Infrared interferometry to spatially and spectrally resolve jets in X-ray binaries

Infrared interferometry is a new frontier for precision ground based observing, with new instrumentation achieving milliarcsecond (mas) spatial resolutions for faint sources, along with astrometry on the order of 10 microarcseconds. This technique has already led to breakthroughs in the observations of the supermassive black hole at the Galactic centre and its orbiting stars, AGN, and exo-planets, and can be employed for studying X-ray binaries (XRBs), microquasars in particular. Beyond constraining the orbital parameters of the system using the centroid wobble and spatially resolving jet discrete ejections on mas scales, we also propose a novel method to discern between the various components contributing to the infrared bands: accretion disk, jets and companion star. We demonstrate that the GRAVITY instrument on the Very Large Telescope Interferometer (VLTI) should be able to detect a centroid shift in a number of sources, opening a new avenue of exploration for the myriad of transients expected to be discovered in the coming decade of radio all-sky surveys. We also present the first proof-of-concept GRAVITY observation of a low-mass X-ray binary transient, MAXI J1820+070, to search for extended jets on mas scales. We place the tightest constraints yet via direct imaging on the size of the infrared emitting region of the compact jet in a hard state XRB.


INTRODUCTION
Radio wave interferometry has been in development for decades, culminating in the exquisite precision of Very Long Baseline Interferometry (VLBI).However as one goes to higher frequencies, atmospheric effects makes visibility corrections more challenging, requiring generally shorter integration times on any given source.In the optical/infrared (OIR) bands the previous generation of instruments could only image very bright sources using interferometry (e.g., V and H-band photometric magnitudes of ≤ 2; Monnier et al. 2007;Che et al. 2011).Current instrumentation includes the Navy Precision Optical Interferometer (NPOI) and the CHARA Array, which consist of 12cm-2m aperture telescopes with sensitivity limits on the order of 6-10 E-mail: s.b.markoff@uva.nlmag (ten Brummelaar et al. 2005;van Belle et al. 2019).The Keck Interferometer (e.g., Swain et al. 2003;Kishimoto et al. 2011) and VLTI/AMBER (Weigelt et al. 2012) observations with 8-10m telescopes have pushed these limits to much fainter sources (K 10).Increasing the sensitivity to still lower fluxes and higher spectral resolution is desirable, since only interferometry provides the precision necessary to resolve individual components in the OIR for many astrophysical systems.
The newest frontier in OIR interferometry is fringe tracking and precision astrometry using a sufficiently bright star within a few arc-seconds of the desired target.Without corrections, atmospheric effects cause too much jitter in the fringes to integrate for periods long enough to detect fainter sources.By phase referencing, the fringes of the target can be actively stabilized with respect to the reference source, allowing for integration times long enough that the target can be much fainter than the reference object.An instrument with these capabilities is now in operation on the Very Large Telescope Interferometer (VLTI), GRAVITY (Gravity Collaboration et al. 2017a).
GRAVITY is a second generation interferometric instrument, commissioned on the VLTI in 2016.It allows observing two objects (one bright fringe-tracking, phase reference object and one fainter science object).When GRAV-ITY is used with the Auxiliary Telescopes (ATs, 1.8m diameter) and the NAOMI adaptive optics system, the brighter phase reference object must have an infrared magnitude of K ≤ 8, and the faint object has to be within 4 arcsec from the bright object but can be as faint as K ≤ 12-13.When GRAVITY is used with the Unit Telescopes (UTs; 8m diameter), the bright object can be K ≤ 11, and potentially even as low as K ∼ 12 under good conditions.The faint object has to be within 2 , with a current limiting magnitude around K ≤ 19 (Gravity Collaboration et al. 2017a, 2018b).The astrometric accuracy is as good as 20 µas in the best cases (Gravity Collaboration et al. 2017a, 2019b), with spectral differential astrometry demonstrated with a precision of 2 µas for high-mass XRBs (Waisberg et al. 2017) and AGN (Gravity Collaboration et al. 2018a).While the small separation between fringe-tracking and phase reference objects is a limitation for finding viable Galactic targets, we here discuss the potential new science cases particularly when considering planned upgrades allowing a separation of ∼ 30 − 40".
The VLT point-spread-function for imaging is ∼ mas, thus the superb stability of GRAVITY allows the determination of relative motions in objects to precisions ∼ 100 times better than the resolution of their structure.GRAVITY was designed primarily to study orbital motions of stars or flare emission in the strong gravitational field of the supermassive black hole Sgr A * (Gravity Collaboration et al. 2020), and has provided the most accurate distance to the Galactic centre (Gravity Collaboration et al. 2018b,c, 2019b), as well as the first detection of an exoplanet by OIR interferometry (Gravity Collaboration et al. 2019a).However GRAV-ITY also has the potential to revolutionise X-ray binary (XRB) studies, and in fact has already been used to study the size, structure and spectra of two Galactic high-mass XRBs, GX 301-2 and SS 433 (Waisberg et al. 2017;Gravity Collaboration et al. 2017b;Waisberg et al. 2019a).While low mass XRBs are generally too small (for their distance) to be spatially resolved on mas scales using the IR band, an IR astrometric accuracy of ∼ 10µas could enable the first direct detection of individual contributions to the IR spectrum, as well as an independent method for obtaining system orbital parameters.
In this paper we propose a feasibility study for how IR interferometry, using GRAVITY in particular, can be exploited to separate emission components in XRBs and thus constrain accretion/outflow physics.In Section 2 we describe the scientific questions that IR interferometry can help address for XRBs, particularly transient microquasars.In Section 3 we explore the feasibility using several typical sources as a guide, particularly for observing faint targets off-axis.In Section 4 we present the first proof-of-concept, mas scale IR interferometric observation of a Galactic transient X-ray binary, MAXI J1820+070, using GRAVITY.Finally, in Section 5 we summarize and make some predictions for the coming decade of all-sky transient detections.

Spatially resolving jets in XRBs
VLBI studies of jets in nearby AGN such as M87 have revealed a spine and sheath geometry, as predicted by theoretical models (Perlman et al. 2011;Walker et al. 2018), as well as the collimation profile of the jet (e.g.Asada & Nakamura 2012).Such images can be used to constrain the equations of force balance (i.e., internal versus external pressure), while variability provides information about turbulence within the flow.M87 is in fact so close and large that the Event Horizon Telescope (global 1 mm VLBI with phased-ALMA at its core) was able to directly image the shadow of the black hole (e.g.Event Horizon Telescope Collaboration et al. 2019).
While Galactic black hole XRBs are much closer than AGN, they are typically millions to billions of times smaller, so direct imaging is a challenge and resolving the black hole shadow or inner accretion disk is well beyond the capabilities of current facilities.With the advent of GRAVITY on the VLTI, however, there is an intriguing possibility to directly resolve expanding mas scale jets in a transient XRB outburst, and to spectrally decompose the accretion components from each other as well as from the companion star.The advantage of XRBs compared to AGN is that one can observe millions more dynamical timescales, thus obtaining constraints on the inner disk physics over much longer relative timescales.Direct imaging provides the best insights into jet morphology, energetics and interactions.Because one of the pressing questions at the moment in modeling accretion flows centres on how and where particles are energised (see, e.g., Romero et al. 2017;Ball et al. 2018), the promise of pinpointing the moment when XRB jets launch and then begin to accelerate high energy particles makes them extremely valuable testbeds for constraining theory.

Compact jets and discrete ejecta
XRBs exist as both persistent (mostly high-mass companions; HMXB) and transient (with low-mass companions; LMXB) sources, the latter of which experience periodic outburst cycles.Within a single outburst we witness the launching and quenching of jets, in some sources repeatedly on a few-year time cycle (e.g.Corbel et al. 2013).Until now direct imaging has focused on radio-VLBI techniques because of the phenomenal spatial resolution, but only three compact, steady jets associated with the non-thermal-dominated 'hard state' have been resolved with radio-VLBI to date: GRS 1915+105 (Dhawan et al. 2000), Cyg X-1 (Stirling et al. 2001) and MAXI J1836-194 (Russell et al. 2015).However during state transitions to the thermal/disk-dominated 'soft state' the jets transform dramatically, and increasingly more radio-VLBI studies have been able to resolve, and track the evolution of, discrete ejecta on mas scales (e.g.Mirabel & Rodríguez 1994;Hjellming & Rupen 1995;Tingay et al. 1995;Fender et al. 1999;Mioduszewski et al. 2001;Miller-Jones et al. 2011, 2019;Brocksopp et al. 2013;Rushton et al. 2017).
The compact jets seen in the hard state also emit IR synchrotron emission, but it originates from too close to the black hole to be directly resolved (e.g.Russell et al. 2006;Gandhi et al. 2011;Buxton et al. 2012).During state transitions, discrete jet ejecta emit optically thin synchrotron from radio to IR, such that the IR flux is generally expected to be fainter than the radio (though see GRS 1915+105;Fender et al. 1997;Eikenberry et al. 1998).Despite this faintness, with the advent of fringe-tracking and phase referencing capabilities with VLTI via the GRAVITY experiment, it may be possible to image XRB jet activity in the IR similar to what has been done with radio-VLBI.

Previous claims of OIR extended jets
There have in fact been claims of a marginal IR detection of a compact jet of 0.2 arcsec in the source GRS 1915+105 (Sams et al. 1996), however this has never been confirmed by later detections.But recently, IR emission lines from plasma in the jets of the exotic Galactic XRB SS 433 have been spatially resolved with GRAVITY (Gravity Collaboration et al. 2017b).On larger scales, extended jets of XTE J1550-564 resolved on arcsec-armin scales, detected at radio and X-ray frequencies, were almost -but not quite -detected by the VLT at optical wavelengths (Corbel et al. 2002).

Detectability with GRAVITY: spatial scales
Because GRAVITY is capable of imaging structures on spatial scales of ∼ 1-50 mas (corresponding to, e.g., ∼0.3-20 AU for a source at 3 kpc; up to ∼60 AU at 8 kpc), transient features such as ejecta or jet-ISM interaction regions may be now be detectable.Specifically, after transition to the soft state the core is no longer active but the ballistic ejecta are still moving.Based on the radio-VLBI observations, we expect these bright ejecta to be spatially resolved with GRAVITY, with motions of ∼ 10s-100 mas/day (note that extremely fast motions of 100 mas/day could result in motion/smearing within a GRAVITY observation itself, depending on integration times).
The mas scale jets seen with radio VLBI are typically discrete ejecta that are themselves unresolved down to < 1 mas (see Table 1 in Miller-Jones et al. 2006), so we do not expect them to be resolved out.One could therefore use a uv binary source model (XRB core and jet ejection, see section 4.1 and Fig. 3) to identify spatially resolved ejecta on scales of 1-50 mas.In the case of a nearby source with high velocity ejecta, the mas scale ejections could move on timescales as short as the exposure time.For these, if the movement is comparable to or longer than the integration time (tens of minutes), these will be detectable.A good example of this is the detection of the resolved S2 star from Sgr A * , in which the dynamical timescale was shorter than the integration time, yet the uv model fitting was successful (Gravity Collaboration et al. 2018c, 2019b, 2020).

Detectability with GRAVITY: fluxes
For a typical XRB, the radio flux densities of discrete ejecta on the 1-50 mas size scales we can probe with GRAVITY are on the order of 10-500 mJy (at 15 GHz, e.g.Fender et al. 2009;Miller-Jones et al. 2019).Assuming a standard optically thin spectrum (α = −0.6 to −0.8) would predict a K ∼ 10-12 magnitude core and a K ∼ 15-16 magnitude discrete ejection, meaning GRAVITY could significantly detect and resolve both components.Because such discrete ejecta would likely be several magnitudes fainter than the compact jet, and the unresolved accretion disc and (in some cases) the star, mas-scale discrete ejecta at these fluxes would never have been noticed before in any IR data.

Detectability with GRAVITY: brief, brighter jets
There may also be bright IR discrete ejecta that are tens of mJy (K∼10 mag), but only briefly near the start of the hardto-soft state transition, before fading to similar or fainter flux later in the radio.For example, the non-spatially resolved jet flares in GRS 1915+105 were a similar flux density (in Jy) in IR and radio, with radio occuring minutes later than IR (Fender et al. 1997;Mirabel et al. 1998).Both IR and radio flares lasted ∼ 20 minutes, strongly suggesting adiabatic losses dominating.However during V404 Cyg's latest outburst, Tetarenko et al. (2017) found that 7 Jy sub-mm flares lasting tens of minutes to an hour at 666 GHz were followed by only ∼ 1 Jy flares in the radio bands.Such flares may have very brief, transient IR counterparts of a few hundred mJy (K 9 mag) or more, lasting timescales of minutes to tens of minutes.To date no such IR flare has been resolved in a typical black hole transient (GRS 1915+105 is considered an outlier), but they may have been missed due to low sampling or short integration times.Such ejecta are likely to emit between K∼ 9 − 16 during the days/week just after launching.In one system, an IR flare peaking at K < 13 magnitude and lasting four days has been detected during state transitions, and may have been brighter on < 1 day timescales (Buxton & Bailyn 2004;Russell et al. 2020).Such flares, on hour-day timescales -if present -will be detectable and spatially resolved if they have typical motions of ∼ 10s-100 mas/day.However, we note that for very rapid flares which change flux on timescales comparable to a single observation, this could introduce image artifacts.As such, the flux variability would likely preclude all but the most basic binary model fitting in these cases.

Consequences of a detection
A clear detection would allow constraining the location, velocity, size/morphology, and evolution of the IR jets.Together with radio-VLBI observations, an IR detection will also provide information about the radiating particle energy distribution of the mas scale discrete ejecta.Any early-time, bright IR detections would be crucial for constraining the launch time of the jets, for comparison to X-ray timing signatures associated with this launching (see, e.g., Miller-Jones et al. 2012), as they are less affected by optical depth effects.Finally, when the steady jet re-establishes itself before the outburst ends, GRAVITY could be used to investigate changes in the inner jet and movement of any interaction hotspots.

Spectral decomposition using interferometry
While challenging, IR interferometry offers an exciting new dimension to the multi-wavelength studies currrently used to deconstruct the physics driving accretion and outflows.
Our understanding of XRB accretion physics has evolved significantly over the last decades, mainly due to the monitoring of entire outburst cycles in the X-ray bands via triggered instruments such as the Rossi X-ray Timing Explorer (RXTE), SWIFT and more recently, NICER (e.g.Belloni et al. 2005;Muñoz-Darias et al. 2011;Motta et al. 2017;Stevens et al. 2018).These observations have led to a greater understanding of the disk/jet coupling driving the discrete accretion states (e.g., McClintock & Remillard 2006;Belloni 2010) that are most pronounced in black hole XRBs, the main focus of this work.The frontier has now shifted to the lower frequency bands, as simultaneous triggering of radio and OIR observations with the X-rays has revealed a parallel evolution in the interplay between the accretion inflow in the accretion disc, jet outflows and sometimes the stellar companion.
The OIR bands in particular offer a valuable new testbed for many aspects of accretion physics in XRBs, as they can be comprised of multiple contributions from the accretion disk, jets and star, the former of which can exchange dominance during state changes.For instance, in the soft state, the outer regions of the accretion flow can re-radiate emission from the inner zones in the OIR bands, as can the companion star itself (e.g.O'Brien et al. 2002;Hynes 2005;Migliari et al. 2007).In the hard state it is now well established that synchrotron emission from the jets extends into the OIR bands (e.g.Corbel & Fender 2002;Russell et al. 2006Russell et al. , 2010;;Buxton et al. 2012;Saikia et al. 2019), either as an extension of the flat/inverted, self-absorbed spectrum, or beyond the synchrotron self-absorption break as an optically thin power-law.The break itself has been explicitly resolved in some observations (e.g.Migliari et al. 2006;Gandhi et al. 2011;Russell et al. 2013) and recent simultaneous broadband campaigns of XRBs in outburst demonstrate that the break dynamically moves up and down in frequency through the band (Russell et al. 2014, Russell et al. subm.).
Understanding the contribution of the jets in the IR and in particular, whether the IR is above or below the break, or how the break evolves, has become a key focus of XRB studies as this places strong constraints on the jet geometry, dynamics and energetics.For instance, recent multi-wavelength variability studies have revealed a characteristic size scale for this break (Gandhi et al. 2017;Paice et al. 2019), as well as very strong near-IR to mid-IR variability from the compact jets (Gandhi et al. 2011;Baglio et al. 2018;Vincentelli et al. 2018;Malzac et al. 2018).Similarly the first ever IR quasiperiodic oscillations (QPOs) with a harmonic of the X-ray QPO frequency (Kalamkar et al. 2016) reveal the tight coupling of jet to disk.If the spectral slope beyond the break can be constrained, this also helps determine the particle acceleration properties and together with limits from the Xrays and γ-rays, the maximum radiative power of the jets (see, e.g.Laurent et al. 2011;Corbel et al. 2012;Zdziarski et al. 2014;Rodriguez et al. 2015;Zanin et al. 2016;Espinasse et al. 2020).However the clear evidence for multiple contributions to the OIR (see, e.g.Homan et al. 2005;Buxton et al. 2012;Baglio et al. 2018) can make identifying the OIR jet contribution challenging.
Isolating the jet contribution to the OIR spectrum is therefore a key new milestone for understanding XRB jet physics in general, and gauging their total power budgets (Corbel et al. 2002;Gallo et al. 2005;Abeysekara et al. 2018).Furthermore, because of the increasing body of evidence that the accretion physics in XRBs and AGN scales predictably with mass (Merloni et al. 2003;Falcke et al. 2004;McHardy et al. 2006;Plotkin et al. 2012;Koljonen et al. 2015;Connors et al. 2017), constraints found from IR studies of XRBs will cast light on larger scale issues in galactic evolution such as the physics governing jet launching and power, and eventually energy released into the environment.

FEASIBILITY STUDY FOR A NEW APPLICATION OF IR INTERFEROMETRY TO XRBS
As typical XRBs have binary separations falling in the range of 1-100 µas, they are not directly resolvable with the VLTI, but the system motion should be detectable.The simplest, but potentially one of the most important, applications of the VLTI for XRBs is the search for a wobble in the light centroid position, which can be used to constrain the mass function of the system.Many systems now have accurately measured orbital periods but the mass of the compact object and/or companion star are, on the whole, poorly constrained.Since the orbital separation, a ∝ P 2/3 (M 1 + M 2 ) 1/3 where P is the orbital period, we can therefore solve for the total system mass with precise determinations of a and P.
For objects with several good reference stars in the field, the VLTI can in principle be used to further constrain the system orientation (in projection on the sky) and inclination.The amount of orbital wobble measured, for non-zero inclination systems, will depend on the angle between the orbital plane of the XRB and the reference star.By measuring the wobble using a number of reference stars at different angles from the XRB, a solution for the orientation of the disc and apparent eccentricity on the plane of the sky can be derived.While for eccentric orbits, speeds will vary from periastron to apastron, the orbits of most XRBs (at least Roche-lobe overflow low-mass X-ray binaries) are circular, and in all cases the inclination angle of the system can also be constrained.If the stellar companion type and mass is known, as is the case for sources with a measured mass function in quiescence, the physical parameters of the system can be completely characterised using this approach.
If both the orientation of the orbital plane as well as the inclination can be constrained, a further interesting test is to compare these with the observed orientation of the radio jets (which are generally well known for most of the prime candidate sources considered in this paper).Such a test could help identify more systems with drastically misaligned jets similar to the 'microblazar' V4641 Sgr (Hjellming et al. 2000;Orosz et al. 2001;Maccarone 2002).The existence of significant numbers of misaligned jets would help constrain the extent to which jet axes align more with the black hole than the outer disk, as predicted by Rees (1978) and now reproduced numerically (e.g.Liska et al. 2018), and enable a study of timescales for which the Bardeen-Petterson effect (Bardeen & Petterson 1975) could bring the jets back into alignment.

Centroid shift and potential target list
The most challenging but potentially most exciting detection beyond orbital effect would be a shift in the image centroid as a function of accretion state, driven by waxing and .Bottom: Same system, at the same orbital phase, after transitioning to the soft state and jet contribution to the IR is quenched, resulting in a shift of the image centroid towards the companion star in the K-band.The orbital wobble, most prominent when the star is producing the IR emission, is largely reduced when the jet is dominating.Note that another centroid shift could be potentially seen between K and J bands during state transitions.
waning in the three main system components in the IR band.Understanding the orbital period via the wobble technique or otherwise will be a necessary first step, to allow comparison of the source at the same orbital phase in different states, and potentially to co-add images from several orbits.A schematic of how this technique would work to identify the jet contribution can be seen in Figure 1.If the system is observed at the same orbital phase during the hard and soft states respectively, and the binary separation is sufficiently large, the shift in centroid position should be detectable for a few systems with GRAVITY.If significant IR emission is thought to be contributed from irradiation in the star, this technique together with spectral modeling would also help to break the degeneracy between that and disk/jet, if comparisions are made between state changes.
For both high-and low-mass XRBs, astrometry with the current specifications of GRAVITY on the VLTI should be achievable if the target has K 16 and another K 11 magnitude star lies within 2 arcsec from the target, or vice versa (brighter target, fainter reference star).For our specific interests, transient LMXBs (or bright flares in persistent LMXBs) are preferable, but in Table 1 we provide a list of all the best known sources which would be good candidates based on the best known estimates of distance, orbital period and component masses from the literature to calculate the orbital separation.Starting from the 40 XRBs with radio detections (i.e.evidence of jets), we find 15 that have apparent orbital separations on the sky a > 10µas (in descending order of a).We include sources too far north for the VLT such as the high-mass X-ray binary (HMXB) Cyg X-1, because it is a canonical object with well-constrained physical parameters that could be useful for future interferometry instruments (on a northern interferometer such as the Large Binocular Telescope, the CHARA Michelson Array and the Magdalena Ridge Observatory Interferometer (MROI); Angel et al. 1998;ten Brummelaar et al. 2005;Buscher et al. 2013;Gies et al. 2019).
These are mostly LMXBs (including black hole and neutron star sources) and also some HMXBs with radio emission.We consider these the current best targets for VLTI attempts with GRAVITY (except for three sources that are too far north, shown in italics in the table); we do not include the other systems in the table as they have smaller apparent orbital separations on the plane of the sky, and are more challenging for GRAVITY.The observed (not dereddened) K-band magnitudes are also tabulated, as are the number of K < 12 stars within 40 of the X-ray binary, listed in the 2MASS catalogue.The reason this list extends beyond GRAVITY's current beam-forming capabilities is because of the proposed enhanced sensitivity and the enlarged field of view of a possible GRAVITY+ upgrade (in prep.), that was presented at the "The Very Large Telescope in 2030" conference, ESO Garching, June 17-20, 2019.All of these objects also have radio flux densities (not shown) which can be used to extrapolate a first order estimate of the expected IR flux from the jets.In some cases the jet contribution to the Kband IR emission has been estimated in the hard state; for these we estimate the phase shift of the centroid between jet on and jet off (if instead the star dominates) states.If instead the shift is from jet to accretion disc over the transition, there would be no phase shift in the XRB during such a transition (this is most likely the case for the LMXBs with the faintest companions, such as GX 339-4, XTE J1550-564 and Cen X-4) and so the phase shift calculated from the ratio I j I j +I s (see below) represents an upper limit in these systems.However in many of the sources in Table 1, the star is large and brighter than (or of comparable brightness to) the accretion flow (GX 301-2, CI CAM, Cyg X-1, SS 433, GRS 1915+105, V4641 Sgr and GRO J1655-40 as shown in Fig. 1; e.g.Kaper et al. 1995;Miroshnichenko et al. 2002;Migliari et al. 2007;Hillwig & Gies 2008;van Oers et al. 2010;Rahoui et al. 2011;MacDonald et al. 2014;Russell & Shahbaz 2014) and so a phase shift is expected.
There are currently at least six known systems with orbital separations a > 50µas, which would yield a 5σ detection with GRAVITY of an astrometric shift over the orbital period.This shift also depends on the mass ratio; for systems in which the black hole mass is much greater than the companion mass, the orbital wobble of the companion could be as large as twice the orbital separation.Most orbital periods of the sources in Table 1 are days to weeks.Exoplanets, by comparison have periods on the order of years, so instrument drifts and systematics over the longer time frame introduce additional astrometric errors which are not relevant for microquasars.
Unfortunately, none of the targets in Table 1 have known nearby stars within 2 in 2MASS, with the closest being GRS 1915+105 with a K = 13.2 star 3.3 from the target.However, a faint star close to the brighter XRB would not be easily detectable in the 2MASS survey, so it is possible some close stars have been missed by 2MASS.We did also check higher resolution images from VISTA surveys (Minniti et al. 2010, including VVV and VHS) for nearby stars.If offaxis capabilities allow a phase reference star within ∼ 30-40 arcsec (as suggested in a GRAVITY+ white paper; Gravity Collaboration et al., in preparation), this dramatically increases the feasibility.Most targets have several (up to 17) bright K < 12 2MASS stars within 40 (Table 1).GX 301-2 and CI Cam have the widest angular orbital separations, but in both these systems the jets never brighten to an IR flux level comparable to that of the companion star.Some of the other sources do have relatively bright jets though, and we investigate these further below.
The spacing of an interferometer's fringes on the sky is λ /B (where B is the baseline length), analogous to the λ /D resolution of a single optical telescope.The phase of the centroid of the compact object (dominated by either the jet or the disk, we will use the jet as an example below) and companion star can be calculated from: where a r is the binary separation in radians and I j and I s are the measured jet and star flux at a given frequency, respectively.This equation assumes (a) 2πa r λ /B (the marginally resolved limit), (b) the angle between the line connecting the XRB and guide star on the sky and the projection on the sky of the line connecting the two telescopes, is zero (this geometry gives the highest resolution; cos(angle) = 1), and (c) sin a r ≈ a r , which is valid for the small angles we are dealing with here.The ratio λ /B for K-band is 4.37 mas (we adopt a baseline of 110 m for the VLTI).For an XRB with an orbital separation on the sky of a r = 100 µas, the maximum phase shift between the hard and soft states (due to jet quenching) is on the order of δ φ ∼ 8 • , which corresponds to ∼ 100 µas on the sky (i.e., the orbital separation), and thus should be detectable with GRAVITY.This maximum shift scenario, in which the jet or disc produces ∼ 100 per cent of the flux in the hard state and the star produces ∼ 100 per cent of the flux in the soft state, will generally not be the case in reality.We therefore estimate the phase shift using the ratio I j I j +I s and these are given in Table 1.The estimates of this ratio are taken from the literature using the relative jet and star contributions at the frequency of K-band (Fender et al. 1997;Migliari et al. 2007;van Oers et al. 2010;Russell et al. 2010;Chaty et al. 2011;Russell et al. 2013Russell et al. , 2018;;Russell & Shahbaz 2014;Bernardini et al. 2016;Maitra et al. 2017).
To test the feasibility of this new class of measurement, we use some examples of known Galactic XRBs where the binary separation and broadband spectral energy distribution are well constrained, allowing an estimation of the potential centroid shift.In Figure 2 we show an example simultaneous, broadband spectrum from the Galactic transient GRO J1655-40, which we have chosen because of its large orbital separation, the fact that in the hard state the jet flux is a reasonable fraction of the K-band flux, and that jet models have been fitted to this data set (Migliari et al. 2007, note that the conclusions would not be affected if the jet synchrotron cuts off well before the X-ray band).This source is visible to the VLT though it has currently returned to quiescence, but during outburst had a K-band magnitude of 11.We have calculated the predicted shift assuming the jet is entirely quenched in the K-band during the soft state (this is supported by the dramatic quenching of radio and mid-IR flux in the soft state of GRO J1655-40; Migliari et al. 2007).Based on the spectrum, the jet contributes ∼ 25% of the total flux in the hard state, leading to a predicted shift in phase of δ φ = 0.5 • , which is in the detectable range by GRAVITY during a future outburst.There are ten field stars brighter than K = 12 within 40" of GRO J1655-40, but none within 2 .If the field of view for phase referencing could be increased to >30", a full orbital solution would be possible for this source.
The 'persistent transient' GRS 1915+105 is another interesting potential target, having been in an outburst state associated periodically with jet ejections for the last 20+ years.During these flares the jet produces almost all of the K-band flux, and the estimated shift in phase of the centroid is δ φ ∼ 5 • .
We should also consider spectro-astrometry.GRAVITY provides a spectral range between 2.00-2.45µm.The astrometric shift between blue K-band (larger star contribution, in the case of GRO J1655-40) and red K-band (dominated more by the jet) is larger than the astrometric shift of the average K-band from photometry.It may be possible to distinguish features in the spectrum from regions dominated by the jet, disc and companion star.For example, a strong Br-γ line is expected from the accretion disc, various absorption lines from the companion star, and the red part of the K-band continuum dominated by the jet.If so, this would also give an interesting astrometric signal of different components at different positions.This has been recently achieved for SS 433, in which emission lines from the jets were found to be spatially offset from the continuum, the jets resolved at ∼ 1-10 mas scales (Gravity Collaboration et al. 2017b;Waisberg et al. 2019b), but this is the only known source with optical and IR emission lines from the jets.
In the last two columns of Table 1 we show the fractional jet contribution, and calculate the centroid phase shift, based on spectra taken from the literature for several of the best candidates.The errors on the phase are propagated from the errors in a and (for three sources) the jet contribution (if it is poorly constrained).Cyg X-1 has the widest orbital separation on the sky for sources with a jet contribution (making it a prime target for measuring the orbital wobble), but since it is a HMXB its IR flux is dominated by the companion, and the jet contributes just ∼ 0.6% of the K-band flux at most.The predicted shift in the phase of the centroid due to the jet quenching is therefore small for Cyg X-1.In contrast, the IR jet flux of V404 Cyg was at least ∼ 80% in the hard state during its outburst in 1989 (and possibly during the flares during the 2015 out-  4 Errors on the estimated values of orbital separation are propagated from the errors in d, P, M 1 and M 2 (if the mass of the neutron star is not known we adopt M 2 = 1.4 ± 0.6M ).For GRO J1655-40 the value of a is given for distance 3.2 ± 0.3 kpc (Gandhi et al. 2019). 5The number of K < 12 stars within 40 of the X-ray binary, and their range of magnitudes (data from the 2MASS catalogue).The K-band jet contributions in the hard state are estimated from (in some cases modelling of) spectral energy distributions in Fender et al. (2000Fender et al. ( , 1997)); Russell et al. (2006); van Oers et al. ( 2010); Migliari et al. (2007); Russell et al. (2010Russell et al. ( , 2013Russell et al. ( , 2018)).The references for the distances, orbital periods and masses can be found in the following articles and references therein: burst; see e.g.Maitra et al. 2017), and the resulting phase shift is large; ∼ 5 • .Both Cyg X-1 and V404 Cyg are located too far north to be observable from the VLTI, however it is likely that XRBs with similar orbital parameters and jet contributions (to the latter transient source at least) will be discovered in the coming years.A recent example is MAXI J1820+070, which was discovered in 2018 and has an orbital separation of a > 10µas (Table 1).We discuss the first GRAVITY observation of this source in the next section.
A good target, observable from VLTI, is GRS 1915+105.During its flaring state the jet produces almost all of the IR emission, so we predict a centroid phase shift of δ φ ∼ 5 • .The three remaining sources with measured IR jet contributions have predicted phase shifts due to a changing jet contribution of ∼ 0.3-1 • , making them the next best currently known sources visible from the VLTI.

Accounting for parallax and proper motion
This technique requires measuring changes in the centroid at the 10 µas level, on timescales of hours-days (for abrupt state changes) to weeks-months (orbital modulation, coadding images from several orbits).Parallax and proper motion will therefore be significant, and their effects will need to be removed, before centroid shifts from orbital motion and state changes can be detected with sufficient accuracy (see e.g., Tomsick & Muterspaugh 2010;Atri et al. 2019, for discussions on this related to X-ray binaries).The targets in Table 1 with estimated centroid phase shifts due to a changing IR jet contribution have known parallax and proper motions measured from Gaia and/or radio VLBI (Gandhi et al. 2019;Atri et al. 2020, and references therein).The uncertainties on these measurements are ± 0.02-0.11mas for the parallax and ± 0.05-0.22mas yr −1 for the proper motion (all except XTE J1550-564 have measurements).By the time of the GRAVITY upgrade, these uncertainties will very likely be smaller, with updated values from subsequent Gaia data releases, and new VLBI observations.
Using these existing astrometric solutions, the positional uncertainties for any given epoch are of order 0.11-0.60µas due to uncertainties in the parallax and 0.14-0.60µas d −1 due to uncertainties in the proper motion (for parallax this will vary depending on location of the target on the sky and the time of year).Star spots on the surface of the companion could also produce light centroid jitter, with a maximum centroid shift of the order of a few µ-AU, with only extreme cases from superflares of some stars producing shifts up to ∼ 100 µ-AU (e.g.Morris et al. 2018), or 0.02 R , or 0.1 µas at a distance of 1 kpc.This effect of star spots is much smaller than the other uncertainties discussed here.2007), illustrating the K band (vertical red line) and the difference in flux between the jet synchrotron emission (dashed green line) and thermal companion star (dashed purple line; note the accretion disk is also present but very distinct at higher energy).
The hot spot/stream impact point can make a small contribution to the optical emission in quiescence (Cherepashchuk et al. 2019).The hot spot is only significant in some LMXBs (not HMXBs) in quiescence as an additional thermal emitter to the optical continuum, and emission lines, but in outburst these are negligible.Since we are interested in the K-band continuum, and the disc dominates the thermal emission in outburst, the hot spot will play an insignificant role in the K-band continuum.Considering these arguments, an abrupt jet contribution change on day timescales at the > 10µas level will be easily detectable over the smoother changes in target position due to parallax and proper motion.Over a period of a month, the uncertainties grow to 3-18 µas and 4-18 µas, which becomes significant for measuring orbital and state changes on the 10 µas level.However, with sufficiently accurate measurements from Gaia and VLBI, it will be possible to remove these effects.In addition, if enough GRAV-ITY measurements are made over year timescales, it may be possible, to independently measure parallax and proper motion using GRAVITY.This would be extremely interesting for constraining the distances, Galactic distribution, natal kicks and origins of the systems (e.g.Mirabel et al. 2001;Miller-Jones 2014;Atri et al. 2019).
Centroid shifts on the 10 µas level also require these target phase shifts to be measured relative to a phase calibrator source.The reference source is typically a star, which has its own parallax and proper motion.One will therefore need to determine the relative parallax and proper motion signatures between the reference star and the target.For the comparison star 2MASS J19053212-0016155 used below with the observation of MAXI J1820+070, we see that it has parallax and proper motion measured by Gaia DR2, with uncertainties of 0.051 mas yr −1 and 0.076 mas yr −1 , respectively.These are very similar to our targets above, and will also be improved with future Gaia releases.One may choose to select reference stars with smaller uncertainties; perhaps more distant stars.For sufficiently high precision astrometry to measure orbital shifts, the systematic uncertainties related to the calibrator throw from the reference star should also be known.While these are believed to be negligible for the current few-arcsecond calibrator throw, they may become important for a wider-field GRAVITY upgrade.We note that for many past and current GRAVITY science cases, true off-axis astrometry to a reference source has not been required, since all extragalactic targets are typically much further than our targets and therefore have negligible proper motion and parallax.

FIRST GRAVITY DETECTION OF A GALACTIC TRANSIENT XRB
As an initial proof-of-concept we here present the first triggered observation of a transient X-ray binary with GRAV-ITY.MAXI J1820+070 is a new black hole candidate XRB that was first detected in March 2018 by the MAXI all sky Xray monitor and ASAS-SN optical transient survey (Tucker et al. 2018;Kawamuro et al. 2018;Denisenko 2018).During its outburst rise it became one of the brightest XRB transients to date, becoming the second brightest X-ray source on the sky after Sco X-1, likely owing to its proximity (2.96 ± 0.33 kpc, recently measured from radio parallax; Atri et al. 2020).Unlike most outbursts, which usually transition from the steady jet-dominated state (hard X-ray state) to the ballistic jet state (transition through the intermediate states), MAXI J1820+070 rose very quickly to its maximum brightness and stayed there for several months, remaining in the steady jet state, meaning that we had an excellent chance to observe a very bright nearby system, with K-band magnitude of ≥ 9.5 (Mandal et al. 2018).A flux density of 300 mJy was measured in the mid-IR from VISIR on VLT UT3 (Russell et al. 2018).
We observed MAXI J1820+070 with GRAVITY on the VLT Interferometer, using all four UTs (DDT 2101.D-0517) on the night of 2018 May 31 -June 1.The X-ray binary was observed at 04:28-05:45 UT and 06:11-06:59 UT on June 1.A comparison star 2MASS J19053212-0016155 (HD 177631) was observed at 05:47-06:10 and 07:01-07:31.All observations were performed under photometric conditions, with a variable seeing of 0.6-0.9 .We first closed the loop of the MACAO visible adaptive optics systems on target with each telescope.We observed in low spectral resolution, placing the science fiber away from the target in order to increase flux in the fringe tracking fiber.
We acquired one (55 mins on source, with 40 mins of science exposure) GRAVITY observation of MAXI J1820+070, when a steady, compact jet was being launched.This observation was a success in terms of feasibility, working remarkably well on a technical level.Despite the source being faint, fringe tracking (Lacour et al. 2019)   (for the comparison star, fringes found in all baselines).The data were reduced with the standard GRAVITY pipeline using the default settings (Lapeyrere et al. 2014).

Results
The GRAVITY data show calibrated squared visibilities (V 2 , squared correlated flux normalized to the value at zero baseline) consistent with a constant value of 0.8-0.85.There is no apparent drop with increasing spatial frequency, i.e. the source is unresolved.We obtain an upper limit to the source size by fitting a Gaussian source model separately to each exposure.We allow for a variable zero-baseline visibility level to allow for coherence loss.The measured sizes are very small, with an upper limit of Gaussian FWHM 0.1 mas.We measure closure phases on all triangles (Fig. 3, upper panel) which are consistent with 0 with an rms of 1 deg.Closure phases of zero are expected for an unresolved source (Lachaume 2003).
A secondary component would show up as an oscillatory signal in the closure phases and from a limit 2 deg the flux ratio is 2% for separations 1 mas.This argues for an unresolved or marginally resolved source, no asymmetry, and possibly some additional (over resolved/extended) background flux, which reduces the visibility at short baselines.
The photometric flux is a factor ∼ 5.9 lower than the calibrator (K = 10.0), which implies the source magnitude was K ∼ 11.9 at the time of observation.The most likely model for the source is an unresolved point source, and some extended background.In the acquisition camera, the H-band flux of the calibrator is a factor of ∼ 3.6 larger, which would correspond to H ∼ 11.4.The unresolved core is fully consistent with expectations from jet models, as the IR synchrotron emission is likely dominated by regions within 10 3 − 10 4 r g , where r g = GM c 2 is the gravitational radius of the black hole (Gandhi et al. 2011(Gandhi et al. , 2017)).Nevertheless, there are no bright jet-ISM interaction sites, constraining the dissipation of energy associated with the steady jet on these scales.This observation was made during the prolonged hard state during the first part of the outburst of MAXI J1820+070.Later in the outburst, the source made a transition to the soft state, but unfortunately GRAVITY was unavailable at the time, and no observations of discrete ejecta were possible during this outburst.
Our size constraint is the the tightest direct (i.e. from imaging) limit on the size of the NIR emitting region in a hard state XRB.The source size limit of 0.1 mas corresponds to a distance of 4.4 × 10 7 km, or ∼ 5 × 10 6 r g for a 5 M black hole at 3.0 kpc (Torres et al. 2019;Atri et al. 2020, 5 M is a lower limit; this source size estimate reduces for higher BH masses).While this size determination is less constraining than indirect methods, it agrees with those inferred from the variability timescales (e.g.Casella et al. 2010;Kalamkar et al. 2016;Gandhi et al. 2017) and model predictions of XRB jet spectra (e.g.Markoff, Falcke & Fender 2001;Markoff, Nowak & Wilms 2005).The 0.5 mas size scale of the extended jet at radio wavelengths (Miller-Jones et al. in prep) is comparable to the resolution of the GRAVITY observation at IR wavelengths, however the size scale of the steady, compact jet is expected to be orders of magnitude smaller at IR wavelengths.Nevertheless, this jet will be expanding and pushing into the surrounding ISM, and the fact that it was in the bright and steady jet state for two months means that the interaction zone with the ISM likely moved out to large scales.Conservatively estimating a velocity of the jet-head to be 0.01c, this would be ∼ 10 15 cm or ∼ 10 −3 pc.At a distance of 3.0 kpc this lengthscale corresponds to 10s of mas, well within the capability of GRAVITY.Our measurement is thus an excellent feasibility study and clearly demonstrates that spatially resolving jet ejecta and jet-ISM interaction regions on scales of 1-50 mas (∼0.3-20AU for a source at 3 kpc; up to ∼60 AU at 8 kpc) is possible with GRAVITY.

DISCUSSION
The case studies presented here demonstrate the untapped potential of upcoming high-precision OIR interferometry instruments such as GRAVITY to open a new discovery space for sources other than their intended targets.It is extremely timely to begin tests of this technique during commissioning of upgrades to GRAVITY for example, because current high-energy wide field monitors (e.g.Swift, Fermi, MAXI ) are being joined by deeper X-ray all-sky instruments such as eRosita (Merloni et al. 2012), and the first generation of mid-to-high frequency range radio all-sky monitors (e.g.MeerKAT;Fender et al. 2017).We expect tens of new XRBs to be discovered in outburst, most of which will likely be in the southern hemisphere and hence visible from the VLT.Well constrained orbital parameters for as many of these systems as possible will be vital for constraining the nature of the various compact primaries, as well as binary evolution models in general.
In the future, other more challenging applications can be considered.For instance, wavelength-dependent centroid shifts may be detectable when the contributions of two components in a single state are oppositely decreasing/increasing very quickly in the IR band.For instance, in the hard to soft state transition, the jet is likely dropping and the relative contribution of the thermal star or disk could be rising.By using, e.g., MATISSE (Lopez et al. 2014) in combination with GRAVITY, a centroid shift between images in, e.g., the K and J bands could be detectable.We explored this idea briefly in an earlier conference presentation (Markoff 2008), and found that for most sources this shift would be a challenge to detect, however it is worth considering for the future generation of interferometers.The results would provide powerful constraints of particle acceleration efficiency and cooling in microquasar jets.

Figure 1 .
Figure1.Schematic of the centroid shift expected during state changes, due to the disappearance of the jet IR synchrotron emission.Top: System in the hard state of a LMXB, where both jet (red broken power law) and companion star (blue blackbody) contribute comparably to the flux density in the IR bands (orange dashed).Bottom: Same system, at the same orbital phase, after transitioning to the soft state and jet contribution to the IR is quenched, resulting in a shift of the image centroid towards the companion star in the K-band.The orbital wobble, most prominent when the star is producing the IR emission, is largely reduced when the jet is dominating.Note that another centroid shift could be potentially seen between K and J bands during state transitions.

Figure 2 .
Figure 2.An example simultaneous, broadband spectrum from GRO J1655-40 in the hard state, from Migliari et al. (2007), illustrating the K band (vertical red line) and the difference in flux between the jet synchrotron emission (dashed green line) and thermal companion star (dashed purple line; note the accretion disk is also present but very distinct at higher energy).

Figure 3 .
Figure 3. Measured closure phases (top) and uv-coverage (bottom) from our GRAVITY observation of MAXI J1820+070, colored by baseline triangle or individual baseline.In the upper panel, colored points with error bars are compared with the prediction of a binary model with a flux ratio of 0.03 and a separation of 10 mas at PA of 45 deg E of N dots).closure phases constrain the flux ratio for any secondary ejected component to be 0.01-0.1 for separations 1-50 mas over all position angles.A single unresolved component would have closure phase = 0 deg at all spatial frequencies; our measured closure phases have median and rms 0.1 ± 1.5 deg, consistent with zero.The data are of sufficient quality to detect a faint, offset second component if present for a future transient.

Table 1 .
The XRBs (with radio detections) possessing the widest orbital separations on the sky 1 (all with a > 10µas).The best interferometry candidates are those that are expected to have a shift of the phase of the centroid due to a changing IR jet contribution (final two columns).We do not include γ-ray binaries in this table, which are not thought to have extended jets. 2 Sources in bold have been observed with GRAVITY on VLTI; sources in italics are too far north for the VLTI (Declination > +25 • ).
was possible for 50% of the total observation time, providing good data quality