# MAXI J1848$-$015: The First Detection of Relativistically Moving Outflows
from a Globular Cluster X-ray Binary

A. Bahramian International Centre for Radio Astronomy Research – Curtin
University, GPO Box U1987, Perth, WA 6845, Australia  E. Tremou National Radio
Astronomy Observatory, Socorro, NM 87801 USA  A. J. Tetarenko Department of
Physics and Astronomy, Texas Tech University, Lubbock, TX 79409-1051, USA
East Asian Observatory, 660 N. A‘ohōkū Place, University Park, Hilo, Hawaii
96720, USA  NASA Einstein Fellow  J. C. A. Miller-Jones International Centre
for Radio Astronomy Research – Curtin University, GPO Box U1987, Perth, WA
6845, Australia  R. P. Fender  Astrophysics, Department of Physics, University
of Oxford, Keble Road, Oxford OX1 3RH, UK  Department of Astronomy, University
of Cape Town, Private Bag X3, Rondebosch 7701, South Africa  S. Corbel
Université Paris Cité and Université Paris Saclay, CEA, CNRS, AIM, F-91190
Gif-sur-Yvette, France  ORN, Observatoire de Paris, Université PSL, Université
Orléans, CNRS, F-18330 Nançay, France  D. R. A. Williams Jodrell Bank Centre
for Astrophysics, School of Physics and Astronomy, The University of
Manchester, Manchester, M13 9PL  J. Strader Center for Data Intensive and Time
Domain Astronomy, Department of Physics and Astronomy, Michigan State
University, East Lansing, MI 48824, USA  F. Carotenuto Astrophysics,
Department of Physics, University of Oxford, Keble Road, Oxford OX1 3RH, UK
R. Salinas Gemini Observatory/NSF’s NOIRLab, Casilla 603, La Serena, Chile  J.
A. Kennea Department of Astronomy and Astrophysics, The Pennsylvania State
University, 525 Davey Lab, University Park, PA 16802, USA  S. E. Motta
Istituto Nazionale di Astrofisica, Osservatorio Astronomico di Brera, via E.
Bianchi 46, I-23807 Merate (LC), Italy  P. A. Woudt Department of Astronomy,
University of Cape Town, Private Bag X3, Rondebosch 7701, South Africa  J. H.
Matthews Astrophysics, Department of Physics, University of Oxford, Keble
Road, Oxford OX1 3RH, UK  T. D. Russell INAF, Istituto di Astrofisica Spaziale
e Fisica Cosmica, Via U. La Malfa 153, I-90146 Palermo, Italy

###### Abstract

Over the past decade, observations of relativistic outflows from outbursting
X-ray binaries in the Galactic field have grown significantly. In this work,
we present the first detection of moving and decelerating radio-emitting
outflows from an X-ray binary in a globular cluster. MAXI J1848$-$015 is a
recently discovered transient X-ray binary in the direction of the globular
cluster GLIMPSE-C01. Using observations from the VLA, and a monitoring
campaign with the MeerKAT observatory for 500 days, we model the motion of the
outflows. This represents some of the most intensive, long-term coverage of
relativistically moving X-ray binary outflows to date. We use the proper
motions of the outflows from MAXI J1848$-$015 to constrain the component of
the intrinsic jet speed along the line of sight,
$\beta_{\textrm{int}}\cos\theta_{\textrm{ejection}}$, to be $=0.19\pm 0.02$.
Assuming it is located in GLIMPSE-C01, at 3.4 kpc, we determine the intrinsic
jet speed, $\beta_{\textrm{int}}=0.79\pm 0.07$, and the inclination angle to
the line of sight, $\theta_{\textrm{ejection}}=76^{\circ}\pm 2^{\circ}$. This
makes the outflows from MAXI J1848$-$015 somewhat slower than those seen from
many other known X-ray binaries. We also constrain the maximum distance to
MAXI J1848$-$015 to be $4.3$ kpc. Lastly, we discuss the implications of our
findings for the nature of the compact object in this system, finding that a
black hole primary is a viable (but as-of-yet unconfirmed) explanation for the
observed properties of MAXI J1848$-$015\. If future data and/or analysis
provide more conclusive evidence that MAXI J1848$-$015 indeed hosts a black
hole, it would be the first black hole X-ray binary in outburst identified in
a Galactic globular cluster.

Radio jets (1347), Low-mass X-ray binary stars (939), Neutron stars (1108),
Black holes (162), Stellar accretion (1578), Globular star clusters (656)

††facilities: VLA, MeerKAT††software: Astropy(Astropy Collaboration et al.,
2013, 2018), CASA (CASA Team et al., 2022), CMasher (van der Velden, 2020),
Corner (Foreman-Mackey, 2016), IPython (Perez & Granger, 2007), Jupyter
(Kluyver et al., 2016), Matplotlib (Hunter, 2007), Numpy (Oliphant, 2006; van
der Walt et al., 2011), PyMC (Salvatier et al., 2016), SAOImage DS9 (Joye &
Mandel, 2003), Scipy (Virtanen et al., 2020).

##  1 Introduction

On 2020-12-20, the Monitor of All-sky X-ray Image (MAXI) mission detected a
bright outburst from the direction of the globular cluster GLIMPSE-C01 (Takagi
et al., 2020). At the time, the source (named MAXI J1848$-$015) was located in
the Sun-constraint zone for most other X-ray observatories. However, follow-up
observations by the Nuclear Spectroscopic Telescope Array (NuSTAR) improved on
localization and found indications of spectral evolution (Pike et al., 2020;
Mihara et al., 2021). A follow-up observation by the X-ray Telescope onboard
the Neil Gehrels Swift Observatory (Swift/XRT) on 2021-02-21 found MAXI
J1848$-$015 still in outburst and localized it to the core of GLIMPSE-C01,
suggesting that this outburst may come from a previously undetected X-ray
binary (XRB) in this star cluster (Kennea et al., 2021). A further follow-up
observation by the Chandra observatory provided improved constraints on the
location (Chakrabarty et al., 2021), while inspection of archival Chandra data
provided a deep upper-limit on the quiescent X-ray luminosity of $\leq
3.3\times 10^{30}$ erg s-1 in the 0.5–10 keV band (Hare et al., 2021).

In contrast with the Galactic field, globular clusters are known to contain an
overabundance of X-ray binaries (XRBs Clark, 1975). This is generally
attributed to dynamical formation of these systems through encounters as
opposed to canonical binary evolution (Sutantyo, 1975; Fabian et al., 1975;
Hills, 1976). Observational evidence in support of this overabundance has been
discussed both for Galactic (Pooley et al., 2003; Heinke et al., 2003;
Bahramian et al., 2013), and extragalactic (Sarazin et al., 2003; Kundu et
al., 2007; Kundu & Zepf, 2007) clusters.

GLIMPSE-C01 is a star cluster located $0.1^{\circ}$ away from the Galactic
plane (Kobulnicky et al., 2005). It is at an estimated distance of 3.4 kpc
(Hare et al., 2018) from us, corresponding to a distance of 6 pc from the
Galactic midplane. This highly extinguished cluster ($E(B-V)\approx 4.85$,
Harris, 1996, version 2010), has been suspected to be a globular cluster
(possibly passing through the Galactic plane or corotating with the Galactic
disk; Salinas et al., in prep.) due to properties including its well-populated
giant branch - indicating an abundance of old low-mass giants, as opposed to
young supergiants, and high stellar density in the core – hinting at mass
segregation, a well-known property of old, relaxed globular clusters
(Kobulnicky et al., 2005; Ivanov et al., 2005; Davidge et al., 2016). In the
X-rays, GLIMPSE-C01 is known to host more than a dozen X-ray sources (Pooley
et al., 2007; Hare et al., 2018).

In this work, we report the detection of radio outflows moving away from the
core of MAXI J1848$-$015, observed by the Karl G. Jansky Very Large Array
(VLA) and MeerKAT. We also detect clear deceleration of these outflows as they
move through the interstellar medium (ISM). Moving outflows have been observed
in a number of black hole XRBs (Mirabel & Rodríguez, 1994; Hjellming & Rupen,
1995; Fomalont et al., 2001a; Corbel et al., 2002, 2005; Yang et al., 2011;
Martí et al., 2017; Rushton et al., 2017; Miller-Jones et al., 2019; Bright et
al., 2020), and with the emergence of facilities such as MeerKAT, decelerating
outflows interacting with the ISM have now been seen in several XRBs at
different distances, opening angles and times (up to months or years).
However, MAXI J1848$-$015 is the first XRB in a globular cluster to be
observed exhibiting such outflows. Furthermore, the outflows from MAXI
J1848$-$015 show some of the most persistent radio emission from
relativistically-moving XRB outflows observed to date (see also XTE
J1550$-$564, XTE J1748$-$288, MAXI J1535$-$571, MAXI J1820+070, MAXI
J1348$-$630; Corbel et al., 2001; Brocksopp et al., 2007; Russell et al.,
2019; Bright et al., 2020; Carotenuto et al., 2021). In §2 we describe the
data presented in this work and details of the data processing. In §3, we
determine the location of a potential compact radio core and measure the
motion of the moving outflows, and finally in §4 we explore the implications
of our findings, considering the host environment and making comparisons with
other, similar, systems. The outflows were also independently identified in
data from the VLA Low-band Ionosphere and Transient Experiment (VLITE) at 340
MHz (Peters et al., in. prep.).

##  2 Data and Reduction

Soon after the localization of MAXI J1848$-$015 to the core of GLIMPSE-C01, we
began an intense monitoring campaign in the radio band to constrain its nature
and study the outflows. The observations analyzed in this work are summarized
in Table LABEL:tab:obs_list.

###  2.1 VLA

MAXI J1848$-$015 was observed with the VLA (Project Code: 21A–400) on
2021-02-27 (MJD 59272), for a total on-source observation time of $\sim 88$
min. During our observations, the array was in its most extended A
configuration, observing in the 8 – 12 GHz band, with the 3-bit samplers. The
correlator was set up to generate 2 base-bands, each with 16 spectral windows
comprised of 64 2-MHz channels, giving a total bandwidth of 2.048 GHz per
base-band. We reduced and imaged the data within the Common Astronomy Software
Application package, casa (version 5.4, CASA Team et al., 2022), using
standard procedures outlined in the casa
Guides111https://casaguides.nrao.edu/index.php/Karl_G._Jansky_VLA_Tutorials.
for VLA data reduction (i.e., a priori flagging, setting the flux density
scale, initial phase calibration, solving for antenna-based delays, bandpass
calibration, gain calibration, scaling the amplitude gains, and final target
flagging). We used 3C286 (J1331+3030) as a flux/bandpass calibrator, and
J1851+0035 as a phase calibrator. We flagged short-spacings ($<400{\rm
k}\lambda$) for J1851+0035, as the VLA calibrator
catalogue222https://science.nrao.edu/facilities/vla/observing/callist#section-0
indicates it is extended at these short-spacings. To image the target source,
we used Briggs weighting with robust parameter 0 (to balance sensitivity and
resolution), two Taylor terms to account for the wide fractional bandwidth,
the multi-scale algorithm (deconvolving with Gaussians of FWHM 5 and 15
pixels, as well as point sources), and placed an outlier field on a bright
source to the south of our target333Likely, GPS5 031.243$-$0.110, a candidate
ultracompact HII region (Becker et al., 1994).. A zoomed-in image of the
target is displayed in Figure 1 (left panel), where we clearly detect two
bright radio lobe structures and potentially see indications of a weak (at
$3.5\sigma$ significance) core component midway between the lobes (see §3.1).

###  2.2 MeerKAT

The field of MAXI J1848$-$015 was first observed with MeerKAT on 2021-02-28
(MJD 59273) as part of the ThunderKAT 444http://www.thunderkat.uct.ac.za/ (The
HUNt for Dynamic and Explosive Radio transients with MeerKAT, Fender et al.,
2016) large survey project. Following the radio detection of MAXI J1848$-$015
(Tremou et al., 2018), we observed the field weekly for 15 minutes of on-
source integration time. Due to the slow evolution of the outflows, in October
2021 we decreased the observations and reduced the monitoring cadence to bi-
weekly (for a total of 54 observations). Our observations were made using the
L-band receiver, centered at 1.284 GHz with a bandwidth of 0.856 GHz.
Observations typically alternated between the target and phase calibrator
(J1911$-$2006), with a single scan on a bandpass and flux calibrator,
J1939$-$6342\. All observations were obtained in full polarization mode. We
flagged the data using Tricolour (Hugo et al., 2022) and calibrated the data
using casa as part of the Oxkat data reduction scripts (Heywood, 2020). For
imaging the field of MAXI J1848$-$015, we used WSClean(Offringa et al., 2014).
The image size was 10240 $\times$ 10240 pixels, the pixel size was set at
1.1$\arcsec$ and we used Briggs weighting with a robust parameter of $-0.6$.
We used the casa task imfit to extract the flux densities and the positions of
the two lobes. The two components were separated significantly and a Gaussian
fit (constrained to the size of the synthesized beam) was applied at each
ejection component. We also account for a 10% of the synthesized beam as a
positional error.

Table 1: VLA and MeerKAT observations of MAXI J1848$-$015 discussed in this work. MJD column represents the modified Julian date at the start of the observation. The VLA X-band observation (performed on 2021-02-27) was centered at 10 GHz. The MeerKAT L-band observations were all centered at 1.284 GHz. Date | MJD | Exposure | Date | MJD | Exposure | Date | MJD | Exposure
---|---|---|---|---|---|---|---|---
2021-02-27 | 59272.522 | 4 hr | 2021-07-04 | 59399.901 | 15 min | 2021-12-18 | 59566.443 | 15 min
2021-03-06 | 59279.221 | 15 min | 2021-07-12 | 59407.019 | 15 min | 2022-01-03 | 59582.381 | 15 min
2021-03-13 | 59286.110 | 15 min | 2021-07-26 | 59421.702 | 15 min | 2022-01-16 | 59595.315 | 15 min
2021-03-20 | 59293.150 | 15 min | 2021-07-31 | 59426.898 | 15 min | 2022-01-29 | 59608.433 | 15 min
2021-03-28 | 59301.290 | 15 min | 2021-08-07 | 59433.909 | 15 min | 2022-02-14 | 59624.221 | 15 min
2021-04-05 | 59309.185 | 15 min | 2021-08-15 | 59441.921 | 15 min | 2022-02-27 | 59637.360 | 15 min
2021-04-10 | 59314.093 | 15 min | 2021-08-22 | 59448.673 | 15 min | 2022-03-16 | 59654.239 | 15 min
2021-04-19 | 59323.003 | 15 min | 2021-08-28 | 59454.676 | 15 min | 2022-03-28 | 59666.106 | 15 min
2021-04-24 | 59328.024 | 15 min | 2021-09-05 | 59462.751 | 15 min | 2022-04-10 | 59679.088 | 15 min
2021-05-01 | 59335.077 | 15 min | 2021-09-13 | 59470.646 | 15 min | 2022-04-25 | 59694.105 | 15 min
2021-05-07 | 59341.109 | 15 min | 2021-09-20 | 59477.678 | 15 min | 2022-05-07 | 59706.052 | 15 min
2021-05-15 | 59349.920 | 15 min | 2021-09-27 | 59484.594 | 15 min | 2022-05-23 | 59722.951 | 15 min
2021-05-22 | 59356.032 | 15 min | 2021-10-04 | 59491.658 | 15 min | 2022-06-03 | 59733.961 | 15 min
2021-05-27 | 59361.965 | 15 min | 2021-10-17 | 59504.508 | 15 min | 2022-06-17 | 59747.929 | 15 min
2021-06-05 | 59370.907 | 15 min | 2021-10-23 | 59510.519 | 15 min | 2022-07-03 | 59763.962 | 15 min
2021-06-12 | 59377.956 | 15 min | 2021-11-08 | 59526.638 | 15 min | 2022-07-15 | 59775.849 | 15 min
2021-06-19 | 59384.910 | 15 min | 2021-11-19 | 59537.677 | 15 min | 2022-07-30 | 59790.750 | 15 min
2021-06-27 | 59392.034 | 15 min | 2021-12-04 | 59552.425 | 15 min |  |  |

##  3 Analysis and Results

###  3.1 Initial identification of moving lobes and a possible compact core

Our first radio observation of MAXI J1848$-$015, performed by the VLA on
2021-02-27, revealed two bright sources with flux densities of $256\pm 11$
(“Northern lobe”) and $176\pm 6$ $\mu$Jy (“Southern lobe”) near the reported
position of the system in the X-rays (Figure 1 \- left), with coordinates:

Northern lobe: R.A.(ICRS)$=18^{h}~{}48^{m}~{}49\fs 7729\pm 0.002$,
Dec.(ICRS)$=-01\arcdeg~{}29\arcmin~{}48\farcs 886\pm 0.03$

Southern lobe: R.A.(ICRS)$=18^{h}~{}48^{m}~{}49\fs 7532\pm 0.002$,
Dec.(ICRS)$=-01\arcdeg~{}29\arcmin~{}50\farcs 725\pm 0.03$

As we discuss below in §3.2, our follow-up MeerKAT monitoring campaign allowed
us to establish that these two are outward-moving lobes. Both of these sources
appear partially resolved when compared to the synthesized beam, indicating
expansion of the outflows.

In addition to the bright lobes, we also notice a faint source approximately
half-way between the two lobes, with a flux density of 17.6 $\mu$Jy,
corresponding to a significance of $3.5\sigma$, when compared to the local
noise R.M.S of 5.0 $\mu$Jy (calculated from an annulus around the source).
Coordinates of this faint source (as estimated from the VLA observation on
2021-02-27) are:

Potential compact core: R.A.(ICRS)$=18^{h}~{}48^{m}~{}49\fs 7628\pm 0.002$,
Dec.(ICRS)$=-01\arcdeg~{}29\arcmin~{}49\farcs 758\pm 0.03$

The location of this faint source is consistent with reported localizations of
MAXI J1848$-$015 in the X-rays by Chandra/ACIS and Swift/XRT, indicating that
it is likely the compact core of MAXI J1848$-$015\. Thus, hereafter, we assume
this to be the case.

Figure 1: Left: VLA 10 GHz image of MAXI J1848$-$015 as observed on
2021-02-27. Two bright lobes are clearly detected. At the midpoint between the
two lobes, a low-significance source (at $3.5\sigma$) is present (denoted by a
gray arrow). We demonstrate the motion of these lobes in §3.2. The white
dashed circle indicates the localization of the X-ray transient by Kennea et
al. (2021) based on Swift/XRT, while the yellow dotted circle represents the
localization by Chakrabarty et al. (2021) based on Chandra/ACIS (both plotted
with 90% confidence localization radii). The VLA synthesized beam is
represented with a filled gray ellipse in the corner of the image. Right:
MeerKAT 1.3 GHz image of outflows from MAXI J1848$-$015 as observed on
2022-06-03 (as an example for comparison with the VLA image on the left). The
MeerKAT synthesized beam is represented with a filled gray ellipse in the
corner of the image. The white box in the center indicates the region shown in
the left panel and the red/orange contours are representative of the VLA flux
densities on 2021-02-27 as shown in the left panel (representing 15, 30 and 60
$\mu$Jy, from red to yellow). Note that the two panels have different spatial
and flux density scales.

###  3.2 Modeling the motion of the outflows

The VLA in its most extended A-configuration provides a resolution (the full-
width at half-maximum of the synthesized beam width) of $\sim 0\farcs 2$ at 10
GHz, whereas MeerKAT at 1.28 GHz provides a resolution of $\sim
6^{\prime\prime}$. Thus, while the lobes were already distinguishable in the
VLA observation in February 2021, it was not until April 2021 that the lobes
were resolved by MeerKAT (Figure 2). Prior to this, MeerKAT only detected a
single source with a flux density of $\approx 2$ mJy at a location consistent
with the X-ray and VLA positions of MAXI J1848$-$015\. It is likely that this
source is confused, as in addition to MeerKAT’s inability to resolve the two
sources at early times, contributions from pulsars, which can be abundant in
globular clusters, may provide additional confusing sources at the frequency
and resolution of our MeerKAT observations. The subsequent brightening of the
lobes as they rose to a peak of $\sim 50$ mJy (Figure 2), led to
distinguishable detection of the two lobes by MeerKAT and enabled us to track
the motion of the lobes and constrain their properties. A full analysis of the
flux density evolution of the lobes will be presented in Tremou et al., in.
prep..

Figure 2: Detection and evolution of the outflows from MAXI J1848$-$015 as
seen by MeerKAT (in L-band at 1.28 GHz), since it was first detected in
February 2021. Following the initial detection, both south and north lobes
showed varying brightness. The two lobes were clearly distinguishable for the
first time in April 2021, approximately two months after the initial detection
of the lobes by the VLA.

We model the outflowing lobes with a kinematic model along their direction of
motion, comprised of proper motion with constant deceleration, and eventual
stalling at zero velocity. To do so, we first apply the following coordinate
transformation to the location of the lobes in each observation:

$\begin{bmatrix}\theta^{N,i}_{\perp}\\\
\theta^{N,i}_{\parallel}\end{bmatrix}=\begin{bmatrix}\cos\phi&-\sin\phi\\\
\sin\phi&\cos\phi\end{bmatrix}\begin{bmatrix}\alpha^{N,i}-\alpha^{0}\\\
\delta^{N,i}-\delta^{0}\\\ \end{bmatrix}$ (1)

where $\alpha$ and $\delta$ are right ascension and declination, with
$[\alpha^{N,i},\delta^{N,i}]$ representing coordinates of the northern lobe in
each individual observation $i$. $[\alpha^{0},\delta^{0}]$ represents the
coordinates of the compact core, and $\phi$ is the jet axis on the sky plane -
the angle between the lobes as initially measured in the first VLA observation
($9.1^{\circ}$ eastward from north in the equatorial coordinate system, §3.1).
This transformation yields the displacement of the lobes as a combination of a
component parallel to the jet axis ($\theta^{N,i}_{\parallel}$) and one
perpendicular to that axis ($\theta^{N,i}_{\perp}$), allowing a simple
ballistic modeling of the motion along the jet axis. An identical
transformation is applied to the co-ordinates of the southern lobe in each
observation. This transformation allows us to track the motions of the lobes
along the jet axis while limiting the influence of any potential scatter as
the lobes expand and their weighted mean position becomes dominated by any hot
spots. Such a scatter is expected, given the resolved nature of the lobes in
our initial VLA epoch. While they may remain unresolved by MeerKAT, their
measured positions will be a weighted mean of the emission, which could be
biased by a hot spot in an expanding lobe (Tremou et al., in. prep.).

With the transformed coordinates, we introduce the following model:

$\displaystyle\theta_{\parallel}^{N}(t)$
$\displaystyle=\begin{cases}\mu_{0,N}(t-t_{0})+\frac{\dot{\mu}_{N}}{2}(t-t_{0})^{2}\quad&t<t_{N,\textrm{stop}}\\\
\mu_{0,N}(t_{N,\textrm{stop}}-t_{0})+\frac{\dot{\mu}_{N}}{2}(t_{N,\textrm{stop}}-t_{0})^{2}\quad&t\geq
t_{N,\textrm{stop}}\\\ \end{cases}$ (2)
$\displaystyle\theta_{\parallel}^{S}(t)$
$\displaystyle=\begin{cases}\mu_{0,S}(t-t_{0})+\frac{\dot{\mu}_{S}}{2}(t-t_{0})^{2}\quad&t<t_{S,\textrm{stop}}\\\
\mu_{0,S}(t_{S,\textrm{stop}}-t_{0})+\frac{\dot{\mu}_{S}}{2}(t_{S,\textrm{stop}}-t_{0})^{2}\quad&t\geq
t_{S,\textrm{stop}},\\\ \end{cases}$ (3)

where $\mu_{0,S}$ and $\mu_{0,N}$ are proper motions at launch, $t_{0}$ is
launch time, $\dot{\mu}_{S}$ and $\dot{\mu}_{N}$ are decelerations, and
$t_{N,\textrm{stop}}=t_{0}-\mu_{0,N}/\dot{\mu}_{N}$ and
$t_{S,\textrm{stop}}=t_{0}-\mu_{0,S}/\dot{\mu}_{S}$ are the times when the
lobes stall completely due to deceleration. Given that the localizations of
the northern and southern lobes are determined independently and that the
lobes potentially move through different environments, we implement this model
of motion with the normal likelihood

$\displaystyle
p(\theta^{N,i}_{\parallel},\theta^{S,i}_{\parallel}|\mu_{0,N},\dot{\mu}_{N},\mu_{0,S},\dot{\mu}_{S},\theta_{\textrm{scatter}},t_{0})=\mathcal{N}(\theta^{N,i}_{\parallel}|\theta_{\parallel}^{N}(t_{i}),\sigma^{N,i})\mathcal{N}(\theta^{S,i}_{\parallel}|\theta_{\parallel}^{S}(t_{i}),\sigma^{S,i}),$
(4)

where $\mathcal{N}$ denotes a normal probability density function, $t_{i}$ is
the time of the observation $i$, and

$\displaystyle\sigma^{N,i}=\sqrt{(\sigma^{N,i}_{\theta,\parallel})^{2}+(\theta^{N,i}_{\parallel}\tan\theta_{\textrm{scatter}})^{2}}$
(5)
$\displaystyle\sigma^{S,i}=\sqrt{(\sigma^{S,i}_{\theta,\parallel})^{2}+(\theta^{S,i}_{\parallel}\tan\theta_{\textrm{scatter}})^{2}}.$
(6)

Here, $\sigma^{N,i}_{\theta,\parallel}$, $\sigma^{S,i}_{\theta,\parallel}$ are
the statistical uncertainties on localizations of the lobes in the
$\theta_{\parallel}$ component. The second term considers an additional
localization uncertainty caused by the expansion of the lobes, characterized
by $\theta_{\textrm{scatter}}$, which is the scatter angle as measured from
the core along the jet axis (Figure 3 \- left). In our model we assume that
the motion of the northern and southern lobes are independent of each other in
most aspects except the time of ejection ($t_{0}$) and the scatter angle
($\theta_{\textrm{scatter}}$). Using the same scatter angle for both lobes
implies that the expansion of the lobes is dictated by their initial
conditions. We assumed uniform priors for all model parameters as tabulated in
Table LABEL:tab:parameters.555We also verified that other choices of
uninformative or weakly informative priors (such as log-uniform priors on
$\mu$ and $\dot{\mu}$, or broad gaussian priors for
$\theta_{\textrm{scatter}}$) do not influence the results. We performed
inference using Hamiltonian Monte-Carlo with No-U-turn sampling through pymc
(version 4.1.2, Hoffman & Gelman, 2011; Salvatier et al., 2016). We verified
chain convergence through the rank-normalized convergence diagnostic (Gelman &
Rubin, 1992; Vehtari et al., 2021), finding $\widehat{R}<1.0001$ for each
model parameter. Model parameter posterior samples are visualized in Figure 4,
with point and interval estimations reported in Table LABEL:tab:parameters.
The posterior sample median for $\theta_{\textrm{scatter}}$ is represented in
Figure 3 \- left, and the median and 90% highest density interval of the
posterior models are plotted against the data in Figure 3 \- right.

The model above allows us to estimate the initial proper motion of the lobes
($\mu_{0,N}=33.1\pm 1.4$ mas d-1 and $\mu_{0,S}=48.1\pm 2.1$ mas d-1), and
provides a constraint on the possible outflow launch time
($59246.4_{-2.5}^{+2.4}$ MJD, corresponding to 2021-02-01). The inferred
launch date suggests the launch of outflows may have occurred
$43.1_{-2.5}^{+2.4}$ days after the discovery of the X-ray outburst on
2021-12-20. These constraints now enable us to explore intrinsic properties of
the outflows and accretion in MAXI J1848$-$015.

It is worth noting that, as shown in Figure 3 \- right, the model fails to
explain the positional scatter of the lobes as observed by MeerKAT between
$\sim$ MJD 59300 and 59550. This scatter cannot be described by any simple
model that does not account for effects such as energy injection or systematic
effects such as uncertain localization of the marginally-resolved lobes due to
the presence of hot spots. Thus, it is likely that the statistical uncertainty
in the launch date inferred from our model is underestimated. It is also
difficult to compare our inferred jet launch date with the date of any
contemporaneous X-ray state transition, as MAXI J1848$-$015 spent a large
fraction of its outburst in sun-constraint for many X-ray observatories.

Table 2: Prior assumptions and posterior estimates for model parameters. All priors were assumed uniform ($\mathcal{U}$) with limits set to physically meaningful boundaries. The choice of prior for $t_{0}$ is to encompass the interval from before the detection of the X-ray outburst to after the first detection of the two lobes. Reported posterior estimates are median, 0.16 and 0.84 quantiles. $\widehat{R}$ is the rank-normalized convergence diagnostic (Gelman & Rubin, 1992; Vehtari et al., 2021) to allow assessment of chain convergence. Parameter | Prior | Posterior estimates | $\widehat{R}$
---|---|---|---
$\mu_{0,N}$ (mas d-1) | $\mathcal{U}(0,1000)$ | $33.1\pm 1.4$ | 1.00004
$\dot{\mu}_{N}$ ($10^{-2}$ mas d-2) | $\mathcal{U}(-1000,0)$ | $-3.0\pm 0.8$ | 1.00006
$\mu_{0,S}$ (mas d-1) | $\mathcal{U}(-1000,0)$ | $-48.1\pm 2.1$ | 1.00006
$\dot{\mu}_{S}$ ($10^{-2}$ mas d-2) | $\mathcal{U}(0,1000)$ | $11.6_{-1.2}^{+1.3}$ | 1.00007
$\theta_{\textrm{scatter}}$ (∘) | $\mathcal{U}(0,90)$ | $6.5_{-0.5}^{+0.6}$ | 1.00003
$t_{0}$ (MJD) | $\mathcal{U}(59100,59300)$ | $59246.4_{-2.5}^{+2.4}$ | 1.00002

Figure 3: Left: Position of the outflows from MAXI J1848$-$015 as observed
over time. Unfilled markers represent observations in which the lobes could
not be distinguished clearly. These observations were not included in the
modeling. The gray line represents the jet axis on the sky plane as determined
by the location of the lobes in the first VLA observation. The shaded gray
interval represents the scatter angle (posterior median) as determined by our
model (§3.2). Right: Proper motion of the radio lobes parallel to the jet axis
(colored triangles) and perpendicular to the jet axis (gray triangles), over
time as observed during our monitoring campaign (errorbars are smaller than
the markers). The yellow line indicates a best-fit model, based on posterior
medians, and the shaded yellow interval represent the 90% highest density
interval of model posteriors. Figure 4: Pairwise plots of the posterior
samples for parameters in the model described in §3.2. All samples appear
unimodal. Significant anti-correlations are noticeable between proper motions
and decelerations of the lobes. This is expected as with a lower initial
proper motion, less deceleration would be needed to achieve a similar
displacement. Initial proper motions and decelerations also show some degree
of (anti-)correlation with the predicted outflow launch date. This is likely
due to the fact that the very early behavior of the outflows is only captured
by a single highly influential observation (the VLA observation in February
2021, see Figure 3).

##  4 Discussion

###  4.1 Distance to MAXI J1848$-$015 and its association with GLIMPSE-C01

In order to interpret the proper motions estimated above, we need to constrain
the distance to MAXI J1848$-$015\. First, we can obtain an upper limit on the
distance using our estimates of the initial proper motions of the lobes
($\mu_{0,N}$, $\mu_{0,S}$), using the constraint that they cannot
intrinsically be moving faster than the speed of light (e.g., Fender et al.,
1999; Fender, 2006). Using the posterior samples discussed in §3.2, we obtain
an upper limit of $d_{\textrm{max}}=4.3\pm 0.2$ kpc, which rules out most of
the Galactic bulge.

Second, while GLIMPSE-C01 is within the Galactic plane (located at $\sim$3.4
kpc, Hare et al., 2018), with most of the Galactic stellar mass in this
direction behind it, the fractional density of X-ray binaries in globular
clusters per unit stellar mass is $\sim 150$ times higher than in the rest of
the Galaxy (e.g., Clark, 1975; Heinke et al., 2003).

Thus, while the probability of a chance coincidence – and that MAXI
J1848$-$015 could be behind GLIMPSE-C01 – might have been worth considering in
the absence of any other independent constraints, the presence of a tight
maximum distance constraint that rejects distances ${\lower
3.44444pt\hbox{$\buildrel>\over{\sim}$}}5$ kpc makes this probability
negligible.

In addition, we should then consider whether MAXI J1848$-$015 could be a
foreground object, in front of GLIMPSE-C01. While this possibility cannot be
ruled out, it is still an unlikely scenario, as there is comparatively little
stellar mass in this direction in front of GLIMPSE-C01.

Therefore, we conclude that MAXI J1848$-$015 is likely located within
GLIMPSE-C01, at a distance of $3.4\pm 0.3$ kpc as estimated by Hare et al.
(2018). Hare et al. (2018) estimate the distance to GLIMPSE-C01 based on
identification of red clump stars in infrared observations. Given the high
levels of extinction and crowding, they perform multiple iterations on
selection and provide an estimate of 3.3–3.5 kpc, with a more conservative
interval of 3.0–3.7 kpc. Thus, based on their work, here we conservatively
assume a distance of $3.4\pm 0.3$ kpc.

###  4.2 A relativistic outflow from a globular cluster XRB and implications
on the accretion properties

Using the constraints on initial proper motions of the lobes ($\mu_{0,N}$,
$\mu_{0,S}$), and assuming that the outflows are intrinsically symmetric, we
can estimate the angle of ejection to the line of sight
($\theta_{\textrm{ejection}}$) and the intrinsic velocity of the lobes
($\beta_{\textrm{int}}=v/c$) following Rees (1966); Blandford et al. (1977);
Mirabel & Rodríguez (1994); Fender (2006). For this purpose, we use our
posterior samples for $\mu_{0,N}$ and $\mu_{0,S}$ and estimate
$\beta_{\textrm{int}}\cos\theta_{\textrm{ejection}}=0.19\pm 0.02$. Following
that, with a randomly generated sample of distance values assuming a normal
probability density function for distance with a mean of 3.4 kpc and a
standard deviation of 0.3 kpc (see §4.1), we estimate
$\theta_{\textrm{ejection}}=77^{\circ}\pm 2$ and subsequently
$\beta_{\textrm{int}}=0.79\pm 0.07$ (Figure 5).

If we assume there is no significant misalignment between the jet and
accretion disk (but see Maccarone, 2002), the inferred
$\theta_{\textrm{ejection}}$ indicates a high inclination angle. A high
inclination angle would be in tension with the inclination angle of the inner
accretion disk estimated by Pike et al. (2022), who used X-ray spectral
modeling to infer a low inclination angle of $\approx 26.4\pm 0.5^{\circ}$ for
the inner accretion disk. This tension may indicate that there is a high
degree of disk-jet misalignment in MAXI J1848$-$015\. However, we note that a
high inclination angle would help explain the apparently low X-ray luminosity
of the outburst states observed in this system (as highlighted by Pike et al.,
2022) through obscuration.

Additionally, Pike et al. (2022) indicate that while their modeling is not
particularly sensitive to the inclination of the outer disk, when left to vary
independently, it yields a suggestive value of $79_{-11}^{+6}$ degrees. This
may suggest that the accretion disk could be warped. If this is indeed the
case, the potential alignment between the jet and the outer accretion disk
(while the inner disk is misaligned with both) may be indicative of the
influence of the outer disk on outflow launching in XRBs (e.g., Liska et al.,
2019).

Our inferred values of the initial proper motions ($\approx$ 34 and 50 mas
day-1) and intrinsic jet speed $\beta_{\textrm{int}}=0.79\pm 0.07$ indicate a
relatively slow moving outflow for MAXI J1848$-$015 as compared to some other
XRBs. For example, outflows from GRS 1915+105 (Mirabel & Rodríguez, 1994;
Fender et al., 1999), GRO J1655$-$40 (Hjellming & Rupen, 1995), XTE
J1550$-$564 (Corbel et al., 2002), GX 339$-$4 (Gallo et al., 2004), XTE
J1550$-$564 (Hannikainen et al., 2009), MAXI J1535$-$571 (Russell et al.,
2019), MAXI J1820+070 (Bright et al., 2020) and MAXI J1348$-$630 (Carotenuto
et al., 2021) have been observed to be faster, and relatively close to the
speed of light666It is worth noting that distance to many of these systems is
not well constrained and very few have measured parallaxes. This can influence
estimated intrinsic velocities significantly (Fender et al., 2003).. In
contrast, systems such as SS 433 (Fabian & Rees, 1979), XTE J1752$-$223 (Yang
et al., 2010; Miller-Jones et al., 2011), XTE J1908+094 (Rushton et al.,
2017), V404 Cygni (Miller-Jones et al., 2019), EXO 1846$-$031 (Williams et
al., 2022) have shown slower-moving outflows, with speeds comparable to MAXI
J1848$-$015, as estimated in this work. In addition, among the large-scale
outflows from XRBs, those observed in MAXI J1848$-$015 have propagated a
relatively small distance at a slow apparent speed - e.g., in contrast with
MAXI J1820+070, MAXI J1348$-$630, XTE J1550$-$564, MAXI J1535$-$571\. However,
some XRBs have been observed to decelerate on smaller angular scales (e.g.,
XTE J1752$-$223, EXO 1846$-$031, Miller-Jones et al., 2011; Williams et al.,
2022).

Lastly, it is worth noting that Pike et al. (2022) detected evolving narrow Fe
emission lines in their observations of MAXI J1848$-$015 in December 2020 –
considerably earlier than our first detection of the outflows at the end of
February 2021, or the projected outflow launch inferred from our model, at the
beginning of February 2021. They discuss jet launching as one possible
scenario for the origin of these lines. While we might have found the jets
predicted by Pike et al. (2022), the timeline of events suggests that there
could potentially have been multiple jet launching events. However, we find no
evidence for multiple sets of jet knots in either the VLA or the MeerKAT
observations. In particular, we imaged the VLA observation out to 4.5′ (the
full-width half-maximum of the VLA primary beam at 10 GHz) and searched along
the jet propagation axis for evidence of ejecta that may have been launched
earlier than the lobes detected in the VLA observation (Figure 1 \- left) and
we found no evidence for the presence of such ejecta.

Figure 5: Pairwise plots for the ejection angle and the intrinsic speed of
ejection ($\beta_{\textrm{int}}=v/c$, where $c$ is speed of light), estimated
using the posterior samples for $\mu_{0,N}$ and $\mu_{0,S}$, and assuming a
distance of $3.4\pm 0.3$ kpc (Hare et al., 2018). The shaded light and dark
gray intervals in the pairwise panels containing distance indicate the median
and 95% quantile, respectively, on the maximum possible distance as inferred
in §4.1.

###  4.3 Nature of the system and the compact object

The likely presence of MAXI J1848$-$015 in a globular cluster indicates that
it is a low-mass X-ray binary (as opposed to a high-mass X-ray binary). Based
on its X-ray temporal and spectral properties, particularly the broad Fe line,
Pike et al. (2022) speculate that the compact object in this system may be a
black hole - while determining the nature of the compact object in XRBs using
such features can be uncertain.

Our observations of strong outflows from MAXI J1848$-$015 also hint at a black
hole nature, as similarly powerful (i.e., bright and moving at relativistic
speeds) outflows are more commonly seen from accreting black holes than from
neutron star systems. However, we can not conclusively rule out a neutron star
nature, as accreting neutron stars with powerful outflows have also been
observed – albeit, much less frequently than black holes. For example, such
outflows have been seen from the neutron star XRBs Circinus X-1 (Fender et
al., 2004; Tudose et al., 2008) and Scorpius X-1 (Fomalont et al., 2001a, b),
although both these sources differ from MAXI J1848$-$015 in some of their key
characteristics. Circinus X-1 is a very young ($\sim 5$ kyr; Heinz et al.,
2013) neutron star high-mass X-ray binary system, which are not found in old
star clusters. Scorpius X-1 is a neutron star low-mass X-ray binary
persistently accreting at close to the Eddington luminosity (in contrast to
the transient nature of MAXI J1848$-$015). While it has shown bright
relativistic outflows, at their brightest these were $\sim$an order of
magnitude fainter than the outflows observed in MAXI J1848$-$015 at their
brightest, despite the distances being comparable.

We detect faint radio emission from a putative compact core (§3.1).
Considering the disk-jet coupling in accreting systems (Fender et al., 2003;
Bahramian & Rushton, 2022), the VLA detection and the Swift/XRT observation
performed on the same day as the VLA observation would place MAXI J1848$-$015
below both the black hole tracks and the vast majority of neutron star systems
(L${}_{\textrm{R}}\approx 3\times 10^{26}$ erg s-1, and an apparent
L${}_{\textrm{X}}\approx 10^{35}$ erg s-1). However, the X-ray spectrum of
that observation and the one performed a few days earlier and reported by
Kennea et al. (2021) both indicate a rather soft spectrum (power-law photon
index $\geq 2$) which suggest that the source was not in a hard state at the
time, and thus it would be inappropriate to place it on the radio/X-ray plane.
The high inclination angle also can lead to underestimation of the X-ray
luminosity, making the source even more underluminous in the radio 777For an
example of how inclination angle affects the disk-jet coupling diagnostics,
see the discussion on GRS 1747$-$312 in Panurach et al. (2021).

Thus, while our observations of the outflows from MAXI J1848$-$015 indicate a
behavior consistent with previously observed black hole candidate Low-mass
X-ray binaries, the nature of the compact object in this system cannot be
definitively confirmed.

It is worth noting that if MAXI J1848$-$015 does host a black hole, it would
be among the very small sample of black holes identified in globular clusters.
While globular clusters are expected to produce a large population of black
holes through stellar evolution, almost all of these black holes are expected
to escape the cluster over a rather short period of time (Sigurdsson &
Hernquist, 1993). However, the presence of black holes in globular clusters
has recently been confirmed through detection of dynamically confirmed
“detached” (non-accreting) black holes in NGC 3201 (Giesers et al., 2018,
2019).

To date, there have been no dynamically confirmed black hole XRBs identified
in any globular cluster, although over the past two decades, a handful of
candidates have been identified in Galactic and extragalactic globular
clusters (e.g., see Maccarone et al., 2007; Strader et al., 2012; Chomiuk et
al., 2013; Miller-Jones et al., 2015; Shishkovsky et al., 2018; Dage et al.,
2019, 2020). All the Galactic candidates among these have been identified in
quiescent/faint states (L${}_{\textrm{X}}\leq 10^{34}$ erg s-1) and none have
so far shown bright (L${}_{\textrm{X}}\geq 10^{35}$ erg s-1) outbursts. In
contrast, almost all the currently known bright persistent and transient
Galactic globular cluster XRBs have been confirmed to contain neutron stars
(see Bahramian & Degenaar, 2022, table 7). Thus, MAXI J1848$-$015 may be the
first outbursting black hole X-ray binary identified in a Galactic globular
cluster.

##  5 Conclusion

In this work we presented results of our radio monitoring of the outburst of
MAXI J1848$-$015and report the first detection of expanding and decelerating
outflows from an XRB in a globular cluster. Using MeerKAT observatory, we
monitored large-scale outflows from MAXI J1848$-$015 regularly for over 500
days, obtaining an extraordinary coverage of such outflows. Using a kinematic
model, we constrain initial proper motion of the outflows and constrain
possible launch date. We find
$\beta_{\textrm{int}}\cos\theta_{\textrm{ejection}}=0.19\pm 0.02$. Assuming
MAXI J1848$-$015 is located in the globular cluster GLIMPSE-C01, at 3.4 kpc,
we determine the intrinsic jet speed, $\beta_{\textrm{int}}=0.79\pm 0.07$, and
the inclination angle to the line of sight,
$\theta_{\textrm{ejection}}=76^{\circ}\pm 2^{\circ}$. Additionally, the
estimated proper motions in our modeling imply a maximum possible distance of
$4.3\pm 0.2$ kpc, and indicate comparatively slow moving outflows in contrast
with XRBs that have been observed with outflows. Our findings also provide
additional circumstantial evidence indicating MAXI J1848$-$015 could be a
black hole X-ray binary, which if confirmed would make it the first such
system in a globular cluster to show a transient outburst.

AB thanks Eric W. Koch for helpful discussions. AJT acknowledges support for
this work was provided by NASA through the NASA Hubble Fellowship grant
#HST–HF2–51494.001 awarded by the Space Telescope Science Institute, which is
operated by the Association of Universities for Research in Astronomy, Inc.,
for NASA, under contract NAS5–26555. FC acknowledges support from the Royal
Society through the Newton International Fellowship programme (NIF/R1/211296).
JS acknowledges support from NASA grant 80NSSC21K0628 and the Packard
Foundation. The MeerKAT telescope is operated by the South African Radio
Astronomy Observatory, which is a facility of the National Research
Foundation, an agency of the Department of Science and Innovation. We
acknowledge the use of the Inter-University Institute for Data Intensive
Astronomy (IDIA) data intensive research cloud for data processing. IDIA is a
South African university partnership involving the University of Cape Town,
the University of Pretoria and the University of the Western Cape. We thank
the VLA director and staff for accommodating our DDT request. The National
Radio Astronomy Observatory is a facility of the National Science Foundation
operated under cooperative agreement by Associated Universities, Inc. We
acknowledge extensive use of NASA’s Astrophysics Data System Bibliographic
Services, Arxiv, and SIMBAD (Wenger et al., 2000).

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