Evidence for a nova super-remnant surrounding the recurrent nova V745 Scorpii using eROSITA

Introduction

Classical novae (CNe) and recurrent novae (RNe) are luminous transient events arising from the surfaces of accreting white dwarfs (WD; Warner [109], and see e.g. Darnley & Henze [16]). A thermonuclear runaway triggers at the base of the accreted material once a critical mass is reached (Shara [88]), resulting in a portion of the accumulated material being ejected in the form of a nova eruption (Starrfield et al. [100]; Prialnik et al. [80]). Observationally, CNe have been observed in eruption once and RNe have exhibited more than one eruption in the last hundred years (Schaefer [85]; Darnley [14]). Yet theoretically, all novae are recurrent and can have periods between eruptions ranging from $10^{-1}$ yr (Hillman et al. [42]) to $10^{6}$ yr (Hillman et al. [43]). Up to $\sim10^{-4}\ M_{\odot}$ of the accreted material is expelled during a nova eruption and can reach velocities of up to 10,000 km s$^{-1}$ (O’Brien et al. [70]). Such ejecta consequently expands to form a shell around the nova (Cohen [12]; Slavin et al. [98]; Gill & O’Brien [26]; Downes & Duerbeck [18] and see Santamaría et al. [83] for a extensive catalogue of known optical nova shells). Though only $\sim10\%$ of Galactic novae have observed nova remnants, these shells can fade within decades (Tappert et al. [102]) so it is probable that all novae host a nova shell and currently only the brightest examples are detectable. Matter retained on the surface after the nova eruption can grow the WD (Yaron et al. [114]; Hillman et al. [42]) towards the Chandrasekhar (1931) mass and result in a type Ia supernova (Whelan & Iben [111]).

Nova super-remnants (NSRs) are greatly-extended shells created as a result of the continual sweeping up of up to thousands of solar masses (Darnley et al. [17]; Healy-Kalesh et al. [36]) of local interstellar medium (ISM) by many prior RN eruptions (Darnley et al. [17]; Healy-Kalesh et al. [36]; Healy-Kalesh [34]). Unlike nova shells observed around CNe (e.g. HR Del: Harman & O’Brien [30] and V4362 Sgr: Harvey et al. [32]), RNe (e.g. RS Oph: O’Brien et al. [69]; Bode et al. [7]; Ribeiro et al. [82] and T Pyx: Shara et al. [97, 96]) and dwarf novae (e.g. Z Cam: Shara et al. [93, 90] and AT Cnc: Shara et al. [94]) which are all less than a parsec across, NSRs are defined as such on account of extending tens of parsecs in diameter (see Healy-Kalesh [34], for a review of NSRs): in particular, the most rapidly recurring nova, M31N 2008-12a, hosts the prototypical NSR with dimensions of 90 × 134 pc (Darnley et al. [17]). Crucially, all RNe should host an NSR (Darnley & Henze [16]; Healy-Kalesh et al. [36]).

Though a narrowband optical search (using $\mathrm{H}\alpha$ and [\mathrm{S,II}] imaging) in M31 and the Large Magellanic Cloud did not recover any further examples in these galaxies, this was likely due to their intrinsic faintness within the data utilised [38], later corroborated using deeper narrowband imaging around the second most rapidly recurring nova M31N 2017-01e [15].

This apparent dearth has been emphatically addressed within the Galaxy by the Condor Array Telescope (Condor; [55]), which can image to very faint surface brightnesses and therefore recover more of the fainter NSRs. Within a short period, Condor has demonstrated that the eleventh Galactic RN, KT Eridani, owns a 50 pc NSR [89, 39]; the Galactic RN, T Coronae Borealis hosts a $\sim$30 pc diameter NSR [92] and the Galactic symbiotic RN, RS Ophiuchi, is surrounded by an NSR 70 pc across [91]. Most recently, the first NSR in the LMC has been found within Magellanic Cloud Emission Line Survey (MCELS; [99]) and DeMCELS survey [78] $\mathrm{H}\alpha$ and [\mathrm{S,II}] images around the RN LMCN 1971-08a and is the largest NSR to date, at $\sim$200 pc in diameter [40].

The continuous stream of NSR discoveries will undoubtedly continue with Condor, supported by possible detections with other optical data, but the search is not constrained to the optical regime. In fact, far-IR data was able to reveal the potential cavity component of the NSR around RS Oph [37] and T Pyx [35]. Additionally, the highly energetic ejecta impacting the high-density inner edge of the NSR shell, in combination with inter-ejecta shocks, will provide a substantial amount of X-ray emission [33, 36, 39], such that the NSR may manifest as an extended X-ray structure.

V745 Scorpii is one of the eleven known Galactic RNe [14, 89] and has a recurrence period of $\sim$25 years, having exhibited nova eruptions in 1897 [86], 1937 [77], 1989 [57] and 2014 [108], and potentially during 1917 and 1963 [14, 86]. The nova system consists of a $>1.3\,M_{\odot}$ WD [75] and a M6 III [21] or M4 III [31] red giant companion and is estimated to be located at a distance of $7.8 \pm1.8$ kpc [85], though recently Molina et al. [63] state a revised estimate distance of $8.2^{+1.2}_{-1.0}$ kpc. During its 2014 eruption, the nova ejected $10^{-7}\,M_{\odot}$ [4, 75, 19] of material at velocities of $\sim$4000 km s$^{-1}$ [2, 4] and declined from peak by three optical magnitudes in 9 days [4]. Over its multiple eruptions, V745 Sco has been observed across optical [87] (Mróz et al. 2014), near-infrared [31, 4, 5], radio [49, 63], UV [75] and X-ray [72, 75, 19] wavelengths as well as being one of the collection of novae to have been detected in $\gamma$-rays [10, 23]. Furthermore, with a WD growing in mass, V745 Sco is proposed to be a SN Ia progenitor (see e.g. Drake et al. [19]).

Here we present evidence for a candidate nova super-remnant surrounding V745 Scorpii in X-ray imaging; the first NSR discovered within the X-ray regime. The paper is organised as follows: in Section 2, we outline the data from which the discovery was made and derive X-ray flux upper limits of the candidate NSR, before quantifying in Section 3 the spatial distribution and luminosity of the emission from the structure. We follow with analyses of the NSR, starting in Section 4 by detailing the detection of a potentially related infrared cavity component and, in Section 5, outlining simple modelling of the shell to estimate NSR characteristics, assuming the X-ray ring and infrared cavity highlight different components of the same structure. In Section 6 we then establish the likelihood of the X-ray shell being an NSR component by testing a coincidental alignment argument. We explore other origins of the X-ray shell in Section 7 before concluding in Section 8.

The search for an NSR surrounding V745 Scorpii

eROSITA data

The extended Roentgen Survey with an Imaging Telescope Array (eROSITA; [61, 79]) is an X-ray telescope consisting of seven telescope modules (TM) on board the Spektrum-Roentgen-Gamma (SRG) observatory [101]. eROSITA has an approximate $1^{\circ}$ diameter field of view covering the soft (0.2 – 2.3 keV) and hard X-ray energy band (2.3 – 8 keV) and since December 2019, has completed four all-sky surveys (eRASS1 – eRASS4). We utilised the eROSITA Science Analysis Software System (eSASS; [8, 60]) in the version eSASSusers_240410 for the analysis of eROSITA data in this work.

With the aim of detecting an NSR in the X-ray regime belonging to Galactic RN, V745 Scorpii, we studied the exposure-subtracted images from the eROSITA all-sky survey around this nova. These data belong to the German eROSITA consortium (eROSITA-DE) as the nova V745 Sco is located in the western Galactic hemisphere.

Discovery image of the X-ray nova super-remnant

In the eROSITA field of V745 Scorpii, an elliptical shell-like structure with semi-major and semi-minor axes of $\sim19$ and $\sim10$ arcminutes, respectively (and position angle of $\sim160^\circ$) was identified. As shown in Figure 1, the centre of the shell is coincident with the nova. For a distance to V745 Sco of $8.2^{+1.2}_{-1.0}$ kpc [63], this elliptical structure has dimensions of $\sim90 \times50$ pc, therefore its size is reminiscent of other NSRs. The predominant X-ray emission from the NSR shell is in the eROSITA $0.5-1.2$ keV waveband.

X-ray flux upper limit of the nova super-remnant

Although there is a ring seen surrounding V745 Sco, we do not see a significant X-ray excess from the region as a whole. As such, we are not able to present any spectral analysis. However, we are able to derive X-ray flux upper limits for the whole region containing the ring using two approaches: a maximum possible count rate (CR$_{\max}$) methodology presented in Khokhriakova et al. [52] and an independent estimate based on the local background fluctuations.

As in Khokhriakova et al. [52], we first used the CR$_{\max}$ approach to ascertain a quantitative measure of any possible extended emission. We extracted photons from an elliptical source region with dimensions of $\sim25^\prime\times15^\prime$ as shown in Figure 2. We determined the background level around the source region by taking the average of the counts from 8 circles with radii of $12^\prime$ employed around the source region, also shown in Figure 2. We masked the two bright sources within the elliptical source region to minimise contamination.

The X-ray counts rate for the source region and background regions were found to be CR$_{\mathrm{s}}=0.261\pm0.002$ cts s$^{-1}$ deg$^{-2}$ and CR$_{\mathrm{b}}=0.263\pm0.001$ cts s$^{-1}$ deg$^{-2}$, respectively, with the source count rate uncertainty and background count rate uncertainty estimated as in Khokhriakova et al. [52]. This analysis reveals that the source region as a whole does not show a significant excess above the surrounding background level. Therefore, as in Khokhriakova et al. [52], we calculated the maximum possible count rate using

where CR$_{\mathrm{s}}$ is the count rate within the elliptical source region, CR$_{\mathrm{b}}$ is the mean count rate within the background regions, and $\sigma_{\mathrm{s}}$ and $\sigma_{\mathrm{b}}$ are the associated uncertainties combined in quadrature, and was found to be CR$_{\max}=6.871\times10^{-3}$ cts s$^{-1}$ deg$^{-2}$.

We then used data from four combined event files of eROSITA (eRASS1 to eRASS4) in order to derive the X-ray flux upper limit. We extracted spectra using the same source region and background regions illustrated in Figure 2 and used all TM cameras of eROSITA except TM5 and TM7, due to the technical problem of optical light contamination in their CCDs [79].

The X-ray Spectral Fitting Package (XSPEC; Arnaud [3]) was utilised to convert the maximum possible count rate, CR$_{\max}$, into flux. As is typically used for modelling the X-ray emitting shock-heated plasma in supernova remnants [84, 53], and the most analogous structures to NSRs, we assumed an absorbed thermal plasma model for the spectrum, namely TBabs * vapec (with abundances fixed to solar values), with TBabs corresponding to X-ray absorption by the ISM [112] and vapec corresponding to a collisionally ionised diffuse gas in thermal equilibrium, and simulated the observations using XSPEC. Within this model, the $N_{\mathrm{H}}$ absorption was fixed at $2.8\times10^{21}$ cm$^{-2}$ to match the Galactic absorption in the direction of V745 Scorpii (from the HI4PI Survey; HI4PI Collaboration et al. 2016). The observations were simulated using XSPEC by assuming this model and examining various values of plasma temperature ($kT=0.2$, $0.5$ and 1 keV). The $3\sigma$ flux upper limit within the energy band $0.5-2$ keV, representing the sensitivity to emission averaged over the full source region, was found to be $(3.5-3.8)\times10^{-14}$ erg s$^{-1}$ cm$^{-2}$, corresponding to a luminosity upper limit of $\sim2.9\times10^{32}$ erg s$^{-1}$ at a distance of $\sim8.2$ kpc to the nova (see § 1).

Secondly, as an independent estimate for the detection threshold, we calculated an upper limit using the background fluctuations measured in the local background regions. The standard deviation was determined from the distribution of background count rates and then scaled to the area of the source region. Assuming the same XSPEC model described above, the $3\sigma$ flux upper limit derived from this was $\sim4.2\times10^{-14}$ erg s$^{-1}$ cm$^{-2}$, corresponding to a luminosity upper limit of $\sim3.4\times10^{32}$ erg s$^{-1}$. This is consistent with the CR$_{\max}$ upper limit.

Annular photometry of the nova super-remnant

Inspection of Figure 1 shows that the shell-like structure is faint and difficult to distinguish from the background (see § 2.3). Therefore, to further quantify the spatial distribution of the emission and investigate the morphology of the structure, we performed annular photometry at the location of V745 Sco. The annular photometry consisted of 500 linearly spaced elliptical annuli with semi-major axes ranging from $0.32-48$ arcminutes ($1-150$ pixels), corresponding to a radial spacing of $\sim0.3$ pixels. All ellipses had ellipticities of 0.5 (to match the semi-major axis of 19 arcmin and semi-minor axis of 10 arcmin) and position angles of $160^\circ$ to match the elliptical shell in the data. Also, before the annular photometry, we applied smoothing to the data ($\sigma= 3$) and masked bright sources with pixel values $> 0.0025$.

The result of our emission radial profile analysis is shown in Figure 3. While the profile shows noticeable scatter, resulting from the large number of annuli used in the process, there is a clear peak at $\sim21$ arcminutes. From Figure 3, we can see that this peak in emission sits within the range of $\sim16$ and 24 arcminutes, consistent with the semi-major axis of the shell-like structure from inspection (19 arcminutes). The inset image of Figure 3 illustrates the (narrow) annuli used for photometry with semi-major axes of 16 and 24 arcminutes. Moreover, the two bright sources in the inset image were masked prior and so do not contribute to the annular photometry.

For comparison, in Figure 3 we have overlaid the H$\alpha$ surface brightness radial profile of the confirmed nova super-remnant around M31N 2008-12a from Healy-Kalesh et al. [38]. This radial profile was created using the same method of annular photometry as applied to the X-ray ring around V745 Sco. Though the shell is faint, from Figure 3 we see that it does stand out from the background and is reminiscent of the radial profile of the M31N 2008-12a NSR: an inner cavity region bound by an over-density and surrounded by a relatively flat ISM.

In order to quantify the X-ray luminosity of the X-ray ring, we took the count rates within each annulus and converted these into fluxes. A local background level was estimated from the background regions and then subtracted from each annulus to derive the net emission associated with the ring. By summing the annuli corresponding to the shell region (between $\sim16$ and 24 arcminutes) we determined the flux of the ring to be $\sim2 \times10^{-12}$ erg s$^{-1}$ cm$^{-2}$, corresponding to a luminosity of $\sim1.6 \times10^{34}$ erg s$^{-1}$. Moreover, summing the fluxes of all annuli within the whole region leads to a luminosity of $\sim2.3 \times10^{34}$ erg s$^{-1}$, revealing that the X-ray ring accounts for $\sim70\%$ of the total emission within this region.

These values are well above the detection thresholds derived in § 2.3, thereby confirming that the observed emission from the X-ray ring represents a significant excess above the background. To reiterate, the upper limits detailed in § 2.3 refer to diffuse emission across the region, whereas the luminosities derived here from annular photometry predominantly trace the ring, which contains the majority ($\sim70\%$) of the emission, is clearly detected above the background, and therefore is unaffected by the diffuse emission upper limits.

Cavity structure in infrared data

We searched through archival multiwavelength data across numerous facilities of the surroundings of V745 Sco with fields of view wide enough to capture associated structures but did not find anything apparent. As the 23.6$^\prime$ $\times$ 23.6$^\prime$ FOV of the X-ray Telescope (XRT) onboard the Neil Gehrels Swift Observatory (Swift; Gehrels et al. 2004) is smaller than the full extent of the X-ray ring, 100 ks of XRT data focused on the location of V745 Sco did not capture the NSR, with only known point sources being visible. Similarly, nothing is found at the location of the X-ray structure in the Australian Square Kilometre Array Pathfinder [47] Rapid ASKAP Continuum Survey or in neutral atomic hydrogen (H I) data from the HI4PI survey (HI4PI Collaboration et al. 2016).

However, motivated by the NSR cavity found around RS Oph in far-infrared data [37], we also checked the location of the X-ray structure within a 3.6$^\circ$ $\times$ 3.6$^\circ$ FOV in the 60$\mu$m waveband of the new generation Infrared Astronomical Satellite (IRAS) catalogue, known as IRIS [62] and found a larger cavity encompassing the position of the X-ray structure, shown in Figure 4. A search through data from other infrared facilities, namely Planck [103, 76] and AKARI [66, 51], shows the same larger infrared cavity shadowing the location of the X-ray shell. In Figure 4, we have overlaid an ellipse approximately outlining the extent of the X-ray structure (from Figure 1) over the infrared data for comparison.

This infrared cavity has semi-major and semi-minor axes of 35 and 25 arcminutes, respectively, which equates to a physical size of 167 $\times$ 120 pc at the distance of V745 Sco, and it also has a similar position angle ($\sim160^\circ$) to the X-ray shell. Further, the approximate centre of the far-infrared cavity is near the location of V745 Sco. From this apparent configuration, a simple interpretation of the two structures could be that the X-ray shell seen in eROSITA data highlights either the boundary between the inner NSR cavity and the ejecta pile-up region or a portion of the ejecta pile-up region, where we find the most extreme temperatures (see § 5.1 for more details on the different components of an NSR), and the large extended cavity revealed in the far-infrared unveils the boundary of the outer NSR shell; this interpretation is explored in § 5. Furthermore, if this were indeed the configuration, then we would expect the optical outer shell of the NSR to be found with dimensions of $\sim167 \times120$ pc.

Probability of finding coincident extended object in infrared data

We determined the probability of finding an extended structure in infrared data at the same position as the X-ray shell with a similar position angle. We note that the morphology of the X-ray ring and cavity appear to be consistent but we do not include this parameter in the following calculation. Given the apparent sizes of the X-ray shell and the infrared cavity, the $3.6^\circ\times3.6^\circ$ field of view of the IRIS 60 µm, and the approximate 5 other cavity-like structures (see the bottom middle panel of Figure 4) present in the data, we estimate a $\sim76\%$ chance of an infrared cavity within the field randomly overlapping with the X-ray shell. However, also accounting for the probability that the position angles of the X-ray shell and infrared cavity also coincide, with a conservative margin of $\pm5^\circ$, we estimate the probability of finding an infrared cavity with a similar position angle overlapping spatially with the X-ray shell to be $\sim4.2\%$, strengthening an association between the two.

Connection between infrared cavity and X-ray shell

As with the X-ray emission from the NSR, we performed the same annular photometry (from § 3) to the far-infrared data focussing on the cavity. The resulting radial profile is illustrated in Figure 5, alongside the radial profile obtained for the X-ray ring (from Figure 3).

The infrared radial profile (red line) in Figure 5 clearly shows lower levels of emission at the centre of the cavity which gradually increases out to a peak of $\sim46$ arcminutes (corresponding to $\sim100$ pc), before flattening off to a relatively constant brightness beyond. This emission profile verifies the cavity-like region seen in the 60 µm IRIS data. Within this infrared cavity sits the peak of the X-ray ring at $\sim21$ arcminutes. This configuration – an X-ray ring encompassed by an infrared cavity – is reminiscent of NSR modelling (presented in § 5) that predicts a structure consisting of an X-ray shell where the highest levels of X-ray emission persist (ejecta pile-up region through to the inner edge of the NSR outer shell) surrounded by an infrared cavity (where the outer shell emits in the optical). Furthermore, an NSR with a non-spherical symmetry would allow for variations of the projected locations of the different NSR components.

Modelling of a V745 Scorpii NSR

To determine the gross properties of the NSR from its angular size in both the eROSITA X-ray and IRIS infrared data, we ran a set of hydrodynamical simulations with the Morpheus code [106], in a similar manner to previous modelling studies of NSRs ([17, 36, 39, 40]), to evolve an NSR to the extent of the larger infrared cavity (containing the X-ray ring component). We adopted a scenario of a static WD (also see [39, 40]) and took the recurrence period of V745 Sco to be 26 years³ ([14]). As the mass loss phase, $t_{\mathrm{ml}}$, of the nova eruption can be approximated by the $t_3$ decline time ([33]), we took $t_{\mathrm{ml}}$ to be 9 days ([4]) and the total mass ejected during each eruption to be $10^{-7}\,M_{\odot}$ ([75, 19]). For the nova ejecta velocity, Banerjee et al. [4] report the near-infrared Pa $\beta$ emission line FWHM to be $\sim4000\ \mathrm{km\ s^{-1}}$ and Anupama et al. [2] concur that all hydrogen Balmer (FWZI $\sim8500\ \mathrm{km\ s^{-1}}$), Fe ii, He i and O i lines have similar profiles to the near-infrared emission lines. As such, we modelled the eruptions with an ejecta velocity of $4000\ \mathrm{km\ s^{-1}}$.

With V745 Sco having a red giant companion ([21]), we adopted a wind loss rate of $2 \times10^{-8}\,M_{\odot}\ \mathrm{yr^{-1}}$ and a wind velocity of $20\ \mathrm{km\ s^{-1}}$ (used to mimic the red giant companion of the Galactic RN RS Oph) as in previous NSR modelling ([17, 36, 39]). In these simulations, we assume one-dimensional spherical symmetry and choose a spatial resolution of 1000 au cell$^{-1}$ as previous studies illustrate that such a resolution is able to capture the full long-term structure of the NSR while helping with computational time ([36, 39]). Healy-Kalesh et al. [36] determined that radiative cooling has a large impact on NSR growth when considering long inter-periods ($>1$ year) and low-energy eruptions. Therefore, we adopted the cooling package ([81]) provided in the Morpheus code as in previous studies ([106, 17, 36, 39]).

The nova eruptions interject the red giant wind mass-loss at intervals set by the recurrence period and are represented by an instantaneous increase in the mass-loss rate and ejecta velocity to match the parameters estimated for V745 Sco. Specifically, each eruption from this modelled nova system ejects $10^{-7}\,M_{\odot}$ at a velocity of $4000\ \mathrm{km\ s^{-1}}$ over 9 days every 26 years into a prepopulated ISM with varying densities. As the ISM density at the location of V745 Sco is not constrained, we chose to sample the density of the ISM over a range of $n = 0.001$ to $n = 10\ \mathrm{cm^{-3}}$ (we will drop the units throughout). The parameters of the set of simulations are detailed in Table 1.

Run #	ISM density	Pile-up boundary (pc)	Shell inner edge (pc)	Shell outer edge (pc)	Eruptions	Elapsed time (yr)	Total KE (erg)
1	0.001	16.9	77.4	83.9	82,615	$2.2 \times10^{6}$	$1.3 \times10^{48}$
2	0.01	9.4	64.6	84.2	158,504	$4.1 \times10^{6}$	$2.5 \times10^{48}$
3	0.1	8.3	72.4	84.0	353,512	$9.2 \times10^{6}$	$5.6 \times10^{48}$
4	1	6.4	82.4	83.9	1,009,812	$2.6 \times10^{7}$	$1.6 \times10^{49}$
5	10	4.7	80.2	84.0	2,441,530	$6.4 \times10^{7}$	$3.9 \times10^{49}$

Results of simulations

In Figure 6, we show the resulting dynamics of an NSR grown in local ISM with densities $n = 0.001, 0.01, 0.1, 1$ and $10$ to the size of the observed infrared cavity (semi-major axis of approximately 84 parsecs) in Figure 4. As detailed in Table 1, there is a large difference in both the amount of time and number of eruptions required to grow the NSR to 84 parsecs across the range of ISM densities. Specifically, it would have taken V745 Sco $\sim6.4 \times10^{7}$ yr to grow the NSR shell to the observed size in an ISM of $n = 10$ compared to $\sim2.2 \times10^{6}$ yr for $n = 0.001$. This is approximately $30 \times$ longer (with $30 \times$ more eruptions) and results from the increasing number of eruptions required to transport the higher density surrounding material to a distance of 84 parsecs.

As shown in the top left panel of Figure 6, the thickness of the outer shell (see Table 1 for the location of the inner edge and outer edge) also differs dramatically across the range of ISM

densities: 7.7% for $n = 0.001$, 23.3% for $n = 0.01$, 13.8% for $n = 0.1$, 1.8% for $n = 1$ and 4.5% for $n = 10$ due to the influence of cooling. The wider low-density shells closely match those NSRs simulated in [17] and [39], in which radiative cooling does not play a substantial role because of the lower densities and shorter evolutionary times involved. Whereas the thin high-density shells seen in Run 4 and Run 5 are reminiscent of the NSR shells presented in Healy-Kalesh et al. [36], which form as a result of high levels of radiative cooling losses early in their formation suppressing the shell width over the longer eruption history (see Appendix § 10 for details on energy losses due to radiative cooling).

In addition to the different shell thicknesses, the structure of the NSR shell varies. The inner edge of the shell is denser than the outer edge for Run 1 ($n_{\mathrm{in}}/n_{\mathrm{out}} \sim2.5$), Run 4 ($n_{\mathrm{in}}/n_{\mathrm{out}} \sim11$) and to a lesser extent for Run 3 ($n_{\mathrm{in}}/n_{\mathrm{out}} \sim1.8$). As with the simulated NSRs presented in Healy-Kalesh et al. [36] which show a similar decrease in density across the radius of the shell, this structure in Run 4 can be attributed to the outer edge depending upon a combination of the $\sim1 \times10^{6}$ prior eruptions, whereas the inner edge is being shaped by the newly incoming ejecta. Though, for Run 1 and Run 3 with fewer eruptions, this similar structure likely comes from the relative ease of manoeuvring the low-density material by the ejecta into a ‘forming wave’ shape. The density gradient of the NSR shell in Run 2 is more constant, in a similar manner to the simulated NSRs in [17] and Healy-Kalesh et al. [39], and likely results from a combination of a higher ISM density compared to $n = 0.001$ but a shorter cooling time compared to $n = 0.1$ preventing significant compression of the shell.

Within the cavity region of the NSRs (contained within the pile-up boundary; see Table 1 for the location of this boundary), Notes. Columns record the simulation number, ISM density, boundary of cavity and ejecta pile-up region, boundary of inner NSR shell, boundary of outer NSR shell, number of eruptions to grow the nova super-remnant to approximately 84 parsecs (the angular semi-major axis of the outer boundary of the infrared NSR cavity around V745 Sco), the elapsed (cumulative) time of the simulation, and the total kinetic energy released. The recurrence period and ejecta velocity for all simulations is 26 years and 4000 km s$^{-1}$, respectively. Please refer to Healy-Kalesh et al. [36] for more information on the defined boundaries of the NSR components (cavity, ejecta pile-up region and NSR shell).

the density of the material drops steeply from the central nova as the ejecta expand, decreasing as low as $n \simeq2.3 \times10^{-7}$ at the ejecta pile-up boundary for Run 1 ($\sim4400\times$ less dense than the density of the surrounding ISM) on account of the ejecta facing negligible resistance. Such a region of near free-expansion also explains the almost identical ejecta velocities of $\sim1400$ km s$^{-1}$ (see bottom left panel of Figure 6), the very low pressures of $1.2 \times10^{-19}$ g cm$^{-1}$ s$^{-2}$–$8.5 \times10^{-18}$ g cm$^{-1}$ s$^{-2}$ for $n = 0.001$–$10$, respectively (see top right panel of Figure 6) and the relatively cool temperatures of 3800–21000 K for $n = 0.001$–$10$, respectively (see bottom right panel of Figure 6) seen in the cavity for Runs 1–5.

Beyond traversing the sparse cavity component of the NSR, the ejecta run into the pile-up region. Here, as seen in the bottom left panel of Figure 6, the ejecta velocities drop considerably for all the runs and smoothly decline through the full pile-up region until the outer shell of the NSR. There are small fluctuations in velocity for Run 5 ($n = 10$) however such perturbations are $\sim1$ km s$^{-1}$ and therefore likely exist in the other runs, but are not evident due to the higher velocities present within those runs. The pressure and temperature of the matter within the pile-up region dramatically increases from the cavity pressure and temperature by $\sim20000 \times$ and $\sim10000 \times$, respectively, for all runs (see top right and bottom right panels of Figure 6) as new energetic ejecta crashing into the inner boundary and continual collisions taking place within the pile-up region leads to extreme levels of shock heating. This extreme region is where we expect the highest levels of X-ray emission from an NSR, powering the X-ray ring in the eROSITA data.

Encompassing the cavity and pile-up regions is the outer shell of the NSR. The outer shell, most apparent in the top left panel of Figure 6, is a high density region predominantly consisting of swept up ISM. Under our interpretation of the X-ray data and infrared data highlighting different components of the NSR, this outer shell would form the boundary of the infrared cavity. The density of the shell for all of the runs is moderately higher than the density of the surrounding medium ($6\times$ for $n = 0.001$, $2\times$ for $n = 0.01$, $4\times$ for $n = 0.1$, $40\times$ for $n = 1$ and $9\times$ for $n = 10$), but is extremely greater than the density of the pile-up (e.g. a factor of $2.4 \times10^{4}$ for $n = 0.001$ and $3.1 \times10^{7}$ for $n = 10$) and pile-up regions (a factor of $4.6 \times10^{3}$ for $n = 0.001$ and $6.8 \times10^{6}$ for $n = 10$). Small spikes of higher pressure are seen in the highest density regions of the outer shell (see top right panel of Figure 6 and also coincide with relatively low temperatures across the inner region of the outer shell ($\sim9.4 \times10^{3}$ K for $n = 0.001$ and $\sim10$ K for $n = 10$). Very low velocities are seen within the shell for all runs with the younger NSR (Run 1) exhibiting velocities of $\sim20$ km s$^{-1}$ compared to the older NSR (Run 5) with velocities of $\sim1$ km s$^{-1}$.

X-ray modelling

As indicated, we would expect considerable X-ray emission from the NSR, just as detected in Figure 1, due to the high levels of shock-heating within the ejecta pile-up regions. Therefore, as in previous modelling studies of NSRs (Darnley et al. [17]; Healy-Kalesh et al. [36, 39]), we model such X-ray emission using XSPEC to compare with the X-ray luminosity upper limit from the eROSITA observation (see § 2.3). We chose to model the same energy bands as for eROSITA, namely 0.2–0.5 keV, 0.5–1.0 keV and 1.0–2.3 keV. The synthetic X-ray luminosity radial profiles summing the three bands are provided in Figure 7.

As seen in Figure 7, the radial distribution of simulated X-ray emission for the modelled NSR in each ISM density shows that the centres of the structures have high luminosities as a result of the nova eruptions emanating from the central binary. This high X-ray luminosity in each model then gives way to a dramatic drop to almost negligible levels as the ejecta freely expand within the cavity regions in which little resistance is experienced. At the respective ejecta pile-up boundaries of each model, the X-ray emission significantly reestablishes ($4.3 \times10^{21}$ erg s$^{-1}$ for $n = 0.001$ to $5.6 \times10^{22}$ erg s$^{-1}$ for $n = 10$) as the new ejecta finally collide with the decelerated debris of thousands of prior eruptions and shock-heat the higher density boundary. The X-ray luminosity then continues to increase by up to 100$\times$ (for the $n = 10$ model) towards the NSR shells as a growing number of ejecta interact and shock-heat the pile-up region. As the density and temperatures are relatively constant across the whole pile-up region (see Figure 6), directly resulting from the continual supply of new ejecta colliding and shocking present material, bright X-ray emission radiating from across this region is feasible.

At the inner edges of the modelled NSRs, the X-ray luminosities then peak, as shown in all panels of Figure 7, ranging from $L_{\mathrm{X-ray}} = 2.7 \times10^{26}$ erg s$^{-1}$ for $n = 0.001$ to $L_{\mathrm{X-ray}} = 2.9 \times10^{28}$ erg s$^{-1}$ for $n = 10$. The total X-ray luminosities predicted from such NSRs are $6.1 \times10^{28}$ erg s$^{-1}$, $4.0 \times10^{28}$ erg s$^{-1}$, $5.2 \times10^{28}$ erg s$^{-1}$, $8.5 \times10^{28}$ erg s$^{-1}$ and $1.7 \times10^{29}$ erg s$^{-1}$ for $n = 0.001$, 0.01, 0.1, 1 and 10, respectively.

Evidently, the brightest NSR model (grown within the $n = 10$ environment) is considerably fainter than both the observed X-ray luminosity of the shell around V745 Sco ($\sim1.6 \times10^{34}$ erg s$^{-1}$) and the X-ray luminosity predictions from previous modelling of the M31N 2008-12a NSR ($\sim3 \times10^{29}$ erg s$^{-1}$ in Darnley et al. 2019 and $\sim1 \times10^{31}$ erg s$^{-1}$ in Healy-Kalesh et al. [36]) and the KT Eri NSR ($\sim6.5 \times10^{32}$ erg s$^{-1}$; Healy-Kalesh et al. [39]). The five-order-of-magnitude discrepancy between the predicted and observed X-ray luminosities is large but not surprising given the fundamental limitations of one-dimensional smooth-shell models. Two physical effects, absent from the simulations, are expected to substantially boost X-ray emission. First, Rayleigh-Taylor and Kelvin-Helmholtz instabilities at the ejecta-shell interface fragment the swept-up ISM into dense clumps with a volume filling factor $f \ll1$ ([107, 11]). Since thermal bremsstrahlung luminosity scales as $n^2V$, concentrating emission into clumps of density $n_\mathrm{clump} \sim n(\mathrm{mean})/f$ while reducing their volume by $f$ yields a net luminosity boost of $\sim1/f$; for $f \sim10^{-2}$, this alone gives a factor of $\sim100$. The highly resolved shell of GK Per ([95]) makes this $f$ very reasonable. Second, radiative shock compression at the ejecta pile-up boundary can locally compress post-shock gas by factors of $\chi\sim10^2 - 10^3$ beyond the standard Rankine-Hugoniot factor of 4 ([6]), and since $L_X \sim n^2V \sim\chi n_0^2V$, this contributes another factor of $10^2 - 10^3$ to the emission. Combining these two effects multiplicatively yields a plausible total boost of $10^4 - 10^5$, which approximately matches the observed $10^5$ discrepancy.

The predicted NSR X-ray luminosities from our one-dimensional simulations therefore represent firm lower bounds rather than realistic estimates. The gap between model and observation upper limit should be interpreted not as evidence against the NSR interpretation, but as a direct consequence of smooth-shell, spherically symmetric hydrodynamics failing to capture the clumping and radiative compression physics that dominate real NSR X-ray emission. Constraining the true X-ray luminosity of NSRs will ultimately require either 3D hydrodynamic simulations (see e.g. the modelled single eruption of the nova V407 Cygni in Orlando & Drake [73] as well as the X-ray emission predicted from simulations of RN eruptions from RS Oph in Martínez-González et al. [58]), or a confirmed X-ray detection of a known NSR from which empirical calibration is possible – precisely what the detection of the V745 Sco NSR candidate would, if confirmed, begin to provide.

To preliminarily explore whether an NSR with the same structure as those grown with hydrodynamic modelling could be responsible for an X-ray ring, we first interpolated the predicted one-dimensional X-ray emission radial profile from Run 5 ($n = 10$), as it is the brightest and most extended (along with Run 4). This profile was then mapped onto a two dimensional grid by computing an elliptical radius to match the elliptical geometry and position of the observed X-ray ring and assigning surface brightness values from the interpolated profile. As it is feasible for bright X-ray emission to be emanating from across this region, we chose to map the modelled X-ray emission from the NSR during the epoch when its radius was 50 pc. This elliptical mapping was smoothed to match the eROSITA image resolution, thereby creating a synthetic ‘on-the-sky’ image (see the purple ring in the inset of Figure 8). Then, as in § 3, annular photometry was performed on the synthetic image to obtain a comparative radial profile. The resulting radial profile of this synthetic X-ray ring is provided in Figure 8 (purple line) alongside the radial profile of the X-ray ring from the eROSITA that the configuration of the synthetic X-ray ring with emission peaking at $\sim$50 pc surrounded by the outer synthetic Hα ring at $\sim$80 pc, used as a proxy for the outer boundary of the infrared cavity, matches the observations shown in Figure 1 and the IRIS 60 μm panel of Figure 4.

Determining association between X-ray structure and V745 Scorpii

As the eROSITA image covers a large area of the sky (5.6° × 5.8°), there are many regions in the data that appear to contain structures. For this reason, we must explore a simple coincidental alignment between V745 Sco and the X-ray structure centred on its location. As such, we follow the same method employed in Healy-Kalesh et al. [37], used to determine the significance of a potential far-infrared NSR cavity being found at the location of the RN RS Ophiuchi.

We firstly define a region which will be used as a reference to compare with other regions of the eROSITA image. As the X-ray structure has a ring-like shape, we chose an annulus as an appropriate region. We now introduce a ratio, $\mathcal{R}$, defined as the ratio of the flux per unit sky area within the annulus to the flux per unit sky area in the surrounding and interior (cavity) regions. For this analysis, we masked all sources above a threshold to remove spurious contributions being made to the ratio (e.g. the two bright sources close to the location of V745 Sco).

For the reference annulus, we fixed the position to the location of V745 Sco and fixed the ellipticity as 0.5 to match the observed shell (semi-major and semi-minor axes of 19 arcmins and 10 arcmins, respectively). The semi-major axis was allowed to vary between 5 – 30 arcmin with 1 arcmin increments and position angle was allowed to range between 0 – 180° with 1° increments. The width of the annulus was fixed at 30% of the annulus semi-major axis and the width of the surrounding ellipse was fixed to 5× the annulus semi-major axis.

We find that a reference annulus fixed to the position of V745 Sco produces the largest ratio of $\mathcal{R} = 0.0262$ with a semi-major axis of 17 arcmins and a position angle of 159°. In Figure 9, we illustrate this best fitting annulus and refer to it as $\mathcal{E}_{\mathrm{annulus}}$. This annulus defines our shell around V745 Sco as it contains the majority of emission from the ring, though we note the lower segment of the shell is not fully accounted for.

For the Monte Carlo analysis, we sampled ∼155,000 annuli on a uniformly distributed spatial grid across an inner 4.1° × 4.7° region of the eROSITA image (as the analysis was constrained at the outer edges of the image by the width of the surrounding ellipse), each with a randomly selected ellipticity, position angle and semi-major axis, and computed $\mathcal{R}$ at each position. The range of ellipticities is derived from the structure having an inclination between 0 – 70°; the range of position angles is between 0 – 180°, and the semi-major axis is taken from a range of radial sizes between 23.85–71.56 pc (10–30 arcmins). The distribution of the computed $\mathcal{R}$ for all ∼155,000 annuli is shown in the right panel of Figure 9 and is normalised to the ratio $\mathcal{R} = 0.0262$.

We find that 83.76% of the sample of annuli (without any fixed parameters) have a ratio $\mathcal{R} < 0.0262$. As such, the probability of a chance alignment of V745 Sco with a structure that has more X-ray emission than the $\mathcal{E}_{\mathrm{annulus}}$ ring is 16.24%, with a large proportion (∼38%) of these annuli clustered around the significantly bright source to the southeast of the nova’s location.

The 16.24% chance alignment probability for the X-ray ring (which we denote as $P(X) = 0.1624$) alone should not be interpreted in isolation. Each of the additional lines of evidence presented in this work carries its own physical constraints, and their conjunction is far more constraining than any single test. The probability of finding an infrared cavity with a matching position angle (within $\pm5^\circ$) spatially coincident with the X-ray shell is $\sim4.2\%$ (denoted as $P(I) = 0.042$; § 4.1). Further, the radial profile of the X-ray ring closely tracking that of the confirmed M31N 2008-12a NSR in both shape and scale (§ 3) is unlikely to arise from a noise fluctuation or unrelated extended source, to which we conservatively assign a probability of $15\%$, interpreted as the conditional probability $P(RP \mid X) = 0.15$.

We now evaluate the joint probability of these combined constraints by considering two limiting scenarios. In these scenarios, we also incorporate a geometric alignment constraint, where the centre of a random X-ray structure must fall within a conservative radius of $5'$ from V745 Sco. Given the $4.1^\circ\times4.7^\circ$ field, this corresponds to an alignment probability of $0.113\%$ (from $78.54\ \mathrm{arcmin}^2 / 69,372\ \mathrm{arcmin}^2$), which we denote as $P(A) = 0.00113$. In the first scenario, we assume all properties are fully correlated and therefore, to avoid compounding their probabilities, we adopt the most conservative constraint, given by the X-ray ring chance alignment ($16.24\%$). This yields a joint probability of $P \approx P(X) P(A) = 0.1624 \times0.00113 \approx1.84 \times10^{-4}$. In the second scenario, we treat the radial profile as conditional on the presence of an X-ray structure, i.e. $P(RP \mid X)$, while treating the infrared cavity and geometric alignment as independent constraints. As such, the joint probability becomes $P = P(X) P(RP \mid X) P(I) P(A) = 0.1624 \times0.15 \times0.042 \times0.00113 \approx1.16 \times10^{-6}$.

While the individual assumptions in such calculations are uncertain, the conclusion is robust across both scenarios: the convergence of spatial coincidence, matching position angle, and NSR-like radial morphology is far more difficult to attribute to chance than the $16.24\%$ figure alone implies. While the resulting probabilities should be taken as order-of-magnitude estimates rather than exact values, they are consistently indicating that a chance alignment is unlikely and thus make a compelling case in favour of a genuine NSR detection.

Other origins of structure

If the structure is indeed real then we must also rule out other possible astrophysical phenomena with similar characteristic sizes as NSRs, including supernova remnants (SNRs) and superbubbles, as well as other responsible sources.

We would expect strong radio emission if the structure were a SNR due to synchrotron radiation from the outer shock front (high velocity shocks at 1000s km s$^{-1}$ combined with strong magnetic fields, e.g. Dubner 2017), yet NSRs will have a weaker magnetic field and exhibit outer shell expansion velocities of $\sim10$ km s$^{-1}$, not energetic enough to accelerate electrons to relativistic velocities and produce strong radio emission. As such, the X-ray ring’s location was examined in various radio surveys. The structure’s location was observed neither with MeerKAT array (Jonas & MeerKAT Team [48]) nor in the ASKAP Evolutionary Map of the Universe survey (ASKAP EMU; Norris et al. [67, 68]). As noted in § 4, its location was covered by the Rapid ASKAP Continuum Survey (RACS; McConnell et al. [59]; Hale et al. [29]) but within these data, there was no radio emission detected coincident with the X-ray ring. As such, we can strongly conclude that we are not detecting a faint SNR in the eROSITA data.

We also cross-matched the location of the candidate X-ray NSR with both the most recent sample of 310 Galactic SNRs from Green [27] and 132 SNRs given in the Chandra Supernova Remnant Catalog⁵ and found that none of the remnants overlapped with the X-ray structure as all SNRs were confined to the Galactic plane. According to Albert & Dwarkadas [1], the X-ray luminosities of many Galactic, LMC and SMC SNRs⁶ are much higher ($10^{35} - 10^{37}$ erg s$^{-1}$) than both the luminosity of the X-ray ring ($\sim1.6 \times10^{34}$ erg s$^{-1}$) and the total emission within the region ($\sim2.3 \times10^{34}$ erg s$^{-1}$; see § 3). Yet, a good proportion have X-ray luminosities of a comparable (e.g. SN 1006 with $\sim3.4 \times10^{34}$ erg s$^{-1}$; Uchida et al. [105]; Albert & Dwarkadas [1], G85.9-0.6 with $\sim1 - 4 \times10^{34}$ erg s$^{-1}$; Jackson et al. [45], and MCSNR J0524–6624 with $\sim1.3 \times10^{34}$ erg s$^{-1}$ Zangrandi et al. [115]), or even lower (e.g. G38.7-1.4 with $\sim7.29 \times10^{33}$ erg s$^{-1}$; Huang et al. [44]; Albert & Dwarkadas [1]) magnitude. Taking the values above as representative of the whole sample of SNR X-ray luminosities, it appears that the Galactic, LMC and SMC SNR X-ray luminosity distribution firmly extends into the regime of the candidate structure, therefore its X-ray luminosity alone is not enough to rule out a faint SNR origin, but rather its lack of radio emission is by far the stronger discriminant.

We explored the possibility of the structure being a superbubble by inspecting the locations of the most well-studied OB associations from Wright [113]. We found that zero OB associations are coincident with the location of the X-ray shell and therefore, along with the non-detection of radio emission, rule out that it is a superbubble formed by an OB association.

The SIMBAD database (Wenger et al. [110]) was utilised to search a radius of 10 arcminutes around V745 Sco to find any other sources potentially responsible for the X-ray ring. Aside from the multitude of variable stars and eclipsing binaries within the $\sim1200$ sources, there were a handful of notable objects (see Figure 10) including the X-ray source NuSTAR J175538-3314.9 (Lansbury et al. [54]); the cataclysmic variable OGLE BLG-DN-306 G357.4-04.0-44 (Mróz et al. 2015); a white dwarf candidate (Gentile Fusillo et al. [25]); and an asymptotic giant branch (AGB) star (Lewis et al. [56]).

While AGB stars do lose material via dusty winds that go on to create extended envelopes (Cox et al. [13]) and bubbles (Ortiz & Guerrero [74]) within the surrounding ISM, these structures are predominantly less than one parsec across (Cox et al. [13]). Secondly, if the X-ray source is an X-ray binary, then it may also be surrounded by an extended shell as a result of winds and outbursts (as is the case for the $9.5 \times14.3$ pc shell around CI Cameleopardalis; Fesen et al. [22]) or from interaction of strong winds with ISM generating bow shocks (Gvaramadze et al. [28]), however it is not known if NuSTAR J175538-3314.9 is an X-ray binary. Cataclysmic variables can indeed host shells if they are systems exhibiting dwarf nova eruptions (e.g. Shara et al. [93, 94, 90]) or nova eruptions (e.g. Santamaría et al. [83]), but these structures are of sub-parsec scales. Lastly, the white dwarf candidate may be surrounded by a planetary nebula, and though they do emit in the X-ray regime as a result of self-shocking winds (Kastner et al. [50]), again the expected sizes of such nebulae are much less than one parsec (Tylenda et al. [104]), much smaller than the X-ray shell.

Therefore, it is unlikely that any of these objects in the vicinity could be responsible for the creation of a much larger $\sim90 \times50$ pc X-ray ring within a $\sim167 \times120$ pc outer shell; if a real structure, the most likely source responsible is the RN, V745 Sco, which has the capability to create a nova super-remnant of this scale via repeated nova eruptions, and in the process, generating X-ray emission through shock-heating.

Conclusions

In this paper, we present the identification of a shell in eROSITA X-ray imaging around the Galactic recurrent nova V745 Scorpii, that we propose to be another Galactic nova super-remnant, and the first to be initially captured through its X-ray emission. The indicators of the structure being a nova super-remnant detailed in this work include:

• (i) it is aligned with V745 Sco, and the nova is in a central location with respect to the structure;

• (ii) its size is consistent with the scales of other NSRs in the Galaxy, M31 and the LMC;

• (iii) the brightness radial profile of the X-ray ring is reminiscent of the H$\alpha$ brightness radial profile of the prototype NSR in M31 thus indicating a common morphology;

• (iv) there is a larger cavity structure in infrared imaging spatially coincident with, and potentially related to, the X-ray NSR with a similar position angle;

• (v) and a synthetic “on-the-sky” NSR derived from the predicted X-ray emission of a modelled V745 Sco NSR mimics the observed X-ray ring.

If this structure is indeed a nova super-remnant belonging to V745 Sco, then much deeper follow up in the optical (and other wavebands) should better reveal the structure, with dimensions of $\sim167 \times120$ pc matching the outer infrared shell, and support our finding of the X-ray emission from the nova super-remnant’s inner component within eROSITA data.

Acknowledgements. We thank the anonymous reviewer for their insightful comments. This work is based on data from eROSITA, the soft X-ray instrument aboard Spektrum-Roentgen-Gamma, a joint Russian-German science mission supported by the Russian Space Agency (Roskosmos), in the interests of the Russian Academy of Sciences represented by its Space Research Institute (IKI), and the Deutsches Zentrum für Luft- und Raumfahrt (DLR). The SRG spacecraft was built by Lavochkin Association (NPO) and its subcontractors, and is operated by NPOL with support from the Max Planck Institute for Extraterrestrial Physics (MPE). The development and construction of the eROSITA X-ray instrument was led by MPE, with contributions from the Dr. Karl Remeis Observatory Bamberg & ECAP (FAU Erlangen-Nuernberg), the University of Hamburg Observatory, the Leibniz Institute for Astrophysics Potsdam (AIP), and the Institute for Astronomy and Astrophysics of the University of Tübingen, with the support of DLR and the Max Planck Society. The Argelander Institute for Astronomy of the University of Bonn and the Ludwig Maximilians Universität Munich also participated in the science preparation for eROSITA. The eROSITA data shown here were processed using the eSASS software system developed by the German eROSITA consortium. This scientific work uses data obtained from manyrāmha Ilgari Bundara / the Murchison Radio-astronomy Observatory. We acknowledge the Wajarri Yamaji People as the Traditional Owners and native title holders of the Observatory site. CSIRO’s ASKAP radio telescope is part of the Australia Telescope National Facility (https://ror.org/05qajvd42). Operation of ASKAP is funded by the Australian Government with support from the National Collaborative Research Infrastructure Strategy. ASKAP uses the resources of the Pawsey Supercomputing Research Centre. Establishment of ASKAP, Inyarrimanha Ilgari Bundara, the CSIRO Murchison Radio-astronomy Observatory and the Pawsey Supercomputing Research Centre are initiatives of the Australian Government, with support from the Government of Western Australia and the Science and Industry Endowment Fund. This paper includes archived data obtained through the CSIRO ASKAP Science Data Archive, CASDA (https://data.csiro.au). MS and SS acknowledges support from the Deutsche Forschungsgemeinschaft through the grants SA 2131/13-1, SA 2131/14-1, and SA 2131/15-1. MMS acknowledges the support of United States National Science Foundation Grants 1910001, 2107954, 2108234, 2407763, and 2407764. This study made use of Prospero high-performance computing facility at Liverpool John Moores University. This research has made use of the SIMBAD database, operated at CDS, Strasbourg, France (see Wenger et al. [110]). This research has made use of the VizieR catalogue access tool, CDS, Strasbourg, France. The original description of the VizieR service was published in Ochsenbein et al. [71].

V745 Sco NSR evolutionary timescale

From the modelling of the NSR around V745 Sco, detailed in § 5, we find that in an ISM with a density of $n = 10$ that it would take $\sim6.4 \times10^{7}$ yr to grow the NSR shell to the observed size. Here, we briefly consider whether this timescale is feasible considering the mass of the system and whether the donor would be able to maintain its mass loss for this period.

Regarding the amount of mass available to the accreting white dwarf over $\sim6.4 \times10^{7}$ yr: assuming a 1 $\mathrm{M}_{\odot}$ WD, then we would require 0.4 $\mathrm{M}_{\odot}$ of retained material to reach the Chandrasekhar limit (the point at which the nova eruptions would cease, and the NSR shell would not have new ejecta to drive its growth). If we also assume a mass accumulation efficiency of $\sim50\%$, then we would require 0.8 $\mathrm{M}_{\odot}$ of material lost by the donor. A recent estimate of the quiescent accretion rate within the V745 Sco system was found to be $5 \times10^{-8}$ $\mathrm{M}_{\odot}$ yr$^{-1}$ [46]. For 0.8 $\mathrm{M}_{\odot}$ of matter to be accreted at this rate, the system would require $\sim1.6 \times10^{7}$ yr – of the same order of magnitude as the $n = 10$ simulation. Furthermore, we note that the mass accretion rate of nova systems will vary over their long-term evolution and this may allow for a more extended period of mass accretion.

Regarding whether the companion star within the V745 Sco system can maintain mass loss for $\sim6.4 \times10^{7}$ yr, we note that while this timescale may be longer than the typical red giant branch lifetime for higher mass stars, mass loss within the binary system would alter the donor’s evolution and thereby increase the donor’s time on the red giant branch. However, the precise extent of this evolutionary lengthening remains an uncertainty.

Radiative cooling energy losses

To determine the amount of energy lost due to radiative cooling within the modelling outlined in § 5 compared to the total amount of energy injected into the simulation through mass loss, we can take the initial energy within the pre-populated ISM plus the total energy from mass loss (given in Table 1) and directly compare this with the total energy within the simulation domain of the final epoch. For each of the five runs, we find the fraction of energy lost due to radiative cooling to be $\sim33\%$, $\sim27\%$, $\sim36\%$, $\sim55\%$ and $\sim67\%$ for ISM $n = 0.001$, 0.01, 0.1, 1 and 10, respectively.

This energy loss within the simulations due to radiative cooling would manifest as either optical emission at the NSR shell (to be searched for, as stated in § 8) or X-ray emission within the interior (which we detail in this current work).