# Thermonuclear explosions on neutron stars reveal the speed of their jets

Thomas D. Russell1∗ Nathalie Degenaar2 Jakob van den Eijnden3,4 Thomas
Maccarone5 Alexandra J. Tetarenko5,6,7† Celia Sánchez-Fernández8 James C. A.
Miller-Jones9
Erik Kuulkers10 Melania Del Santo

Relativistic jets are observed from accreting and cataclysmic transients
throughout the Universe, and have a profound affect on their surroundings[1,
2]. Despite their importance, their launch mechanism is not known. For
accreting neutron stars, the speed of their compact jets can reveal whether
the jets are powered by magnetic fields anchored in the accretion flow [3] or
in the star itself [4, 5], but to-date no such measurements exist. These
objects can display bright explosions on their surface due to unstable
thermonuclear burning of recently accreted material, called type-I X-ray
bursts [6], during which the mass accretion rate increases [7, 8, 9]. Here, we
report on bright flares in the jet emission for a few minutes after each X-ray
burst, attributed to the increased accretion rate. With these flares, we
measure the speed of a neutron star compact jet to be
$v=0.38^{+0.11}_{-0.08}$c, much slower than those from black holes at similar
luminosities. This discovery provides a powerful new tool in which we can
determine the role that individual system properties have on the jet speed,
revealing the dominant jet launching mechanism.

The accreting neutron stars 4U 1728$-$34 and 4U 1636$-$536 (hereafter, 4U1728
and 4U1636, respectively) both exhibit frequent type-I X-ray bursts, with
recurrence rates of $\approx$0.3 bursts per hour [10, 11]. For each of these
two sources we carried out an intensive, simultaneous radio and X-ray
observing campaign. The radio observations, which probe the jet emission, were
taken over a three day period with the Australia Telescope Compact Array
(ATCA), with $\sim$30 hours of time on source for each individual source.
Radio data were recorded simultaneously at two frequency bands, 5.5 and 9 GHz.
X-ray monitoring, tracing the accretion flow, consisted of a single long
observation for each source with the INTErnational Gamma-Ray Astrophysics
Laboratory (INTEGRAL), lasting an entire satellite orbit of around 51 hours
and ensuring strictly simultaneous monitoring with our radio campaign. During
the observations, the persistent X-ray emission from both sources was
consistent with being in a hard X-ray spectral state known to be associated
with jets.

Fig. 1:  Strictly simultaneous X-ray and multi-band radio light curves of
4U1728. For the X-rays, we show the 2-second 3–25 keV count rate for each
epoch (panels a, b, c, where each panel corresponds to a different epoch). For
the radio (panels d, e, f), we show the flux densities of the target during
each epoch, measured at 5.5 GHz (red circles) and 9 GHz (blue squares) for
10-minute time-bins. Error bars show the 1-sigma uncertainties on the flux
density. The timing of the X-ray bursts in the X-ray light curves are shown by
the grey vertical lines in the lower panels. We detect 10 X-ray bursts
coincident with our radio monitoring. For all X-ray bursts we find clearly
defined radio counterparts, although for the final bursts of epoch 1 and 2 the
data are not as clear due to the low source elevation and the radio
observation ending close to the burst.

Fourteen type-I X-ray bursts occurred during our INTEGRAL monitoring of
4U1728, ten of which occurred when the source was visible to ATCA. In the 3–25
keV energy band the X-ray bursts all have a similar duration of $\sim$10 s,
but differ in peak brightness by a factor $\sim$2\. Following every X-ray
burst exhibited by 4U1728, we detected a clear radio flare with the radio
emission brightening by a factor of 1.36–1.90 in the minutes after each X-ray
burst (Fig. 1), where the range represents the errors on the average light
curves. The timing of the radio flare peak was frequency dependent; on
average, the 5.5 GHz radio emission peaked 3.5$\pm$0.5 mins after the onset of
the X-ray flare, before fading back to pre-burst levels 20–25 mins after the
X-ray burst (Fig. 2). In contrast, at 9 GHz, the emission peaked 2.5$\pm$0.5
mins after the start of the burst, fading back to pre-burst levels within
$12\pm 2$ mins. Analysis of each individual radio flare shows variability in
both the rise and decay times, as well as the brightening factor (Fig. 2). The
combination of the flare arriving first at higher frequencies and strong
variations between individual flares points to a jet origin of the radio
enhancement. While reflection can also produce time lags at higher
frequencies, reflected emission from the disk or companion star is expected to
occur within a few seconds of the burst, and for the observed radio emission
to arise from thermal reprocessing then the emission region required would
dominate the total emission, being far brighter than even the burst itself
(following arguments in [12]). Furthermore, calculating the brightness
temperature, $T_{\rm b}$, from the brightness and rise times of the radio
flares ($T_{\rm b}>4.5\times 10^{9}$ K) implies that the emission must be non-
thermal in origin. The radio flare properties also suggest that the emission
originates from outside of the orbit of the neutron star, and that it is
unlikely to arise from a disk wind, as its speed would well exceed those
typically observed from accreting neutron stars (by a factor of $\gtrsim 7$).
As such, our observations imply that the radio flares associated with the
type-I X-ray bursts originate from an out-flowing jet.

Fig. 2:  Radio light curves of 4U1728 showing the radio response to each of
the ten individual bursts detected in the radio band. Here we show the
4-minute time intervals at 5.5 GHz (panel a) and 9 GHz (panel b), where the
data points show the centre of the time bin. The width of each time bin is
shown by the error bar in the lower right of each panel and errors on the flux
density are 1-sigma. By combining all of the radio data following a burst, we
show the average response at each frequency on 1-minute timescales (grey
shaded area, where the height represents the uncertainties in the flux
density, and the width is the duration of the time bin), as well as the
average radio flux density at non-burst times (hatched area, where the width
is the uncertainty), determined by randomly sampling the non-burst light
curve. Bursts are numbered according to their detection in the X-ray
monitoring, where 14 bursts were detected. However, only 10 bursts occurred
with simultaneous radio data. Here we see that the radio response from each
single burst show significant variability in brightness, and the rate at which
they brighten.

During their hard states, accreting neutron stars launch a partially self-
absorbed compact jet, that is characterised by a flat to inverted synchrotron
spectrum that extends from the radio to the infrared band. However, at their
highest mass accretion rates during the transition to their soft X-ray state
the jet emission changes dramatically, where discrete, ballistic ejecta can be
launched. The radio emission can show bright flares as the ejecta travel
outwards and interact with their local environment [13], with a radio spectrum
that becomes steep as the peak of the self-absorbed synchrotron spectrum
shifts to lower frequency as the ejecta expand. A steep radio spectrum is
observed even in the case of short-lived, faint ejections from accreting
neutron stars [14]. Throughout our radio monitoring, and in particular during
the radio flares, the radio spectrum remained flat or inverted at all times
indicating that the flares occurred within a compact jet (see Methods
section).

For 4U1636, twelve bursts occurred during our INTEGRAL monitoring, with ten
occurring during our radio observations. However, 4U1636 was radio faint
during our observations such that we were not able to detect flaring at such
low levels of emission on the short timescales required to repeat the
individual burst analysis that we were able to complete for 4U1728. By
combining all of the 4U1636 radio data from the onset of the X-ray burst to 20
mins post-burst we do indeed find an enhancement of the radio emission when
compared to the emission prior to and after the flares. Using the timescales
of the radio flares observed from 4U1728, we place an estimate on the
brightening factor of $\sim$1.2 – 1.8 for 4U1636, similar to results from
4U1728.

Observational and theoretical evidence shows that for the duration of an X-ray
burst, the mass accretion rate onto the neutron star increases [15] by up to a
factor of $\sim$10 [8, 9]. The increased influx of photons from an X-ray burst
onto the accretion flow can be expected to cause two changes to the accretion
flow’s properties driving the increase in the jet emission: first, hot
geometrically thick, optically thin accretion flows, like those seen in hard
state accretion, will be cooled via inverse Compton processes and will hence
collapse geometrically, as their random thermal motions will no longer exceed
their ordered orbital motions. The strong reduction of the hard X-rays in
several systems during type-I bursts has been observed, supporting this
picture [16]. Secondly, Poynting-Robertson drag effects rapidly cool plasma
within the geometrically thin, optically thick disc causing the matter in the
accretion flow to collapse vertically and fall in faster than the standard
viscous timescale, increasing the accretion rate in the disk for the duration
of the X-ray burst [17, 8, 9].

In magneto-centrifugal jet launching models developed to include objects
without an event horizon, such as the Blandford-Payne jet model classically
assumed for weak-magnetic field neutron stars [3], the magnetic field
responsible for jet launching is generated by and anchored in the inner disk.
In this case, the kinetic power entering a relativistic jet is typically
believed to be correlated with the poloidal component of the magnetic field of
the accretion disk [18]. The increase of the mass accretion rate from the
Poynting-Robertson drag will then lead to an increase in magnetic field
strength in the inner accretion disk. However, if the magnetic fields collapse
inward with the gas in the disk, then the poloidal magnetic field component
weakens, which would lead to a suppression of the jet power even with the
increase in the accretion rate. Alternatively, if the magnetic field either
remains static, or collapses more slowly than the gas in the disk, then the
increase in accretion rate simply leads to an increase of kinetic power into
the jet, driven by the burst, in agreement with our observations of a radio
flare associated with each X-ray burst. We note that the radio brightening
could also arise from magnetospheric jet mechanisms, where the neutron star’s
magnetic field is responsible for launching the jet [4, 5], either in powering
the jet continuously, or in the jet’s brightening as it takes over from
weakened magneto-centrifugal launching.

Both accreting stellar-mass black holes and neutron stars launch jets. Despite
these two classes of systems having profoundly different physical
characteristics, i.e., an event horizon versus a stellar surface, very few
differences between the emitted jets have been identified, beyond the jets
appearing to be generally more luminous in black hole systems at similar X-ray
luminosities [19]. In the few cases that it has been estimated, the compact
jet speed from black holes has been shown to be highly relativistic, where
$\beta>0.63$ ($\beta=v/{\rm c}$, where $v$ is velocity and c is the speed of
light[12, 20, 21, 22, 23]), but the most robust constraints generally exceed
$\beta=0.9$. Discrete, ballistic ejecta can also be launched from black holes
as they approach high mass accretion rates ($\sim$a few to tens of percent of
the Eddington luminosity), as well as highly-accreting, persistent (Z-type)
neutron star systems. The speeds of these discrete ejecta can be variable, in
the few cases they have been detected in neutron star systems, the ejecta
travel outwards at mildly relativistic speeds [24, 25] but for black hole
systems, the ejecta can be either highly- or mildly-relativistic [26, 27].
However, to date, no robust measurements have been made for the compact jets
from the transient (atoll-type) neutron star systems, for comparison with the
fast compact jets from black holes. While it is often assumed that the compact
jets from accreting neutron stars should be slower than their black hole
counterparts due to a lower escape velocity, the lack of any observational
evidence to support this has prevented a clear comparison of jet launching
between these objects. The detection of radio bursts allows for such a
comparison for the very first time; different radio frequencies probe emission
from a narrow range of distances downstream in the jet, where higher
frequencies arise from the more compact regions of the jet, closer to the
compact object [28]. As such, by measuring the time delay between the X-ray
burst and the radio flare at each radio frequency (i.e., the time lags), we
are able to measure the compact jet speed[21] from 4U1728 (see Methods section
for more details). We measure a jet speed of $v=0.38^{+0.11}_{-0.08}$ c. This
is the first time robust constraints have been placed on the compact jet speed
from a confirmed accreting neutron star. This result is much slower than
measurements made for the compact jets from black hole systems, and is similar
to the expected escape velocity for a neutron star.

The discovery of jet flares associated with type-I X-ray bursts presents the
first indication that the disk magnetic field collapses more slowly than the
gas in the disk and the first measurement of the compact jet speed from a
neutron star system. Neutron stars offer a unique laboratory to study jet
launching; the spin and magnetic field can often be measured in these systems,
both of which are believed to fundamentally affect jet launching [29, 4]. As
such, the discovery of jet flares associated with type-I X-ray bursts offers a
completely new and robust way in which we can tie the jet speeds to
fundamental jet powering properties. This phenomenon opens a new window into
the dominant jet launching mechanism; measuring the jet speeds from a large
enough population with a variety of mass and spin rates will reveal if there
is a direct connection to these properties, and how they compare to black
holes. For example, magnetospheric jet models predict a connection between the
compact jet speed and neutron star spin [4, 5], while testing how the jet
speed is affected by the neutron star mass can reveal if the jets are
connected to the escape velocity of the system [30]. In addition, a more
detailed study of how individual X-ray bursts, which produce different
increases to the mass accretion rate, impact the jets will significantly
advance our knowledge of jet launching. In particular, the jet response at
higher frequencies would enable even tighter constraints on the jet speed.
Therefore, upgrades to existing facilities such as ATCA, ALMA, SMA, NOEMA, and
new radio and millimetre telescopes such as the Next-Generation Very Large
Array, the Africa Millimetre Telescope, and the Square Kilometre Array will
provide the sensitivity and frequency coverage required to analyse single
radio bursts in much greater detail from many systems.

## References

  * [1] Gallo, E. _et al._ A dark jet dominates the power output of the stellar black hole Cygnus X-1.  _Nature_ 436, 819–821 (2005).
  * [2] Fabian, A. C.  Observational Evidence of Active Galactic Nuclei Feedback.  _ARA &A_ 50, 455–489 (2012).
  * [3] Blandford, R. D. & Payne, D. G.  Hydromagnetic flows from accretion disks and the production of radio jets.  _MNRAS_ 199, 883–903 (1982).
  * [4] Parfrey, K., Spitkovsky, A. & Beloborodov, A. M.  Torque Enhancement, Spin Equilibrium, and Jet Power from Disk-Induced Opening of Pulsar Magnetic Fields.  _ApJ_ 822, 33 (2016).
  * [5] Das, P., Porth, O. & Watts, A. L.  GRMHD simulations of accreting neutron stars with non-dipole fields.  _MNRAS_ 515, 3144–3161 (2022).
  * [6] Galloway, D. K. & Keek, L.  Thermonuclear X-ray Bursts.  In Belloni, T. M., Méndez, M. & Zhang, C. (eds.) _Timing Neutron Stars: Pulsations, Oscillations and Explosions_ , vol. 461 of _Astrophysics and Space Science Library_ , 209–262 (2021).
  * [7] Degenaar, N. _et al._ Accretion Disks and Coronae in the X-Ray Flashlight.  _Space Sci. Rev._ 214, 15 (2018).
  * [8] Fragile, P. C., Ballantyne, D. R., Maccarone, T. J. & Witry, J. W. L.  Simulating the Collapse of a Thick Accretion Disk due to a Type I X-Ray Burst from a Neutron Star.  _ApJ_ 867, L28 (2018).
  * [9] Fragile, P. C., Ballantyne, D. R. & Blankenship, A.  Interactions of type I X-ray bursts with thin accretion disks.  _Nature Astronomy_ 4, 541–546 (2020).
  * [10] Galloway, D. K., Yao, Y., Marshall, H., Misanovic, Z. & Weinberg, N.  Radius-expansion Burst Spectra from 4U 1728-34: An Ultracompact Binary?  _ApJ_ 724, 417–424 (2010).
  * [11] Lewin, W. H. G. _et al._ EXOSAT Observations of 4U/MXB 1636-53: On the Relation between the Amount of Accreted Fuel and the Strength of an X-Ray Burst.  _ApJ_ 319, 893 (1987).
  * [12] Casella, P. _et al._ Fast infrared variability from a relativistic jet in GX 339-4.  _MNRAS_ 404, L21–L25 (2010).
  * [13] Fender, R.  Jets from X-ray binaries.  In Lewin, W. & van der Klis, M. (eds.) _Compact stellar X-ray sources_ , vol. 39 of _Cambridge Astrophysics_ , 381–419 (Cambridge University Press, 2006).
  * [14] Vincentelli, F. M. _et al._ A shared accretion instability for black holes and neutron stars.  _Nature_ 615, 45–49 (2023).
  * [15] in’t Zand, J. J. M. _et al._ A bright thermonuclear X-ray burst simultaneously observed with Chandra and RXTE.  _A &A_ 553, A83 (2013).
  * [16] Maccarone, T. J. & Coppi, P. S.  Hysteresis in the light curves of soft X-ray transients.  _MNRAS_ 338, 189–196 (2003).
  * [17] Ballantyne, D. R. & Everett, J. E.  On the Dynamics of Suddenly Heated Accretion Disks around Neutron Stars.  _ApJ_ 626, 364–372 (2005).
  * [18] Meier, D. L.  The Association of Jet Production with Geometrically Thick Accretion Flows and Black Hole Rotation.  _ApJ_ 548, L9–L12 (2001).
  * [19] Gallo, E., Degenaar, N. & van den Eijnden, J.  Hard state neutron star and black hole X-ray binaries in the radio:X-ray luminosity plane.  _MNRAS_ 478, L132–L136 (2018).
  * [20] Saikia, P. _et al._ Lorentz Factors of Compact Jets in Black Hole X-Ray Binaries.  _ApJ_ 887, 21 (2019).
  * [21] Tetarenko, A. J. _et al._ Radio frequency timing analysis of the compact jet in the black hole X-ray binary Cygnus X-1.  _MNRAS_ 484, 2987–3003 (2019).
  * [22] Tetarenko, A. J. _et al._ Measuring fundamental jet properties with multiwavelength fast timing of the black hole X-ray binary MAXI J1820+070.  _MNRAS_ 504, 3862–3883 (2021).
  * [23] Zdziarski, A. A., Tetarenko, A. J. & Sikora, M.  Jet Parameters in the Black Hole X-Ray Binary MAXI J1820+070.  _ApJ_ 925, 189 (2022).
  * [24] Fomalont, E. B., Geldzahler, B. J. & Bradshaw, C. F.  Scorpius X-1: The Evolution and Nature of the Twin Compact Radio Lobes.  _ApJ_ 558, 283–301 (2001).
  * [25] Spencer, R. E. _et al._ Radio and X-ray observations of jet ejection in Cygnus X-2.  _MNRAS_ 435, L48–L52 (2013).
  * [26] Mirabel, I. F. & Rodríguez, L. F.  A superluminal source in the Galaxy.  _Nature_ 371, 46–48 (1994).
  * [27] Wood, C. M. _et al._ The varying kinematics of multiple ejecta from the black hole X-ray binary MAXI J1820 + 070.  _MNRAS_ 505, 3393–3403 (2021).
  * [28] Blandford, R. D. & Königl, A.  Relativistic jets as compact radio sources.  _ApJ_ 232, 34–48 (1979).
  * [29] Blandford, R. D. & Znajek, R. L.  Electromagnetic extraction of energy from Kerr black holes.  _MNRAS_ 179, 433–456 (1977).
  * [30] Livio, M.  Astrophysical jets: a phenomenological examination of acceleration and collimation.  _Phys. Rep._ 311, 225–245 (1999).

##  1 Methods

###  1.1 X-ray observations

Both 4U1728 and 4U1636 alternate between hard and soft X-ray states on a time
scale of weeks [1]. To ensure that a compact radio jet was present, our ATCA
and INTEGRAL observations were aimed to be performed in the hard X-ray
spectral state. To this end, we triggered our campaigns based on the spectral
state evolution seen from the publicly available X-ray monitoring light curves
of the Monitor of All-sky X-ray Image mission (MAXI, 2–20 keV[2]) and the
Burst Alert Telescope (BAT, 15–50 keV[3]) on board the Swift satellite [4].

####  1.1.1 INTEGRAL data reduction and analysis

INTEGRAL [5, 6] observed 4U1728 from 2021-04-03 14:26 UT to 2021-04-05 23:26
UT (MJD 59,307.6014 – MJD 59,309.9764; obsID 18700020001), and 4U1636 from
2021-10-04 04:10 UT to 2021-10-05 12:05 UT (MJD 59,491.1736 – MJD 59,492.5035;
obsID 18700050001), for total exposure times of 186.6 and 182.6 kiloseconds
(corresponding to 51.83 and 50.72 hours, respectively). These observations
took place in satellite revolutions 2350 (4U1728) and 2419 (4U1636). The
observations were scheduled in the Hexagonal dither pattern (HEX), consisting
of one source-on-axis pointing, six source-off-axis pointings 2.17∘ apart in a
hexagonal pattern centred on the nominal target position. Each target was
monitored almost continuously for an entire revolution, except for the small
slews from pointing to pointing in the pattern, which resulted in periodic
2-minute gaps in the exposures.

In this work we analyse the data provided by INTEGRAL’s instruments JEM-X [7]
and IBIS [8]. JEM-X, the Joint European X-ray Monitor for X-rays, is sensitive
in the 3–35 keV energy range, with a timing resolution capable of reaching 122
$\mu$s and an angular resolution of $3^{\prime}$. It consists of two identical
units X1 and X2, which operated simultaneously. ISGRI, the INTEGRAL Soft
Gamma-Ray detector of the IBIS (Imager on-Board the INTEGRAL Satellite)
instrument is sensitive in the 15 keV to 1 MeV range, and provides an angular
resolution of $12^{\prime}$. The data were reduced using the INTEGRAL Offline
Science Analysis (OSA) v.11.2 [9], provided by the ISDC Data Centre for
Astrophysics (http://www.isdc.unige.ch/, using standard reduction steps.

####  1.1.2 X-ray burst detection

X-ray bursts from 4U1728 and 4U1636 were identified on the 1-s binned JEM-X
light curves extracted in the 3–25 keV band at the science window observation
level (3393 and 3320 seconds duration, respectively). X-ray light curves are
shown in the top panel of Extended Data Figure 1. We computed the mean and
standard deviation of the source count rate during each science window, and
recursively compared the source count rate with these values for each time
bin. When a bin rate exceeded 6$\sigma$ of the persistent level emission we
identified the potential onset of an X-ray burst. The peak of the burst and
subsequent burst decay, which we fitted with an exponential function, were
identified in the system light curve to verify that the rise and decay profile
were consistent with those of a type-I X-ray burst, and to discard potential
disturbances in the system light curve. The burst detection was further
confirmed by extracting the image of the field within a time interval
restricted to the burst duration, to discard contamination to the source light
curve by an event originating in another source in the field of view (FOV).
The burst search resulted in a sample of 14 X-ray bursts for 4U1728 and 12
X-ray bursts for 4U1636.

####  1.1.3 X-ray spectral analysis

Time-resolved analysis of bursts: To derive the main properties of each burst,
such as the temperature, emitting radius and total radiated energy, we
extracted JEM-X and IBIS/ISGRI time-resolved spectra, varying exposure times
as a function of the count rate to ensure similar total numbers of counts in
each spectrum. On the time scales relevant for our current analysis, the
source was not detected by IBIS/ISGRI. For the time-resolved analysis we
therefore only fitted the JEM-X spectra of individual bursts.

We fitted the burst emission with an absorbed black body model (bbodyrad)
after accounting for the underlying persistent accretion emission. To this
end, we extracted JEM-X and ISGRI time-averaged spectra for both 4U1728 and
4U1636 from all data that did not contain a burst. To build these spectra, we
excluded an interval of [-20, 200] seconds around the X-ray burst peak of
4U1728 and [-20, 250] seconds around the (generally longer) 4U1636 bursts. We
further excluded the first six science windows of each revolution to minimise
the possibility of noise in the source spectrum due to instrument activation
after perigee passage. After making these selections, the total exposure time
of the persistent emission spectra was 130.5 ks for 4U1728 and 126.9 ks for
4U1636.

The persistent emission parameters during the time-resolved analysis were
fixed to the values obtained from fitting the pre-burst spectra (see below),
because the data quality and restricted energy range (only JEM-X) did not
allow the persistent emission parameters to be variable during the bursts
[10].

Fits to persistent emission spectra: To characterise the persistent accretion
emission, we performed joint fits to JEM-X (5–-20 keV) and ISGRI (40–100 keV),
where the instruments are well calibrated. Spectral data of each source were
fit using XSpec version 12.11.0 [11]. A multiplicative constant factor was
included in the fits to take into account the uncertainty in the cross-
calibration of the instruments. A systematic error of 2% was applied to the
JEM-X/ISGRI spectra which corresponds to the current uncertainty in the
response matrix. Uncertainties in the results are provided at a 90% confidence
level for a single parameter.

The average spectrum of 4U1728 was fitted with a model consisting of a thermal
Comptonisation component and a hard power-law tail, modified by the
interstellar absorption in the direction of the source ($N_{H}=2.6\times
10^{22}$ cm-2)[10], for which we used the tbabs model [12], available in
XSpec, adopting wilms abundances [12] and vern [13] cross sections. The
spectrum does not display residuals at soft X-ray energies that would be
indicative of thermal emission from the inner regions of the accretion disk
and/or neutron star vicinity. The thermal Comptonisation component was taken
into account using a phenomenological cutoff power-law model, cutoffpl
($\chi^{2}/{\rm d.o.f.}$ = 20.56/22; shown in Extended Data Table 1), and the
more physical nthcomp model ($\chi^{2}/{\rm d.o.f.}$ = 22.34/22; shown in
Extended Data Table 2). In both cases we described the hard power law tail
using the powerlaw model. We note that when fitting the Comptonised emission
using the nthcomp model, the normalization of the hard power-law tail is
poorly constrained. Hence, although a priori the $\chi^{2}/{\rm d.o.f.}$
statistics could favour the more physical nthcomp+powerlaw model, we have used
the cutoffpl+powerlaw model to describe the persistent emission in our fits to
the burst spectra.

The average spectrum of 4U1636 was consistent with a thermal Comptonisation
model, modified by the interstellar absorption in the direction of the source
($N_{H}=4.4\times 10^{21}$ cm-2)[14]. The spectrum does not display residuals
that indicate the need to include a component at soft X-ray energies. The
thermal Comptonisation component was fit with the cutoff powerlaw, cutoffpl
($\chi^{2}/{\rm d.o.f.}$ = 12.86/11; Extended Data Table 1), and nthcomp
($\chi^{2}/{\rm d.o.f.}$ = 8.94/11; Extended Data Table 2) models available in
XSpec. As in the case for 4U1728 we chose the cutoffpl model to fit the data.
We observe some residuals above 70 keV which we tried to model by adding an
additional powerlaw component powerlaw. This resulted in worse statistics but
gave similar results to those obtained for the Comptonisation-only model
($\chi^{2}/{\rm d.o.f.}$ = 12.2/9) so the powerlaw was not included in our
further analysis.

Fits to the burst spectra: The results of our time-resolved spectroscopy of
the bursts, carried out as described above, are listed in Extended Data Table
LABEL:tab:resolved_1728 for 4U1728 and in the Supplementary Information for
4U1636. For both sources, the temperatures near the burst peak are found to be
$\sim$2.5–3 keV, and decrease to $\sim$1–1.5 keV as the burst proceeds. We
measure burst fluences of $\sim 1-3\times 10^{-6}$ erg cm-2 for both sources,
which implies total radiated burst energies of $\sim 10^{39}$ erg. Both the
observed cooling and total radiated energy output are characteristic of
(normal) type-I X-ray bursts [15].

Time-resolved spectroscopy of the INTEGRAL data does not reveal if the bursts
exhibited photo-spheric radius expansion (PRE). Based on the duration of the
bursts we observed ($\sim$10 s for 4U1728 versus $\sim$1 min for 4U1636), we
suspect that the 4U1728 bursts result from the ignition of a pure He layer,
which are bursts that often exhibit PRE. The longer bursts of 4U1636 are more
likely caused by ignition in a mixed He/H layer, which often do not display
PRE [15]. Studying hundreds of bursts observed with RXTE, it was found that
the average increase in the persistent accretion emission (hence presumably
the mass-accretion rate) was similar for non-PRE bursts and PRE bursts, but
that for the latter higher values could be recorded for individual bursts
[16].

###  1.2 Radio observations

####  1.2.1 4U 1728$-$34

We observed 4U1728 with ATCA over three epochs in early June 2021, under
project code C3433. Epoch 1 was carried out between 2021-04-03 12:44:49 UT and
2021-04-04 01:05:59 UT (MJD 59,307.5311 – MJD 59,308.0458), epoch 2 ran from
2021-04-04 13:17:40 UT to 2021-04-05 01:04:29 UT (MJD 59,308.5539 –
59,309.0448), while the shorter epoch 3 was taken between 2021-04-05 13:08:59
UT and 2021-04-05 18:58:39 UT (MJD 59,309.5479 – 59,309.7907). For all
observations, ATCA was in its extended 6 km (6D) configuration
(https://www.narrabri.atnf.csiro.au/operations/array_configurations/configurations.html).
Data were recorded simultaneously in two sub-bands with central frequencies of
5.5 and 9 GHz, with 2 GHz of bandwidth at each central frequency. Each sub-
band was composed of 2048 1-MHz channels. We used PKS 1934$-$638 for bandpass
and flux density calibration, and the nearby (3∘ away) source B1714$-$336 was
used for phase calibration. Using the Common Astronomy Software Applications
(casa version 5.1.2[17]), data were first edited for radio frequency
interference (RFI) and systematic issues, before being calibrated and imaged
following standard procedures (see https://casaguides.nrao.edu/).

####  1.2.2 4U 1636$-$536

4U1636 was also observed by ATCA over three epochs in October 2021 under
project code C3433. Observations occurred between 2021-10-04 00:53:29 UT and
2021-10-04 13:30:09 UT (epoch 1; MJD 59,491.03714120 – MJD 59,491.56260417),
2021-10-04 22:26:20 UT and 2021-10-05 13:17:00 UT (epoch 2; MJD
59,491.93495370 – MJD 59,492.55347222), and 2021-10-05 22:13:19 UT and
2021-10-06 06:02:29 UT (epoch 3; MJD 59,492.92591435 –MJD 59,493.25172454).
ATCA was in its extended 6 km (6A) configuration throughout all observations.
Data were taken at central frequencies of 5.5 and 9 GHz, with 2 GHz of
bandwidth at each frequency, comprised of 2048 1-MHz channels. PKS 1934$-$638
was used for bandpass and flux density calibration, while B1657$-$56 (4.18∘
away) was used for phase calibration. Data were edited and calibrated
following standard procedures in casa.

####  1.2.3 Imaging and variability analysis

Data were initially imaged with the CLEAN task in casa. Initial imaging was
carried out using a Briggs robust parameter of 0 to balance sensitivity and
resolution, while mitigating effects from any side-lobes present in the
images. 4U1728 had an average flux density of $788\pm 6$ $\mu$Jy at 5 GHz and
$880\pm 6$ $\mu$Jy at 9 GHz, corresponding to a radio spectral index,
$\alpha$, of $0.23\pm 0.06$. The measured flat/slightly inverted radio
spectrum is consistent with emission from a self-absorbed compact jet [13].
4U1636 was much more radio faint, where we measured an average flux density of
$45\pm 4$ $\mu$Jy and $55\pm 8$ $\mu$Jy at 5.5 and 9 GHz, respectively, where
$\alpha=0.4\pm 0.5$, also consistent with emission from a compact jet.

To analyse the short-timescale variability of the sources, we first removed
the inner 10kilolambda baselines to remove any diffuse emission in the field.
Second, we subtracted all sources in the field (in the $uv$-plane) using the
casa task uvsub, leaving only the target, a nearby check source to ensure that
the radio flares were intrinsic to the source, and a bright source towards the
edge of our images. The bright source was left in as we were not able to
extract it out sufficiently such that on short timescales significant noise
and variability was introduced into the target and check source light curves
as the bright source moved through the sidelobes in the telescope response.
Keeping the bright source in the $uv$-data well accounted for such effects (as
shown by the stability of the check source in Extended Data Figure 1). For
4U1728, the additional two sources were located at positions of right
ascension (R.A.) of $17^{\rm h}31^{\rm m}48.5^{\rm s}$ and declination (Dec.)
of $-33^{\circ}46^{\prime}56.1^{\prime\prime}$ (check source) and R.A.
$17^{\rm h}31^{\rm m}15.0^{\rm s}$ and Dec.
$-33^{\circ}51^{\prime}16.3^{\prime\prime}$ (bright source). For 4U1636, we
also extracted all sources in the field except a check source (located at R.A.
$16^{\rm h}41^{\rm m}12.9^{\rm s}$ and Dec.
$-53^{\circ}46^{\prime}00.7^{\prime\prime}$) and a bright source (located at
$16^{\rm h}40^{\rm m}38.5^{\rm s}$ and Dec.
$-53^{\circ}45^{\prime}35.05^{\prime\prime}$).

Earlier work on 4U1728 has presented radio observations taken at the time of
type-I X-ray bursts [18]. That work was carried out prior to the upgrade to
the ATCA radio telescope, meaning that the observations were sensitivity
limited, especially at short timescales. As such, [18] were not able to detect
any effects on the radio emission, but their limits are larger than the effect
detected in our study.

For 4U1636, the radio source was a factor of $\approx$17 fainter than 4U1728,
such that we were unable to significantly detect any radio variability on
short timescales for single bursts (due to sensitivity limitations). As such,
we searched for a radio response to the bursts by stacking the burst and non-
burst times together, where the burst duration was taken from the 4U1728
results. Stacking the two (5.5 and 9 GHz) bands provides average flux
densities of $68\pm 9$ $\mu$Jy in the 20 mins after each X-ray burst, and
$46\pm 4$ $\mu$Jy outside of the burst times. Although we were not able to
measure such a clear radio brightening for each individual X-ray burst from
4U1636, our results do indicate that there was indeed radio flaring associated
with the X-ray bursts. Despite the limitations with sensitivity, we place an
estimate on the brightening factor of $\sim$1.2 – 1.8 for this source, similar
to results from 4U1728.

Radio emission can arise from either thermal or non-thermal processes, which
could originate from either a jet, the accretion flow, or wind emission.
However, from our radio light curves, we measure a lower-limit on the
brightness temperature of $T_{\rm b}>4.5\times 10^{9}$ K (assuming a distance
to source, D, of $5.2\pm 0.5$ kpc[15]), indicating that the emission must
arise from non-thermal processes [19, 20]. In addition, assuming that the
inverse Compton limit is not violated, the rise and brightness of the radio
flares suggests a minimum size scale of the emission that is beyond the
orbital period expected for 4U1728 [10, 21, 22, 23, 24]. Taking the minimum
size scale limit, we also find that for the emission to originate from a disk
wind, the wind must be travelling at a speed well in excess of those typically
observed from accreting neutron stars, by a factor of at least seven [25]. As
such, the timescales and brightness of the radio flares indicate a jet origin
of the emission. Throughout our observations, the radio spectrum remained flat
to inverted, and did not show a steepening of the spectrum at any time
(Extended Data Figure 2). This evolution is typical of compact jet emission,
and suggests that these flares do not arise from ballistic ejection events.

Assuming equipartition between the magnetic field and the electrons, and one
proton per electron, from the observed (average) brightening and flare times
we estimate a minimum energy of $\sim(2-3)\times 10^{37}$ erg required to
produce the jet flares (Following equations 9.2, 9.3, and 9.4 presented in
[13]). This corresponds to a mean jet power of $\sim 1\times 10^{35}$ erg s-1
with an equipartition magnetic field of $\sim$1 G. If we assume that the
flares are indeed optically-thick, we also find similar estimates (see Section
3 in [26]).

####  1.2.4 Measuring and modelling multi-band radio time-lags in 4U1728

To search for time-lags between the burst signals in different electromagnetic
frequency bands from 4U1728, we first identify segments of the light curves
for which each burst is contributing enhanced emission over the quiescent
level in both the radio and X-ray light curves (see shaded regions in Extended
Data Figure 1, where each burst is labelled according to Extended Data Table
LABEL:tab:resolved_1728). As we wish to remain consistent across all bursts,
we define the burst segments as beginning right before the respective X-ray
burst until +120 minutes after the X-ray burst (with the exception of Burst 8
(B8), where we truncate the burst segment to +60 minutes after the X-ray burst
in order to avoid overlap with the next X-ray burst). For each burst segment,
we then created cross-correlation functions with these respective time
segments as inputs, comparing both the X-ray to radio and 9 GHz to 5.5 GHz
signals (using the z-transformed discrete correlation function algorithm
[ZDCF][27, 28]). Further, we also repeated this procedure for an average
’stacked’ version of all of the 9 GHz to 5.5 GHz bursts (see Extended Data
Figure 2 and 3). The resulting measured time-lags are shown in Extended Data
Figure 4 and Extended Data Table 4. Note that we do not consider Burst 3 and
Burst 11 in our cross-correlation analysis of single bursts, as they occur
close to the end of the radio observing window on that date and the radio
signal is cut off before the flare decays. However, they are included in our
stacked analysis (Fig. 2).

As our measured time-lags have an electromagnetic frequency dependence, which
is characteristic of out-flowing jet emission, we choose to implement the
model used in [21], appropriate for modelling the time-lags from a compact
jet. We only use the more statistically robust lags from the stacked signals
of all the bursts for our modelling analysis (see Extended Data Table 4;
although the individual burst lags are consistent within uncertainties of the
stacked values). In this model, we assume a continuous, conical, constant bulk
Lorentz factor jet, where the X-ray emission originates in a region close to
the neutron star and information from this region propagates down the jet axis
towards the radio emission regions. Therefore, the time-lags can be
represented as:

$\tau_{\rm lag}=\frac{z_{{\rm
norm}}}{\beta\,c}\,(\xi_{2}-\xi_{1})\,(1-\beta\cos\theta)\,.$ (1)

Here, $\beta$ represents the bulk jet speed (units of $v/c$, where $c$
indicates the speed of light, and the bulk Lorentz factor,
$\Gamma=(1-\beta^{2})^{-1/2}$) and $\theta$ represents the inclination angle
of the jet axis to our line of sight. To relate the jet size scale to the
electromagnetic frequency scale, we use the metric $z=z_{\rm norm}\xi=z_{\rm
norm}{\nu}^{-1}$ ($\xi_{\rm 1}$ and $\xi_{\rm 2}$ are the inverse of the
electromagnetic frequencies between which the time-lags were measured). Note
that we introduce the $\xi$ parameter in the model formalism implemented in
this work, rather than directly use the electromagnetic frequencies, as was
done in [21]. We do this as we wish to simultaneously model X-ray to radio
lags (at both radio bands), as well as lags between the 9 GHz and 5.5 GHz
radio bands, and the $\xi$ formalism allows us to place all of these lags on a
common axis of $\xi_{2}-\xi_{1}$). We also note that the $z\propto\nu^{-1}$
follows the standard jet model of [28], well-fitting the data. To obtain a
more physically motivated prior for the jet size scale normalization parameter
in our modelling, we use a one-zone synchrotron model [29, 30] to express this
normalization in terms of observationally measurable parameters of the system.
Following the procedure outlined in Appendix C of [31], we can relate this
normalization to an estimate of the size-scale of the emitting region at the
jet base, which is defined primarily by the shape of the synchrotron spectrum.

$z_{\rm norm}=z_{\rm base}\nu_{\rm
base}=C_{1}S_{\mathrm{\nu,b}}^{(p+6)/(2p+13)}\nu_{\mathrm{b}}^{-1}D^{\frac{2p+12}{2p+13}}\nu_{\rm
base}$ (2)

Here, $\nu_{\mathrm{b}}$ is the synchrotron break frequency in the broad-band
spectrum, $S_{\mathrm{\nu,b}}$ is the flux density at the break, $D$ is the
distance to the source, $p$ is the power law index of the electron energy
distribution (where $p$ is related to the optically thin synchrotron spectral
index via $p=-2\alpha_{\rm thin}+1$), $C_{1}$ is a constant term dependent on
properties of the non-thermal electron population and fundamental constants,
where we assume that the energy of the non-thermal electrons equals the
magnetic energy density, and average over an isotropic distribution of pitch
angles for the electrons, and assume $\nu_{\rm base}=\nu_{\mathrm{b}}$. To
cross-check this jet size-scale method, we compare our estimate to the
benchmark value presented in [32]. In that work, the neutron star jet base
size-scale was estimated to be $\sim 6\times 10^{8}\,{\rm cm}$, based on
scaling the known jet base size-scale in stellar-mass black holes (calculated
from the measured $\sim 100$ ms time-lag between X-ray and optical/infrared
emission found in several stellar-mass black hole systems) down by a factor of
5 due to the typical compact object mass difference. Our modelling yields a
neutron star jet base size-scale of $\sim 1.3\times 10^{8}\,{\rm cm}$, which
is reasonably consistent with the estimate from [32], validating the jet size-
scale used in our modelling. We note that any possible signal from the
counter-jet, on top of the brighter approaching jet, will not affect our lag
measurements as the emissions from the approaching and counter-jet have been
shown to arrive at the observer at the same time, assuming both jets are
symmetric [33].

We fit Equation 1 to our measured time-lags using a Markov Chain Monte-Carlo
algorithm (MCMC [34]). In our fitting runs, we allow the bulk Lorentz factor
($\Gamma$) to be a free parameter, while we sample from known distributions of
inclination angle (uniform distribution in $\cos(\theta)$, where
$\theta=25-53^{\circ}$ [35]), synchrotron break frequency (normal
distribution, $\nu_{\mathrm{b}}=(6\pm 5)\times 10^{13}$ Hz[36]), flux density
at the break (normal distribution, $S_{\mathrm{\nu,b}}=4\pm 2$ mJy[36]),
distance (normal distribution, $D=5.2\pm 0.5$ kpc[15]), and optically thin
synchrotron spectral index (normal distribution, $\alpha_{\rm thin}=-0.8\pm
0.7$[36]). We note that for definite positive priors, such as the flux density
and synchrotron break frequency, negative values were prohibited. The best-fit
result is taken as the median of the one-dimensional posterior distributions
and the uncertainties are reported as the range between the median and the
15th percentile (-), and the 85th percentile and the median (+), corresponding
approximately to $1\sigma$ errors. Our best-fit bulk Lorentz factor is
$\Gamma=1.08^{+0.06}_{-0.03}$, corresponding to a jet velocity of
$\beta=0.38^{+0.11}_{-0.08}\,v/{\rm c}$, and the best-fit model is overlaid on
the measured lags in Extended Data Figure 5. We note that we choose to fit for
the bulk Lorentz factor $\Gamma$, rather than the dimensionless jet speed
$\beta$ (where $\Gamma=(1-\beta^{2})^{-1/2}$), as it is computationally easier
to avoid the hard limits on $\beta$. Using these best-fit values, the ratio of
the approaching to counter-jet flux density is dependent upon jet speed
($\beta$), inclination angle ($\theta$), and spectral index ($\alpha$)
according to, $\frac{F_{\rm app}}{F_{\rm
counter}}=\left(\frac{1+\beta\cos\theta}{1-\beta\cos\theta}\right)^{2-\alpha}$.
Inputting our best-fit values for 4U1728, with a flat spectrum ($\alpha=0$)
yields $\frac{F_{\rm app}}{F_{\rm counter}}\sim 2-4$.

## References

  * [1] authorMuñoz-Darias, T., authorFender, R. P., authorMotta, S. E. & authorBelloni, T. M.  titleBlack hole-like hysteresis and accretion states in neutron star low-mass X-ray binaries.  _journal MNRAS_ volume443, pages3270–3283 (year2014).
  * [2] authorMatsuoka, M. _et al._ titleThe MAXI Mission on the ISS: Science and Instruments for Monitoring All-Sky X-Ray Images.  _journalPASJ_ volume61, pages999 (year2009).
  * [3] authorKrimm, H. A. _et al._ titleThe Swift/BAT Hard X-Ray Transient Monitor.  _journal ApJS_ volume209, pages14 (year2013).
  * [4] authorGehrels, N. _et al._ titleThe Swift Gamma-Ray Burst Mission.  _journal ApJ_ volume611, pages1005–1020 (year2004).
  * [5] authorWinkler, C. _et al._ titleThe INTEGRAL mission.  _journal A&A_ volume411, pagesL1–L6 (year2003).
  * [6] authorKuulkers, E. _et al._ titleINTEGRAL reloaded: Spacecraft, instruments and ground system.  _journalNewAR_ volume93, pages101629 (year2021).
  * [7] authorLund, N. _et al._ titleJEM-X: The X-ray monitor aboard INTEGRAL.  _journal A&A_ volume411, pagesL231–L238 (year2003).
  * [8] authorUbertini, P. _et al._ titleIBIS: The Imager on-board INTEGRAL.  _journal A&A_ volume411, pagesL131–L139 (year2003).
  * [9] authorCourvoisier, T. J. L. _et al._ titleThe INTEGRAL Science Data Centre (ISDC).  _journal A&A_ volume411, pagesL53–L57 (year2003).
  * [10] authorWorpel, H., authorGalloway, D. K. & authorPrice, D. J.  titleEvidence for Accretion Rate Change during Type I X-Ray Bursts.  _journal ApJ_ volume772, pages94 (year2013).
  * [11] authorArnaud, K.  titleXSPEC: The First Ten Years.  In editorJacoby, G. & editorBarnes, J. (eds.) _booktitleAstronomical Data Analysis Software and Systems V_ , vol. volume101 of _seriesAstronomical Society of the Pacific Conference Series_ , pages17 (year1996).
  * [12] authorWilms, J., authorAllen, A. & authorMcCray, R.  titleOn the Absorption of X-Rays in the Interstellar Medium.  _journal ApJ_ volume542, pages914–924 (year2000).
  * [13] authorVerner, D. A. & authorYakovlev, D. G.  titleAnalytic FITS for partial photoionization cross sections.  _journal A&AS_ volume109, pages125–133 (year1995).
  * [14] authorGüver, T. _et al._ titleBurst-Disk Interaction in 4U 1636-536 as Observed by NICER.  _journal ApJ_ volume935, pages154 (year2022).
  * [15] authorGalloway, D. K., authorMuno, M. P., authorHartman, J. M., authorPsaltis, D. & authorChakrabarty, D.  titleThermonuclear (Type I) X-Ray Bursts Observed by the Rossi X-Ray Timing Explorer.  _journal ApJS_ volume179, pages360–422 (year2008).
  * [16] authorWorpel, H., authorGalloway, D. K. & authorPrice, D. J.  titleEvidence for Enhanced Persistent Emission During Sub-Eddington Thermonuclear Bursts.  _journal ApJ_ volume801, pages60 (year2015).
  * [17] authorCASA Team _et al._ titleCASA, the Common Astronomy Software Applications for Radio Astronomy.  _journalPASP_ volume134, pages114501 (year2022).
  * [18] authorMigliari, S. _et al._ titleDisc-jet coupling in an atoll-type neutron star X-ray binary: 4U 1728-34 (GX 354-0).  _journal MNRAS_ volume342, pagesL67–L71 (year2003).
  * [19] authorRybicki, G. B. & authorLightman, A. P.  _titleRadiative processes in astrophysics_ (publisherA Wiley-Interscience Publication, New York: Wiley, year1979).
  * [20] authorLongair, M. S.  _titleHigh energy astrophysics. Vol.1: Particles, photons and their detection_ (publisherCambridge University Press, Cambridge, UK, year1992).
  * [21] authorHeinke, C. O. _et al._ titleGalactic Ultracompact X-Ray Binaries: Disk Stability and Evolution.  _journal ApJ_ volume768, pages184 (year2013).
  * [22] authorDubus, G., authorDone, C., authorTetarenko, B. E. & authorHameury, J.-M.  titleThe impact of thermal winds on the outburst lightcurves of black hole X-ray binaries.  _journal A&A_ volume632, pagesA40 (year2019).
  * [23] authorVincentelli, F. M. _et al._ titleDiscovery of a thermonuclear Type I X-ray burst in infrared: new limits on the orbital period of 4U 1728-34.  _journal MNRAS_ volume495, pagesL37–L41 (year2020).
  * [24] authorVincentelli, F. M. _et al._ titleSub-second infrared variability from the archetypal accreting neutron star 4U 1728-34.  _journal MNRAS_ volume525, pages2509–2518 (year2023).
  * [25] authorDíaz Trigo, M. & authorBoirin, L.  titleAccretion disc atmospheres and winds in low-mass X-ray binaries.  _journalAstronomische Nachrichten_ volume337, pages368 (year2016).
  * [26] authorFender, R. & authorBright, J.  titleSynchrotron self-absorption and the minimum energy of optically thick radio flares from stellar mass black holes.  _journal MNRAS_ volume489, pages4836–4846 (year2019).
  * [27] authorAlexander, T.  titleIs AGN Variability Correlated with Other AGN Properties?—ZDCF Analysis of Small Samples of Sparse Light Curves.  _journalAstronomical Time Series_ volumeEds. D. Maoz, A. Sternberg, and E.M. Leibowitz, pages163 (year1997).
  * [28] authorAlexander, T.  titleImproved AGN light curve analysis with the z-transformed discrete correlation function.  _journalArXiv e-prints_ (year2013).
  * [29] authorChaty, S., authorDubus, G. & authorRaichoor, A.  titleNear-infrared jet emission in the microquasar XTE J1550-564.  _journal A&A_ volume529, pagesA3 (year2011).
  * [30] authorRybicki, G. & authorLightman, A.  titleRadiative Processes in Astrophysics.  _journalRadiative Processes in Astrophysics_ volumeWiley Interscience Publication (year1979).
  * [31] authorRussell, T. D. _et al._ titleRapid compact jet quenching in the Galactic black hole candidate X-ray binary MAXI J1535-571.  _journal MNRAS_ volume498, pages5772–5785 (year2020).
  * [32] authorMaccarone, T. J., authorvan den Eijnden, J., authorRussell, T. D. & authorDegenaar, N.  titleEclipses of jets and discs of X-ray binaries as a powerful tool for understanding jet physics and binary parameters.  _journal MNRAS_ volume499, pages957–973 (year2020).
  * [33] authorMaccarone, T. J., authorPattie, E. C. & authorTetarenko, A. J.  titleThe simultaneity of emission from approaching and receding jets.  _journal MNRAS_ volume517, pagesL76–L80 (year2022).
  * [34] authorForeman-Mackey, D., authorHogg, D. W., authorLang, D. & authorGoodman, J.  titleemcee: The MCMC Hammer.  _journalPASP_ volume125, pages306–312 (year2013).
  * [35] authorWang, Y. _et al._ titleStudy of the X-ray properties of the neutron star binary 4U 1728-34 from the soft-to-hard state.  _journal MNRAS_ volume484, pages3004–3016 (year2019).
  * [36] authorDíaz Trigo, M. _et al._ titleALMA observations of 4U 1728-34 and 4U 1820-30: first detection of neutron star X-ray binaries at 300 GHz.  _journal A&A_ volume600, pagesA8 (year2017).

### Acknowledgments

We thank the anonymous referees for their excellent comments and suggestions
on the manuscript. This research was made possible by an XS grant
OCENW.XS3.096 from the Netherlands Organisation for Scientific Research (NWO),
awarded to ND. We thank participants of the ISSI Beijing, Charleston, and
Vasto meetings for very useful discussions. This research was partly based on
observations with INTEGRAL, an ESA project with instruments and science data
centre funded by ESA member states (especially the PI countries: Denmark,
France, Germany, Italy, Switzerland, Spain) and with the participation of
Russia and the USA. We thank the INTEGRAL staff for coordinating the X-ray
observations possible. We also thank Jamie Stevens and ATCA staff for
scheduling the ATCA observations. ATCA is part of the Australia Telescope
National Facility (https://ror.org/05qajvd42) which is funded by the
Australian Government for operation as a National Facility managed by CSIRO.
We acknowledge the Gomeroi people as the Traditional Owners of the ATCA
observatory site. TDR acknowledges support as an INAF IAF research fellow. AJT
acknowledges partial 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.

### Author contributions statement

TDR, ND, JvdE, JCAM-J, and TM coordinated the radio and X-ray observations.
CSF analysed the X-ray data. TDR carried out and analysed the radio
observations, with help from JCAM-J. AJT performed the time lag analysis. TDR,
ND, JvdE, TM, AJT, and CSF interpreted the results. All authors made
significant contributions to the writing of the manuscript. ND and JvdE wrote
the NWO XS grant to secure ATCA observing time. TM and ND worked on the
original idea of looking for a jet response to thermonuclear bursts.

### Competing Interest Statement

The authors declare no competing interests

### Data availability

Data from INTEGRAL are publicly available online
(https://www.isdc.unige.ch/integral/archive). Raw ATCA data are provided at
the Australia Telescope Online Archive (https://atoa.atnf.csiro.au/query.jsp),
under project code C3433. Calibrated radio and X-ray light curve data (as
shown in Figure 1 and 2, and Extended Data Figures 1 and 2) are available
online at https://github.com/russell1/jet-burst-data.git. Radio timing scripts
are provided online at https://github.com/tetarenk/AstroCompute_Scripts.
Calibrated measurement sets as well as time-lag analysis scripts (Extended
Data Figures 3, 4, and 5) can be requested from the corresponding author.

### Corresponding author

All correspondence, including requests for data and scripts, and reprints and
permissions should be sent to T. D. Russell (email: thomas.russell@inaf.it).

Extended Data Table 1: Results from fitting the persistent X-ray spectrum to a phenomenological model (using cutoffpl+powerlaw). For both the cutoffpl (cut) and powerlaw (PL) model, the flux, $F$, is in units of erg cm-2 s-1, $\Gamma_{\rm X}$ is the photon index of the powerlaw, and $K$ is the normalisation in photons keV-1 cm-2 s-1 at 1 keV. $E$ is the energy of the cutoffpl in units of keV. Model: | cutoffpl+powerlaw
---|---
Parameter | 4U1728 | 4U1636
$\Gamma_{\rm cX,ut}$ | $1.8_{-0.1}^{+0.1}$ | $1.83_{-0.09}^{+0.09}$
$E_{\rm cut}$ | $11_{-1}^{+1}$ | $96_{-14}^{+20}$
$K_{\rm cut}$ | $1.2_{-0.2}^{+0.2}$ | $0.30_{-0.01}^{+0.01}$
$F_{\rm cut}(\times 10^{-9})$ | $3.89_{-0.1}^{+0.03}$ | $2.1_{-0.1}^{+0.1}$
$\Gamma_{\rm X,PL}$ | $1.7_{-0.1}^{+0.1}$ | –
$K_{\rm PL}$ | $0.04_{0.01}^{0.02}$ | –
$F_{\mathrm{PL}}(\times 10^{-9})$ | $0.273_{-0.006}^{+0.005}$ | –
$\chi^{2}/{\rm d.o.f.}$ | $20.56/22$ | 12.86/11

Extended Data Table 2: Results from fitting the persistent X-ray spectrum to a more physical (nthcomp+powerlaw) model. For both the nthcomp (nthcomp) and powerlaw (PL) model, the flux, $F$, is in units of erg cm-2 s-1, $\Gamma_{\rm X}$ is the photon index of the powerlaw, and $K$ is the normalisation in photons keV-1 cm-2 s-1 at 1 keV. For nthcomp alone, $kT_{\rm e}$ is the electron temperature in keV, while $kT_{\rm bb}$ is the seed photon temperature in keV. Model: | nthcomp+powerlaw
---|---
Parameter | 4U1728 | 4U1636
$\Gamma_{\rm X,nthcomp}$ | $2.2_{-0.2}^{+0.1}$ | $1.90_{-0.06}^{+0.06}$
$kT_{\rm e}$ | $6_{-1}^{+2}$ | $31_{-6}^{+13}$
$kT_{\rm bb}$ | ${0.1}$ | ${0.1}$
$K_{\rm nthcomp}$ | $2.0_{-0.2}^{+0.2}$ | $0.31_{-0.03}^{+0.04}$
$F_{\rm nthcomp}(\times 10^{-9})$ | $3.6_{-0.2}^{+0.2}$ | $2.0_{-0.1}^{+0.1}$
$\Gamma_{\rm X,PL}$ | $2.2_{-0.8}^{+0.3}$ | –
$K_{\rm PL}$ | $0.2_{-0.2}^{+0.5}$ | –
$F_{\rm PL}(\times 10^{-9})$ | $0.5_{-0.5}^{+0.2}$ | –
$\chi^{2}/{\rm d.o.f.}$ | $22.34/22$ | 8.94/11

Extended Data Table 3: Time resolved spectroscopy of the 4U1728 X-ray bursts. For each burst spectra were extracted in three time bins. Burst 9 was excluded from fitting due to artefacts in the X-ray data immediately before and after the burst. Burst | Start | Stop | Exp. | $kT_{\rm bb}$ | $R_{\rm km}^{2}/D_{10}^{2}$ | Flux |  $\chi^{2}$/d.o.f.
---|---|---|---|---|---|---|---
| (MJD) | (MJD) | (sec) | (keV) |  | $\times 10^{-8}$ |
|  |  |  |  |  |  (erg/cm2/s) |
B1 | 59,307.719803 | 59,307.719837 | 2.38 | $2.3_{-0.7}^{+0.9}$ | $195_{-68}^{+68}$ | $6_{-2}^{+2}$ | 1.76/4
| 59,307.719837 | 59,307.719895 | 3.95 | $1.5_{-0.5}^{+0.6}$ | $606_{-249}^{+249}$ | $4_{-2}^{+1}$ | 1.89/4
| 59,307.719895 | 59,307.720011 | 7.97 | – | – | – | –
B2 | 59,307.899837 | 59,307.899872 | 2.33 | $2.7_{-0.6}^{+0.8}$ | $134_{-35}^{+35}$ | $8_{-2}^{+2}$ | 0.54/4
| 59,307.899872 | 59,307.899930 | 3.89 | $2.4_{-0.6}^{+0.7}$ | $113_{-32}^{+32}$ | $4_{-1}^{+1}$ | 0.40/4
| 59,307.899930 | 59,307.900046 | 7.98 | $1.5_{-0.6}^{+0.7}$ | $160_{-71}^{+71}$ | $0.9_{-0.4}^{+0.4}$ | 1.30/4
B3 | 59,308.035578 | 59,308.035613 | 2.35 | $2.2_{-0.6}^{+0.7}$ | $288_{-80}^{+80}$ | $8_{-2}^{+2}$ | 1.04/4
| 59,308.035613 | 59,308.035671 | 3.91 | $2.5_{-0.7}^{+0.7}$ | $104_{-35}^{+35}$ | $4_{-1}^{+1}$ | 2.35/4
| 59,308.035671 | 59,308.035787 | 8.00 | $<2$ | $<11$ | $0.4_{-1}^{+1}$ | 1.14/2
B4 | 59,308.163425 | 59,308.163460 | 2.38 | $2.6_{-0.7}^{+0.8}$ | $132_{-45}^{+45}$ | $7_{-2}^{+2}$ | 0.93/4
| 59,308.163460 | 59,308.163518 | 3.94 | $2.4_{-0.8}^{+1.4}$ | $86_{-38}^{+38}$ | $3_{-1}^{+1}$ | 0.89/4
| 59,308.163518 | 59,308.163634 | 7.99 | $<4.2$ | $137_{-97}^{+97}$ | $0.7_{-0.5}^{+1}$ | 1.23/3
B5 | 59,308.281990 | 59,308.282025 | 2.37 | $2.6_{-0.9}^{+1.2}$ | $104_{-45}^{+45}$ | $5_{-2}^{+2}$ | 1.13/4
| 59,308.282025 | 59,308.282083 | 3.97 | $2.7_{-1.0}^{+1.7}$ | $62_{-27}^{+27}$ | $4_{-2}^{+2}$ | 0.62/4
| 59,308.282083 | 59,308.282199 | 8.00 | $<3.3$ | – | – | –
B6 | 59,308.401388 | 59,308.401423 | 2.38 | $2.5_{-0.7}^{+1.1}$ | $93_{-35}^{+35}$ | $4_{-1}^{+1}$ | 0.27/4
| 59,308.401423 | 59,308.401481 | 3.93 | $2.2_{-0.5}^{+0.7}$ | $152_{-44}^{+44}$ | $4_{-1}^{+1}$ | 0.09/4
| 59,308.401481 | 59,308.401597 | 7.98 | $<4.1$ | $100_{-75}^{+75}$ | $0.5_{-0.3}^{+1.0}$ | 0.85/3
B7 | 59,308.563761 | 59,308.563796 | 2.37 | $3.0_{-0.8}^{+1.4}$ | $75_{-26}^{+26}$ | $7_{-2}^{+3}$ | 1.27/4
| 59,308.563796 | 59,308.563854 | 3.97 | $1.9_{-0.6}^{+0.9}$ | $246_{-94}^{+94}$ | $4_{-1}^{+1}$ | 2.35/4
| 59,308.563854 | 59,308.563969 | 7.95 | – | – | – | –
B8 | 59,308.732175 | 59,308.732210 | 2.35 | $2.0_{-0.5}^{+0.5}$ | $368_{-100}^{+100}$ | $7_{-2}^{+2}$ | 1.25/4
| 59,308.732210 | 59,308.732268 | 3.94 | $1.7_{-0.6}^{+0.6}$ | $450_{-127}^{+127}$ | $4_{-1}^{+1}$ | 2.94/4
| 59,308.732268 | 59,308.732384 | 7.96 | $1.3_{-1.3}^{+1.5}$ | $207_{-135}^{+135}$ | $0.8_{-0.4}^{+1}$ | 0.54/3
B9 | 59,308.887569 | 59,308.887604 | 2.37 | $2.2_{-0.7}^{+0.9}$ | $224_{-82}^{+82}$ | $6_{-2}^{+2}$ | 0.40/4
| 59,308.887604 | 59,308.887662 | 3.95 | $2.5_{-0.6}^{+0.8}$ | $112_{-34}^{+34}$ | $5_{-2}^{+2}$ | 0.79/4
| 59,308.887662 | 59,308.887777 | 7.95 | – | – | – | –
B10 | 59,309.029884 | 59,309.029918 | 2.36 | $2.3_{-0.6}^{+0.8}$ | $209_{-60}^{+60}$ | $6_{-2}^{+2}$ | 1.40/4
| 59,309.029918 | 59,309.029976 | 3.96 | $2.6_{-0.8}^{+1.1}$ | $49_{-21}^{+21}$ | $2_{-1}^{+1}$ | 0.56/4
| 59,309.029976 | 59,309.030092 | 7.97 | $1.0_{-1.0}^{+0.8}$ | $844_{-512}^{+512}$ | $<2$ | 0.45/3
B11 | 59,309.277905 | 59,309.277939 | 2.38 | $<4.8$ | $91_{-47}^{+47}$ | $3_{-2}^{+3}$ | 2.04/4
| 59,309.277939 | 59,309.277997 | 3.97 | $1.8_{-0.7}^{+0.8}$ | $172_{-80}^{+80}$ | $2_{-1}^{+1}$ | 1.14/4
| 59,309.277997 | 59,309.278113 | 7.98 | $<2.6$ | $<299$ | $<2$ | 0.62/3
B12 | 59,309.426932 | 59,309.426967 | 2.33 | $2.7_{-0.6}^{+0.8}$ | $134_{-35}^{+35}$ | $8_{-2}^{+2}$ | 0.54/4
| 59,309.426967 | 59,309.427025 | 3.93 | $2.0_{-0.5}^{+0.6}$ | $228_{-71}^{+71}$ | $4_{-1}^{+1}$ | 1.07/4
| 59,309.427025 | 59,309.427141 | 7.92 | $<3.6$ | $45_{-27}^{+27}$ | $<2$ | 2.39/3
B13 | 59,309.596493 | 59,309.596527 | 2.37 | $2.5_{-0.9}^{+1.4}$ | $89_{-38}^{+38}$ | $4_{-2}^{+2}$ | 0.90/4
| 59,309.596527 | 59,309.596585 | 3.93 | $2.1_{-0.5}^{+0.6}$ | $287_{-78}^{+78}$ | $5_{-1}^{+2}$ | 1.85/4
| 59,309.596585 | 59,309.596701 | 7.95 | $1.5_{-0.7}^{+1.0}$ | $211_{-108}^{+108}$ | $<2$ | 0.22/3
B14 | 59,309.729525 | 59,309.729560 | 2.38 | $2.2_{-0.9}^{+1.1}$ | $183_{-74}^{+74}$ | $4_{-2}^{+2}$ | 0.85/4
| 59,309.729560 | 59,309.729618 | 3.98 | $1.4_{-0.6}^{+0.9}$ | $495_{-218}^{+218}$ | $2_{-1}^{+2}$ | 1.51/4
| 59,309.729618 | 59,309.729733 | 7.98 | – | – | – | –

Extended Data Table 4: Time-lag measurements for the stacked signals of 4U1728. Here ${\xi_{2}-\xi_{1}=\left(\frac{1}{\nu_{2}}\right)-\left(\frac{1}{\nu_{1}}\right)}$. $\nu_{1}$ | $\nu_{2}$ | $\xi_{2}-\xi_{1}$ | Lag (min)
---|---|---|---
$1.2\times 10^{18}$ GHz/5 keV | 9 GHz | 0.11 | $2.5^{+0.7}_{-1.1}$
$1.2\times 10^{18}$ GHz/5 keV | 5.5 GHz | 0.18 | $3.5^{+1.2}_{-0.7}$
9 GHz | 5.5 GHz | 0.07 | $1.0^{+1.0}_{-0.9}$

Extended Data Figure 1:  X-ray and multi-band radio light curves of 4U1728 on
10-minute timescales for our three radio epochs. For the X-rays we show the
1-second 3–25 keV light curves (panels a, b, s). For the radio, we show the
flux densities of the target at 5.5 GHz (panels d, e, f; red circles) and 9
GHz (panels g, h, i; blue circles), as well as a nearby check source (grey
squares), where error bars are 1-sigma. We detected 10 X-ray bursts coincident
with our radio monitoring. For all X-ray bursts, we find clearly defined radio
counterparts, with the only exceptions being two that occurred right at the
end of our observation when the source elevation was low and the observation
ended during the 10-minute time bin, however, radio brightening is detected on
shorter timescales for these two bursts (Fig. 2). No radio brightening was
detected in the nearby check source. Burst times are shown by the vertical
black lines in the lower two rows, while the vertical shaded purple regions
mark the time chunks used for our cross-correlation analysis (see Section
1.2.4) of each burst, where the bursts are labelled as in Extended Data Table
LABEL:tab:resolved_1728 (we exclude the two bursts close to the end of epoch 1
and 2, labelled as B3 and B11, from our cross-correlation analysis of single
bursts (but not for the stacked analysis), as such there is no vertical shaded
region for these two bursts).
Extended Data Figure 2:  Stacked radio light curves and time-resolved radio
spectral indices of 4U1728. To create these light curves (panel a), we stacked
all of the radio bursts from 4U1728 separately in the 5.5 GHz and 9.0 GHz
bands, with respect to the time of the partner X-ray burst (indicated by the
vertical black dotted line). Panel b displays the stacked spectral index
showing the flare starting as optically thick. There is a clear time-lag
between the X-ray and radio burst signals, where the radio signal lags the
X-ray signal by several minutes and this lag is dependent on electromagnetic
frequency (smaller electromagnetic frequencies yield longer lags). All errors
are 1-sigma.

Extended Data Figure 3:  Cross-correlation functions created with the ZDCF
algorithm from stacked versions of the X-ray and radio signals; X-ray to 9 GHz
radio (panel a), X-ray to 5.5 GHz radio (panel b), and 9 GHz to 5.5 GHz radio
(panel c), with 1-sigma errors. The resulting lag measurements and their
uncertainties are shown with the dotted black lines and shaded gray regions,
respectively. The lag measurements from these CCFs are also tabulated in
Extended Data Table 4.

Extended Data Figure 4:  Measured time-lags between the X-ray and radio bands
in 4U1728. Here we show the lags between the X-ray and stacked signal, as well
as those for individual bursts (panel a), as well as the lag between the 9 and
5.5 GHz signal (panel b). In both panels, the data points represent lags
measured from cross-correlation functions comparing signals from individual
bursts, while the shaded regions represent lags measured from cross-
correlation functions comparing signals from the stacked bursts. We show the
results of both 2 min and 10 min time-binned radio light curves for the 9 GHz
to 5.5 GHz radio lags (which are consistent within errors with each other),
while we show only the results from the 10 min time-binned radio light curves
for the X-ray to radio lags for clarity. In both cases, the individual burst
lags are consistent with the stacked measurement within (the 1-sigma)
uncertainties.

Extended Data Figure 5:  Results of modelling the stacked burst time-lags from
4U1728. Panel a: The best-fit model (solid orange line) overlaid on the time-
lag measurements, with 1-sigma errors. Here the shaded orange region
represents the model predictions from the final position of the MCMC walkers
in our parameter space. The three lag measurements correspond to lags between
the X-ray and the 9 GHz and 5 GHz radio data, as well as the lag between the 9
GHz and 5.5 GHz radio data (as shown in Extended Data Figure 3 and Extended
Data Table 4). Panel b: The residuals of the fit (data–model/uncertainties).
Panel c: Two-parameter correlations in our modelling for the free parameters
and those with informative (non-uniform) priors. Our model fits the measured
time-lags reasonably well, suggesting the radio counterparts to the X-ray
bursts in 4U1728 originate in an out-flowing compact jet.

Supplementary Table 1: Time resolved spectroscopy of the 4U1636 X-ray bursts. For each burst, spectra were extracted in five time bins. Burst | Start | Stop | Exp. | $kT_{\rm bb}$ | $R_{\rm km}^{2}/D_{10}^{2}$ | Flux |  $\chi^{2}$/d.o.f.
---|---|---|---|---|---|---|---
| (MJD) | (MJD) | (sec) | (keV) |  | $\times 10^{-8}$ |
|  |  |  |  |  |  (erg/cm2/s) |
B1 | 59,491.256215 | 59,491.256261 | 3.20 | $1.9_{-0.6}^{+0.7}$ | $165_{-71}^{+71}$ | $2_{-1}^{+1}$ | 1.28/3
| 59,491.256261 | 59,491.256307 | 3.19 | $1.9_{-0.8}^{+1.0}$ | $167_{-86}^{+86}$ | $2_{-2}^{+2}$ | 1.98/3
| 59,491.256307 | 59,491.256400 | 6.39 | $1.8_{-0.7}^{+0.8}$ | $171_{-68}^{+68}$ | $1.7_{-0.7}^{+0.7}$ | 0.31/3
| 59,491.256400 | 59,491.256585 | 12.88 | $1.9_{-1.0}^{+1.7}$ | $34_{-20}^{+20}$ | $0.5_{-0.2}^{+1.3}$ | 0.42/3
| 59,491.256585 | 59,491.256956 | 25.77 | $1.8_{-0.8}^{+1.3}$ | $34_{-18}^{+18}$ | $0.3_{-0.2}^{+0.2}$ | 1.26/3
| 59,491.256956 | 59,491.257696 | 51.65 | $<2.4$ | – | – | –
B2 | 59,491.450034 | 59,491.450081 | 3.19 | $2.1_{-0.8}^{+1.3}$ | $116_{-50}^{+49}$ | $2_{-1}^{+1}$ | 0.85/3
| 59,491.450081 | 59,491.450127 | 3.19 | $1.9_{-0.7}^{+1.0}$ | $130_{-68}^{+68}$ | $1.5_{-0.7}^{+8.9}$ | 2.12/3
| 59,491.450127 | 59,491.450219 | 6.40 | $1.7_{-0.6}^{+0.8}$ | $140_{-62}^{+62}$ | $1.2_{-0.6}^{+0.6}$ | 0.56/3
| 59,491.450219 | 59,491.450405 | 12.83 | $1.7_{-0.6}^{+0.7}$ | $119_{-46}^{+46}$ | $0.9_{-0.4}^{+0.3}$ | 0.10/3
| 59,491.450405 | 59,491.450775 | 25.73 | $1.7_{-0.7}^{+1.1}$ | $35_{-21}^{+20}$ | $0.3_{-0.2}^{+0.2}$ | 1.03/3
| 59,491.450775 | 59,491.451516 | 51.55 | $<2.6$ | $<81$ | $<0.2$ | 1.02/3
B3 | 59,491.791631 | 59,491.791678 | 3.19 | $1.4_{-0.7}^{+1.1}$ | $433_{-208}^{+208}$ | $2_{-9}^{+1}$ | 0.69/3
| 59,491.791678 | 59,491.791724 | 3.19 | $1.3_{-0.9}^{+1.3}$ | $851_{-399}^{+400}$ | $2.1_{0.9}^{+1.3}$ | 2.23/3
| 59,491.791724 | 59,491.791817 | 6.40 | $1.6_{-0.5}^{+0.7}$ | $232_{-89}^{+88}$ | $1.7_{-0.7}^{+0.6}$ | 0.54/3
| 59,491.791817 | 59,491.792002 | 12.86 | $1.7_{-0.6}^{+0.7}$ | $101_{-42}^{+42}$ | $0.9_{-0.4}^{+0.3}$ | 0.55/3
| 59,491.792002 | 59,491.792372 | 25.73 | $1.6_{-0.7}^{+0.9}$ | $56_{-27}^{+26}$ | $0.4_{-0.2}^{+0.2}$ | 0.80/3
| 59,491.792372 | 59,491.793113 | 51.55 | $<6.4$ | $<2$ | $<0.2$ | 1.12/3
B4 | 59,492.095034 | 59,492.095081 | 3.21 | $<3$ | $339_{-162}^{+162}$ | $2_{-1}^{+1}$ | 1.44/3
| 59,492.095081 | 59,492.095127 | 3.21 | $2.8_{-1.2}^{+3.6}$ | $36_{-18}^{+18}$ | $2_{-1}^{+2}$ | 0.13/3
| 59,492.095127 | 59,492.095219 | 6.42 | $2.1_{-0.9}^{+1.7}$ | $53_{-28}^{+28}$ | $1.2_{-0.7}^{+0.7}$ | 0.11/3
| 59,492.095219 | 59,492.095405 | 12.87 | $1.6_{-0.7}^{+0.9}$ | $115_{-53}^{+53}$ | $0.7_{-0.3}^{+0.3}$ | 0.34/3
| 59,492.095405 | 59,492.095775 | 25.78 | $1.8_{-0.9}^{+1.7}$ | $29_{-16}^{+15}$ | $0.3_{-0.2}^{+0.2}$ | 1.42/3
| 59,492.095775 | 59,492.096516 | 51.65 | $<4.1$ | $<11$ | $<0.2$ | 0.57/3
B5 | 59,492.246238 | 59,492.246284 | 3.18 | $1.9_{-0.5}^{+0.7}$ | $184_{-66}^{+65}$ | $3_{-1}^{+1}$ | 0.28/3
| 59,492.246273 | 59,492.246319 | 3.17 | $2.2_{-0.7}^{+0.9}$ | $109_{-41}^{+40}$ | $5_{-1}^{+1}$ | 0.53/3
| 59,492.246319 | 59,492.246412 | 6.36 | $1.8_{-0.5}^{+0.6}$ | $170_{-58}^{+58}$ | $1.7_{-0.5}^{+0.7}$ | 0.37/3
| 59,492.246412 | 59,492.246597 | 12.80 | $1.9_{-0.9}^{+1.7}$ | $49_{-22}^{+22}$ | $0.8_{-0.3}^{+1.3}$ | 1.36/3
| 59,492.246597 | 59,492.246967 | 25.74 | $1.5_{-0.7}^{+0.9}$ | $63_{-31}^{+30}$ | $0.3_{-0.1}^{+0.1}$ | 1.27/3
B6 | 59,492.399918 | 59,492.399965 | 3.20 | $2.3_{-0.8}^{+1.2}$ | $103_{-41}^{+41}$ | $3_{-1}^{+1}$ | 0.56/3
| 59,492.399965 | 59,492.400011 | 3.20 | $1.2_{-0.6}^{+1.2}$ | $875_{-403}^{+404}$ | $2.9_{-0.9}^{+1.9}$ | 1.83/3
| 59,492.400011 | 59,492.400104 | 6.39 | $2.3_{-0.9}^{+1.7}$ | $40_{-20}^{+20}$ | $1.2_{-0.6}^{+1.7}$ | 0.58/3
| 59,492.400104 | 59,492.400289 | 12.83 | $1.6_{-0.9}^{+1.1}$ | $85_{-40}^{+40}$ | $0.6_{-0.3}^{+1.3}$ | 0.44/3
| 59,492.400289 | 59,492.400659 | 25.75 | $1.6_{-0.7}^{+1.0}$ | $44_{-23}^{+23}$ | $0.3_{-0.2}^{+0.2}$ | 1.01/3
| 59,492.400659 | 59,492.401400 | 51.57 | $<3$ | $448_{-276}^{+277}$ | $0.2_{-0.1}^{+1.0}$ | 1.41/3
B7 | 59,492.550995 | 59,492.551041 | 3.18 | $2.9_{-1.0}^{+2.0}$ | $34_{-14}^{+14}$ | $3_{-1}^{+1}$ | 0.38/3
| 59,492.551041 | 59,492.551087 | 3.18 | $2.0_{-0.7}^{+0.9}$ | $115_{-45}^{+45}$ | $2.1_{-0.9}^{+0.9}$ | 0.36/3
| 59,492.551087 | 59,492.551180 | 6.39 | $1.9_{-0.7}^{+1.0}$ | $80_{-37}^{+37}$ | $1.0_{-0.5}^{+1.5}$ | 0.64/3
| 59,492.551180 | 59,492.551365 | 12.79 | $1.7_{-0.6}^{+0.7}$ | $75_{-27}^{+27}$ | $0.8_{-0.3}^{+0.2}$ | 0.49/3
| 59,492.551365 | 59,492.551736 | 25.70 | $1.3_{-0.9}^{+2.3}$ | $68_{-46}^{+45}$ | $0.2_{-0.1}^{+0.5}$ | 1.07/3
| 59,492.551736 | 59,492.552476 | 51.38 | $<0.8$ | – | – | –
B8 | 59,492.700995 | 59,492.701041 | 3.19 | $1.9_{-0.6}^{+0.9}$ | $131_{-56}^{+56}$ | $2_{-1}^{+8}$ | 2.49/3
| 59,492.701041 | 59,492.701087 | 3.19 | $1.8_{-0.6}^{+0.7}$ | $196_{-80}^{+79}$ | $2.1_{-0.9}^{+1.0}$ | 0.96/3
‘ | 59,492.701087 | 59,492.701180 | 6.39 | $2.2_{-0.7}^{+1.0}$ | $70_{-23}^{+23}$ | $1.9_{-0.6}^{+1.7}$ | 0.43/3
| 59,492.701180 | 59,492.701365 | 12.83 | $1.2_{-0.5}^{+0.6}$ | $420_{-171}^{+171}$ | $0.8_{-0.4}^{+0.5}$ | 1.38/3
| 59,492.701365 | 59,492.701736 | 25.70 | $1.0_{-1.0}^{+1.0}$ | $292_{-146}^{+146}$ | $0.3_{-0.2}^{+0.8}$ | 2.33/3
| 59,492.701736 | 59,492.702476 | 51.50 | $<3.5$ | $40_{-28}^{+27}$ | $0.8_{-0.1}^{+0.1}$ | 0.98/3
B9 | 59,492.887604 | 59,492.887650 | 3.18 | $1.6_{-0.5}^{+0.6}$ | $330_{-117}^{+117}$ | $2_{-1}^{+7}$ | 0.66/3
| 59,492.887650 | 59,492.887696 | 3.17 | $1.9_{-0.5}^{+0.6}$ | $207_{-61}^{+61}$ | $3.0_{-1}^{+0.9}$ | 0.51/3
| 59,492.887696 | 59,492.887789 | 6.35 | $2.3_{-0.8}^{+1.2}$ | $52_{-18}^{+17}$ | $1.5_{-0.5}^{+1.7}$ | 1.15/3
| 59,492.887789 | 59,492.887974 | 12.80 | $1.4_{-0.4}^{+0.7}$ | $182_{-62}^{+62}$ | $0.8_{-0.3}^{+0.2}$ | 2.02/3
| 59,492.887974 | 59,492.888344 | 25.69 | $1.4_{-0.6}^{+0.8}$ | $108_{-44}^{+44}$ | $0.4_{-0.2}^{+0.2}$ | 0.42/3
| 59,492.888344 | 59,492.889085 | 51.42 | $1.2_{-1.2}^{+1.1}$ | $58_{-36}^{+36}$ | $0.11_{-0.07}^{+0.11}$ | 0.08/3
B10 | 59,493.035509 | 59,493.035555 | 3.18 | $1.8_{-0.6}^{+0.8}$ | $241_{-89}^{+89}$ | $3_{-1}^{+1}$ | 0.51/3
| 59,493.035555 | 59,493.035601 | 3.17 | $2.0_{-0.7}^{+1.3}$ | $133_{-53}^{+53}$ | $2.2_{-0.9}^{+0.9}$ | 2.72/3
| 59,493.035601 | 59,493.035694 | 6.38 | $1.9_{-0.7}^{+0.8}$ | $96_{-38}^{+38}$ | $1.2_{-0.4}^{+0.5}$ | 1.19/3
| 59,493.035694 | 59,493.035879 | 12.84 | $1.6_{-0.7}^{+0.9}$ | $59_{-31}^{+31}$ | $0.4_{-0.2}^{+0.2}$ | 1.44/3
| 59,493.035879 | 59,493.036250 | 25.72 | $<2.9$ | $66_{-32}^{+32}$ | $0.3_{-0.1}^{+0.1}$ | 1.81/3
| 59,493.036250 | 59,493.036990 | 51.46 | $<2$ | $145_{-87}^{+87}$ | $0.21_{-0.09}^{+0.21}$ | 0.69/3
B11 | 59,493.183449 | 59,493.183495 | 3.21 | $2.0_{-0.5}^{+0.7}$ | $164_{-64}^{+64}$ | $3_{-1}^{+1}$ | 1.61/3
| 59,493.183495 | 59,493.183541 | 3.18 | $2.6_{-2.6}^{+3.7}$ | $34_{-20}^{+19}$ | $3_{-1}^{+1}$ | 1.76/3
| 59,493.183541 | 59,493.183634 | 6.38 | $1.9_{-0.7}^{+1.0}$ | $77_{-37}^{+36}$ | $1.1_{-0.5}^{+1.5}$ | 0.43/3
| 59,493.183634 | 59,493.183819 | 12.83 | $1.8_{-0.8}^{+1.3}$ | $62_{-27}^{+27}$ | $0.6_{-0.3}^{+0.3}$ | 0.77/3
| 59,493.183819 | 59,493.184189 | 25.71 | $<2.5$ | $98_{-48}^{+48}$ | $0.3_{-0.2}^{+0.2}$ | 0.62/3
| 59,493.184189 | 59,493.184930 | 51.51 | $<1.8$ | $1653_{-1306}^{+1311}$ | $0.22_{-0.10}^{+0.22}$ | 0.29/3
B12 | 59,493.334872 | 59,493.334918 | 3.19 | $2.8_{-2.8}^{+9.3}$ | $22_{-15}^{+13}$ | $10_{-9}^{+7}$ | 0.97/3
| 59,493.334918 | 59,493.334965 | 3.19 | $2.0_{-0.9}^{+1.5}$ | $158_{-63}^{+62}$ | $4_{-2}^{+1}$ | 2.22/3
| 59,493.334965 | 59,493.335057 | 6.37 | $1.8_{-0.6}^{+0.7}$ | $167_{-58}^{+58}$ | $2.0_{-0.6}^{+0.7}$ | 1.64/3
| 59,493.335057 | 59,493.335243 | 12.83 | $1.7_{-0.7}^{+1.0}$ | $95_{-39}^{+39}$ | $0.7_{-0.3}^{+0.3}$ | 0.68/3
| 59,493.335243 | 59,493.335613 | 25.70 | $1.9_{-0.9}^{+1.8}$ | $22_{-11}^{+11}$ | $0.3_{-0.2}^{+0.2}$ | 0.51/3
| 59,493.335613 | 59,493.336354 | 51.46 | $<3.9$ | $46_{-41}^{+41}$ | $0.10_{-0.09}^{+0.1}$ | 1.18/3