Complex K: Supernova Origin of Anomalous-velocity H i Structure

We address one of the lingering mysteries of high-velocity clouds: If the anomalous negative velocities are the result of the approaching gas from old supernovae, then where are the receding counterparts of the expanding shells? Data from the λ-21 cm Galactic neutral hydrogen EBHIS survey (Winkel et al.) show multiple signatures of the expanding shells. The near-side (approaching) H i shells form part of Complex K. The high blueshifted velocities result from the H i moving into the low-density environment of inter-arm space. The H i data also show a distinctive, bow-shaped feature, the signature of the far-side (receding) emission of an expanding shell. The low redshifted velocity results from the gas expanding into volumes of space with a higher density. If we make the simplifying assumptions that the expansion of the shells is uniform and spherically symmetric, then the explosions took place about ⪅3 × 105 yr ago. The momentum, p ∼ 7 × 104 M ⊙ km s−1, agrees with recent model estimates for supernova evolution. Supernova explosions attributed to the unseen companion in several binary systems identified by the Third Gaia Data Release may be responsible for anomalous-velocity H i gas in Complex K. Four binary star systems with neutron-star candidates are located at the edge of the Sagittarius spiral arm and used to determine the distance to the H i features discussed here.


Introduction
Complex K is composed of neutral hydrogen clouds and filaments with radial velocities that are inconsistent with the regular rotation of the the Milky Way.It was originally considered part of Complex C, but the global view of the hydrogen sky revealed by the Leiden-Dwingeloo H I Survey (Hartmann & Burton 1997) was used to separate it out in both position and velocity space (Wakker 2001).The components of Complex K have Galactic longitudes, l = 30°-70°, Galactic latitudes, b = 25°-68°, and radial velocities between −60 and −90 km s −1 .Although the traditional boundary between High-Velocity Clouds (HVCs) and Intermediate-Velocity Clouds (IVCs) is −80 km s −1 , radial velocity is used as one of the parameters to distinguish IVC Complex K from HVC Complex C. Kerr & Knapp (1972) first observed 21 cm emission from Complex K, de Boer & Savage (1983) detected Mg II toward the star Barnard 29, and Shaw et al. (1996) observed Na I toward several stars in M13.The Mg II and Na I detections set an upper limit to the distance of Complex K of 6.8 kpc, but it may be much closer.Haffner et al. (2001) detected Hα emission and Savage et al. (2003) observed O VI absorption, indicating that ionized gas is also part of Complex K although no one-to-one relationship between H I and Hα was found.The absorption studies, although limited, indicate that the metallicity of Complex K is approximately solar.
Despite observations going back over 50 yr, the distance and origin of Complex K as well as many other HVCs and IVCs remain unknown.Most models place them in the Galactic Halo (see, e.g., van Woerden et al. 2004) so some early models, such as old supernova explosions, were rejected because they could not generate enough energy to propel the required mass to the observed high velocities (Oort 1966).
Recent results have resurrected the supernova model for HVC MI (Schmelz & Verschuur 2022) and HVC Complex M (Schmelz & Verschuur 2023;Verschuur & Schmelz 2023).The invisible companion of the yellow giant star, 56 Ursae Majoris, may be the remains of the supernova (Escorza et al. 2023) that accelerated HVC MI to 120 km s −1 .The distance to 56 Ursae Majoris itself, 163 pc, is then used to determine a distance to MI and subsequently to Complex M, 150 pc.Since these distances are substantially lower than the upper limits estimated from absorption line studies, the mass and energy of both the MI and Complex M are easily in line with what is expected from a supernova.Both cavities also have the high-energy signatures expected from supernovae: X-rays observed by ROSAT for MI (Herbstmeier et al. 1995) and γ-rays observed by COMPTEL for Complex M (Schoenfelder et al. 1993).The supernova that created the Complex M Cavity may have carved out the Local Chimney (Welsh et al. 1999;Lallement et al. 2003), a low-density extension of the Local Bubble (Zucker et al. 2022) that reaches all the way into the Galactic halo.
Motivated by the results for MI and Complex M, Schmelz et al. (2023) investigated a supernova-related cavity centered at (l, b) ∼(145°, 34°) with a radius of about 11°and an expansion velocity of 55 km s −1 .The H I gas of the approaching shell is part of the Low-Latitude-Intermediate-Velocity Arch.The H I gas on the receding side appears to be interacting with the gas approaching us on the near side of a second elongated cavity; Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence.Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
the North-Celestial-Pole Loop is located at the intersection of these two expanding features at a distance of a few hundred parsecs.
In this paper, we investigate the possible association of the anomalous-velocity gas of Complex K with low-velocity H I cavities centered at (l, b) ∼(49°, 32°).We also address one of the lingering mysteries of HVCs: If the anomalous negative velocities are the result of the approaching gas from old supernovae, then where are the receding halves of the expanding shells?In other words, where are all the positive HVCs?The analysis is described in Section 2 followed by the discussion in Section 3 and conclusions in Section 4. The Appendix gives the details of the binary-star analysis that provides the distance to the Complex K H I features, which is required for calculations of physical properties like mass, momentum, and energy.

Analysis
The λ-21 cm Galactic neutral atomic hydrogen data from the Effelsberg-Bonn H I Survey (EBHIS) covers the northern sky with a declination greater than −5°and an angular resolution of 10′8 (Winkel et al. 2016).Figure 1 shows EBHIS area maps of the H I brightness temperature centered at (l, b) ∼(49°, 32°).Although there is a lot of complicated structure, Figure 1(a) reveals two cavities centered at 0 km s −1 with respect to the local standard of rest.Throughout this paper, we will refer to the feature at lower longitudes (right) as Cavity 1 and the one at higher longitudes (left) as Cavity 2. Figure 1(b) shows the anomalous-velocity gas features identified as Complex K in an image integrated from −20 to −100 km s −1 .The four numbered symbols mark the location of candidate neutron stars summarized below.
Figure 2 shows a series of (b − v) maps at different longitudes chosen to cover the cavities seen in Figure 1.These plots were drawn from a complete set produced at 0.°5 intervals for longitudes from l = 44°to 56°Each plot was integrated over of 0.°2 in longitude and covers a latitude range from b = 25°to 40°The symbols mark the location of the same candidate neutron stars that appear in Figure 1.
Figure 2(a) at l = 44°is just beyond the high-longitude boundary of shell.It shows the expected ridge of H I emission around 0 km s −1 that represents relatively undisturbed gas in the Galactic disk.Features appear at higher and lower velocities, typical of the complex, interstellar H I structure throughout the Milky Way.
Figure 2(b) at l = 47°.5 is close to the longitude of Star 1 (l = 47°35).This image shows the first indication of the anomalous-velocity gas that forms Complex K at (b, v) = (36°, −70 km s −1 ).The emission around 0 km s −1 shows a distinct hole at the location of the star.This is Cavity 1 seen in Figure 1.There is also a displacement of the H I peaks in that direction to positive velocities of order 15 km s −1 .
In Figure 2(c) at l = 49°, the emission from Complex K is more extensive in latitude.The negative-velocity gas around −30 km s −1 shows considerable substructure, indicating that the hydrogen is patchy or cloudy.The ridge around 0 km s −1 fills in slightly and the bulge to positive velocity is nearly continuous in latitude.This distinctive, bow-shaped feature is the signature of the far-side (receding) emission of an expanding shell.
Figure 2(d) at l = 50°.5 is at the longitude of Star 3. The lowvelocity H I shows a hole, and the positive-velocity gas is again distorted.Emission at the velocities of Complex K is less pronounced, although it does appear that the negative-velocity protrusion to around b = 28°may be related.
Figure 2(e) at l = 52°is at the longitude of Star 4. The negative-velocity emission is similar to that seen in Figure 2(d), and the low-velocity H I shows a small hole.The positivevelocity structure is similar to Figure 2(c), but the bow-shaped feature-the receding emission of an expanding shell-is significantly less pronounced.
Figure 2(f) at l = 53°is at the longitude of Star 2. Emission at negative velocities shows distinct peaks at velocities from −50 to −15 km s −1 with little trace of gas from Complex K.The positive-velocity bulge in H I is less well-defined and appears to extend over a larger latitude range than seen in the previous plots, which is consistent with the appearance of Cavity 2 in Figure 1.
Figure 3 shows a series of (l − v) maps at three latitudes chosen to highlight the features discussed in Figures 1 and 2. These were drawn from an extended set made at 1°intervals each covering 1°in latitude from b = 30°to 46°I n Figure 3(a) at b = 34°, the ridge of local gas at 0 km s −1 breaks up at b = 46°-49°, which corresponds to Cavity 1.The H I emission from Complex K dominates at velocities beyond −30 km s −1 , and the positive-velocity gas shows a fragmented bow-shaped signature of the far side of an expanding shell.
Figure 3(b) at b = 33°is close to the latitude of Star 1 (32°.88).The zero-velocity ridge is disrupted, and the positivevelocity bulge is clearly evident.The Complex K emission is extended with a bow-shaped continuity across the longitude range of the image.This extension in longitude of the Complex K emission may be a consequence of more than one supernova event occurring in this area of sky.
Figure 3(c) at b = 32°shows that the zero-velocity ridge is strengthening, the Complex K emission is fading, and a gap in the positive-velocity bulge is beginning to close.
The presence of the shell-like structures referred to above prompted us to search for possible neutron-star candidates that could provide the location and distance of the supernova events responsible for the H I cavities.Following the procedure outlined in Schmelz et al. (2023), we queried the Gaia Nonsingle-star (Gaia-NSS) catalog (Gaia Collaboration et al. 2023a) and retrieved all binaries within the following target areas seen in Figure 1: Cavity 1 centered at (l, b) = (49°, 32°) with a radius of 5°and Cavity 2 centered at (l, b) = (53°5, 32°) with a radius of 3°The details of the binary-star analysis are described in the Appendix and Table 1 summarizes the results for four possible neutron-star candidates.Table 1 shows the Gaia DR3 ID number followed by a star number identifier that will be used in the discussion below.For each binary system, the distance derived from parallax measurements is followed by the z height above the Galactic plane and the R distance along the Galactic plane.Table 1 also lists the center-of-mass velocity, V CM , as well as the mass of the primary star, M 1 , and the mass of the secondary star, M 2 , the neutron-star candidate.
The values of R and V CM are not consistent with simple models of H I moving in orderly orbits around the Galactic center due to differential rotation (see, e.g., Figure 7.7 of Burton 1988).The traditional explanation for these so-called forbidden velocities would place the stars at distances well beyond the solar circle, more than 12 kpc at these longitudes, but the precise distances from parallax exclude this possibility.If, instead, the binary systems are inside the solar circle, the observed velocities would imply that they may have experienced a kick of order 20-30 km s −1 as a result of the supernova event (see, e.g., Fortin et al. 2022 for post-supernovae highmass X-ray binaries).

Discussion
The positions on the sky of the four candidate stars listed in Table 1 place them within the cavities of H I emission at low   velocities (Figure 1).In addition, the position-velocity plots (Figures 2 and 3) in these directions show distinct disturbances in the low-velocity hydrogen emission.The negative-velocity emission peaks of Complex K are the near-side (approaching) gas of the explosive events.The positive-velocity gas shows a bow-shaped feature, a signature of the far-side (receding) emission of an expanding shell.

Snowplow Model
A supernova remnant goes through various phases as it expands (e.g., Haid et al. 2016 and references therein).
The first is the Free Expansion Phase where the ejecta expand freely until they sweep up their own weight in circumstellar and interstellar matter.This phase can last tens to hundreds of years, depending on the density of the surrounding gas.The remnant is faint at all wavelengths except for the synchrotron emission from high-energy electrons accelerated in the shock.
The second is the Sedov-Taylor Phase that occurs when the remnant expands adiabatically.The forward shock heats the interstellar material, and the reverse shock heats the ejecta.These remnants are typically X-ray bright and last a few thousand years.
The subsequent Pressure-Driven Snowplow Phase occurs when the shock velocity decreases to 200 km s −1 , the temperature of the gas drops below 10 6 K, and radiative cooling begins to affect the dynamics.The remnants become bright in optical emission from recombining atoms.This phase lasts tens of thousands of years.
The Momentum-Conserving Snowplow Phase occurs when the interior cools and the shell continues to expand due to its own momentum.The electrons associated with the expanding gas are moving at sub-relativistic speeds, much too slowly to generate significant synchrotron emission.The generation of cosmic rays has also diminished, so any associated synchrotron emission has faded.This phase is best seen in the radio emission from neutral hydrogen atoms (like that seen in Figures 2 and 3 for Complex K) and lasts hundreds of thousands of years.
Finally, the Dissipation Phase describes the condition when the remnant begin to merge with the surrounding interstellar medium and the expansion speed has slowed to approach the random velocities of the surrounding matter.Its remaining kinetic energy contributes to interstellar turbulence.This dissipation begins about a million years after the supernova explosion.
In general, the signatures of a supernova remnant in the momentum-conserving snowplow phase will not be recognizable unless the explosion occurred in a region of space where the ambient interstellar density is low.This condition is met at the surfaces of spiral arms, in inter-arm space, and at large distances above the Galactic disk.The radio signatures of the remnant expansion are present in the EBHIS position-velocity maps seen in Figures 2 and 3, with the Complex K anomalousvelocity features expanding toward us into a low-density medium and the positive-velocity gas receding into denser spiral arm material.Using the distance to the stars, we can determine the momentum of the features associated with the cavities for each star.
The derivation of momentum begins with average spectra produced from the EBHIS data.Two sets were produced for each of the cavities associated with Stars 1, 2, and 3. Figure 1 shows that Star 1 and Star 3 are found inside the boundary of Cavity 1, which appears to have two main segments.Star 2 lies inside Cavity 2. At this point in the analysis, it is not obvious that Star 4 is associated with its own cavity.
Average profiles were created for two areas associated with Star 1.The first encompasses the anomalous Complex K features on the approaching side of the expanding shell structure; the second includes the gas moving away from the observer, i.e., the bow-shaped bulge at positive velocities seen in Figures 2(b) and 3.For the appropriate velocity ranges, the area under the curve of these average profiles can be estimated using Gaussian or histogram analysis.The resulting column densities are 12 × 10 18 cm −2 and 69 × 10 18 cm −2 for the approaching and receding sides, respectively.Using the distance of Star 1 as the center of the explosion, the corresponding masses are approximately 1000 and 6000 M e .
The calculation of momenta requires the velocities of the expanding gas on the near and far sides of the shell with respect to the velocity of the star at the time of the explosive event.
Since the supernova imparted a kick of unknown magnitude to the binary system, the best approximation for the preexplosion value is the radial velocity of the Sagittarius arm, −2 km s −1 (please see Section 3.2).
The near-side velocity for Complex K is then about −68 km s −1 ; see Figure 2. Combining this with the mass results in a momentum of ∼7.3 × 10 4 M e km s −1 .Similarly, the far-side velocity is about +22 km s −1 , and the momentum is ∼13.2 × 10 4 M e km s −1 .The total momentum of the expanding shell is then ∼20.5 × 10 4 M e , in good agreement with the models of Haid et al. (2016, please see their Figure 3).
If we make the simplifying assumptions that the expansion is uniform and spherically symmetric, then the explosion took place about 3 × 10 5 yr ago.Since we know the expansion is slowing down, this value would be an upper limit.The lower limit corresponds to the time required for the optical emission of the supernova to fade, about 1 × 10 5 yr, thus 1 × 10 5 yr age 3 × 10 5 yr.
Similar calculations using the appropriate spectra for the H I gas surrounding Star 3 and Star 2 show that the total momentum of the expanding H I is 4.4 × 10 4 M e km s −1 and 1.9 × 10 4 M e km s −1 , respectively.The corresponding ages are ∼4 × 10 5 yr and ∼3 × 10 5 yr, consistent with theoretical models of a supernova remnant in the momentum-driven snowplow phase.Cavities in interstellar space carved out by supernova events such as those discussed above as well as those associated with HVC MI (Schmelz & Verschuur 2022), Complex M (Schmelz & Verschuur 2023;Verschuur & Schmelz 2023), and the Low-Latitude-Intermediate-Velocity Arch/North-Celestial-Pole Loop, Schmelz et al. (2023), should be recognizable in images of face-on galaxies.A dramatic example is found in the JWST image of M74, which shows a distinct honeycomb appearance consistent with the effect of a large number of supernova events that sculpted the spiral arms of that galaxy.Examination of the M74 image shows cavities that exhibit a range of diameters that span at least a factor of ten in size. 7If our galaxy is similarly honeycombed by past explosive events, we will only find the necessary evidence by searching for them in areas of sky that are minimally affected by the confusing presence of intervening H I gas in the Galactic disk, that is, at intermediate or high Galactic latitudes.
This raises the intriguing possibility that Galactic cavities would be observed in other circumstances.Those may include the shell-like objects (Heiles 1984), worms (de Avillez & Berry 2001), and chimneys (Lallement et al. 2003).With as many as 10 9 neutron stars in the galaxy (Sartore et al. 2010) and only ∼10 3 observed directly as either pulsars or accreting X-ray sources, the overwhelming majority of those will have affected the gas dynamics of the interstellar medium without leaving a clue as to their distance or when the supernova event occurred.Identifying binary systems with a candidate neutron star adds the fundamental parameter of distance to the analysis and allows estimate to be made of the physical conditions in the surrounding, churned-up interstellar matter.The signatures of past supernova events become recognizable in the morphology and dynamics of surrounding interstellar gas over a range of scales that depend on the energy of explosion, the age of the event, and the preexisting structure and density of the surrounding medium.The phenomenon is most readily identified in areas of sky devoid of the clutter in the Galactic disk which, from our vantage point, renders a search for such cavities in those directions nearly impossible.

Where in the Galaxy is Complex K?
The (b − v) plot in Figure 2(b) cuts close to Star 1 and shows a clear minimum in the low-velocity H I consistent with the area map in Figure 1.A bright segment of Complex K peaking at −75 km s −1 is found at a slightly higher latitude than the star.The clear bulge in the H I emission toward positive velocity, the far side of the shell, surrounds a minimum at about +10 km s −1 .The bulge to positive velocities is even more evident in Figure 2(c).
As a first step to locating the stars and Complex K with respect to the Sun, Figure 4(a) is a plan view of the second quadrant of the galaxy with the four target stars plotted at their distances projected onto the Galactic disk.Their longitudes range from 47°to 53°, close to the tangent direction of the Sagittarius spiral arm at l = 50° (Vallee 2014a(Vallee , 2014b)).The distance from the Sun to the center of the Sagittarius spiral arm measured along the plane by various tracers considered in the literature (e.g., Vallee 2008;Steiman-Cameron et al. 2010;Hou & Han 2014;Reid et al. 2014;Hu et al. 2016;Griv et al. 2017;Hou 2021;Vallee 2022) is 964 ± 157 pc.Using the same references, we can estimate the distance to the tangent point at the center of the arm, 1180 ± 230 pc.Assuming the width of the arm in the plane is 1 kpc, the near side of the arm is about 460 pc from the Sun. Figure 4(a) shows that Stars 1 and 4 are located at the surface of the Sagittarius spiral arm while Stars 2 and 3 are probably in inter-arm space.
How then do we account for the apparent offset in latitude between the location of Complex K and Star 1? Figure 4(b) shows the location of the 4 stars with respect to a crosssectional view of the Sagittarius arm in the direction of l = 50°T he dashed dark lines indicate the latitude values of interest.The series of blue dashed lines represent H I density gradientlevels that decrease with distance from the center of the Sagittarius arm.
The H I scale height of the Sagittarius spiral arm in the direction of l = 50°can be estimated from a (b − v) plot produced using Leiden-Argentina Bonn survey data (Hartmann & Burton 1997) averaged over a range of longitudes from 48°to 50°The amplitude of the H I emission at velocities of 5, 10 and 15 km s −1 was measured on the (b − v) plot as a function of latitude, and the dependence of brightness on latitude was found to be exponential.The average scale height estimates at the three velocities give 300 ± 42 pc.When applied to Figure 4(b), this suggests that Star 4 lies in the Sagittarius spiral arm at about two-scale heights above the Galactic plane.The other three stars are located at the outer edges of the Sagittarius arm.
The schematic in Figure 4(b) serves to illustrate why H I emission from Complex K in Figures 2 and 3, the gas approaching the Sun, is offset in latitude from the direction of Star 1.In the presence of a radial H I density gradient (symbolized by the blue curves in Figure 4(b)), expansion of gas away from the star will have a component of motion toward the Sun (blue arrows) that travels into regions of lower density.The gas moving away from the Sun (red arrows) moves into volumes of space with a higher density.Figure 4(b) shows that, in general, the approaching gas will be observed at a higher latitude than the star while the receding gas will be observed at a lower latitude than the star.
Therefore, the H I in the shell created by a supernova in the momentum-conserving snowplow phase will appear asymmetric in a (b − v) plot.This is consistent with what is observed for Star 1 in Figure 2 The detailed outcome of this phenomenon will be modulated by the presence of unknown, preexisting structure in the interstellar medium.In addition, the actual density in a spiral arm crosssection is, at best, poorly known.What does emerge from Figure 4(b) is that anomalous-velocity H I is found where the expansion is toward regions of lower density.This is in contrast to a symmetric shell that would be created if the supernova event occurred in a region of relatively uniform density.

Conclusions
Supernova explosions attributed to the unseen companion in several binary systems identified by Gaia DR3 may be responsible for the anomalous-velocity H I gas in IVC Complex K.
Slices from the Longitude-Latitude-Velocity data cube of the λ-21 cm Galactic neutral atomic hydrogen HI4PI survey show multiple signatures of expanding shells.The two cavities associated with these explosions are best seen at low velocities.Cavity 1 is centered at (l, b) = (49°, 32°) with a radius of 5°Cavity 2 is centered at (l, b) = (53°5, 32°) with a radius of 3°T he near-side (approaching) H I shell of Cavity 1 is part of IVC Complex K.The high blueshifted velocities result from the H I moving into inter-arm space with a lower density.
This distinctive, bow-shaped H I feature best seen in Figure 2(c) is the signature of the far-side (receding) emission of an expanding shell.The low redshifted velocity results from the gas expanding into volumes of space with a higher density.
Complex K and the associated H I gas address one of the lingering mysteries of HVCs-if the anomalous negative velocities are the result of the approaching gas from old supernovae, then where are the receding portions of the expanding shells?The answer, in this case, is that the gas is moving into a high-density environment so, due to momentum conservation, it has a lower velocity.
The total momentum for the far and near sides of the shell of H I surrounding Star 1 (Cavity 1) is ∼21 × 10 4 M e km s −1 , in agreement with recent model estimates for a supernova (Haid et al. 2023).
The lower limit for the age of the supernova corresponds to the time required for the optical emission to fade.We can estimate the upper limit by assuming a uniform expansion of the explosion.We find 1 × 10 5 yr age 4 × 10 5 yr.
Four binary-star systems with neutron-star candidates were used to determine the distance to IVC Complex K and the other H I features discussed here.These stars are located at the upper, outer edges of the Sagittarius spiral arm.Complex K itself has been blasted into inter-arm space.
of the queried binaries among the different Gaia-NSS solutions is as follows: About 140 binaries with an AstroSpectroSB1 solution.This model is the most complete because the binaries are detected with both astrometric and spectroscopic data so that the full set of orbital parameters, and in particular the inclination and, in most cases, the masses of the two components, can be obtained for these targets that are not accessible from one type of data only.
About 450 binaries with an Orbital or astrometric solution, for which M 2 (the mass of the secondary) cannot be derived from Gaia data alone.M 1 (the mass of the primary) must be estimated independently using other stellar parameters locating the star in the Hertzsprung-Russell diagram.
About 350 binaries with an SB1 solution, which relies only on the spectroscopic signal.For these systems, even when M 1 can be derived from its stellar parameters, only a lower limit is available for M 2 .Additionally, one can draw a relation between M 2 and the orbital inclination to find systems that could host a massive faint companion given a specific orbital orientation.
Additionally, we find about a thousand targets with a nonlinear proper motion that is compatible with an acceleration solution.About 150 of these that show a spectroscopic trend, and although these systems are very likely binaries, the currently available data do not constrain their orbits, probably due to their long periods.These systems are useful to highlight the incompleteness of the current Gaia-NSS catalogs.
For all these Gaia sources, we also queried the masses of their components in the gaiadr3.binary_massestable of the NSS catalog.
Table 2 lists the parameters of the binary systems of interest.The column head shows their Gaia DR3 ID numbers in two rows.The next row lists the Star ID number used in the Discussion above.The first column lists the parameters: the binary type, Galactic longitude l, Galactic latitude b, parallax ϖ, period P, eccentricity e, semimajor axis a 1 of the photocenter around the barycenter, inclination i, semi-amplitude K 1 of the radial velocity curve, center-of-mass velocity V CM , mass function f (m), effective temperature T eff , g log , iron abundance [Fe/H], astrometric mass ratio function AMRF, primary mass M 1 , and secondary mass M 2 .

A.1. AstroSpectroSB1 Binaries
Among the AstroSpectroSB1 binaries with mass information, no obvious neutron-star candidate was found.There are a few binaries with an M 2 upper limit larger than 1.2 M e ; however, the lower limit is in all cases smaller than M 1 , making a low-mass main-sequence companion or white-dwarf companion much more likely.
For the fraction of AstroSpectroSB1 binaries that were not part of the gaiadr3.binary_massestable, we computed the spectroscopic mass function ( f (m)) from the Gaia-NSS orbital parameters as follows: where P is the orbital period in days, e is the eccentricity, and K 1 is the semi-amplitude of the radial velocity curve in km s −1 .The latter was computed from the orbital parameters available for the Gaia AstroSpectroSB1 sample: Here, a 1 is the primary semimajor axis in AU and i is the orbital inclination.We assume that the secondary contributes no light to the system.We used the calculated f (m) values to look for significantly high values that could indicate the presence of massive companions in systems without mass information.In contrast with our study of the LLIV arch and the NCP loop (Schmelz et al. 2023), this time we decided to set a much more conservative cut-off of f (m) = 0.075 M e .This lower value allows us to explore a much larger parameter space and many more mass combinations, allowing systems with more massive primary stars to be considered as well as neutron-star hosting systems.We collected the Gaia stellar parameters for all systems with f (m) > 0.075 M e and within 2 degrees of the centers of Cavity 1 and Cavity 2.
Columns (2)-( 5) of Table 2 list the four systems with f (m) > 0.075 M e Type AstroSpectroSB1.The orbital Gaia DR3 stellar parameters (Creevey et al. 2023) are used to locate the primary stars on a Hertzsprung-Russell diagram along the lines followed in Schmelz et al. (2023).We then compared their location with evolutionary tracks to get a rough estimate of M 1 that can be used to estimate M 2 .The errors on the Gaia stellar parameters are small, but large errors can be caused by the choice of the grid of models (Escorza et al. 2017) and its metallicity.Since two of the targets have sub-solar metal content, we also considered tracks from the same grid with [Fe/H] = −0.25.
With this secondary mass estimation, we find two massive companions.The first one is in the system Gaia DR3 4572271657605887616, Star 1, but the primary star in this system seems to be a massive (M 1 ∼ 4.5 M e ) evolved star given its log g value.A main-sequence companion with M 2 ∼ 1.44 M e could possibly hide next to such a primary.In addition, Star 2 (Gaia DR3 4598657875087627648; TYC 2087-1193-1) is also a good neutron-star candidate.The primary mass was estimated to be between 1 and 1.5 M e from the location on the Hertzsprung-Russell diagram using the Gaia stellar parameters.The spectroscopic mass function of the system was calculated from the Gaia orbital parameters to be f (m) = 0.17 M e , and the orbital inclination is close to 50°, as directly reported by Gaia.With these numbers, we find that Star 2 has a faint companion (not seen as SB2 by Gaia) in the neutron-star mass regime.Moreover, the estimated secondary mass is larger than M 1 , allowing us to eliminate the possibility of a main-sequence companion (but not a close pair).

A.2. Orbital or Astrometric Binaries
Among the astrometric binaries with mass information, we find no clear neutron-star candidates.There are many systems where the upper boundary of M 2 is massive enough to allow a neutron star, but again, in all cases the lower boundary is significantly smaller than M 1 , which favors a lower-mass companion.There are two marginal exceptions, Gaia DR3 4575217421055072768 and Gaia DR3 4574196868106419200, hereafter Star 3, where the lower boundary of M 2 (0.92 M e and 0.53 M e , respectively) is only marginally smaller than M 1 (1.01 M e and 0.71 M e , respectively) whereas the upper bound is compatible with a neutron star (1.22 M e and 1.35 M e , respectively).The properties of these two systems are summarized in columns (6)-(7) of Table 2 for Type Astrom.
In the case of pure astrometric binaries, we do not have enough information to compute K 1 and f (m), but we carefully checked the astrometric mass ratio function (AMRF) defined by Gaia-NSS as follows: where a 0 is the angular semimajor axis of the photocentric orbit, ϖ is the parallax, M 1 is the mass of the primary star, and P is the orbital period of the binary.Following Gaia Collaboration et al. (2023a) and using their Figure 33 as a reference, we looked for additional systems that could host a massive faint companion but found none.Additionally, the AMRF computed for Gaia DR3 4575217421055072768 is quite low, making a neutron star unlikely.

A.3. SB1 Binaries
Less than half of the systems among the Gaia SB1 binaries present in the cavity had information about the mass of its components, and in those cases, only M 1 and the lower boundary allowed for M 2 were available.For the SB1 subsample, we again computed the spectroscopic mass functions of all the systems within 2°of each cavity center and tried to put additional constraints on the component masses for the binaries with f (m) > 0.075.We found 18 systems fulfilling these two criteria.Eight of them had an M 1 value in the gaiadr3.binary_massestable, and for the remaining ten, we queried the Gaia stellar parameters to locate the primary stars on the Hertzsprung-Russell diagram as we did above and compare their location with our STAREVOL grids of different metallicities.Only five of these eight systems had stellar parameters available and additional metallicity grids were also considered for the mass determination when appropriate.
This additional analysis left us with 13 SB1 systems for which we have an estimate of M 1 and a f (m) value.As mentioned above, for pure SB1 binaries, we do not have inclination information, and the constraints that we can set for M 2 are dependent on the inclination.Using the following relation: we plotted M 2 as a function of i for the 13 mentioned systems.Star 4 (Gaia DR3 4575599875005089280), last column in Table 2, Type SB1, is the best candidate system to host a neutron-star companion.Assuming that there are only two bodies in the system, the mass range covered by M 2 does not leave space for a second main-sequence star, because we should have detected the system as an SB2 and not as an SB1.
In any case, once again, we cannot discount the possibility of this faint companion being a close pair of lower-mass stars.Additionally, Gaia DR3 4574036236330142464 has a mass function above 0.3 M e , indicative of a reversed mass ratio.However, without an M 1 value, it is impossible to say more about its components.For completeness, we also note that 12 additional SB1 systems were identified within 2°of the cavity centers with f (m) > 0.075 M e but that have smaller ranges of favorable inclinations or primary masses high enough to hide a main-sequence star companion with a mass in the neutron-star range.Unfortunately, the inclinations of many of the systems considered here will not be available before the Gaia DR4 release, which is expected in 2025.

Figure 1 .
Figure 1.(a) EBHIS area map of the H I brightness temperature centered at (l, b) ∼(49°, 32°5) that reveals two distinct cavities in a 5.0 km s −1 wide band centered at 0 km s −1 w.r.t. the local standard of rest.(b) Structure of the anomalous-velocity H I in the direction of the cavities integrated from −20 to −100 km s −1 .The location of Stars 1, 2, 3, and 4 suspected of having neutron stars in orbit as discussed in the text, Section 3, are indicated by the symbols.H I emission associated with Complex K is located mostly north of Star 1.All legends are in Kelvin.

Figure 2 .
Figure 2. Examples of (b − v) maps at different longitudes from a large set described in the text.(a) At l = 44°, outside the area of the cavity seen in Figure 1, the expected ridge of H I emission around 0 km s −1 due to H I in the Galactic disk, is undisturbed.(b) At l = 47°.5, the longitude of Star 1, the first sign of the anomalousvelocity gas that forms Complex K is seen at (b − v)=(30°, −65 km s −1 ).The clear cavity seen at 0 km s −1 aligns with the star as does a bulge of emission that extends to small (10-20 km s −1 ) positive velocities.(c) At l = 49°the ridge around 0 km s −1 begins to fill in, Complex K becomes more pronounced, and the positivevelocity bulge is most clearly defined.(d) At l = 50°.5, the longitude of Star 3, both the negative and positive-velocity gas show complex, multicomponent structure.(e) At l = 52°, the longitude of Star 4, the positive-velocity gas shows a hint of a bowed signature of the far side of an expanding shell.(f) At l = 53°, the longitude of Star 2, the zero-velocity ridge is shifted to a small positive velocity.The minimum in the ridge is not as pronounced as in the examples above.Anomalous negativevelocity H I bears similarities to the structure seen in the other plots in this figure.

Figure 4 .
Figure 4. (a) A plan view of the second quadrant of Galactic longitude with the distances of the four stars of interest projected onto the Galactic disk shown by the star symbols along the tangent direction of the Sagittarius spiral arm at l = 50°The center of the arm is represented by the dark arc and the near side by a blue, dashed arc.(b) A schematic cross-section of the Sagittarius spiral arm seen in the tangent direction of l = 50°The Sun is located at the origin of the (X, Z) plane.Distances are in pc.Latitudes 30°, 32°and 33°are shown as dashed dark lines.Levels of decreasing density in the Sagittarius spiral arm are symbolized by the concentric blue, dashed arcs.Blue arrows represent the expansion of a supernova shell along the direction of the density gradient that would have a component of motion toward the observer, while red arrows represent the receding gas.In the presence of a density gradient in surrounding gas, the approaching and receding faces of a shell are offset in latitude from the direction of the central star.

Table 1
Binary Systems with Possible Neutron-star Companions

Table 2
Binary Data and Astrophysical Parameters Extracted from Gaia DR3 Astrophysical parameters are described in Gaia Collaboration et al. (2023b) and binary parameters in Gaia Collaboration et al. (2023a). a