 1996a), and PSR J0437$-$4715, a nearby MSP. The reason for the large
discrepancy in the latter case is not clear, but it might be related to the
faintness of the optical counterpart and the proximity of the system to Earth.

In the rest of this section we discuss the properties of confirmed matches and
candidates in more detail.

###  3.1 Millisecond Pulsars

We found 18 matches to known MSPs including PSR J0348+0432 which, even though
does not satisfy our formal MSP definition, is most likely a fully-recycled
pulsar (Antoniadis et al., 2013). With the exception of PSRs B1953+29,
B1957+20 and J1435$-$6100, these _Gaia_ counterparts have also been identified
by Jennings et al. (2018), Mingarelli et al. (2018) and Igoshev & Perets
(2019).

The majority of these sources are eclipsing MSPs with stellar- or Jupiter-
mass companions (often referred to as “redbacks” and “black widows”
respectively). As can be seen in Figure 2 these sources occupy sparsely
populated regions on the HR and RPM diagrams: they are both bluer and
significantly brighter compared to MS stars of comparable masses. This
supports the idea that they either have a high helium content (i.e. they are
stripped), or that their atmospheres are highly irradiated. On the RPM
diagram, MSP companions are even more separated from MS stars. On average,
they have large proper-motion moduli, suggestive of high velocities that are
likely a fossil signature of the SN explosion.

|
---|---
Figure 2: Positions of known and candidate pulsar companions and with _Gaia_
counterparts on the observational HR (left) and RPM diagrams (right). Scatter
points and the overlaid histogram shows field stars with precise parallax
measurements within 200 pc from the Sun. The positions of known pulsars and
candidate associations are shown in black and gray respectively. The dashed
lines show the empirical cuts of Eq. 3 (see text for details).

We find that most eclipsing MSPs, as well as three MSPs with low-mass white
dwarf (WD) companions, satisfy the following conditions:

$\begin{array}[]{rcl}M_{\rm G}&\leq&2.7(G_{\rm BP}-G_{\rm RP})+10.5,\\\ M_{\rm
G}&>&3.7(G_{\rm BP}-G_{\rm RP})+2.4,\\\ H_{\rm g}&>&5.3(G_{\rm BP}-G_{\rm
RP})+5.9,\\\ \end{array}$ (3)

where $G_{\rm BP}$ and $G_{\rm RP}$ are the mean magnitudes in the _Gaia_ BP
and RP photometric bands. These empirical criteria are efficient in filtering
out 99.8% of the field stars shown in Figure 2. They are also robust against
selecting high-velocity MS stars with similar $H_{\rm g}$ values. However,
some overlap is expected with early-type sub-dwarfs and extremely-low mass
white dwarfs and their precursors (Pelisoli & Vos, 2019; Pelisoli et al.,
2019a). Utilizing color and Hg information only (i.e. the last two relations)
results in significant overlap with WDs and higher contamination from halo
stars (at the $\sim 1-2\%$ level), but has the benefit of being applicable to
sources for which a reliable parallax measurement is not available. This can
be compensated by additional criteria (e.g. $H_{\rm g}\leq 6.9(G_{\rm
BP}-G_{\rm RP})+13.0$) to filter out WDs, or multi-wavelength information
(e.g. the presence of X-ray, $\gamma-$ray or radio counterparts). We provide
some practical examples for identifying pulsar candidates in a python notebook
accompanying this paper33310.5281/zenodo.4075042.

#### Individual sources and comparison to previous work

##### PSR J1024$-$0719

This MSP was long thought to be isolated. However Bassa et al. (2016) and
Kaplan et al. (2016) identified a $\sim 0.4$ M⊙ MS K-dwarf as a potential
companion in a very long period (2-20 kyr) orbit. Our search identified _Gaia_
3775277872387310208 as the pulsar companion (see also Jennings et al., 2018)
with a true angular separation of $\theta=0\aas@@fstack{\prime\prime}076(3)$
(without accounting for systematic uncertainties which are likely not dominant
in this case). At the inferred distance of $3.4^{+4.6}_{-2.0}$ kpc, this
implies a projected separation of $260^{+852}_{-195}$ AU, or an orbital period
between $\sim 0.75$ and 12 kyr. The uncertainty is clearly dominated by the
distance estimate and thus it will improve significantly with further timing
observations and the next _Gaia_ data release. This source clearly
demonstrates the complementary of optical astrometry and radio timing for
identifying binary pulsars.

##### PSR B1957+20

This pulsar is the prototypical “black widow” system, a 2-ms MSP with a
Jupiter-mass companion in a 9 h orbit. Jennings et al. (2018) discuss a
counterpart $\sim 0\aas@@fstack{\prime\prime}7$ away from the timing position
but they conclude that this source is unrelated. Here, we identify a faint
source within 0$\aas@@fstack{\prime\prime}$1 of the pulsar (_Gaia_
1823773960079216896). We are confident that this is the counterpart to PSR
B1957+20 based on available optical photometry (e.g. Reynolds et al., 2007)
and the good match between the _Gaia_ and timing proper motion measurements.
Combining the negative parallax measurement with DM-based distance estimate,
yields $d=1.9^{+1.0}_{-0.9}$ kpc, consistent with the constraints based on
spectroscopy (van Kerkwijk et al., 2011).

##### PSR B1953+29

This system is the second MSP discovered after PSR B1937+21 and the first one
in a binary (Boriakoff et al., 1983). It has a low-mass companion ($\lesssim
0.18$ M⊙; Gonzalez et al., 2011) in a 117 d orbit. Source _Gaia_
2028584968839606784 was identified as a possible counterpart based on its
angular separation of $0\aas@@fstack{\prime\prime}1$ from the pulsar position,
and the low stellar density in the field which implies a small probability for
chance alignment ($\leq 3$%). However, the error budget is dominated by the
systematic uncertainty which is likely overestimated, given that the timing
position is being updated regularly (Arzoumanian et al., 2018, 2020). The same
source has been investigated as the possible companion to PSR B1953+29 by
Boriakoff et al. (1996) and Mignani et al. (2014). It has a red featureless
spectrum suggestive of an evolved star. Indeed, the inferred colors and
absolute luminosity place the source above the MS. However, the _Gaia_
parallax measurement implies a distance of $2.3^{+2.9}_{-1.0}$ kpc which is
$\sim 2$ times smaller than the DM-based estimate. In addition, the proper
motion does not agree well with that of the pulsar. We therefore conclude that
the _Gaia_ source is probably unrelated to the pulsar and that the true
companion of the latter is a low-mass WD, as suggested by the radio timing
solution.

##### PSR J1435$-$6100

This is a 9 ms pulsar with a massive, $\sim 1$ M⊙ companion in a 32 h orbit.
This particular combination of fast spin, short orbital period and high
companion mass is challenging to explain. The compactness of the orbit
suggests that the system is the survivor of a CE episode. To reach the
observed spin frequency, the pulsar must have accreted $\mathcal{O}(0.1$ M⊙)
of material from the donor star (Podsiadlowski et al., 2002; Tauris et al.,
2012). This happened either during the CE event or after, via Case BB mass
transfer from the stripped, post-CE companion. In either case, the short
evolutionary timescales suggest that the system experienced a phase of
supercritical accretion in which a very high accretion flow that led to
efficient neutrino cooling (Tauris et al., 2011, 2012).

We identified a 18.9m source (_Gaia_ 5878387705005976832)
0$\aas@@fstack{\prime\prime}$3 away from the pulsar timing position. The
object has a probability of true association $\sim 95\%$, and a trigonometric
parallax that is consistent with the pulsar DM distance estimate. However, the
inferred absolute magnitude of $M_{\rm G}\simeq-2.7^{\rm m}$ means that this
cannot be the companion responsible for recycling the pulsar. Deep photometric
observations obtained by Jacoby et al. (2006) failed to detect any fainter
counterpart closer to the pulsar position, which is consistent with the
expected WD nature of the companion. Based on that, we conclude that this is
either a chance coincidence or, less likely, the system is part of a wide
triple. The latter possibility can be tested if the pulsar proper motion is
measured.

##### PSRs J1311$-$3430, J1628$-$3205 and J2129$-$0429

_Gaia_ counterparts to these systems were identified by Jennings et al.
(2018), but did not show up in our search. The position of PSR J1628$-$3205 is
not well known and hence, it was not included in our final sample. For PSR
J1311$-$3430, the nearest source was filtered out due to its large position
error of $2\aas@@fstack{\prime\prime}9$. Similarly, for PSR J2129$-$0429, the
inferred angular separation of the nearest source
(1$\aas@@fstack{\prime\prime}$3 for _Gaia_ 2672030065446134656) was larger
than our formal $2\sigma$ threshold. However, for all these cases the
association is confirmed by phase-resolved photometry and spectroscopy. We
include these sources in Table 1 for completeness.

##### PSRs J1843$-$1113, J1732$-$5049 and J1949+3106

Possible associations to these pulsars were discussed by Mingarelli et al.
(2018). For the nearest source to PSR J1843$-$1113 (Gaia 4106823440438736384),
we infer a separation of 1$\aas@@fstack{\prime\prime}$44\. Long-term timing of
this pulsar (Desvignes et al., 2016) strongly suggests that it is isolated.
Hence, we conclude that the _Gaia_ source is most likely unrelated.

For PSRs J1732$-$5049 and J1949+3106 which are known binaries, we again infer
large separations to the proposed counterparts
(2$\aas@@fstack{\prime\prime}$26 and 2$\aas@@fstack{\prime\prime}$82 for
_Gaia_ 5946288492263176704 and 2033684267592307584 respectively). In addition,
the inferred colors, luminosities and proper motions are inconsistent with the
white-dwarf nature of the pulsar companions and the pulsar timing constraints.
We therefore conclude that these sources are also unrelated.

###  3.2 Young and mildly-recycled pulsars

Of the 1440 pulsars with $B>10^{9}$ G in our sample, 11 were found to have a
close astrometric pair. Of these, only three are known binaries: PSR
J0045$-$7319 is an LMC pulsar with a B1V companion in a 51 day orbit (Kaspi et
al., 1996a; Kaspi et al., 1996b). PSR B1259$-$63 is in a highly-eccentric
3.4-yr orbit with a rapidly-rotating OB star (Chernyakova et al., 2014). The
system is well known for its 40-day long radio eclipses near periastron.
Finally, PSR J2032+4127 is a pulsar in the Cygnus OB2 association. It is in a
$\sim$30-yr orbit around a Be star. It’s binary nature was revealed only after
long-term timing (Lyne et al., 2015).

In addition to the aforementioned sources, our sample contained a further 59
young and mildly-recycled pulsars in known binaries. Upon investigation we
find that all their companions were too faint to be detected by _Gaia_ (van
Kerkwijk et al., 2005; Mignani et al., 2014). We identified 8 new close
astrometric pairs to which we discuss below.

#### Candidates

##### PSR J0534$-$6703

This source is a slow pulsar in the LMC (Manchester et al., 2006). We found a
bright star within $\sim 0\aas@@fstack{\prime\prime}5$ of the timing position.
Its propoerties are consistent with an early-type MS star at the LMC. The
positional offset is similar to the one between PSR J0045$-$7319 and its
optical counterpart. Given that the ATNF timing solution is over 15 years old,
this could be attributed to systematics. Interestingly, the pulsar has an
unusually high spin period derivative, which might be caused by orbital
acceleration. We conclude that a true association between the pulsar and the
_Gaia_ source is plausible and cannot be ruled out based on existing
information. We therefore recommend further radio timing observations.

##### PSR J1624$-$4411

The nearest counterpart to PSR J1624$-$4411 has a positional offset of
0$\aas@@fstack{\prime\prime}$3 from the timing position (Lorimer et al.,
2006). The _Gaia_ source is consistent with an MS star at the inferred
distance of $2.7^{+4.6}_{-1.8}$ kpc. The latter also agrees well with the DM-
based estimate of $\sim 3.3$ kpc and hence a true association is possible.

##### PSR J1638$-$4608

_Gaia_ 5992089022760118400 has a separation of only
0$\aas@@fstack{\prime\prime}$14 from the timing position of this pulsar.
Unfortunately, only a 2-parameter astrometric solution is available and hence
the true separation might be larger. At the DM-distance of the pulsar, the
source would have an absolute magnitude of $M_{\rm G}=0.3^{+1.5}_{-1.6}$.
Interestingly, Kerr et al. (2016) report a 450-day periodic modulation in the
timing residuals. If interpreted as a Røemer, the observed amplitude would
suggest a planetary companion of a few Earth masses. Such an object would be
much fainter than the _Gaia_ source. Under these considerations, we conclude
that this is either a chance alignment or that the _Gaia_ source is in a very
wide orbit. The next _Gaia_ data releases will hopefully result in more
stringent constraints on this system.

##### PSR J1838$-$0549

The nearest _Gaia_ entry has an angular separation of $\sim
0\aas@@fstack{\prime\prime}5$ from the pulsar. Its distance is somewhat
smaller but still consistent with the pulsar’s DM distance. The inferred
distance implies that source is a giant star off the MS. Parthasarathy et al.
(2019) recently presented timing data spanning 4 years that show no signs of
periodicity. Based on the available information, we conclude that the _Gaia_
source is either in a wide orbit around the pulsar or a foreground star.

##### PSR J1852+0040

PSR J1852+0040 is a radio-quiet pulsar associated with the SN remnant Kes 79
(Halpern & Gotthelf, 2010). The _Gaia_ source identified in our search has a
distance that is only marginally consistent with that of the pulsar. Hence, we
conclude that this is either a chance coincidence or that the source is the
ejected companion of the pulsar progenitor.

##### PSR J1903$-$0258

This pulsar is located 0$\aas@@fstack{\prime\prime}$4 away from _Gaia_
4261581076409458304 (Lorimer et al., 2006). The measured color and luminosity
suggest that the latter is an intermediate mass MS star. Given that the timing
solution has not been updated for over 15 years, the two objects may be
physically associated.

##### PSR J1958+2846

This is a radio-quiet pulsar that has been timed using the Fermi-LAT
instrument. The $\gamma-$ray timing solution (Kerr et al., 2016) derived using
$\sim 1.5$-yr of data shows no sign of binarity. However, given the low
accuracy of the time-of-arrival measurements and the small span of the data,
an association with _Gaia_ 2030000280820200960, located $\sim
0\aas@@fstack{\prime\prime}4$ from the formal position is still possible.

##### PSR J2027+4557

This pulsar was found in a radio survey of Cygnus OB associations (Janssen et
al., 2009). The _Gaia_ source that showed up in our search is consistent with
an early-type MS star at the inferred distance of $1.96^{+0.25}_{-0.20}$ kpc.
The latter is smaller than the DM distance estimate. The pulsar bears
similarities to PSR J2032+4127, located inside the Cygnus OB2 region. The
latter has a DM of 115 pc cm-3, i.e. $\sim 2$ times smaller. Hence, a local
un-modelled contribution to the DM would be needed, which is not impossible
given the complexity of the region.

##  4 The multiplicity fraction among young pulsars

The results presented in Section 3 confirm that the _observed_ multiplicity
fraction (henceforth $f_{\rm young}^{\rm obs}$) among young pulsars is small:
of the 1377 galactic pulsars444 (here we do not consider extragalactic
pulsars, since some of the processes impacting $f_{\rm young}^{\rm true}$
depend strongly on metallicity) with $B>10^{10}$ G in our sample, only 22(16)
are in binaries with(without) considering the candidates described in the
previous section, thus $f_{\rm young}^{\rm obs}=1.16-1.59\%$. The latter is
considerably smaller than the multiplicity fraction among MSPs and mild-MSPs
($f_{\rm MSP}^{\rm obs}\simeq 79\%$ and $f_{\rm mild}^{\rm obs}\simeq 85\%$
respectively).

In interpreting these results, one has to consider two strong selection
effects: 1) Radio timing is not sensitive to binaries with orbital periods
considerably longer than the observational timespan and Røemer delays much
smaller than the amplitude of the timing noise, and b) _Gaia_ cannot detect
sources fainter than $m_{\rm g}\gtrsim 20.5^{\rm m}$. To examine the impact of
these biases and place a constraint on the true multiplicity fraction among
young pulsars, $f_{\rm young}^{\rm true}$, we constructed a toy model to
simulate various scenarios for the orbital and optical properties of possible
companions stars and estimate their detectability at radio and optical
wavelengths.

In these simulations, we split the 1377 young Galactic pulsars in our sample
in three categories: the first contained all known binaries ($P_{\rm b}\geq 0$
in PSRCat), the second the seven Galactic candidates of Table 1 and the third,
the remaining seemingly isolated pulsars. We then used a Monte-Carlo sampling
scheme with $10^{5}$ iterations to estimate the number of binaries in each
group and infer the probability distribution for $f_{\rm young}^{\rm true}$.
All pulsars belonging to the first group were obviously always counted as
binaries. For the second group, we decided on whether the candidates of Table
1 are true binary companions using their inferred probabilities of chance
coincidence. For the third group, we assigned a companion with a separation
and mass drawn from various astrophysically-motivated distributions (see
below). The brightness was inferred using a mass-luminosity relation for MS
stars, the extinction curves of Green et al. (2019) (see Section 3), and a
distance normally distributed about the DM distance with a fractional
uncertainty of 20%. The multiplicity fraction for each sample population was
inferred by counting all binaries in the first two categories and adding those
systems from the final category that had orbital periods and apparent
magnitudes above a certain detectability threshold, $P_{\rm b}\geq P_{\rm
b}^{\rm thres}$ and $m_{\rm g}\geq m_{\rm g}^{\rm thres}$.

Figure 3 shows the results for various simulated scenarios. For our fiducial
model (shown in blue), companion masses were inferred by combining a Salpeter
mass function in the 10…50 M⊙ range for the pulsar progenitors, with the best-
fit mass ratio distribution of Sana et al. (2012). Orbital periods ranging
from 1 d to 1000 yr, were also distributed according to the results of the
latter work, while for the _Gaia_ and radio timing detectability thresholds we
assumed $P_{\rm b}^{\rm thres}=50$ yr and $m_{\rm g}^{\rm thres}=20.5^{\rm
m}$. This scenario — which we consider to be the most realistic, given all
underlying uncertainties — places an upper limit of $b_{\rm young}^{\rm
true}\leq 5.3\%$ at the 99.8% confidence level (CL). Radio timing appears to
be the most sensitive probe of binarity ($f_{\rm young}^{\rm true}\leq 8.3\%$
at 99.8% CL for $P_{\rm b}^{\rm thres}=10$ yr), while massive companions would
be the easiest to detect with _Gaia_ ($f_{\rm young}^{\rm OB}\leq 3.6\%$ at
99.8% CL for early-type companions brighter than $M_{g}=-2.6^{\rm M}$).
Overall, we find that the binary fraction could still be $\sim 3$ to 8 times
higher than the observed one, given present limitations.

An additional selection effect against pulsars in binaries that is unaccounted
for in the aforementioned models is the stellar wind of the companion which
may be opaque to radio emission. The high mass-loss rates expected for upper-
MS stars could create a dense environment leading to free-free absorption. For
pulsars in our sample, this means that certain combinations of orbits and
companion masses are ruled out (given that a pulsar _is_ observed).

Figure 3: The probability density function for $f_{\rm young}^{\rm true}$
given different detectability thresholds and scenarios discussed in the text
(see Sections 4 and 5). Dashed lines show the results of simulations in which
the possibility of free-free absorbtion of pulsar emission from the stellar
wind is taken into account.

For a circular orbit (i.e. constant separation), the minimum period below
which 21-cm radiation would be eclipsed by a 1000 km s-1 outflow with a
temperature of $10^{4}$ K (Illarionov & Sunyaev, 1975) is:

$P_{\rm b}^{\rm min}\simeq 0.28\left(\frac{\dot{M}}{4.8\times 10^{-12}{\rm
M_{\odot}\,yr^{-1}}}\right)\left(\frac{M_{\rm tot}}{{\rm
M_{\odot}}}\right)^{-1}\,{\rm days}$ (4)

where $\dot{M}$ is the wind mass-loss rate and Mtot is the total mass of the
binary. In practice, we find that taking this effect into account in our toy
model – assuming standard mass-loss recipes for the MS (Kippenhahn et al.,
2012) — has a very small impact on the results described above (see dashed
lines in Figure 3). This is because free-free absorption only becomes relevant
for large companion masses and short separations. For the models discussed
here, most such systems are assumed to be within the sensitivity of exiting
timing programs and are thus already ruled out. However, Eq. 4 also suggests
that some rotation-powered pulsars with massive companions are obscured at
radio wavelengths and therefore, the intrinsic binary fraction could be even
larger. Some clues about the influence of this effect is obtained from the
properties of known systems: Of the pulsars investigated here, only the
1237-day binary PSR B1259$-$63 is eclipsed over $\sim 3$% of its orbit near
periastron (Johnston et al., 1992, 1994; Johnston et al., 2005). Considering
the shape of the mass function, this suggests that stellar winds should only
affect a small fraction of pulsars when they approach their massive companions
(either due to compact orbits or high eccentricities). On the other hand,
pulsars in sufficiently close orbits around massive stars would become wind-
fed high-mass X-ray binaries (HMXBs). Indeed, most known wind-fed HMXBs have
orbital periods in the 3…300 d range and X-ray luminosities that roughly scale
as $L_{\rm x}\propto P_{\rm b}^{-4/3}$, as expected for spherical accretion
(e.g. Lutovinov et al., 2013; Chaty, 2013; Walter et al., 2015; Tauris et al.,
2017, and references therein). However, these sources are accretion-powered
and hence not directly relevant to the population of pulsars considered here.

To conclude, we believe that absorption is only relevant to a small fraction
of pulsars orbiting massive companions with periods of up to few years. To be
hidden, these pulsars must approach their companions sufficiently close to
intersect the optically-thick part of the wind, but not too close so as to
become persistent HMXBs. In turn, this means that the constraints on $f_{\rm
young}^{\rm true}$ inferred in this section should be a reliable proxy of the
true frequency of pulsars in stellar binaries.

##  5 Conclusions and Prospects

We have performed a search for optical counterparts to 1534 rotation-powered
pulsars. By utilizing the _Gaia_ DR2 catalogue and back-propagating its
astrometric solution to the reference epoch of each pulsar’s ephemeris
(Section 2), we were able to search for close astrometric pairs. We identified
20 previously known binary companions — the majority of which are companions
to MSPs — and 8 tentative new matches to young pulsars. For these candidates,
we find that their _Gaia_ parallaxes are broadly consistent with the pulsar
distance estimates and recommend further timing observations to test if they
are true binary companions.

Most MSP companions in _Gaia_ DR2 are early-type sub-dwarfs significantly
bluer and more luminous than MS stars with similar masses. Their colours,
luminosities and reduced proper motions sets them apart from the majority of
stars on the HR and RPM diagrams. In Section 3.1, we inferred empirical color-
magnitude-Hg criteria (Equation 3) that satisfy the observed properties of
eclipsing and WD companions to MSPs and filter out $\gtrsim 99.8\%$ of field
stars. While some contamination is expected by sdA stars (Pelisoli et al.,
2019b; Pelisoli & Vos, 2019; Pelisoli et al., 2019a), these selection criteria
allow to single out _Gaia_ sources that might be orbited by neutron stars.
Deep targeted radio surveys of these candidates might be proven a viable path
towards discovering new MSPs. Because of the information provided by _Gaia_ ,
pulsars discovered in this way would be extremely valuable for a broad range
of astrophysical inquiry (Antoniadis et al., 2012; Mingarelli et al., 2018;
Arzoumanian et al., 2020). For instance, MSPs with bright WD companions enable
precise NS mass measurements, which are important for constraining the mass
function of compact stars and the equation-of-state of super-dense matter
(Antoniadis et al., 2013; Antoniadis et al., 2016). Similarly, eclipsing MSPs
are key in understanding NS recycling and the end-states of low-mass XRBs
(e.g. van Kerkwijk et al., 2011; Tauris et al., 2015a; Strader et al., 2019,
and references therein).

In Section 4, we used a toy model to investigate the impact of observational
selection effects on the detectability of pulsar companions. We constrained
the true multiplicity fraction among young pulsars to be $\leq 5.3\%$ under
the assumption that all binaries with orbital periods shorter than 50 years
and companions brighter than $20.5^{m}$ would have been detected by _Gaia_ and
ongoing timing programs. We also concluded that the number of pulsars with
longer orbital periods that are obscured by the wind of their companions
should be small.

Given that our toy model only considers stellar binaries, the number of
pulsars with planetary companions could still be considerably larger. Indeed,
low-mass objects are considered as the possible cause of the low-amplitude
periodic signals found in the timing residuals of several young pulsars. (e.g.
Ray et al., 2011; Parthasarathy et al., 2019). With this caveat in mind, our
constraints on $f_{\rm young}^{\rm true}$ should be reliable proxy for the
number of young pulsars orbited by stars. While our analysis confirms that
$f_{\rm young}^{\rm true}$ is low, we find that it could still be a factor 5–8
larger than previously thought. Hence, there could still be of order $\sim
100$ hidden binaries in the known pulsar population. For massive companions in
particular, we inferred a more stringent limit of $f_{\rm OB}^{\rm true}\leq
3.7\%$. Combined with the Milky-Way core-collapse SN rate ($r_{\rm
SN}=0.01-0.02$ yr-1, see Diehl et al., 2006; Keane & Kramer, 2008, and
references therein), this places a very conservative, but independent upper
limit on the Galactic NS coalescence rate, $r_{\rm mergers}\lesssim f_{\rm
OB}^{\rm true}\times r_{\rm SN}=(3.7-7.4)\times 10^{-4}$ yr-1 (with the caveat
that some close binaries may be HMXBs, see Section 4). The former is
consistent with (but more conservative than) the more direct constraints based
on double neutron star systems (Kalogera et al., 2004; Pol et al., 2020), the
observed number of HMXBs in the Galaxy (Tauris et al., 2017) and the advanced
LIGO/Virgo constraint of $(3.2^{+4.9}_{-2.4})\times 10^{-5}$ yr-1 (Abbott et
al., 2020).

There are several evolutionary pathways leading to the formation of isolated
young pulsars. Theoretical models predict that while $\sim$one third originate
from single stars or binaries that merge during the MS (Portegies Zwart &
Yungelson, 1999), the majority must be due to SNe in massive binary systems.
The relative number of pulsars released during the first and second explosion,
as well as the frequency of surviving binaries depends sensitively on the
magnitude distribution of natal SN kicks. A binary system with a given
separation is more likely to survive a kick of a certain magnitude during the
first SN explosion, when the secondary is still a massive star. The second SN
can then release up to two NSs (one young and one midly recycled). In this
case one would expect a relatively large number of isolated mild MSPs, which
appears to disagree with observations ($f_{\rm mild}^{\rm obs}\simeq 85\%$,
see Section 4). This suggests that most young pulsars originate from the first
SN in a wide binary, or the released secondary star. On the other hand,
compact orbits, stripping of the secondary star prior to its core collapse and
electron-capture SNe lead to increased binary survival rates and therefore,
they can help explain the properties of the observed binary pulsar population
(Podsiadlowski et al., 2004; Tauris et al., 2013; Tauris et al., 2015b, 2017).
Nevertheless our results appear to be in broad agreement with kick amplitudes
of few 100 km s-1 for core-collapse SNe (Schneider et al., 2020), while
extremely small-amplitude kicks are disfavoured given the small number of
pulsars in wide binaries (see also Igoshev & Perets, 2019). Detailed
population-synthesis studies and comparison with all available observational
benchmarks will be required to reach more quantitative conclusions.

It is evident that this study will benefit significantly by future iterations
of the _Gaia_ catalogue that will provide improved astrometry for a larger
number of stars. Next-generation surveys such as the _Vera C. Rubin Large
Synoptic Survey Telescope_ (Kessler et al., 2019) will be even more important
in identifying dimmer and less massive pulsar companions (Figure 3) as well as
optical emission from young pulsars similar to the Crab. Close astrometric
pairs — even those that are not true binary companions — can also be promising
targets for pulsar scintillation studies (Simard & Pen, 2018; Main et al.,
2018, 2020). Finally, an extension of the method presented here combined with
improved astrometry will also allow to identify potential future micro-lensing
events (Dai et al., 2015) and stars ejected during SNe.

Despite the current importance of optical astrometry in constraining the
frequency of binary pulsars, our simulation suggest that pulsar timing remains
the most sensitive probe of multiplicity. Until recently, regular monitoring
of all known pulsars was impractical due to limited telescope availability and
resources. The advent of large-scale monitoring projects such as the
CHIME/pulsar project (Ng, 2018; Ng et al., 2020) and its southern counterpart
HIRAX (Newburgh et al., 2016), MeerTime (Bailes et al., 2016, 2020; Johnston
et al., 2020) and eventually the Square Kilometre Array (Tauris et al., 2015a;
Antoniadis et al., 2015) will therefore lead to significantly more stringent
constraints on the young pulsar multiplicity fraction in the near future.

## Data availability

The python/jupyter notebook to reproduce the results of this article is
available at https://dx.doi.org/10.5281/zenodo.4075042.

## Acknowledgements

Support was provided by the Hellenic Foundation for Research and Innovation
(HFRI) and the Stavros Niarchos Foundation (SNF) under grant agreement No.
72-1/11.8.2020. I am grateful to the referee for their constructive report. I
am also grateful to Philipp Podsiadlowski, Paulo Freire, Michael Kramer and
Vivek Venkatraman Krishnan for discussions. This work relies on data from the
European Space Agency (ESA) mission _Gaia_ (https://www.cosmos.esa.int/gaia),
processed by the _Gaia_ Data Processing and Analysis Consortium (DPAC,
https://www.cosmos.esa.int/web/gaia/dpac/consortium). This research made use
of NumPy (Harris et al., 2020), Matplotlib (Hunter, 2007) and Astropy
(http://www.astropy.org), a community-developed core Python package for
Astronomy (Astropy Collaboration et al., 2013, 2018) and of NASA’s
Astrophysics Data System Bibliographic Services.

Table 1: Catalogued and derived properties of confirmed and candidate cross-
matches between the _Gaia_ DR2 and the ATNF pulsar catalogues. A complete
catalogue of all _Gaia_ sources within 20″ of ATNF pulsars, including more
columns is available online (see Appendix).

Known Binaries |
---|---
Name | $\theta$ | $\sigma_{\rm pos}$ | $\hat{\pi}_{\rm GAIA}$ | $\hat{\pi}_{\rm r}$ | $\mu_{\alpha}$ | $\mu_{\delta}$ | $\mu_{\alpha,r}$ | $\mu_{\delta,r}$ | $P_{s}$ |  Pb | DM |  mg |  Passoc. | d |  Mg
| arcsec | mas |  mas yr-1 | s | d |  pc cm-3 |  |  | kpc |
J0045$-$7319 | 0.5149 | 0.2689 | 0.04(6) | - | 0.30(11) | $-0.9(1)$ | - | - | 0.926 | 51.169 | 105.4 | 16.22 | 0.90 | $62.1^{+1.9}_{-1.9}$ | $-5.30^{+0.06}_{-0.07}$
J0337+1715 | 0.0064 | 0.2501 | 0.73(25) | - | 4.8(5) | $-4.4(4)$ | - | - | 0.003 | 1.629 | 21.3 | 18.08 | 0.99 | $1.49^{+0.66}_{-0.47}$ | $6.88^{+0.79}_{-0.82}$
J0348+0432 | 0.0018 | 0.2519 | $-1.9(12)$ | - | 3.1(20) | $-0.1(1.4)$ | 4.04(16) | 3.5(6) | 0.039 | 0.102 | 40.5 | 20.64 | 0.99 | $2.49^{+1.17}_{-1.01}$ | $7.86^{+0.84}_{-1.13}$
J0437$-$4715 | 0.3286 | 0.2506 | 8.32(68) | 6.37(9) | 122.8(12) | $-71.2(1.7)$ | 121.438(2) | $-71.475(2)$ | 0.006 | 5.741 | 2.6 | 20.41 | 0.99 | $0.157^{+0.003}_{-0.004}$ | $14.43^{+0.04}_{-0.06}$
J1012+5307 | 0.0165 | 0.2501 | 1.32(41) | 0.71(17) | 2.97(52) | $-26.94(63)$ | 2.609(8) | $-25.482(11)$ | 0.005 | 0.605 | 9.0 | 19.63 | 0.99 | $1.73^{+1.62}_{-0.58}$ | $8.40^{+1.43}_{-0.89}$
J1023+0038 | 0.0042 | 0.2500 | 0.73(14) | 0.731(22) | 4.75(14) | $-17.35(14)$ | 4.76(3) | $-17.34(4)$ | 0.002 | 0.198 | 14.3 | 16.27 | 0.99 | $1.371^{+0.072}_{-0.065}$ | $5.51^{+0.11}_{-0.10}$
J1024$-$0719 | 0.0765 | 0.2503 | 0.53(43) | 0.8(3) | $-35.52(64)$ | $-47.93(66)$ | - | - | - | 0.005 | 6.5 | 19.18 | 0.99 | $3.4^{+4.6}_{-2.0}$ | $6.41^{+1.86}_{-1.99}$
J1048+2339 | 0.0103 | 0.2511 | 0.96(80) | - | $-16.3(10)$ | $-11.70(13)$ | $-18.7$ | $-9.4$ | 0.005 | 0.251 | 16.7 | 19.65 | 0.99 | $2.1^{+1.2}_{-1.0}$ | $7.99^{+0.97}_{-1.45}$
J1227$-$4853 | 0.0618 | 0.2500 | 0.62(17) | - | $-18.7(2)$ | 7.4(1) | - | - | 0.002 | 0.288 | 43.4 | 18.08 | 0.99 | $2.0^{+2.2}_{-0.7}$ | $6.41^{+1.69}_{-1.04}$
J1311$-$3430∗ | 0.0416 | 2.89 | - | - | - | - | - | - | 0.002 | 0.065 | 37.84 | 20.52 | - | $2.43^{+0.48}_{-0.48}$ | $8.54^{+0.41}_{-0.50}$
B1259$-$63 | 0.0590 | 0.2500 | 0.42(3) | - | $-6.986(43)$ | $-0.416(44)$ | $-6.6(18)$ | $-4.4(14)$ | 0.048 | 1236.725 | 146.7 | 9.63 | 0.96 | $2.42^{+0.33}_{-0.26}$ | $-7.05^{+0.94}_{-0.77}$
J1417$-$4402 | 0.3818 | 0.2805 | 0.22(7) | - | $-4.7(1)$ | $-5.1(1)$ | - | - | 0.003 | 5.374 | 55.0 | 15.79 | 0.99 | $4.6^{+3.1}_{-1.5}$ | $2.25^{+1.26}_{-0.93}$
J1431$-$4715 | 0.0485 | 0.2500 | 0.64(16) | - | $-12.01(33)$ | $-14.50(26)$ | $-7(3)$ | $-8(4)$ | 0.002 | 0.450 | 59.4 | 17.75 | 0.99 | $2.0^{+2.1}_{-0.7}$ | $6.13^{+1.68}_{-1.03}$
J1723$-$2837 | 0.3122 | 0.2500 | 1.077(54) | - | $-11.71(8)$ | $-23.99(6)$ | - | - | 0.002 | 0.615 | 19.7 | 15.55 | 0.93 | $0.94^{+0.086}_{-0.073}$ | $4.19^{+0.20}_{-0.18}$
J1810+1744 | 0.0689 | 0.2519 | 1.04(70) | - | 6.4(18) | $-7.2(21)$ | - | - | 0.002 | 0.150 | 39.7 | 20.08 | 0.99 | $2.3^{+1.4}_{-1.2}$ | $7.76^{+1.02}_{-1.70}$
J1816+4510 | 0.0016 | 0.2501 | 0.22(15) | - | $-0.16(30)$ | $-4.41(33)$ | 5.3(8) | $-3(1)$ | 0.003 | 0.361 | 38.9 | 18.22 | 0.99 | $4.2^{+2.2}_{-1.6}$ | $5.03^{+0.92}_{-1.056}$
J1957+2516 | 0.0066 | 0.2512 | 0.69(86) | - | $-5.7(11)$ | $-8.8(15)$ | - | - | 0.004 | 0.238 | 44.1 | 20.30 | 0.96 | $2.6^{+1.5}_{-1.3}$ | $5.47^{+1.96}_{-2.59}$
B1957+20 | 0.1016 | 0.2509 | $-0.6(16)$ | - | $-19.1(12)$ | $-23.5(19)$ | $-16.0(5)$ | $-25.8(6)$ | 0.002 | 0.382 | 29.1 | 20.30 | 0.96 | $1.9^{+1.0}_{-0.9}$ | $7.88^{+1.06}_{-1.56}$
J2032+4127 | 0.0480 | 0.2500 | 0.69(3) | - | $-2.991(48)$ | $-0.742(55)$ | - | - | 0.143 | 16835.000 | 114.7 | 11.36 | 0.99 | $1.45^{+0.13}_{-0.11}$ | $-3.19^{+1.51}_{-1.40}$
J2129$-$0429∗ | 1.388 | 0.2500 | 0.424(88) | - | 12.38(15) | 10.18(15) | - | - | 0.007 | 0.635 | 16.9 | 16.83 | - | $2.60^{+1.48}_{-0.71}$ | $4.69^{+0.98}_{-0.70}$
J2215+5135 | 0.0887 | 0.2502 | 0.27(37) | - | 0.3(5) | 1.9(6) | 170(22) | 82(24) | 0.003 | 0.173 | 69.2 | 19.24 | 0.98 | $2.9^{+1.5}_{-1.2}$ | $6.46^{+1.17}_{-1.35}$
J2339$-$0533 | 0.1247 | 0.2505 | 0.75(26) | - | 4.1(5) | $-10.3(3)$ | 11(4) | $-29(10)$ | 0.003 | 0.193 | - | 18.97 | 0.99 | $1.35^{+0.55}_{-0.40}$ | $8.27^{+0.73}_{-0.76}$
Single Pulsars |
B0531+21 | 0.0268 | 0.2500 | 0.27(12) | - | $-11.82(22)$ | 2.65(17) | $-14.7(8)$ | 2.0(8) | 0.033 | - | 56.8 | 16.43 | 0.99 | $4.0^{+3.6}_{-1.6}$ | $2.14^{+1.64}_{-1.16}$
B0540$-$69 | 0.0163 | 0.2503 | $-0.53(14)$ | - | 2.8(28) | 2.1(32) | - | - | 0.051 | - | 146.5 | 20.31 | 0.93 | $62.1^{+1.89}_{-1.89}$ | $-6.30^{+0.06}_{-0.07}$
Small angular separations but likely not associated |
B1953+29 | 0.1401 | 0.2501 | 0.60(19) | - | $-3.1(3)$ | $-7.96(32)$ | - | - | 0.006 | 117.349 | 104.5 | 18.71 | 0.97 | $2.3^{+2.9}_{-1.0}$ | $4.54^{+2.70}_{-1.91}$
J1435$-$6100 | 0.3993 | 0.2500 | $-0.26(35)$ | - | $-5.28(33)$ | $-2.34(45)$ | - | - | 0.009 | 1.355 | 113.7 | 18.94 | 0.95 | $3.3^{+1.5}_{-1.2}$ | $-2.70^{+4.92}_{-4.45}$
Candidates |
J0534$-$6703 | 0.5130 | 0.2872 | 0.14(18) | - | 1.7(5) | 0.3(5) | - | - | 1.818 | - | 94.7 | 18.90 | 0.94 | $49.97^{+1.13}_{-1.13}$ | $-0.12^{+0.05}_{-0.05}$
J1624$-$4411 | 0.3068 | 0.2514 | 1.14(59) | - | $-2.6(11)$ | $-8.6(8)$ | - | - | 0.233 | - | 139.4 | 19.93 | 0.94 | $2.7^{+4.6}_{-1.8}$ | $6.32^{+4.63}_{-3.38}$
J1638$-$4608 | 0.1407 | 0.2553 | - | - | - | - | - | - | 0.278 | - | 423.1 | 19.38 | 0.93 | - | -
J1838$-$0549 | 0.5015 | 0.2536 | 0.65(19) | - | 1.55(26) | 1.62(23) | - | - | 0.235 | - | 276.6 | 17.71 | 0.98 | $2.0^{+2.5}_{-0.8}$ | $1.73^{+2.84}_{-1.60}$
J1903$-$0258 | 0.4002 | 0.2505 | 0.95(30) | - | $-1.7(6)$ | 3.40(46) | - | - | 0.301 | - | 113.0 | 18.93 | 0.96 | $1.7^{+3.2}_{-0.8}$ | $7.55^{+5.49}_{-1.53}$
J1958+2846 | 0.3912 | 0.2537 | 0.59(34) | - | $-4.0(5)$ | $-6.1(6)$ | - | - | 0.290 | - | - | 19.36 | 0.98 | $2.0^{+1.0}_{-0.8}$ | $5.34^{+1.45}_{-1.71}$
J2027+4557 | 0.2904 | 0.2500 | 0.52(3) | - | 2.12(7) | $-2.06(6)$ | - | - | 1.100 | - | 229.6 | 15.73 | 0.98 | $1.96^{+0.25}_{-0.20}$ | $1.60^{+0.32}_{-0.56}$
J1852+0040 | 0.5067 | 0.2571 | 2.1(12) | - | -0.9(17) | -4.9 | - | - | 0.105 | - | - | 20.23 | 0.98 | $2.93^{+4.83}_{-2.20}$ | $3.23^{+4.78}_{-4.14}$

(∗) Sources identified only after visual inspection

##  Appendix A Description of columns in online catalogue

The full catalogue of sources withing 20″ of ATNF pulsars is available on
VizieR (http://cdsarc.u-strasbg.fr/viz-bin/). The table below provides a
summary of the information available in the catalogue.

Table 2: Catalogue Format

Name | Format | Description
---|---|---
angDist | float64 | angular Separation from the pulsar (in degrees)
id | int64 | pulsar identification number
name | <U12 | pulsar name
survey | <U48 | survey that discovered the pulsar as defined in psrcat
BinComp | <U6 | companion type as defined in psrcat
Type | int64 | pulsar type as defined in psrcat
raj | float64 | pulsar right ascension at PosEpoch (in degrees)
rajerr | float64 | error in pulsar right ascension at PosEpoch (in degrees)
decj | float64 | pulsar right ascension at PosEpoch (in degrees)
decjerr | float64 | error in pulsar right ascension at PosEpoch (in degrees)
pmra$\\_$radio | float64 | radio timing proper motion in RA (mas/yr)
pmraerr | float64 | error of radio timing proper motion in RA (mas/yr)
pmdec_radio | float64 | radio timing proper motion in DEC (mas/yr)
pmdecerr | float64 | error of radio timing proper motion in DEC (mas/yr)
px | float64 | radio timing parallax (mas)
pxerr | float64 | error of radio timing parallax (mas)
posepoch | float64 | position epoch of the radio timing solution
p0 | float64 | spin period (s)
p0err | float64 | error of spin period (s)
p1 | float64 | spin-period derivative
p1err | float64 | error of spin-period derivative
dm | float64 | dispersion measure (pc/cm3)
dmerr | float64 | error of dispersion measure (pc/cm3)
dist | float64 | DM distance estimate (see text)
pb | float64 | orbital period (days)
pberr | float64 | error of orbital period (days)
raj_now | float64 | RA of source at posepoch
decj_now | float64 | DEC of source at posepoch
ra_epoch2000 | float64 | RA of source at J2000
dec_epoch2000 | float64 | DEC of source at J2000
source_id | int64 | GAIA source ID
ra | float64 | RA of source at J2015.5
ra_error | float64 | RA uncertainty of source at J2000
dec | float64 | DEC of source at J2000
dec_error | float64 | DEC uncertainty of source at J2000
parallax | float64 |  _Gaia_ parallax (mas)
parallax$\\_$error | float64 |  _Gaia_ parallax error (mas)
pmra | float64 |  _Gaia_ proper motion in RA (mas/yr)
pmra_error | float64 | error of _Gaia_ proper motion in RA (mas/yr)
pmdec | float64 |  _Gaia_ proper motion in DEC (mas/yr)
pmdec_error | float64 | error of _Gaia_ proper motion in DEC (mas/yr)
phot_g_mean_mag | float64 |  _Gaia_ mean magnitude
phot_bp_mean_mag | float64 |  _Gaia_ mean magnitude in BP band
phot_rp_mean_mag | float64 |  _Gaia_ mean magnitude in RP band
bp_rp | float64 |  _Gaia_ BP-RP mean color
poserror | float64 | position error of the source at posepoch (arcsec)
poserror_sys | float64 | position error of the source including systematics at posepoch (arcsec)
angDist | float64 | angular separation from the nearest pulsar (arcsec)
TrueAngDist | float64 | angular separation from the nearest pulsar at posepoch (arcsec)
Pass | float64 | probability of Association (1 - Probability of chance coincidence)
g_abs∗ | float64 | Absolute G magnitude corrected for extinction
b_r_abs∗ | float64 |  $B-R$ color corrected for extinction
distance∗ | float64 | Median distance (kpc)
distance_min∗ | float64 | 16% lower bound on distance (kpc)
distance_max∗ | float64 | 68% upper bound on distance (kpc)
dust | float64 | median E(B-V) extinction
dust_min | float64 | 16% lower bound on extinction
dust_max | float64 | 68% upper bound on extinction

∗ Calculated only for the sources in Table 1

## References

  * Abadie et al. (2010) Abadie J., et al., 2010, Classical and Quantum Gravity, 27, 173001
  * Abbott et al. (2017) Abbott B. P., et al., 2017, Physical Review Letters, 119, 161101
  * Abbott et al. (2020) Abbott R., et al., 2020, arXiv e-prints, 2010, arXiv:2010.14533
  * Antoniadis et al. (2011) Antoniadis J., Bassa C. G., Wex N., Kramer M., Napiwotzki R., 2011, Monthly Notices of the Royal Astronomical Society, 412, 580
  * Antoniadis et al. (2012) Antoniadis J., van Kerkwijk M. H., Koester D., Freire P. C. C., Wex N., Tauris T. M., Kramer M., Bassa C. G., 2012, Monthly Notices of the Royal Astronomical Society, 423, 3316
  * Antoniadis et al. (2013) Antoniadis J., et al., 2013, Science, 340, 448
  * Antoniadis et al. (2015) Antoniadis J., et al., 2015, Advancing Astrophysics with the Square Kilometre Array (AASKA14), p. 157
  * Antoniadis et al. (2016) Antoniadis J., Tauris T. M., Ozel F., Barr E., Champion D. J., Freire P. C. C., 2016, arXiv e-prints, 1605, arXiv:1605.01665
  * Arzoumanian et al. (2018) Arzoumanian Z., et al., 2018, The Astrophysical Journal Supplement Series, 235, 37
  * Arzoumanian et al. (2020) Arzoumanian Z., et al., 2020, arXiv e-prints, 2009, arXiv:2009.04496
  * Astraatmadja & Bailer-Jones (2016) Astraatmadja T. L., Bailer-Jones C. A. L., 2016, The Astrophysical Journal, 832, 137
  * Astropy Collaboration et al. (2013) Astropy Collaboration et al., 2013, Astronomy and Astrophysics, 558, A33
  * Astropy Collaboration et al. (2018) Astropy Collaboration et al., 2018, The Astronomical Journal, 156, 123
  * Bailer-Jones (2015) Bailer-Jones C. A. L., 2015, PASP, 127, 994
  * Bailer-Jones et al. (2018) Bailer-Jones C. A. L., Rybizki J., Fouesneau M., Mantelet G., Andrae R., 2018, The Astronomical Journal, 156, 58
  * Bailes (1989) Bailes M., 1989, The Astrophysical Journal, 342, 917
  * Bailes et al. (2016) Bailes M., et al., 2016, arXiv:1803.07424, p. 11
  * Bailes et al. (2020) Bailes M., et al., 2020, Publications of the Astronomical Society of Australia, 37, e028
  * Bassa et al. (2016) Bassa C. G., et al., 2016, Monthly Notices of the Royal Astronomical Society, 460, 2207
  * Boriakoff et al. (1983) Boriakoff V., Buccheri R., Fauci F., 1983, Nature, 304, 417
  * Boriakoff et al. (1996) Boriakoff V., Beskin G., Dossa D., Fauci F., Oke J. B., Tella L., 1996, in Johnston S., Walker M. A., Bailes M., eds, Astronomical Society of the Pacific Conference Series Vol. 105, IAU Colloq. 160: Pulsars: Problems and Progress. p. 303
  * Chaty (2013) Chaty S., 2013, Advances in Space Research, 52, 2132
  * Chernyakova et al. (2014) Chernyakova M., et al., 2014, Monthly Notices of the Royal Astronomical Society, 439, 432
  * Dai et al. (2015) Dai S., Smith M. C., Lin M. X., Yue Y. L., Hobbs G., Xu R. X., 2015, The Astrophysical Journal, 802, 120
  * Deller et al. (2019) Deller A. T., et al., 2019, The Astrophysical Journal, 875, 100
  * Desvignes et al. (2016) Desvignes G., et al., 2016, Monthly Notices of the Royal Astronomical Society, 458, 3341
  * Diehl et al. (2006) Diehl R., et al., 2006, Nature, 439, 45
  * Ding et al. (2020) Ding H., Deller A. T., Freire P., Kaplan D. L., Lazio T. J. W., Shannon R., Stappers B., 2020, The Astrophysical Journal, 896, 85
  * Ferdman et al. (2020) Ferdman R. D., et al., 2020, Nature, 583, 211
  * Gaia Collaboration et al. (2016) Gaia Collaboration et al., 2016, Astronomy and Astrophysics, 595, A1
  * Gonzalez et al. (2011) Gonzalez M. E., et al., 2011, The Astrophysical Journal, 743, 102
  * Graczyk et al. (2013) Graczyk D., et al., 2013, The Astrophysical Journal, 780, 59
  * Green (2018) Green G. M., 2018, Journal of Open Source Software, 3, 695
  * Green et al. (2014) Green G. M., et al., 2014, The Astrophysical Journal, 783, 114
  * Green et al. (2019) Green G. M., Schlafly E., Zucker C., Speagle J. S., Finkbeiner D., 2019, The Astrophysical Journal, 887, 93
  * Halpern & Gotthelf (2010) Halpern J. P., Gotthelf E. V., 2010, The Astrophysical Journal, 709, 436
  * Harris et al. (2020) Harris C. R., et al., 2020, Nature, 585, 357–362
  * Hobbs et al. (2005) Hobbs G., Lorimer D. R., Lyne A. G., Kramer M., 2005, Monthly Notices of the Royal Astronomical Society, 360, 974
  * Hunter (2007) Hunter J. D., 2007, Computing in Science Engineering, 9, 90
  * Igoshev & Perets (2019) Igoshev A. P., Perets H. B., 2019, Monthly Notices of the Royal Astronomical Society, 486, 4098
  * Illarionov & Sunyaev (1975) Illarionov A. F., Sunyaev R. A., 1975, Astronomy and Astrophysics, 39, 185
  * Ivanova et al. (2013) Ivanova N., et al., 2013, Astronomy and Astrophysics Review, 21, 59
  * Jacoby et al. (2006) Jacoby B. A., Chakrabarty D., van Kerkwijk M. H., Kulkarni S. R., Kaplan D. L., 2006, The Astrophysical Journal Letters, 640, L183
  * Janka (2013) Janka H.-T., 2013, Monthly Notices of the Royal Astronomical Society, 434, 1355
  * Janssen et al. (2009) Janssen G. H., Stappers B. W., Braun R., van Straten W., Edwards R. T., Rubio-Herrera E., van Leeuwen J., Weltevrede P., 2009, Astronomy and Astrophysics, 498, 223
  * Jennings et al. (2018) Jennings R. J., Kaplan D. L., Chatterjee S., Cordes J. M., Deller A. T., 2018, The Astrophysical Journal, 864, 26
  * Johnston et al. (1992) Johnston S., Manchester R. N., Lyne A. G., Bailes M., Kaspi V. M., Qiao G., D’Amico N., 1992, The Astrophysical Journal Letters, 387, L37
  * Johnston et al. (1994) Johnston S., Manchester R. N., Lyne A. G., Nicastro L., Spyromilio J., 1994, Monthly Notices of the Royal Astronomical Society, 268, 430
  * Johnston et al. (2005) Johnston S., Ball L., Wang N., Manchester R. N., 2005, Monthly Notices of the Royal Astronomical Society, 358, 1069
  * Johnston et al. (2020) Johnston S., et al., 2020, Monthly Notices of the Royal Astronomical Society, 493, 3608
  * Kalogera et al. (2004) Kalogera V., et al., 2004, The Astrophysical Journal Letters, 601, L179
  * Kaplan et al. (2016) Kaplan D. L., et al., 2016, The Astrophysical Journal, 826, 86
  * Kaspi et al. (1996a) Kaspi V. M., Bailes M., Manchester R. N., Stappers B. W., Bell J. F., 1996a, Nature, 381, 584
  * Kaspi et al. (1996b) Kaspi V. M., Tauris T. M., Manchester R. N., 1996b, The Astrophysical Journal, 459, 717
  * Keane & Kramer (2008) Keane E. F., Kramer M., 2008, Monthly Notices of the Royal Astronomical Society, 391, 2009
  * Kerr et al. (2016) Kerr M., Hobbs G., Johnston S., Shannon R. M., 2016, Monthly Notices of the Royal Astronomical Society, 455, 1845
  * Kessler et al. (2019) Kessler R., et al., 2019, arXiv:1903.11756 [astro-ph]
  * Kippenhahn et al. (2012) Kippenhahn R., Weigert A., Weiss A., 2012, Stellar Structure and Evolution, second edn. Astronomy and Astrophysics Library, Springer-Verlag, Berlin Heidelberg, doi:10.1007/978-3-642-30304-3
  * Lindegren et al. (2018) Lindegren L., et al., 2018, Astronomy & Astrophysics, 616, A2
  * Lorimer et al. (2006) Lorimer D. R., et al., 2006, Monthly Notices of the Royal Astronomical Society, 372, 777
  * Luri et al. (2018) Luri X., et al., 2018, Astronomy & Astrophysics, 616, A9
  * Lutovinov et al. (2013) Lutovinov A. A., Revnivtsev M. G., Tsygankov S. S., Krivonos R. A., 2013, Monthly Notices of the Royal Astronomical Society, 431, 327
  * Lutz & Kelker (1973) Lutz T. E., Kelker D. H., 1973, PASP, 85, 573
  * Luyten (1922) Luyten W. J., 1922, Lick Observatory Bulletin, 10, 135
  * Lyne et al. (2015) Lyne A. G., Stappers B. W., Keith M. J., Ray P. S., Kerr M., Camilo F., Johnson T. J., 2015, Monthly Notices of the Royal Astronomical Society, 451, 581
  * Main et al. (2018) Main R., et al., 2018, Nature, 557, 522
  * Main et al. (2020) Main R. A., et al., 2020, arXiv e-prints, 2009, arXiv:2009.10707
  * Manchester et al. (2005) Manchester R. N., Hobbs G. B., Teoh A., Hobbs M., 2005, The Astronomical Journal, 129, 1993
  * Manchester et al. (2006) Manchester R. N., Fan G., Lyne A. G., Kaspi V. M., Crawford F., 2006, The Astrophysical Journal, 649, 235
  * Mignani et al. (2014) Mignani R. P., et al., 2014, Monthly Notices of the Royal Astronomical Society, 443, 2223
  * Mignard et al. (2018) Mignard F., et al., 2018, Astronomy & Astrophysics, 616, A14
  * Mingarelli et al. (2018) Mingarelli C. M. F., Anderson L., Bedell M., Spergel D. N., 2018, arXiv e-prints, 1812, arXiv:1812.06262
  * Newburgh et al. (2016) Newburgh L. B., et al., 2016, arXiv:1607.02059, 9906, 99065X
  * Ng (2018) Ng C., 2018,  arXiv:1711.02104, 337, 179
  * Ng et al. (2020) Ng C., et al., 2020, Monthly Notices of the Royal Astronomical Society, 496, 2836
  * Parthasarathy et al. (2019) Parthasarathy A., et al., 2019, Monthly Notices of the Royal Astronomical Society, 489, 3810
  * Pelisoli & Vos (2019) Pelisoli I., Vos J., 2019, Monthly Notices of the Royal Astronomical Society, 488, 2892
  * Pelisoli et al. (2019a) Pelisoli I., Bell K. J., Kepler S. O., Koester D., 2019a, Monthly Notices of the Royal Astronomical Society, 482, 3831
  * Pelisoli et al. (2019b) Pelisoli I., Bell K. J., Kepler S. O., Koester D., 2019b, Monthly Notices of the Royal Astronomical Society, 482, 3831
  * Pietrzyński et al. (2013) Pietrzyński G., et al., 2013, Nature, 495, 76
  * Podsiadlowski et al. (2002) Podsiadlowski P., Rappaport S., Pfahl E. D., 2002, The Astrophysical Journal, 565, 1107
  * Podsiadlowski et al. (2004) Podsiadlowski P., Langer N., Poelarends A. J. T., Rappaport S., Heger A., Pfahl E., 2004, The Astrophysical Journal, 612, 1044
  * Pol et al. (2020) Pol N., McLaughlin M., Lorimer D. R., 2020, Research Notes of the AAS, 4, 22
  * Portegies Zwart & Yungelson (1999) Portegies Zwart S. F., Yungelson L. R., 1999, Monthly Notices of the Royal Astronomical Society, 309, 26
  * Ray et al. (2011) Ray P. S., et al., 2011, The Astrophysical Journal Supplement Series, 194, 17
  * Reynolds et al. (2007) Reynolds M. T., Callanan P. J., Fruchter A. S., Torres M. a. P., Beer M. E., Gibbons R. A., 2007, Monthly Notices of the Royal Astronomical Society, 379, 1117
  * Sana et al. (2012) Sana H., et al., 2012, Science, 337, 444
  * Schneider et al. (2020) Schneider F. R. N., Podsiadlowski P., Müller B., 2020, arXiv e-prints, 2008, arXiv:2008.08599
  * Simard & Pen (2018) Simard D., Pen U.-L., 2018, Monthly Notices of the Royal Astronomical Society, 478, 983
  * Strader et al. (2019) Strader J., et al., 2019, The Astrophysical Journal, 872, 42
  * Tauris et al. (2011) Tauris T. M., Langer N., Kramer M., 2011, Monthly Notices of the Royal Astronomical Society, 416, 2130
  * Tauris et al. (2012) Tauris T. M., Langer N., Kramer M., 2012, Monthly Notices of the Royal Astronomical Society, Volume 425, Issue 3, pp. 1601-1627., 425, 1601
  * Tauris et al. (2013) Tauris T. M., Langer N., Moriya T. J., Podsiadlowski P., Yoon S.-C., Blinnikov S. I., 2013, The Astrophysical Journal Letters, 778, L23
  * Tauris et al. (2015a) Tauris T. M., et al., 2015a, Advancing Astrophysics with the Square Kilometre Array (AASKA14), p. 39
  * Tauris et al. (2015b) Tauris T. M., Langer N., Podsiadlowski P., 2015b, Monthly Notices of the Royal Astronomical Society, 451, 2123
  * Tauris et al. (2017) Tauris T. M., et al., 2017, ApJ, 846, 170
  * Walter et al. (2015) Walter R., Lutovinov A. A., Bozzo E., Tsygankov S. S., 2015, Astronomy and Astrophysics Review, 23, 2
  * van Kerkwijk et al. (2005) van Kerkwijk M. H., Bassa C. G., Jacoby B. A., Jonker P. G., 2005, in Rasio F. A., Stairs I. H., eds, Astronomical Society of the Pacific Conference Series Vol. 328, Binary Radio Pulsars. p. 357 (arXiv:astro-ph/0405283)
  * van Kerkwijk et al. (2011) van Kerkwijk M. H., Breton R. P., Kulkarni S. R., 2011, The Astrophysical Journal, 728, 95