# 4FGL J1120.0–2204: A Unique Gamma-ray Bright Neutron Star Binary with an
Extremely Low Mass Proto-White Dwarf

Samuel J. Swihart  National Research Council Research Associate, National
Academy of Sciences, Washington, DC 20001, USA,
resident at Naval Research Laboratory, Washington, DC 20375, USA  Jay Strader
Center for Data Intensive and Time Domain Astronomy, Department of Physics and
Astronomy,
Michigan State University, East Lansing, MI 48824, USA  Elias Aydi  Center for
Data Intensive and Time Domain Astronomy, Department of Physics and Astronomy,
Michigan State University, East Lansing, MI 48824, USA  Laura Chomiuk  Center
for Data Intensive and Time Domain Astronomy, Department of Physics and
Astronomy,
Michigan State University, East Lansing, MI 48824, USA  Kristen C. Dage
Department of Physics, McGill University, 3600 University Street, Montréal, QC
H3A 2T8, Canada  McGill Space Institute, McGill University, 3550 University
Street, Montréal, QC H3A 2A7, Canada  Adam Kawash  Center for Data Intensive
and Time Domain Astronomy, Department of Physics and Astronomy,
Michigan State University, East Lansing, MI 48824, USA  Kirill V. Sokolovsky
Center for Data Intensive and Time Domain Astronomy, Department of Physics and
Astronomy,
Michigan State University, East Lansing, MI 48824, USA  Elizabeth C. Ferrara
Department of Astronomy, University of Maryland, College Park, MD, 20742, USA
Center for Exploration and Space Studies (CRESST), NASA/GSFC, Greenbelt, MD
20771, USA  NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA

###### Abstract

We have discovered a new X-ray emitting compact binary that is the likely
counterpart to the unassociated _Fermi_ -LAT GeV $\gamma$-ray source 4FGL
J1120.0–2204, the second brightest _Fermi_ source that still remains formally
unidentified. Using optical spectroscopy with the SOAR telescope, we have
identified a warm ($T_{\textrm{eff}}\sim 8500$ K) companion in a 15.1-hr orbit
around an unseen primary, which is likely a yet-undiscovered millisecond
pulsar. A precise _Gaia_ parallax shows the binary is nearby, at a distance of
only $\sim 820$ pc. Unlike the typical “spider” or white dwarf secondaries in
short-period millisecond pulsar binaries, our observations suggest the $\sim
0.17\,M_{\odot}$ companion is in an intermediate stage, contracting on the way
to becoming an extremely low-mass helium white dwarf (a “pre-ELM” white
dwarf). Although the companion is apparently unique among confirmed or
candidate millisecond pulsar binaries, we use binary evolution models to show
that in $\sim 2$ Gyr, the properties of the binary will match those of several
millisecond pulsar–white dwarf binaries with very short ($<1$ d) orbital
periods. This makes 4FGL J1120.0–2204 the first system discovered in the
penultimate phase of the millisecond pulsar recycling process.

##  1 Introduction

Millisecond pulsars (MSPs) are neutron stars that have been spun-up (recycled)
to very rapid spin periods via accretion from a binary companion (Alpar et
al., 1982). Despite the fact that this recycling process should be long-lived
(Tauris & Savonije, 1999), most MSPs in the field of the Galaxy have completed
the spin-up process, such that accretion has ceased, and the neutron star is
left with a low-mass, helium white dwarf as a companion. This process is in
contrast to MSPs in globular clusters, which likely acquired their current
binary companion(s) via dynamical exchange interactions (e.g., Hui et al.,
2010; Bahramian et al., 2013; Ye et al., 2019).

Nearly all MSPs emit $\gamma$-rays (Abdo et al., 2013), and multiwavelength
follow-up observations of previously unidentified _Fermi_ -LAT GeV
$\gamma$-ray sources have resulted in an enormous increase in the number of
known MSPs in the Galactic field (e.g., Ray et al., 2012), particularly those
in compact binaries that have non-degenerate, Hydrogen-rich companions. These
binary systems are commonly referred to as “spiders,” due to the evaporative
effects that the MSP has on its companion, and are further subdivided into
“black widows” with ultra-light companions ($M_{c}\lesssim 0.05\,M_{\odot}$),
and “redbacks” with more massive companions ($M_{c}\gtrsim 0.1\,M_{\odot}$)
(Roberts, 2013; Strader et al., 2019).

Prior to the launch of _Fermi_ , most of these MSPs remained elusive: the
energetic pulsar wind leads to substantial mass loss from the non-degenerate
companion, eclipsing the radio emission and making it challenging to discover
these systems in the short-timescale observations of all-sky radio surveys,
especially at low observing frequencies (e.g., Archibald et al., 2013).
However, this radio eclipsing material does not affect the GeV emission,
making follow-up of _Fermi_ sources a successful method for identifying new
MSP binaries with companions other than He white dwarfs.

One approach that has been used successfully to identify MSP counterparts in
the unassociated _Fermi_ sources is to search for X-ray/optical matches inside
the LAT error ellipses. X-rays in these binary systems are often produced by
an intrabinary shock at the interface between the pulsar and companion winds
(e.g., Gentile et al., 2014; Romani & Sanchez, 2016; Wadiasingh et al., 2017),
while the non-degenerate stellar companions typically display optical periodic
variability due to tidal distortion of the secondary and/or irradiative
heating of the tidally-locked companion surface (e.g., McConnell et al., 2015;
Sanchez & Romani, 2017; Cho et al., 2018; Swihart et al., 2018; Draghis et
al., 2019; Swihart et al., 2019; Yap et al., 2019; Swihart et al., 2021).

Although the number of spider MSPs has increased dramatically in recent years,
binary evolution models predict these systems will not end up being the MSP–He
white dwarf binaries that make up the bulk of the MSP binary population (e.g.,
Benvenuto et al., 2012; Chen et al., 2013). In contrast to redbacks in
particular, systems with companions in the late stages of becoming a He white
dwarf do not fill significant fractions of their Roche lobe since most of the
companion envelope has either been accreted or ejected during MSP spin-up
(e.g., Podsiadlowski et al., 2002; Postnov & Yungelson, 2014; Ablimit, 2019).
Such systems will not show substantial optical variability, and so have
remained relatively elusive.

The standard evolutionary pathway for creating MSP binaries with short-period,
extremely-low-mass (ELM, $M\lesssim 0.3\,M_{\odot}$) white dwarfs is well-
understood (e.g., Tauris & Savonije, 1999; Lin et al., 2011; Istrate et al.,
2014, 2016). However, there should be a population of systems in which the
companion is still in an intermediate stage—after the outer envelope of the
star has been lost during MSP spin-up, but before the companion fully
contracts and reaches the white dwarf cooling branch (e.g., Sarna et al.,
2001; Althaus et al., 2013).

Here we present the discovery of a new low-mass X-ray binary inside the
bright, previously unassociated _Fermi_ $\gamma$-ray source 4FGL J1120.0–2204,
and show it is likely a MSP with a warm companion in a relatively face-on
orbit. Despite some similarities with the spider class of MSP binaries, the
companion is more consistent with being a precursor to an extremely-low-mass
white dwarf, commonly referred to as a “pre-ELM” white dwarf (e.g., Maxted et
al., 2011; Rappaport et al., 2015; Pelisoli et al., 2019). This places the
system in an intermediate stage on its way to becoming a short-period MSP–He
white dwarf binary, and so is likely in the late phases of the standard
evolutionary pathway leading to the bulk of the MSP population.

(a)  (b)

Figure 1: Left: _XMM-Newton_ /EPIC X-ray image of the field showing the
positions and overlapping 95% error ellipses from the 1FGL, 2FGL, and 3FGL
catalogs corresponding to the $\gamma$-ray source 4FGL J1120.0–2204 (magenta).
The likely counterpart to the $\gamma$-ray source that is the subject of this
work is marked in blue. The fainter X-ray source visible in the 4FGL ellipse
is a galaxy unrelated to the $\gamma$-ray emission (Salvetti et al., 2017).
Right: Optical Pan-STARRS $i^{\prime}$ image zoomed-in on the 4FGL region. The
inset displays a further zoomed-in view showing the positions (90% confidence)
of the _Swift_ and _XMM_ source marked in the left panel. The optical source
coincident with the X-rays (hereafter, J1120) is the likely companion in a MSP
binary (see Sec. 3).

##  2 Observations

###  2.1 The $\gamma$-ray Source

The unassociated _Fermi_ source 4FGL J1120.0–2204 is a bright, persistent
$\gamma$-ray source that has been known since it was first catalogued as 1FGL
J1119.9–2205 based on the first eleven months of survey data. Since then, it
has appeared in each subsequent LAT catalog (2FGL J1120.0–2204, 3FGL
J1119.9–2204), and is currently listed in the 4FGL-DR2 catalog (Ballet et al.,
2020) with a detection significance of 54.9$\sigma$, making it the second
brightest _Fermi_ source that still remains formally unidentified (the
brightest is 4FGL J2112.5–3043, which has a detection significance of
56.3$\sigma$). The updated 4FGL 95% confidence error ellipse lies within the
3FGL region and is 69% smaller in area (Figure 1). The $\gamma$-ray spectrum
is highly curved, with a curvature significance of 16.0$\sigma$ for a
LogParabola model (16.3$\sigma$ for a cut-off power law), a common feature
among _Fermi_ -detected MSPs (Abdo et al., 2010). In fact, a number of
independent groups have classified this _Fermi_ source as a highly-likely MSP
based on machine learning classifications using the $\gamma$-ray data (Saz
Parkinson et al., 2016; Kaur et al., 2019; Finke et al., 2020; Kerby et al.,
2021; Bhat & Malyshev, 2021).

The 0.1–100 GeV flux, $F_{\gamma}=(1.69\pm 0.06)\times 10^{-11}$ erg
cm${}^{\textrm{-2}}$ s${}^{\textrm{-1}}$, corresponds to a luminosity of
$(1.35\pm 0.05)\times 10^{33}\,(d/0.82\,\textrm{kpc})^{\textrm{2}}$ erg
s${}^{\textrm{-1}}$, assuming the geometric distance estimate from a
significant _Gaia_ parallax measurement of the suspected optical counterpart
(Sec. 3.3.2).

###  2.2 X-rays

####  2.2.1 Swift

The field containing 4FGL J1120.0–2204 was observed with _Swift_ /XRT,
targeting the 1FGL and 2FGL regions on 27 epochs between 2010 Nov and 2013
Mar, for a total of $\sim$65 ksec. After the release of the 3FGL catalog, Hui
et al. (2015) first reported on the X-ray sources inside the overlapping 2FGL
and 3FGL regions. Their analysis found two X-ray sources detected at
$>4\sigma$ inside the 3FGL error ellipse. These sources also lie within the
4FGL region. The brightest of these sources (listed as J1120_X1 in Hui et al.
2015) is the subject of this work and, as we argue below, is the likely MSP
counterpart to the $\gamma$-ray source. Hereafter, we refer to this X-ray
source (and the corresponding optical source, see below) as J1120.

Hui et al. (2015) calculated the X-ray flux of this source by assuming the
Galactic HI column density ($N_{H}=3.9\times
10^{20}\,\textrm{cm}^{\textrm{-2}}$) (Kalberla et al., 2005) and a power-law
model with $\Gamma=2$, finding an unabsorbed 0.3–10 keV flux of $(4.7\pm
0.5)\times 10^{-14}$ erg cm${}^{\textrm{-2}}$ s${}^{\textrm{-1}}$. No spectral
or temporal analysis of these data was carried out by this group.

Kerby et al. (2021) performed a more detailed spectral analysis of this
source, finding a best fit power law index of $\Gamma=1.89^{+0.18}_{-0.17}$
and unabsorbed 0.3–10 keV flux of $(7.9^{+1.2}_{-1.0})\times 10^{-14}$ erg
cm${}^{\textrm{-2}}$ s${}^{\textrm{-1}}$. It is notable that despite using the
same datasets, these two flux estimates do not agree within the uncertainties.
Even if we account for the slightly different spectral models assumed, we find
no straightforward explanation for this discrepancy, though it does not
substantively affect any of our conclusions.

For the remainder of this work, we assume the X-ray properties derived from
the more recent _XMM_ data presented below.

####  2.2.2 XMM

This region was also observed by _XMM-Newton_ for $\sim$74 ksec in 2014 June.
Prior to the release of the 4FGL catalog, Salvetti et al. (2017) analyzed data
from all sources inside and around the 3FGL region, focusing specifically on
sources that had optical counterparts spatially coincident with the X-ray
source positions. Three of the X-ray sources they analyzed had plausible
optical counterparts, and two of these are present within the 4FGL 95%
confidence ellipse (see Figure 1; we note these are the same two sources
identified by Hui et al. (2015) from the _Swift_ data). As pointed out by
Salvetti et al. (2017), the fainter of these two X-ray sources is a known
galaxy, and is unlikely to be the source of the $\gamma$-ray emission,
especially given the highly curved $\gamma$-ray spectrum; Kerby et al. (2021)
estimate the probability that this 4FGL source is a blazar is only $\sim$3%,
supporting the inference that the fainter X-ray source is unrelated to the
$\gamma$-ray emission.

The brightest _XMM_ source in the 4FGL ellipse (Figure 1, left panel, blue
circle) is spatially coincident with an optical source whose properties are
consistent with a stellar companion to a yet-undiscovered MSP (see Sec. 3).
Salvetti et al. (2017) analyzed the _XMM_ X-ray spectrum of this source
(assuming a Galactic column density of $N_{H}=4\times 10^{20}$ cm-2), finding
$\Gamma=2.63^{+0.12}_{-0.11}$ and an unabsorbed 0.3–10 keV flux of
$(7.3^{+0.6}_{-0.5})\times 10^{-14}$ erg cm${}^{\textrm{-2}}$
s${}^{\textrm{-1}}$ (68% confidence), equivalent to a 0.5–10 keV X-ray
luminosity of $(4.1\pm 0.3)\times 10^{30}$ erg s-1 at the _Gaia_ distance of
the source.

While the X-ray fluxes of the _XMM_ and _Swift_ observations match within
their uncertainties, the photon indices do not; formally the _XMM_ spectral
fit is softer at the $>3\sigma$ level. Either value is within the range of
photon indices observed for known MSP binaries at this X-ray luminosity (Lee
et al., 2018). One possibility is that the uncertainty in one or both of the
measurements is underestimated; another is that the X-ray spectrum has changed
between the two observations. In close MSP binaries where the X-rays originate
from an intrabinary shock at the interface between the pulsar and companion
winds, the X-rays can vary on both orbital and secular timescales (e.g., Al
Noori et al. 2018). However, the X-ray fluxes of the two observations are
consistent with each other, and Salvetti et al. (2017) found no evidence for
variability in the _XMM_ light curve. We also checked to see whether the GeV
flux and spectrum changed between the _Swift_ and _XMM_ observations, but
found no evidence for a change in either quantity, and we find no significant
variability in the long-term $\gamma$-ray light curve. It is therefore likely
safe to assume that the X-ray spectral index change between the _Swift_ and
_XMM_ observations is not associated with a genuine state-transition as is
observed in the known transitional MSPs (e.g., Torres et al., 2017).

We folded the _XMM_ data on the orbital period derived in Sec. 3.2 and confirm
the source shows no orbital variability, which may be due to a combination of
a weak expected intrabinary shock and the relatively face-on orbital geometry
of the system (Sec. 3). Future X-ray observations would be useful to further
explore the X-ray spectrum and variability of J1120.

###  2.3 Optical Counterpart

The brightest X-ray source in the 4FGL region clearly matches to a bright
($G=15.5$) and relatively blue ($BP-RP=0.24$) source in _Gaia_ EDR3 (Gaia
Collaboration et al., 2021), with a ICRS position of (R.A., Dec.) =
(11:19:58.309, –22:04:56.33), which we take as the best position available. No
other optical sources are present within $14\arcsec$ (down to a limiting
magnitude of $i^{\prime}\sim 22.5$ mag). This source has a significant EDR3
parallax, 1.18 $\pm$ 0.04 mas, corresponding to a precise geometric distance
of $816.8^{+22.0}_{-24.8}$ pc (Bailer-Jones et al., 2021) after a parallax
zeropoint correction (Lindegren et al., 2021), and as discussed below (Sec.
3.3.2), has a large proper motion due to its high space velocity.

This optical source (J1120) is also present in the Pan-STARRS DR2 (Chambers et
al., 2016) and Skymapper DR2 (Onken et al., 2019) surveys. The right panel of
Figure 1 shows a Pan-STARRS $i^{\prime}$ image of the field corresponding to
4FGL J1120.0–2204 with the positions (90% confidence) of the _Swift_ and _XMM_
X-ray sources overlaid in the inset.

As discussed in Hui et al. (2015) and Salvetti et al. (2017), J1120 is also
detected in Catalina Sky Survey data (CSS; Drake et al., 2009) and by the
Gamma-Ray Burst Optical/Near-Infrared Detector (GROND, Greiner et al., 2008).
Both groups attempted to find periodic variations in these photometry but were
unsuccessful. Previewing our conclusions about this source, we suspect no
variations are present due to the relatively face-on orientation of the binary
orbit, the secondary underfilling its Roche lobe, and negligible current
heating of the companion.

This source is also present in the All-Sky Automated Survey for Supernovae
(ASAS–SN, Shappee et al., 2014; Kochanek et al., 2017), with a brightness of
$g^{\prime}=14.42$ mag. However, the ASAS–SN pixels are large ($\sim
8\arcsec$), so this measurement may be confused by the bright ($V=12.4$)
source that is only $14.5\arcsec$ away (the saturated star in the right panel
of Figure 1). Similar to the CSS and GROND datasets, no periodic variability
is present in the ASAS-SN photometry.

###  2.4 Optical Spectroscopy

Motivated by the spatial coincidence between the X-ray and optical source, we
obtained 40 usable spectra of J1120 with the Goodman Spectrograph (Clemens et
al., 2004) on the 4.1-m SOAR telescope between 2019 Apr and 2021 Jul. Nearly
all the data were obtained in 2021.

The spectra were obtained in three main configurations, depending on the
observing conditions and grating availability: a 1200 l mm-1 grating with a
resolution of 1.7 Å FWHM and wavelength coverage $\sim 5500$–6750 Å; a 2100 l
mm-1 grating with a resolution of 0.8 Å FWHM and wavelength coverage $\sim
5630$–6230 Å; and the same 2100 l mm-1 grating, instead covering $\sim
6020$–6610 Å. The spectra were taken through a 0.95″ longslit. Typical
exposure times were 1200s per spectrum, though a few were slightly shorter or
longer.

The data were reduced and optimally extracted in the standard manner using
tools in IRAF (Tody, 1986). We derived radial velocities through cross-
correlation with the highest signal-to-noise spectrum of J1120 obtained in
each setup. These velocities are listed in Table A1.

##  3 Results and Analysis

###  3.1 Stellar Parameters and Unusual Abundances

The single low-resolution flux-calibrated spectrum of J1120 has a blue
continuum dominated by broad Balmer absorption lines (Figure 2), strongly
suggesting an early to mid-A spectral type. No He I lines are visible. Other
moderately strong absorption lines include Ca K (the Ca H line is buried in
H$\epsilon$), the Mg triplet, and what appears to be O I at 7773 Å. Absorption
at the Na doublet is also present, which is a blend of interstellar and
stellar absorption (see below). We do not see any emission lines.

To help constrain the effective temperature and gravity of the star, we fit
the highest signal-to-noise 1200 l mm-1 spectra to a grid of solar metallicity
PHOENIX models (Husser et al., 2013) in the region of the H$\alpha$ line that
were smoothed to the resolution of the SOAR data. Given the stellar radius and
binary inclination inferred below, the projected rotation of the star can be
neglected at our spectral resolution. We find best-fit values of $T_{\rm
eff}=8650\pm 110$ K and log $g=4.6\pm 0.2$ cm s-2
($\chi^{2}/\textrm{dof}=212.8/211$). Since J1120 likely has an unusual
structure and abundances (see below), these values could have substantial
systematic uncertainties, and we take them more as general guidance than
precise measurements. In Figure 3, we overplot the closest template to these
best-fit values ($T_{\rm eff}=8600$ K; log $g=4.5$ cm s-2) on one of the
medium-resolution J1120 spectra from 2021 Feb 19 in the region of the
H$\alpha$ line.

Figure 2: Low-resolution SOAR spectrum of J1120 with a relative flux
calibration applied. The star has a blue continuum, and the strongest
intrinsic features visible are broad Balmer lines. Weak Mg and Na absorption
is also apparent.

While these solar metallicity models do a reasonable job of matching the
H$\alpha$ region, they poorly fit most of the metal lines. We also
experimented with fits of different bulk metallicity ($Z$), finding that these
were much worse fits than solar metallicity. This indicates that the poor
metal-line fits are due to unusual abundances rather than solar-scaled
abundances at a lower or higher metallicity.

One clear example of this is for Na I. In the two high signal-to-noise 2100 l
mm-1 spectra covering the Na doublet, there are two clear doubled-lined
components. The weaker component (equivalent width 0.26 Å summed across both
lines), with a velocity near rest, is consistent with interstellar absorption.
The stronger component (summed equivalent width $0.51\pm 0.02$ Å) has a
velocity consistent with the other absorption lines and hence is associated
with J1120. These lines are stronger than predicted for a star with solar
abundances and the inferred $T_{\rm eff}$ and log $g$, which from the
appropriate PHOENIX models is an equivalent width of $\sim 0.20$ Å. Even for
somewhat cooler temperatures (i.e., $T_{\rm eff}\sim 8000$ K, as inferred from
the photometry presented below), the observed Na I line strength is
significantly larger than predicted. This hints at an overabundance of Na in
J1120.

Figure 3: Continuum-normalized medium-resolution spectrum of J1120 (solid
line) from 2021 Feb 19 in the region of H$\alpha$. A resolution-matched solar
metallicity PHOENIX template with $T_{\rm eff}=8600$ K and log $g=4.5$ cm s-2
is overplotted (dashed line). The Li I line at 6708 Å in the J1120 spectrum is
very strong.

The other unusual line apparent in the 1200 l mm-1 spectra is Li I at 6708 Å
(Figure 3). It is among the strongest metal lines visible in these spectra
(equivalent width $0.34\pm 0.03$ Å), but is predicted to be quite weak
(equivalent width 0.04 Å). As for Na, this comparison again suggests a
substantial overabunance of Li.

It should be noted that this is not the only suspected MSP binary that shows a
substantial overabundance of Li. In the stripped redback PSR J1740–5340 in the
globular cluster NGC 6397, a very high Li content is observed in a series of
high-resolution spectra (Sabbi et al., 2003). Those authors suggest the most
plausible explanation for this overabundance is that fresh 7Li is being
produced on the stellar surface due to bombardment from the high-energy pulsar
wind. Since we currently observe minimal heating on the companion surface, it
is difficult to explain the high Li abundance with this scenario. However,
heating from the suspected neutron star may have been much more significant in
the past, and large amounts of Li may still be present from these times.
Additional explanations are also possible, such as a recent shell flash in the
proto-white dwarf that could have produced some of the Li. Further study will
be needed in order to properly interpret the high Li abundance.

The secondaries of other low-mass X-ray binaries have also shown Li
overabundances (e.g., Cen X-4; González Hernández et al. 2005). For the
purpose of this paper, the main implication of the Li measurement is that it
proves that the companion star is definitely unusual and provides additional
evidence that J1120 is indeed the counterpart to the GeV $\gamma$-ray source.

Given the modest resolution of our data and the non-standard structure of the
star, we do not attempt to convert the above equivalent widths into
abundances. Due to the brightness of the star ($G=15.5$), it should be
feasible to obtain a high-resolution spectrum of sufficient quality to allow a
proper abundance analysis in the future.

Figure 4: Circular Keplerian fit to the SOAR/Goodman barycentric radial
velocities of the optical counterpart to 4FGL J1120.0–2204.

###  3.2 Orbital Paramters

We fit circular Keplerian models to the radial velocities using the Markov
Chain Monte Carlo sampler TheJoker (Price-Whelan et al., 2017), fitting for
the binary period $P$, BJD time of ascending node $T_{0}$, orbital semi-
amplitude $K_{2}$, and systemic velocity $\gamma$. We find $P=0.630398(27)$ d,
$T_{0}=2459307.116\pm 0.031$ d, $K_{2}=83.3\pm 1.7$ km s-1, and
$\gamma=10.4\pm 1.3$ km s-1. Uncertainties are given at 1$\sigma$. We show
this best-fit model along with the data in Figure 4. This is a good fit with
$\chi^{2}$/d.o.f. = 30/36 and an r.m.s. scatter of 6.8 km s-1. We also
experimented with eccentric fits, finding an eccentricity posterior peaked at
$e=0$ and no improvement in the reduced $\chi^{2}$. Hence we see no evidence
for a non-zero eccentricity.

We use the posterior samples from the circular fit to derive the binary mass
function $f(M)$,

$f(M)=\frac{PK_{2}^{3}}{2\pi
G}=\frac{M_{1}\,(\textrm{sin}\,i)^{3}}{(1+q)^{2}}$ (1)

for mass ratio $q=M_{2}/M_{1}$ and inclination $i$, finding $f(M)=0.0377\pm
0.0023\,M_{\odot}$. Since this value represents the lower limit on the mass of
the primary object for an edge-on (90∘) orbit, these results immediately
suggest the orbit must be relatively face-on in order to accommodate a neutron
star-mass primary.

Figure 5: The range of possible inclinations and companion masses that can
accommodate a neutron star-mass primary (solid lines), given our spectroscopic
results. The shaded region represents the most likely mass of the secondary
based on the system parameters and our binary evolution models (see below),
which suggest the system is on its way to becoming a low-mass white dwarf
($M\sim 0.17\,M_{\odot}$), and implying an inclination of $i\sim
16^{\circ}$–$19^{\circ}$ for typical neutron star masses.

Figure 5 shows the range of inclinations and companion masses that are
possible given the spectroscopic results for a range of neutron star masses
(solid lines). The shaded region represents the most likely mass of the
secondary based on the system parameters and binary evolution models of the
system (see below), which suggest the system is on its way to becoming a low-
mass white dwarf ($M\sim 0.17\,M_{\odot}$), implying an inclination of $i\sim
16^{\circ}$– $19^{\circ}$ for a neutron star in the mass range $\sim
1.4-2.0\,M_{\odot}$. This very face-on inclination is the likely explanation
for the lack of obvious orbital variability (see Sec. 3.3.3).

###  3.3 Properties of the Companion

####  3.3.1 Colors & Temperature

As mentioned in Sec. 2.3, J1120 has a blue color in _Gaia_. This is confirmed
in the Pan-STARRS and Skymapper data: the dereddened
$(g^{\prime}-i^{\prime})_{0}$ colors are –0.28 and –0.32, respectively, where
band-dependent extinction corrections were applied using the Schlafly &
Finkbeiner (2011) reddening maps. In fact, this source lies in a peculiar
region of the color-magnitude diagram (CMD), as shown in Figure 6. This
figure, which has been adapted from Antoniadis (2021), shows an observational
color–absolute magnitude diagram of field stars with precise parallax
measurements within 200 pc from the Sun (scatter points), along with the
positions of the known (black circles) and candidate (grey circles) MSP
companions that are listed in _Gaia_ EDR3. Most of these MSP companions are
bluer and brighter than main-sequence stars of similar masses, suggesting they
are highly irradiated or have been stripped of their outer envelopes
(Antoniadis, 2021). The black dashed lines are empirical relations that filter
99.8% of the field stars and white dwarfs in this figure.

Figure 6: Observational color–absolute magnitude diagram (data from _Gaia_
EDR3) of field stars with precise parallax measurements within 200 pc from the
Sun (scatter points & colored histogram). The positions of confirmed and
candidate MSP companions are shown with black and grey circles, respectively.
The black dashed lines are empirical relations that filter 99.8% of the field
stars and white dwarfs in this figure. Most of the MSP companions are bluer
and brighter than main-sequence stars of similar masses, suggesting they are
highly irradiated or have been stripped of their outer envelopes. The
suspected optical counterpart to 4FGL J1120.0–2204 (gold star) is much warmer
than main-sequence stars at a similar brightness and is significantly brighter
than white dwarfs with comparable colors. The two sources blueward of J1120
and with similar $M_{G}$ are PSR J1816+4510 (Kaplan et al., 2012, 2013) (see
Sec. 4.2) and PSR J0337+1715, a MSP in a triple system with two low-mass white
dwarfs (Ransom et al., 2014). Figure adapted from Antoniadis (2021).

J1120, the suspected optical counterpart to 4FGL J1120.0–2204, clearly lies in
a sparsely populated region on this diagram (Figure 6, gold star), with a blue
color suggestive of a warm atmosphere compared to main sequence stars, but
with a luminosity significantly brighter than white dwarfs with comparable
colors.

The temperature of J1120 was estimated by Bai et al. (2019) using a machine
learning algorithm to predict the effective temperatures of $\sim$133 million
stars in _Gaia_ DR2 using their proper motions and ($G-G_{\textrm{RP}}$) and
($G_{\textrm{BP}}-G$) colors. Using this technique, they estimate
$T_{\textrm{eff}}=8001\pm 304$ K. We note that given the unusual abundances
presented above, this estimate should not be taken as a precise measurement.

As an independent estimate of the temperature inferred from the photometry, we
compare the de-reddened Pan-STARRS and Skymapper colors to the theoretical
colors of main sequence stars using a 100 Myr solar metallicity isochrone
(Bressan et al., 2012), similar to the procedure described in Swihart et al.
(2020). We find $T_{\textrm{eff}}=8430$ K and $T_{\textrm{eff}}=8530$ K for
the Pan-STARRS and Skymapper colors, respectively. Assuming a more metal-poor
star with [Fe/H] = –1 gives consistent results within $\sim$100 K. These
values are broadly consistent with our estimate from the spectral modeling
(Sec. 3.1). Overall, given our analysis of the spectra and colors, for the
remainder of the paper we assume $T_{\rm eff}=8500\pm 200$ K.

####  3.3.2 Distance and Kinematics

J1120 has a significant Gaia EDR3 (Gaia Collaboration et al., 2021) parallax,
corresponding to a geometric distance of $d=816.8^{+22.0}_{-24.8}$ pc (Bailer-
Jones et al., 2021). It also has a large proper motion ($36.33\pm 0.02$ mas
yr${}^{\textrm{-1}}$), corresponding to a tangential space velocity of
$140.6^{+3.9}_{-4.3}$ km s${}^{\textrm{-1}}$. High space velocities are
expected in binary MSPs (e.g., Hobbs et al., 2005; Desvignes et al., 2016;
Lynch et al., 2018), providing additional supporting evidence for the MSP
nature of this system. If our MSP interpretation is correct, this large space
velocity is likely the signature of a natal kick from the supernova that
birthed the suspected neutron star primary.

The Galactic coordinates of J1120 are ($l\sim 276.5^{\circ}$, $b\sim
36.0^{\circ}$), which corresponds to a height of $\sim$480 pc above the
midplane of the Galactic disk given its distance $d$. Assuming the systemic
radial velocity from Sec. 3.2 together with the distance and proper motion
measurements from _Gaia_ (and their 1$\sigma$ uncertainties), we derive the
3-D space motion of the system corrected to the local standard of rest
(Coşkunoǧlu et al., 2011), finding $(U,V,W)_{\rm{LSR}}=(130\pm 4,-14.2\pm
0.6,8.0\pm 0.4)$ km s${}^{\textrm{-1}}$. The corresponding 3-D space velocity
($131\pm 4$ km s${}^{\textrm{-1}}$) is consistent with the velocities of
binary MSPs (e.g., Gonzalez et al., 2011; Matthews et al., 2016). Another
explanation for the high velocity could be that the star is a member of the
Galactic halo. However, typical halo stars in the solar neighborhood
($d\lesssim 3$ kpc) have 3-D space velocities $\gtrsim$220 km s-1 (e.g.,
Nissen & Schuster, 2010; Bonaca et al., 2017), so it is unlikely J1120 is a
member of the halo.

####  3.3.3 Companion Size & Lack of Variability

The lack of optical variability in J1120 suggests the system is relatively
face-on, which is supported by our spectroscopic results, but also is
consistent with the secondary only partially filling its Roche lobe. We test
this hypothesis by estimating the size of the companion and comparing it to
the size of its full Roche lobe.

Assuming the _Gaia_ $G$ mag of the secondary, including extinction from the
Green et al. (2019) dustmaps, and a distance of 817 pc, the absolute magnitude
is $M_{G}=5.85$. Assuming $T_{\textrm{eff}}=8500\pm 200$ K (Sec. 3.3.1), we
calibrate to the absolute magnitude and temperature of the Sun (Casagrande &
VandenBerg, 2018), giving a radius of $R_{2}=0.27\pm 0.02\,R_{\odot}$. Looking
ahead to our interpretation of the source, this radius is $\sim 5\times$
larger than white dwarf radii with similar colors/temperatures, explaining its
relatively high optical luminosity (Figure 6).

As an initial estimate of the mass of the secondary, we use our spectroscopic
measurement of log $g=4.6\pm 0.2$ cm s-2, which formally gives
$M_{2}=0.11^{+0.06}_{-0.04}M_{\odot}$ when combined with the $R_{2}$
measurement above. While we do not take this precise value too seriously given
the systematic uncertainties in the spectroscopic fit, the binary evolution
modelling presented in Section 4.1 predicts a secondary mass near the upper
end of this range, suggesting a consistent scenario.

For a neutron star in the mass range $1.4-2.0\,M_{\odot}$, the implied mass
ratio $q=M_{2}/M_{1}\sim 0.03$–0.12, giving an effective Roche lobe radius in
the range $\sim 0.6$–0.8 $R_{\odot}$ (Eggleton, 1983). Hence, given
$R_{2}=0.27\pm 0.02\,R_{\odot}$, the secondary in J1120 is strongly
underfilling its Roche lobe ($R_{2}/R_{L}\lesssim 0.45$). A more massive
secondary would have a larger Roche lobe and hence would underfill it to an
even greater degree.

At the system inclinations inferred from Figure 5, the amplitude of the
optical light curve due to tidal distortion of the secondary would be $<0.02$
mag in $V$-band (Orosz & Hauschildt, 2000), much less than the typical
magnitude uncertainties from the ASAS-SN and CSS data (0.04 and 0.08,
respectively). We show the CSS photometry folded on our spectroscopic period
along with a light curve model assuming $i=19^{\circ}$ in Figure 7.

Hence, the small size of the secondary relative to its Roche lobe and the
face-on system inclination readily explain the lack of detectable orbital
variability in the available optical data. With knowledge of the binary orbit
from our spectroscopic results, future high-cadence, high-precision photometry
could in principle be able to be searched for orbital modulation.

###  3.4 High-Energy Properties

Using the precise _Gaia_ parallax distance and the unabsorbed _XMM_ X-ray
flux, the 0.5–10 keV X-ray luminosity is $(4.1\pm 0.3)\times 10^{30}$ erg s-1.
The 0.1–100 GeV $\gamma$-ray luminosity is $L_{\gamma}=(1.35\pm 0.05)\times
10^{33}$ erg s-1, giving an X-ray to $\gamma$-ray luminosity ratio of $0.003$.
This is lower than typical for redbacks (Miller et al., 2020), with the only
comparably low ratios observed for PSR J1622–0315 (Gentile, 2018; Strader et
al., 2019) and the unusual source PSR J1816+4510 (Kaplan et al., 2013),
discussed in more detail below. Instead, the X-ray to $\gamma$-ray flux ratios
and X-ray luminosities are more similar to black widows (e.g., Lee et al.
2018), though nearly all black widows have shorter orbital periods than J1120.
Given the face-on inclination of the binary, any relativistic Doppler boosting
is expected to be minimal compared to a typical spider MSP intrabinary shock.

While the relatively soft X-ray photon index from the _XMM_ observation and
low X-ray luminosity are consistent with a weak, black widow-like intrabinary
shock, they could also be consistent with thermal and/or magnetospheric
emission entirely from the millisecond pulsar, with little or no contribution
from a shock (e.g., Bogdanov et al. 2006). Given the weaker wind expected from
a warm, non-Roche lobe-filling companion compared to a cooler, more bloated
star, and the marginal predicted irradiation of the secondary (the intrinsic
optical surface flux is a factor of $\gtrsim 150$ larger than the $\gamma$-ray
flux), the lack of a shock may indeed be expected.

Figure 7: Unfiltered Catalina Sky Survey photometry of J1120 folded on our
spectroscopic period, along with a light curve model assuming an inclination
consistent with a neutron star-mass primary ($i=19^{\circ}$). The
uncertainties on individual measurements are clearly much larger than the
amplitude of the model light curve. Data have been repeated $1.5\times$.

##  4 Discussion

The observations presented thus far suggest the secondary has unusual
properties compared to the companions of most known MSPs associated with
_Fermi_ sources. However, here we show that in the context of the canonical
formation scenario for MSPs, this system actually appears to be on the
standard evolutionary pathway for forming a MSP–He white dwarf binary, albeit
one with an especially short orbital period and extremely low-mass white
dwarf.

In this standard scenario, the secondary is born with a relatively low mass
($\lesssim 2\,M_{\odot}$), and depending on the initial orbital period, can
initiate mass transfer on the main sequence or as an evolved star. The
accretion fully recycles the neutron star and the envelope of the secondary is
completely stripped, leaving behind an extremely-low-mass ($\sim 0.1$–0.3
$M_{\odot}$) Helium white dwarf companion (an ELM white dwarf; Brown et al.,
2010). There is strong theoretical and observational support for this scenario
(e.g., Savonije 1987; Rappaport et al. 1995; Tauris & Savonije 1999;
Podsiadlowski et al. 2002; Istrate et al. 2014; Strader et al. 2019), which
predicts a correlation between the final orbital period of the binary and the
mass of the He white dwarf.

In recent years, ELM white dwarfs have seen increasing study outside of the
context of MSP binaries (e.g., Brown et al. 2010; Kilic et al. 2011; Brown et
al. 2020), where surveys such as SDSS have allowed the selection of hot, high
surface gravity objects with masses too low to have been formed except through
close binary evolution. _Gaia_ has allowed the efficient expansion of these
studies to include somewhat cooler and more bloated stars (e.g., Pelisoli et
al. 2019; El-Badry et al. 2021) which can be interpreted as “pre-ELM” stars
(e.g., Maxted et al., 2014), i.e., stripped stars still in the process of
contracting to sit on a He white dwarf cooling track.

The properties of J1120 are fully consistent with being in this intermediate
stage, on its way to eventually becoming a short period MSP–He white dwarf
binary. We explore this hypothesis with binary evolution models in the
following subsection.

###  4.1 Binary Evolution Models: A pre-ELM companion

In order to understand the possible evolution of J1120, we performed a series
of binary evolution simulations using Modules for Experiments in Stellar
Astrophysics (MESA, version 15140; Paxton et al., 2011, 2013, 2015, 2018,
2019).

We initialize our models with a zero-age main sequence (ZAMS) star orbiting a
more massive neutron star represented as a point mass. Mass transfer occurs
once the companion overfills its Roche lobe with rates determined following
the prescriptions of Kolb & Ritter (1990) (mdot_scheme = ‘Kolb’). The mass
transfer (accretion) efficiency of the neutron star is defined as
$\epsilon=1-(\alpha+\beta+\delta)$, where $\alpha$, $\beta$, and $\delta$
denote the mass fraction lost from the vicinity of the donor, accretor, and
from a circumbinary coplanar toroid, respectively (Tauris & van den Heuvel,
2006). For all our models we assume $\delta=0$. We implement magnetic braking
following the prescription from Rappaport et al. (1983) with a braking index
$\gamma_{\textrm{mb}}=3$. The remainder of the MESA parameters were left to
their default values.

Similar to the method employed by Bellm et al. (2016) for their models of the
redback binary PSR J2129–0429, we utilize our observational constraints on the
companion orbital period, log $g$, radius, and temperature to establish
feasible evolutionary models by requiring that these observables are matched
at a particular age.

We simulated a large range of models assuming a neutron star born with a mass
of either 1.4 $M_{\odot}$ or 1.6 $M_{\odot}$, with initial orbital periods in
the range 0.9–2.7 days and companion masses between 0.9–1.3 $M_{\odot}$. We
show some of these models in Figure 8, highlighting the effects of varying the
accretion efficiency parameters $\alpha$ and $\beta$ (colored lines).

We note that the bifurcation period (separating models that diverge to long
periods and those that evolve to shorter periods) is highly sensitive to the
companion mass and the magnetic braking prescription. Soethe & Kepler (2021)
found that using a magnetic braking prescription that considers the wind mass
loss and rotation of the donor as well as the magnetic fields generated by the
outer convective zone (Van & Ivanova, 2019) shifts the bifurcation period to
longer initial orbital periods.

Figure 8: The evolution of the orbital period, log $g$, radius, and effective
temperature of the companion for our MESA models simulating a $1.2\,M_{\odot}$
zero-age main sequence companion orbiting a $1.6\,M_{\odot}$ neutron star
primary with an initial orbital period of 1.0 d. The different colors denote
the effects of varying the mass loss efficiency at the companion ($\alpha$)
and at the neutron star ($\beta$) (see text). In each panel, the horizontal
shaded region corresponds to the range of values inferred from our
observations. The “best” model is shown with a thick blue line, where all the
model values are consistent with the observations at a single age (vertical
shaded region).

We first attempted to find compatible solutions assuming a relatively non-
conservative mass transfer rate, $\alpha=0.2$ and $\beta=0.5$, implying
$\epsilon=0.3$. We were unable to find models that reproduced our observations
with this accretion efficiency, except for when $P_{\textrm{init}}=2.6$ d.
However, the age at which this solution was compatible with our observations
is $\sim$19 Gyr (greater than a Hubble time). At this $\epsilon$, models with
smaller initial orbital periods were able to match the observed values for log
$g$, $R_{2}$, and $T_{\rm eff}$ but none could simultaneously reproduce the
observed period for J1120, always resulting in periods that were too low
(e.g., the red model line in Figure 8). A similar issue was found by Mata
Sánchez et al. (2020) trying to model PSR J1012+5307, which also hosts a very
low-mass He white dwarf.

For some models with shorter initial periods and larger mass transfer
efficiencies, the results agree very well with our observations. The “best”
model we find has $\epsilon\sim 0.75$, $P_{\rm init}=1.0$ d, and initial
component masses $M_{\rm NS}=1.6\,M_{\odot}$ and $M_{2}=1.2\,M_{\odot}$. In
Figure 8 we show this model in blue. With these initial conditions, mass
transfer onto the neutron star begins while the secondary is still on the main
sequence ($\sim$4 Gyr after ZAMS), and lasts for $\sim$3 Gyr. Figure 8 shows
that at an age of $\sim$8.1 Gyr (vertical shaded region), all the model
parameters match our observations (horizontal shaded regions). At this stage
of the evolution, mass transfer is completely finished, as is the bulk of the
orbital period evolution, and the companion is slowly contracting towards the
He white dwarf cooling sequence, consistent with a pre-ELM companion.

The final component masses associated with this “best” model are $M_{\rm
NS}\sim 2.2\,M_{\odot}$ and $M_{2}=0.17\,M_{\odot}$. Although the final mass
of the neutron star is somewhat high compared to known systems, due primarily
to the low mass-loss efficiency, it is a generic prediction of evolutionary
models that on average the binaries with shorter initial orbital periods will
have more massive neutron stars (Tauris & Savonije, 1999). In addition, such
neutron stars should have among the fastest spin periods and hence high spin-
down luminosities, leading to a bias for _Fermi_ to find the fastest spinning
(and more massive) MSPs. We note that this particular system does not appear
to be among the more luminous _Fermi_ -detected MSPs (with a 0.1–100 GeV
luminosity of only $\sim 1.4\times 10^{33}$ erg s-1), which could be either
intrinsic or due to geometric factors. In any case, we do expect the neutron
star to be massive. The neutron star mass could potentially be measurable if
it were detected as a radio or $\gamma$-ray pulsar and if an improved proto-
white dwarf mass could be measured from optical spectroscopy.

Independent of our specific choices made for the MESA models, we can use other
published orbital period–secondary mass correlations to check the robustness
of our conclusions. Istrate et al. (2016) predict that at solar metallicity,
an orbital period of 0.6304 d implies a secondary mass of $0.17M_{\odot}$,
exactly matching our result. Even for other metallicities, a mass below $\sim
0.15M_{\odot}$ or above $\sim 0.2M_{\odot}$ seems relatively unlikely. While
this is consistent with our rough mass estimate from fitting the medium-
resolution SOAR spectra, it would be beneficial to have an improved white
dwarf mass estimate from properly modeled high-resolution spectroscopy.

While we found no other comparably good solution for another combination of
parameters, we did not search the entirety of the parameter space for all
combinations of donor and accretor mass or efficiency, nor for varying
assumptions about the magnetic braking law (e.g., Van & Ivanova 2019). Hence
we do not claim that this is the only solution, but rather that this general
area of initial condition parameter space can lead to systems whose properties
match that of J1120 at the present day. Other evolutionary scenarios are not
ruled out. Future, more detailed modeling will be useful once the suspected
pulsar is found and timed, either in radio or $\gamma$-rays. This system may
be especially valuable for further study due to its precise parallax, allowing
an unusually accurate determination of the luminosity of the source.

###  4.2 Comparison to Other Systems and The End Fate of 4FGL J1120.0–2204

The results presented above suggest a unique system is associated with 4FGL
J1120.0–2204—a MSP binary with a pre-ELM white dwarf companion in a short-
period orbit. To our knowledge, there is no other similar system, though the
expected mechanism for forming MSP–ELM white dwarf binaries can generally
explain its evolution. Perhaps the most similar MSP binary is PSR J1816+4510
(Kaplan et al., 2012, 2013), which is an eclipsing MSP often classified as a
redback but with an unusually hot ($T_{\rm eff}\sim 16000$ K) secondary and a
strongly supersolar metal abundance. While its mass and radius are inferred to
be similar to that of J1120, it has a much shorter orbital period (8.7 hr),
and the secondary may still be eroding in mass, more akin to known spider
systems.

The end fate of J1120, after the secondary has contracted to the white dwarf
cooling sequence, is a reasonable match to several known MSP–He white dwarf
binaries. The MSPs PSR J1012+5307, PSR J1906+0055, and PSR J2006+0148 all have
ELM white dwarf companions, with masses well established from radio pulsar
timing campaigns and/or optical radial velocity measurements (Mata Sánchez et
al., 2020; Stovall et al., 2016; Deneva et al., 2021). These systems have
orbital periods ranging from $14.5-15.6$ hours, and secondary masses between
$\sim 0.12-0.17\,M_{\odot}$. These values are consistent with the orbital
period and suspected mass of J1120 from our spectroscopic results and our
binary evolution models, though at present the radius of J1120 is a factor of
$\sim 6$ larger than these end-stage binaries. Our MESA models predict that in
$\sim 2$ Gyr, J1120 will have a radius and log $g$ fully consistent with these
ELM white dwarfs ($R_{2}\sim 0.04\,R_{\odot}$, $\textrm{log}\;g\sim 6.5$).

The long lifespan of the system in this intermediate stage means that such
systems should not be too uncommon, and that more could be discovered through
follow-up of unassociated _Fermi_ sources. Unlike the case for typical spider
MSP binaries, pre-ELM MSP binaries may show little or no optical variability
and weak X-ray emission, so would be best identified through their blue
colors.

Table 1: Summary of Properties Parameter | Value
---|---
Opt. R.A. (ICRS h:m:s) | 11:19:58.309
Opt. Dec. (ICRS ∘:$\arcmin$:$\arcsec$) | –22:04:56.33
$G_{\rm{mag}}$ (mag) | $15.538\pm 0.003$
Period (d) | $0.630398\pm 0.000027$
$K_{2}$ (km s-1) | $83.3\pm 1.7$
$T_{0}$ (d) | $2459307.116\pm 0.031$
$v_{sys}$ (km s-1) | $10.4\pm 1.3$
$i$ (∘) | $\sim 16-19$
$T_{\rm{eff}}$ (K) | $8500\pm 200$
log $g$ (cm s-2) | $4.6\pm 0.2$
$R_{2}$ ($R_{\odot}$) | $0.27\pm 0.02$
$M_{2}$ ($M_{\odot}$) | $\sim 0.17$
$L_{X}/L_{\gamma}$ | $0.0030\pm 0.0003$
$\mu_{\alpha}$cos $\delta$ (mas yr-1) | $-33.442\pm 0.033$
$\mu_{\delta}$ (mas yr-1) | $14.182\pm 0.028$
$(U,V,W)$ (km s-1) | ($130\pm 4$, $-14.2\pm 0.6$, $8.0\pm 0.4$)
Distance (pc) | $816.8^{+22.0}_{-24.8}$

##  5 Conclusions and Future Work

We have presented the discovery of the X-ray emitting compact binary inside
the error ellipse of the unassociated _Fermi_ $\gamma$-ray source 4FGL
J1120.0–2204. This source shows some properties similar to those of spider
MSPs, including an overluminous secondary, a large spatial velocity, and a
highly curved $\gamma$-ray spectrum, as well as other unusual properties such
as an overabundance of Li. However, binary evolution modeling of the
temperature, radius, gravity, and orbital period of the system together
suggest the companion is a pre-ELM white dwarf star and that the binary is
evolving toward being a short-period MSP–He white dwarf binary. We summarize
many of the system properties in Table LABEL:tab:summary_table.

In contrast to many recently discovered MSPs associated with _Fermi_ sources,
which have tidally distorted or significantly irradiated secondaries, the
optical companion shows no evidence for periodic orbital modulation in the
optical light curves. This can be explained by a combination of the companion
significantly underfilling its Roche lobe, a face-on orientation, and the
rather low X-ray luminosity (implying a weak or absent intrabinary shock). The
lack of orbital variability in this system highlights the value of using a
range of approaches to identify counterparts to _Fermi_ sources.

For a neutron star primary, we find a face-on inclination of $\sim
16^{\circ}$–$19^{\circ}$. The a priori probability of such a face-on
orientation is low, $\lesssim 6$%, though there may be a selection bias: if
the orientation were more edge-on, there might have been optical variability
that would have allowed an earlier discovery of the binary.

The X-ray luminosity of J1120 is somewhat low compared to most redbacks,
though more similar to black widows. Together with the lack of orbital
variability and the absence of optical emission lines, we find that it is
plausible that there is no intrabinary shock in this system, with the X-ray
emission entirely originating from the MSP.

Although J1120 appears to be on an evolutionary path that will eventually
result in a binary that looks similar to several known short-period MSP–He
white dwarfs binaries, there is no other known system in a similar pre-ELM
stage. The best comparison is the strange eclipsing MSP PSR J1816+4510 (Kaplan
et al., 2013), which differs in several key aspects from 4FGL J1120.0–2204,
but clearly deserves further attention.

The suspected MSP nature of 4FGL J1120.0–2204 is likely given the current
data, but detecting the pulsar in either radio or $\gamma$-rays is still
needed. The distance to the source is well-constrained, so detection of the
pulsar would immediately allow a determination of the efficiency of the pulsar
at converting its spin-down power to $\gamma$-rays. Pulsar searches of the
1FGL and 2FGL regions were performed a number of times between 2009–2012 with
the GBT, GMRT, Effelsburg, and Parkes radio telescopes, and one brief search
of the 3FGL region was executed in late-2016 with Parkes, all resulting in no
detections (Pulsar Search Consortium, private comm.). Unlike typical spider
MSPs, it is unclear whether 4FGL J1120.0–2204 should show radio eclipses, and
it is possible that the radio beam from this pulsar is never pointed at Earth.
Nonetheless, additional radio searches that use our optical ephemerides for
scheduling would be valuable, and we have recently begun a GBT program
utilizing this strategy. An independent, promising route to a pulsar detection
would be to search for $\gamma$-ray pulsations, with the computationally-
expensive search (e.g., Nieder et al., 2020; Clark et al., 2021) constrained
via our optical orbital parameters. The detection of the pulsar, combined with
new high-resolution optical spectroscopy, could also allow a mass measurement
of the neutron star, which is predicted to be high. Confirmation of an unusual
and luminous MSP binary would provide yet more evidence of how incomplete the
MSP census is, even at close distances ($<1$ kpc) to the Sun.

## Acknowledgements

Special thanks to E. Brown and K. El-Badry for assistance with MESA.

This research was performed while SJS held a NRC Research Associateship award
at the Naval Research Laboratory. Work at the Naval Research Laboratory is
supported by NASA DPR S-15633-Y.

We also acknowledge support from NSF grant AST-1714825 and the Packard
Foundation.

Some material is based upon work supported by NASA under award number
80GSFC21M0002.

Based on observations obtained at the Southern Astrophysical Research (SOAR)
telescope, which is a joint project of the Ministério da Ciência, Tecnologia e
Inovações (MCTI/LNA) do Brasil, the US National Science Foundation’s NOIRLab,
the University of North Carolina at Chapel Hill (UNC), and Michigan State
University (MSU).

This work was based on observations obtained with XMM–Newton, an ESA science
mission with instruments and contributions directly funded by ESA Member
States and NASA.

We acknowledge the use of public data from the Swift data archive.

This research has made use of data and software provided by the High Energy
Astrophysics Science Archive Research Center (HEASARC), which is a service of
the Astrophysics Science Division at NASA/GSFC and the High Energy
Astrophysics Division of the Smithsonian Astrophysical Observatory.

## References

  * Abdo et al. (2010) Abdo, A. A., Ackermann, M., Ajello, M., et al. 2010, ApJS, 188, 405
  * Abdo et al. (2013) Abdo, A. A., Ajello, M., Allafort, A., et al. 2013, ApJS, 208, 17
  * Ablimit (2019) Ablimit, I. 2019, ApJ, 881, 72
  * Al Noori et al. (2018) Al Noori, H., Roberts, M. S. E., Torres, R. A., et al. 2018, ApJ, 861, 89
  * Alpar et al. (1982) Alpar, M. A., Cheng, A. F., Ruderman, M. A., & Shaham, J. 1982, Nature, 300, 728
  * Althaus et al. (2013) Althaus, L. G., Miller Bertolami, M. M., & Córsico, A. H. 2013, A&A, 557, A19
  * Antoniadis (2021) Antoniadis, J. 2021, MNRAS, 501, 1116
  * Archibald et al. (2013) Archibald, A. M., Kaspi, V. M., Hessels, J. W. T., et al. 2013, arXiv e-prints, arXiv:1311.5161
  * Bahramian et al. (2013) Bahramian, A., Heinke, C. O., Sivakoff, G. R., & Gladstone, J. C. 2013, ApJ, 766, 136
  * Bai et al. (2019) Bai, Y., Liu, J., Bai, Z., Wang, S., & Fan, D. 2019, AJ, 158, 93
  * Bailer-Jones et al. (2021) Bailer-Jones, C. A. L., Rybizki, J., Fouesneau, M., Demleitner, M., & Andrae, R. 2021, AJ, 161, 147
  * Ballet et al. (2020) Ballet, J., Burnett, T. H., Digel, S. W., & Lott, B. 2020, arXiv e-prints, arXiv:2005.11208
  * Bellm et al. (2016) Bellm, E. C., Kaplan, D. L., Breton, R. P., et al. 2016, ApJ, 816, 74
  * Benvenuto et al. (2012) Benvenuto, O. G., De Vito, M. A., & Horvath, J. E. 2012, ApJ, 753, L33
  * Bhat & Malyshev (2021) Bhat, A., & Malyshev, D. 2021, arXiv e-prints, arXiv:2102.07642
  * Bogdanov et al. (2006) Bogdanov, S., Grindlay, J. E., Heinke, C. O., et al. 2006, ApJ, 646, 1104
  * Bonaca et al. (2017) Bonaca, A., Conroy, C., Wetzel, A., Hopkins, P. F., & Kereš, D. 2017, ApJ, 845, 101
  * Bressan et al. (2012) Bressan, A., Marigo, P., Girardi, L., et al. 2012, MNRAS, 427, 127
  * Brown et al. (2010) Brown, W. R., Kilic, M., Allende Prieto, C., & Kenyon, S. J. 2010, ApJ, 723, 1072
  * Brown et al. (2020) Brown, W. R., Kilic, M., Kosakowski, A., et al. 2020, ApJ, 889, 49
  * Casagrande & VandenBerg (2018) Casagrande, L., & VandenBerg, D. A. 2018, MNRAS, 479, L102
  * Chambers et al. (2016) Chambers, K. C., Magnier, E. A., Metcalfe, N., et al. 2016, arXiv e-prints, arXiv:1612.05560
  * Chen et al. (2013) Chen, H.-L., Chen, X., Tauris, T. M., & Han, Z. 2013, ApJ, 775, 27
  * Cho et al. (2018) Cho, P. B., Halpern, J. P., & Bogdanov, S. 2018, ApJ, 866, 71
  * Clark et al. (2021) Clark, C. J., Nieder, L., Voisin, G., et al. 2021, MNRAS, 502, 915
  * Clemens et al. (2004) Clemens, J. C., Crain, J. A., & Anderson, R. 2004, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 5492, Ground-based Instrumentation for Astronomy, ed. A. F. M. Moorwood & M. Iye, 331–340
  * Coşkunoǧlu et al. (2011) Coşkunoǧlu, B., Ak, S., Bilir, S., et al. 2011, MNRAS, 412, 1237
  * Deneva et al. (2021) Deneva, J. S., Ray, P. S., Camilo, F., et al. 2021, ApJ, 909, 6
  * Desvignes et al. (2016) Desvignes, G., Caballero, R. N., Lentati, L., et al. 2016, MNRAS, 458, 3341
  * Draghis et al. (2019) Draghis, P., Romani, R. W., Filippenko, A. V., et al. 2019, ApJ, 883, 108
  * Drake et al. (2009) Drake, A. J., Djorgovski, S. G., Mahabal, A., et al. 2009, ApJ, 696, 870
  * Eastman et al. (2010) Eastman, J., Siverd, R., & Gaudi, B. S. 2010, PASP, 122, 935
  * Eggleton (1983) Eggleton, P. P. 1983, ApJ, 268, 368
  * El-Badry et al. (2021) El-Badry, K., Rix, H.-W., Quataert, E., Kupfer, T., & Shen, K. J. 2021, MNRAS, arXiv:2108.04255
  * Finke et al. (2020) Finke, T., Krämer, M., & Manconi, S. 2020, arXiv e-prints, arXiv:2012.05251
  * Gaia Collaboration et al. (2021) Gaia Collaboration, Brown, A. G. A., Vallenari, A., et al. 2021, A&A, 649, A1
  * Gentile (2018) Gentile, P. A. 2018, PhD thesis, West Virginia University
  * Gentile et al. (2014) Gentile, P. A., Roberts, M. S. E., McLaughlin, M. A., et al. 2014, ApJ, 783, 69
  * Gonzalez et al. (2011) Gonzalez, M. E., Stairs, I. H., Ferdman, R. D., et al. 2011, ApJ, 743, 102
  * González Hernández et al. (2005) González Hernández, J. I., Rebolo, R., Israelian, G., et al. 2005, ApJ, 630, 495
  * Green et al. (2019) Green, G. M., Schlafly, E., Zucker, C., Speagle, J. S., & Finkbeiner, D. 2019, ApJ, 887, 93
  * Greiner et al. (2008) Greiner, J., Bornemann, W., Clemens, C., et al. 2008, PASP, 120, 405
  * Hobbs et al. (2005) Hobbs, G., Lorimer, D. R., Lyne, A. G., & Kramer, M. 2005, MNRAS, 360, 974
  * Hui et al. (2010) Hui, C. Y., Cheng, K. S., & Taam, R. E. 2010, ApJ, 714, 1149
  * Hui et al. (2015) Hui, C. Y., Park, S. M., Hu, C. P., et al. 2015, ApJ, 809, 68
  * Husser et al. (2013) Husser, T. O., Wende-von Berg, S., Dreizler, S., et al. 2013, A&A, 553, A6
  * Istrate et al. (2016) Istrate, A. G., Marchant, P., Tauris, T. M., et al. 2016, A&A, 595, A35
  * Istrate et al. (2014) Istrate, A. G., Tauris, T. M., & Langer, N. 2014, A&A, 571, A45
  * Kalberla et al. (2005) Kalberla, P. M. W., Burton, W. B., Hartmann, D., et al. 2005, A&A, 440, 775
  * Kaplan et al. (2013) Kaplan, D. L., Bhalerao, V. B., van Kerkwijk, M. H., et al. 2013, ApJ, 765, 158
  * Kaplan et al. (2012) Kaplan, D. L., Stovall, K., Ransom, S. M., et al. 2012, ApJ, 753, 174
  * Kaur et al. (2019) Kaur, A., Falcone, A. D., Stroh, M. D., Kennea, J. A., & Ferrara, E. C. 2019, ApJ, 887, 18
  * Kerby et al. (2021) Kerby, S., Kaur, A., Falcone, A. D., et al. 2021, AJ, 161, 154
  * Kilic et al. (2011) Kilic, M., Brown, W. R., Allende Prieto, C., et al. 2011, ApJ, 727, 3
  * Kochanek et al. (2017) Kochanek, C. S., Shappee, B. J., Stanek, K. Z., et al. 2017, PASP, 129, 104502
  * Kolb & Ritter (1990) Kolb, U., & Ritter, H. 1990, A&A, 236, 385
  * Lee et al. (2018) Lee, J., Hui, C. Y., Takata, J., et al. 2018, ApJ, 864, 23
  * Lin et al. (2011) Lin, J., Rappaport, S., Podsiadlowski, P., et al. 2011, ApJ, 732, 70
  * Lindegren et al. (2021) Lindegren, L., Bastian, U., Biermann, M., et al. 2021, A&A, 649, A4
  * Lynch et al. (2018) Lynch, R. S., Swiggum, J. K., Kondratiev, V. I., et al. 2018, ApJ, 859, 93
  * Mata Sánchez et al. (2020) Mata Sánchez, D., Istrate, A. G., van Kerkwijk, M. H., Breton, R. P., & Kaplan, D. L. 2020, MNRAS, 494, 4031
  * Matthews et al. (2016) Matthews, A. M., Nice, D. J., Fonseca, E., et al. 2016, ApJ, 818, 92
  * Maxted et al. (2011) Maxted, P. F. L., Anderson, D. R., Burleigh, M. R., et al. 2011, MNRAS, 418, 1156
  * Maxted et al. (2014) Maxted, P. F. L., Bloemen, S., Heber, U., et al. 2014, MNRAS, 437, 1681
  * McConnell et al. (2015) McConnell, O., Callanan, P. J., Kennedy, M., et al. 2015, MNRAS, 451, 3468
  * Miller et al. (2020) Miller, J. M., Swihart, S. J., Strader, J., et al. 2020, ApJ, 904, 49
  * Nieder et al. (2020) Nieder, L., Allen, B., Clark, C. J., & Pletsch, H. J. 2020, ApJ, 901, 156
  * Nissen & Schuster (2010) Nissen, P. E., & Schuster, W. J. 2010, A&A, 511, L10
  * Onken et al. (2019) Onken, C. A., Wolf, C., Bessell, M. S., et al. 2019, PASA, 36, e033
  * Orosz & Hauschildt (2000) Orosz, J. A., & Hauschildt, P. H. 2000, A&A, 364, 265
  * Paxton et al. (2011) Paxton, B., Bildsten, L., Dotter, A., et al. 2011, ApJS, 192, 3
  * Paxton et al. (2013) Paxton, B., Cantiello, M., Arras, P., et al. 2013, ApJS, 208, 4
  * Paxton et al. (2015) Paxton, B., Marchant, P., Schwab, J., et al. 2015, ApJS, 220, 15
  * Paxton et al. (2018) Paxton, B., Schwab, J., Bauer, E. B., et al. 2018, ApJS, 234, 34
  * Paxton et al. (2019) Paxton, B., Smolec, R., Schwab, J., et al. 2019, ApJS, 243, 10
  * Pelisoli et al. (2019) Pelisoli, I., Bell, K. J., Kepler, S. O., & Koester, D. 2019, MNRAS, 482, 3831
  * Podsiadlowski et al. (2002) Podsiadlowski, P., Rappaport, S., & Pfahl, E. D. 2002, ApJ, 565, 1107
  * Postnov & Yungelson (2014) Postnov, K. A., & Yungelson, L. R. 2014, Living Reviews in Relativity, 17, 3
  * Price-Whelan et al. (2017) Price-Whelan, A. M., Hogg, D. W., Foreman-Mackey, D., & Rix, H.-W. 2017, ApJ, 837, 20
  * Ransom et al. (2014) Ransom, S. M., Stairs, I. H., Archibald, A. M., et al. 2014, Nature, 505, 520
  * Rappaport et al. (2015) Rappaport, S., Nelson, L., Levine, A., et al. 2015, ApJ, 803, 82
  * Rappaport et al. (1995) Rappaport, S., Podsiadlowski, P., Joss, P. C., Di Stefano, R., & Han, Z. 1995, MNRAS, 273, 731
  * Rappaport et al. (1983) Rappaport, S., Verbunt, F., & Joss, P. C. 1983, ApJ, 275, 713
  * Ray et al. (2012) Ray, P. S., Abdo, A. A., Parent, D., et al. 2012, arXiv e-prints, arXiv:1205.3089
  * Roberts (2013) Roberts, M. S. E. 2013, in Neutron Stars and Pulsars: Challenges and Opportunities after 80 years, ed. J. van Leeuwen, Vol. 291, 127–132
  * Romani & Sanchez (2016) Romani, R. W., & Sanchez, N. 2016, ApJ, 828, 7
  * Sabbi et al. (2003) Sabbi, E., Gratton, R. G., Bragaglia, A., et al. 2003, A&A, 412, 829
  * Salvetti et al. (2017) Salvetti, D., Mignani, R. P., De Luca, A., et al. 2017, MNRAS, 470, 466
  * Sanchez & Romani (2017) Sanchez, N., & Romani, R. W. 2017, ApJ, 845, 42
  * Sarna et al. (2001) Sarna, M. J., Ergma, E., & Gerskevits, J. 2001, Astronomische Nachrichten, 322, 405
  * Savonije (1987) Savonije, G. J. 1987, Nature, 325, 416
  * Saz Parkinson et al. (2016) Saz Parkinson, P. M., Xu, H., Yu, P. L. H., et al. 2016, ApJ, 820, 8
  * Schlafly & Finkbeiner (2011) Schlafly, E. F., & Finkbeiner, D. P. 2011, ApJ, 737, 103
  * Shappee et al. (2014) Shappee, B. J., Prieto, J. L., Grupe, D., et al. 2014, ApJ, 788, 48
  * Soethe & Kepler (2021) Soethe, L. T. T., & Kepler, S. O. 2021, MNRAS, 506, 3266
  * Stovall et al. (2016) Stovall, K., Allen, B., Bogdanov, S., et al. 2016, ApJ, 833, 192
  * Strader et al. (2019) Strader, J., Swihart, S., Chomiuk, L., et al. 2019, ApJ, 872, 42
  * Swihart et al. (2021) Swihart, S. J., Strader, J., Aydi, E., et al. 2021, ApJ, 909, 185
  * Swihart et al. (2019) Swihart, S. J., Strader, J., Chomiuk, L., & Shishkovsky, L. 2019, ApJ, 876, 8
  * Swihart et al. (2018) Swihart, S. J., Strader, J., Shishkovsky, L., et al. 2018, ApJ, 866, 83
  * Swihart et al. (2020) Swihart, S. J., Strader, J., Urquhart, R., et al. 2020, ApJ, 892, 21
  * Tauris & Savonije (1999) Tauris, T. M., & Savonije, G. J. 1999, A&A, 350, 928
  * Tauris & van den Heuvel (2006) Tauris, T. M., & van den Heuvel, E. P. J. 2006, Formation and evolution of compact stellar X-ray sources, Vol. 39, 623–665
  * Tody (1986) Tody, D. 1986, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 627, Instrumentation in astronomy VI, ed. D. L. Crawford, 733
  * Torres et al. (2017) Torres, D. F., Ji, L., Li, J., et al. 2017, ApJ, 836, 68
  * Van & Ivanova (2019) Van, K. X., & Ivanova, N. 2019, ApJ, 886, L31
  * Wadiasingh et al. (2017) Wadiasingh, Z., Harding, A. K., Venter, C., Böttcher, M., & Baring, M. G. 2017, ApJ, 839, 80
  * Yap et al. (2019) Yap, Y. X., Li, K. L., Kong, A. K. H., et al. 2019, A&A, 621, L9
  * Ye et al. (2019) Ye, C. S., Kremer, K., Chatterjee, S., Rodriguez, C. L., & Rasio, F. A. 2019, ApJ, 877, 122

Table A1: Modified Barycentric Radial Velocities of 4FGL J1120.0–2204

MBJD | RV | unc.
---|---|---
(d) | (km s-1) | (km s-1)
58580.0292230 | 79.1 | 10.2
59263.2108944 | –43.1 | 8.8
59263.2252614 | –33.7 | 8.4
59265.1105358 | –24.8 | 6.5
59265.1607660 | 5.0 | 6.4
59265.1747837 | 14.9 | 7.3
59275.0714854 | –75.2 | 7.6
59275.0854903 | –70.4 | 8.8
59275.1026843 | –72.5 | 7.8
59275.1169088 | –73.2 | 8.6
59275.1483191 | –52.4 | 7.7
59277.0835264 | –29.8 | 9.7
59277.0978731 | –20.1 | 8.9
59277.1145712 | –3.0 | 10.8
59277.1287851 | –9.4 | 6.9
59277.1454170 | 14.7 | 6.8
59277.1578828 | 13.9 | 7.4
59306.0077810 | –77.5 | 5.0
59306.0268962 | –70.2 | 5.2
59306.9965064 | 85.6 | 5.4
59307.0163584 | 64.4 | 5.3
59307.0370772 | 57.1 | 5.4
59307.0552111 | 35.4 | 5.2
59345.9653099 | 89.0 | 6.3
59345.9831531 | 92.5 | 5.5
59348.0915650 | –4.2 | 6.7
59348.1100869 | –20.0 | 6.1
59348.1304595 | –30.0 | 9.8
59364.0891693 | –29.8 | 12.2
59364.1609283 | 10.3 | 15.4
59374.0215399 | –68.3 | 10.4
59374.0405526 | –72.1 | 8.2
59374.1021232 | –68.8 | 9.6
59375.0215555 | 86.1 | 7.4
59375.0362274 | 80.4 | 9.6
59375.0838375 | 63.3 | 9.5
59375.1181126 | 43.0 | 6.2
59375.1320182 | 44.9 | 7.6
59410.9891252 | 94.1 | 8.3
59411.0032804 | 74.9 | 6.5

Note. — All dates are Modified Barycentric Julian Dates (BJD–2400000.5) on the
TDB system (Eastman et al., 2010).