3D hydrodynamic simulations of white dwarf-main-sequence star collisions-II. Off-centre collisions

MNRAS 538, 1384–1396 (2025) https://doi.org/10.1093/mnras/staf328 Advance Access publication 2025 February 25 3D hydrodynamic simulations of white dwarf-main-sequence star collisions – II. Off-centre collisions C. J. T. van der Merwe , 1 , 2 ‹S. S. Mohamed, 1 , 2 , 3 , 4 , 5 J. Jos ´ e, 6 , 7 M. M. Shara 8 and T. Kami ´ nski 9 1 Department of Astronomy, University of Cape Town, Private Bag X3, Rondebosch, 7701, Cape Town, South Africa 2 South African Astronomical Observatory, P. O Box 9, Observatory, 7935, Cape Town, South Africa 3 Department of Astronomy, University of Virginia, Charlottesville, VA 22904, USA 4 NITheCS National Institute for Theoretical and Computational Sciences, South Africa 5 Virginia Institute for Theoretical Astronomy, University of Virginia, Charlottesville, VA 22904, USA 6 Departament de F ´ ısica, EEBE, Universitat Polit ` ecnica de Catalunya, c/Eduard Maristany 16, E-08019 Barcelona, Spain 7 Institut d’Estudis Espacials de Catalunya, c/Esteve Terradas 1, E-08860 Castelldefels, Spain 8 Department of Astrophysics, American Museum of Natural History, Central Park West at 79th Street, New York, NY 10024, USA 9 Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences, Rabia ´ nska 8, PL-87-100 Toru ´ n, Poland Accepted 2025 February 17. Received 2025 February 4; in original form 2024 November 20 A B S T R A C T Stellar collisions have garnered renewed attention for their role in the formation of peculiar objects, such as blue stragglers, and their potential to explain transients with atypical observational and spectroscopic signatures. Among these, white dwarf– main sequence (WD–MS) collisions are particularly intriguing due to the di verse e volutionary pathways they can produce – such as peculiar red giants, novae, or sub-Chandrasekhar supernovae. We present 3D smoothed particle hydrodynamics (SPH) simulations of WD–MS collisions, exploring a range of mass ratios and impact parameters. We analyze the dynamics, energetics, gas morphology, and mass-loss from these interactions. Using a 34-isotope nuclear network, we further predict the nucleosynthesis products generated during these collisions. Our models suggest that at early times the ejecta have a bipolar structure and, along with the stellar remnant, may be enriched in isotopes such as 13 C, 15 N, and 17 O. In the case of near head-on collisions, the ejecta may also show an o v erabundance of 7 Li relative to solar values. Key words: hydrodynamics – nuclear reactions, nucleosynthesis, abundances – binaries: general – stars: mass-loss – globular clusters: general. 1 INTRODUCTION The detection of peculiar stellar populations (e.g. blue stragglers and lithium-rich giants) and transients with observational and spectroscopic characteristics that differ from the more well-known transient subclasses (Tylenda & Soker 2006 ; Karambelkar et al. 2023 ; CastroTapia, Aguilera-G ´ omez & Chanam ´ e 2024 ) has renewed interest in stellar collisions as a possible formation pathway for these objects within dense stellar environments such as the cores of globular clusters (GCs) (e.g. Chatterjee et al. 2013b ; Rozner & Perets 2022 ). Population synthesis models suggest that the most common interactions that occur in GCs are main-sequence-main-sequence (MS–MS) star and white-dwarf-main-sequence star (WD–MS) interactions (Chatterjee et al. 2013a ; Kremer et al. 2020 , 2021 , 2022 ; Rui et al. 2021 ). The reason for this is the large abundance of WDs in these environments and also the large MS star geometrical cross-sections. Additionally, the low dispersion velocity within GCs amplify the effect of gravitational focusing between stars, leading to larger collisional cross-sections and a higher probability of interactions (Freitag & Benz 2005 ; Kremer et al. 2021 ). The WD–MS star interactions are particularly interesting as they can lead to a variety of energetic  E-mail: christian[email protected] phenomena that may be detectable with the upcoming time-domain transient surv e ys such as the Rubin Observatory Le gac y Surv e y of Space and Time 1 (RO–LSST) and Square Kilometer Array 2 (SKA). These instruments and surv e ys will detect up to 10 million transients every day, and predictions towards the energetics and observational signatures of these various interactions will be needed in order to successfully distinguish them among the large influx of detections. It is thus important and advantageous to model dynamic WD–MS star collisions within these dense stellar environments to make theoretical predictions towards their expected observational signatures. A recent example of a successful identification of a transient caused by a stellar collision involving a WD is the case of CK Vul or Nova 1670. Initially proposed to be a WD-brown dwarf collision (Eyres et al. 2018 ), based on the composition of the ejecta and the energetics, it is now thought to result from a WD–red giant interaction (Tylenda, Kami ´ nski & Smolec 2024 ). It had been suggested that mergers of helium WDs with red giant branch (RGB) stars are relatively common and can explain the population of early R-type stars, which are lithium-rich carbon stars with very specific ratios of carbon and nitrogen isotopes, but do not have enhancement of 1 https:// www.lsst.org/ 2 https:// www.skao.int/ © 2025 The Author(s). Published by Oxford University Press on behalf of Royal Astronomical Society. This is an Open Access article distributed under the terms of the Creative Commons Attribution License ( https:// creativecommons.org/ licenses/ by/ 4.0/ ), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited. Downloaded from https://academic.oup.com/mnras/article/538/3/1384/8042563 by UPC Btca Rector G Ferrate user on 22 April 2025 3D models of WD–MS star collisions in GCs 1385 MNRAS 538, 1384–1396 (2025) s-process elements. The link to mergers was based on population synthesis studies of collisions and coalescence products (e.g. Izzard, Jeffery & Lattanzio 2007 ; Zhang et al. 2020 ). These theoretical models suggested that some of the mergers acti v ate helium burning. It was a rather surprising notion that the remnant of the ancient event Nov a 1670, kno wn as CK Vul and classified today as a red nova, is surrounded by circumstellar material that can only be explained by a WD–RGB merger that acti v ated partial helium burning and dispersed 26 Al into the surrounding medium, as expected by some of the models (Tylenda et al. 2024 ). This example demonstrates that, beyond the WD–WD collisions that are the focus of Type Ia supernovae studies, there may be transients produced by WD collisions that are yet to be identified. Hydrodynamic simulations investigating head-on WD–MS collisions (Shara & Shaviv 1977 , 1978 ; Shara & Regev 1986 ; Rozyczka et al. 1989 ; Ruffert & Mueller 1990 ; Ruffert 1992 , 1993 ) showed that the MS star is completely disrupted during these collisions, leading to large amounts of material being ejected ( ∼50 per cent of the MS star). As the WD mo v es through the central regions of the MS star, the MS star material closest to it reached temperatures and densities of ∼10 8 K and ∼10 3 g cm −3 , respectively. Under these conditions, it was proposed that significant nuclear burning can occur (Shara & Shaviv 1977 , 1978 ; Michaely & Shara 2021 ). However, the importance of nuclear reactions was thought to be negligible, i.e. the nuclear energy released is insufficient to have a dynamical effect, and therefore need not be considered in head-on WD–MS collisions (Rozyczka et al. 1989 ). Our own results (van der Merwe et al. 2024 , hereafter P1), which explicitly included a nuclear reaction network for WD-MS collisions for the first time, showed conclusively that the energy contribution from nuclear reactions is far from negligible. On the contrary, it is comparable to the 3 ×10 47 er g kinetic ener gy of each star relative to the other, and to the MS star binding energy. The large amount of material that remained bound to the WD after the collision led to suggestions that the stellar remnant will e ventually e volve into a red giant. If nuclear reactions were shown to be significant in these interactions, these collisions may lead to the formation of peculiar red giant populations that have unusual spectroscopic signatures. Further investigation into these questions has recently been done in P1, where the importance of nuclear burning for different stellar mass-ratios was studied using high resolution, 3D models. In P1, our simulations showed that MS star material can reach temperatures and densities of T > 1 ×10 8 K and ρ∼1 ×10 3 g cm −3 , respectively. Under these conditions, hot CNO-cycles contribute significantly towards the total energy released during the collision, becoming even more significant for lower mass ratios ( q ≤0 . 5) where the amount of nuclear energy generated during the collision was similar to the binding energy of the MS star ( ∼10 47 erg). Furthermore, signs of incomplete CNO burning are predicted to be evident in the ejecta and stellar remnant with enriched values for 13 C, 15 N, and 17 O isotopes compared to solar values. Using simple analytical estimates, it is predicted that these head-on collisions could reach bolometric luminosities similar to or higher than that of classical novae ( ∼10 5 –10 7 L ). However, head-on collisions are not expected to occur frequently; we thus need to look into off-axis collisions which are more probable, and likely to be less energetic. Previous models of parabolic WD–MS star collisions have shown that these collisions are less disruptive than head-on collisions and may lead to the formation of massive disks around the WD (Soker et al. 1987 ; Ruffert & Mueller 1990 ; Ruffert 1992 ). These studies, which were primarily conducted at low resolution and implemented point-mass approximations for the WD, suggest that temperatures and densities reached in off-axis collisions are too low ( T ≤10 7 K) for any significant nuclear energy to be generated during the collision (Soker et al. 1987 ; Ruffert 1992 ). Ho we ver, implementing a finite radius for the WD surface and increasing the resolution closer to the WD in these models led to higher temperature ( T ∼10 8 K) and density ( ρ∼10 2 –10 3 g cm −3 ) estimates in the vicinity of the WD that may lead to non-negligible contributions from nuclear reactions during the collision (Ruffert 1993 ). In this work, we utilize the smoothed particle hydrodynamics (SPH) method (Lucy 1977 ; Monaghan 1992 ), specifically a modified version of the GADGET-4 code (Springel et al. 2021 ), to further our investigation into the energetics and hydrodynamics of WD-MS collisions in GCs, specifically focusing on off-axis collisions. We will impro v e on the previous work by simulating these collisions at higher resolution and in 3D to investigate the dynamics, energetics, mass loss, and morphology of the stellar remnant for different stellar mass ratios and impact angles. We implement a simplified nuclear network, with 34-isotopes ranging from 1 H to 56 Ni, to assess the impact of nuclear burning during these collisions, and to also estimate the elemental abundances and potentially observable isotopic ratios. The paper is structured as follows: in Section 2 , we give a description of the code set-up, as well as the initial conditions for our models. In Section 3 , we present our results for the different stellar mass ratios and impact parameters considered. We discuss observational predictions in Section 4 , followed by an investigation into angular momentum and possible disk formation during these collisions in Section 5 . We present our conclusions in Section 6 . 2 NUMERICAL METHODS AND SET-UP 2.1 The Code In this work, we use a modified version of the GADGET-4 code. We adopt the entropy-density formulation, together with the Wendland C4 kernel with N ngb = 137 neighbours, time-dependent artificial viscosity (AV), and fast multipole method (FMM), and include an updated equation of state (EOS) with radiation pressure. We further include artificial conductivity (AC) which provides better estimates for hydrodynamic quantities o v er steep gradients that exist between the WD surface and surrounding MS star material (see Merwe et al. 2024 , and references therein for details). Additionally, we have coupled a 34-isotope nuclear reaction network 3 (Timmes 1999 ) that includes 125 reactions; this network includes pp-chains, cold and hot CNO-cycles, as well as the triplealpha process. We tested and compared various networks and found that this network is sufficient to estimate the energy release due to nuclear burning during the conditions found in these collisions, i.e. T max ∼10 8 K and ρmax ∼10 3 g cm −3 . We refer the reader to P1 and Springel et al. ( 2021 ) for more details of our numerical approach and GADGET-4 code modifications. 2.2 Initial conditions The stars are modelled as n = 1 . 5 polytropes of solar composition (Shara & Shaviv 1977 , 1978 ; Soker et al. 1987 ; Rozyczka et al. 1989 ; Ruffert 1993 ; Lodders 2021 ). As mentioned in P1, the use of polytropic models is not ideal when modelling stellar interactions. Using realistic stellar profiles derived from stellar evolution codes has been shown to significantly affect the structure of the stellar remnant 3 https:// cococubed.com/ code pages/ burn helium.shtml Downloaded from https://academic.oup.com/mnras/article/538/3/1384/8042563 by UPC Btca Rector G Ferrate user on 22 April 2025 1386 C. J. T. van der Merwe et al. MNRAS 538, 1384–1396 (2025) Figure 1. Density (top) and temperature (bottom) profiles for the 0 . 3 M  (red) and 0 . 6 M (blue) MS star, respectively. o v er long time-scales (Sills & Lombardi Jr 1997 ). The simulations in this work ho we v er co v er the first few hours of the interaction, focusing on the energetics of the collision and not the long-term evolution of the stellar remnant. Thus, we implemented polytropic profiles for the stars with solar metallicity as this also enabled better comparison with previous works to more clearly identify the effects of the additional physics in our models. To set up these polytropes, we used the weighted Voronoi tessellation initial configuration ( WVTIC ) code (Arth et al. 2019 ) to generate a constant density sphere with the desired radius of the star. This constant density sphere is then evolved with a constant specific entropy profile, which after a few dynamical times relaxes into hydrostatic equilibrium with the desired density and temperature profiles (see P1 for more details). We use N = 2 . 5 –5 ×10 5 equal-mass particles to represent each polytrope in the various models, as it was shown in P1 to result in sufficient convergence of our results. Follo wing pre vious works and recent population synthesis models of GCs (Shara & Regev 1986 ; Soker et al. 1987 ; Rozyczka et al. 1989 ; Ruffert & Mueller 1990 ; Kremer et al. 2022 ) our models comprise of MS stars with masses, M MS = 0 . 3 M and 0 . 6 M , and radii, R MS = 0 . 28 R and 0 . 56 R , respectively, and a WD with mass, M WD = 0 . 6 M , and radius, R WD = 0 . 01 R (see Fig. 1 for the stellar profiles). We define the mass-ratio as q = M MS /M WD . The initial position and velocity of the stars in our models are determined as follows: we use a simplified N -body code 4 to simulate the initial parabolic orbit of the stars, which is only influenced by the gravitational forces between the stars, approximated as point-masses. We choose the collision axis to be in the xy-plane and therefore place the stars d x ∼4 ( R MS + R WD ) apart in the x -axis, and separate the stars in the y -axis by a value b, the impact parameter. The initial 4 https:// github.com/ pmocz/ nbody-python velocity of the stars at the initial separation ( d 0 ) is equal to v esc ∼ 2 G ( M WD + M MS ) d 0 , (1) where G is the gravitational constant, and d 0 =  d 2 x + b 2 . We choose b such that the periastron distance between the cores of the stars are d min = 0 . 25 , 0 . 5 ( R MS + R WD ). We select these values as we are interested in the most energetic off-axis scenarios; intuitively larger d min values will lead to less energetic interactions. Once the point-masses (stars) are d min = 2 ( R MS + R WD ) apart, we extract their position and velocities and assign them to the polytropes used in our hydrodynamic models as the starting conditions. This distance is chosen to ensure that we can fully model the tidal distortion of the MS star expected during the initial interaction. The model parameters are given in Table 1 . Column (2) indicates the minimum separation, d min , of the centre of the stars during the collision. Columns (3)–(6) show the MS/WD mass and radii used in the different models. Columns (7) and (8) give the number of particles used to model each star in the collision. Energy conservation is within < 1 per cent for all models in this work. Lastly, in many of the figures below, we refer to normalized time ( t norm ), which is simply the ratio of the physical time of the simulation and the dynamical time-scale of the MS star for each model. The dynamical time-scales for the MS stars used in this work are: t dyn , 0 . 3 M ∼478 s and t dyn , 0 . 6 M ∼955 s. The following assumptions are implemented in our models: (i) We assume the stars are on parabolic orbits. (ii) We do not include the effect of magnetic fields. (iii) The stars are non-rotating. (iv) Only MS star particles enter the nuclear reaction network. (v) We neglect relativistic effects, since the velocities reached are small compared to the velocity of light ( v max ∼10 3 km/s). 2.3 Bound mass calculation As in P1, we implement an iterative method to estimate the mass bound to the WD during the interaction. An initial guess for the bound material is estimated as follows: We define particle j to be bound to the WD if 1 2 m j ( v j −v WD ) 2 + U j −G m j ( M WD + M bound ) d < 0 , (2) where d is the distance between the particle of interest and the WD’s centre of mass, U j is the particle’s internal energy, v j is the velocity of particle j, v WD is the WD centre-of-mass (COM) velocity, G is the gravitational constant, and M bound is the mass of bound MS star material which is set to zero in the initial guess; the first term is the kinetic energy of the particle and the final term represents the particle’s gravitational potential energy. We then set M bound equal to the amount of MS star material that is calculated to be bound to the WD in the initial estimate. Thus, the subsequent iterations of the equation now also take into account the gravitational influence of bound material in addition to M WD . This step is repeated (updating M bound ) until the bound mass fraction converges to within 0.01 per cent. Downloaded from https://academic.oup.com/mnras/article/538/3/1384/8042563 by UPC Btca Rector G Ferrate user on 22 April 2025 3D models of WD–MS star collisions in GCs 1387 MNRAS 538, 1384–1396 (2025) Table 1. Properties of the stars in this work modelled as n = 1 . 5 polytropes. Model name d min ( R MS + R WD ) M MS ( M ) R MS ( R ) M WD ( M ) R WD ( R ) N MS N WD q1 dmin0 0.00 0.60 0.56 0.60 0.01 5 ×10 5 5 ×10 5 q1 dmin025 0.25 0.60 0.56 0.60 0.01 5 ×10 5 5 ×10 5 q1 dmin05 0.50 0.60 0.56 0.60 0.01 5 ×10 5 5 ×10 5 q05 dmin0 0.00 0.30 0.28 0.60 0.01 2 . 5 ×10 5 5 ×10 5 q05 dmin025 0.25 0.30 0.28 0.60 0.01 2 . 5 ×10 5 5 ×10 5 q05 dmin05 0.50 0.30 0.28 0.60 0.01 2 . 5 ×10 5 5 ×10 5 3 RESULTS AND DISCUSSION 3.1 Equal mass stars: q = 1 3.1.1 Near head-on collision: d min = 0 . 25 The dynamics of the interactions between the WD and MS star mentioned in P1 (head-on collisions) change significantly when introducing a non-zero impact parameter as in model q1 dmin025. In this scenario, the WD and MS star are separated initially such that their periastron distance would be equal to d min = 0 . 25( R WD + R MS ) if the stars were represented by point masses as described in Section 2.2 . At t = 0 s the stars are separated by a distance of ∼2( R WD + R MS ) with a relative velocity equal to that of the escape velocity of the stars at that distance, i.e. ∼700 km s −1 . As the stars accelerate towards each other, material from the MS star’s outer envelope is focused towards the WD. As the WD starts to penetrate the MS star envelope (normalized time ∼0 . 73), MS star material is ejected at velocities of ∼10 3 km s −1 , preferentially along the ne gativ e pressure gradient behind the WD as it enters the MS star (Fig. 2 , left panels). Some of the shocked material is flung around the WD to the extent that it collides with undisturbed MS star material in the outer envelope on the other side of the WD. This latter interaction results in a shock front that runs rapidly along the outer edges of the MS star (left-hand side of the WD in Fig. 2 ). The flow of the material in front of the faster shock is towards the WD, whereas the material behind the fast shock flows away from the WD. This is a result of the strong anisotropic, counter-clockwise flow of MS star material that was set up as the WD entered the MS star. The material in front of the slow shock, which propagates perpendicular to the entry direction of the WD, flows away from the WD along the shock, while the material behind the slow shock either gets flung around the WD or gets ejected downstream via the ne gativ e pressure gradient. The flow differs from that in head-on collisions (see P1) where the shock is symmetric about the collision axis, and remains within the MS star for most of the collision. Thus, whereas head-on collisions may exhibit a soft X-ray/UV flash when the, initially hidden, shock breaks through the outer surface of the MS star (Rozyczka et al. 1989 ), we do not expect such a flash for off-centre interactions. The averaged maximum temperature and density reached within 2 R WD of the WD surface during the off-centre collision are T ave ∼8 ×10 7 K and ρave ∼130 g cm −3 , respectively. The maximum temperatures and densities reached during the run for each model can be found in Table 2 . As expected, these values are lower compared to the head-on case ( T ave ∼1 . 03 ×10 8 K and ρave ∼230 g cm −3 , model q1 dmin0) since the WD passes through regions with lower densities and temperatures as they are farther from the central part of the MS star (see Fig. 3 ). Our temperature and density estimates are similar to the T ∼8 . 3 ×10 7 K and ρ∼10 2 g cm −3 predicted near the WD surface in Ruffert ( 1993 ). Deviations are due in part to differing initial conditions, e.g. slightly smaller and less massive stars, higher resolution, and also the fact that we selected a larger radius o v er which to calculate the average temperature and densities near the WD surface compared to Ruffert ( 1993 ). In off-axis collisions, the WD mo v es through regions with lower density, which leads to less kinetic energy being converted into heat due to hydrodynamical and gravitational drag compared to the headon case, as shown in the top and bottom panels of Fig. 4 . An order of magnitude calculation for the total drag experienced by the WD in the time interval t, is estimated by combining the hydrodynamic and gravitational drag as E hydro , drag = πR 2 WD ρave v 2 rel D, (3) E grav , drag = G 2 M 2 WD ρave D / v 2 rel , (4) respectively, where ρave is the average density within 3 R WD of the WD, v rel is the maximum relativ e v elocity between the MS star material near the WD and the WD’s COM velocity, and D = v WD ×t is the distance the WD travelled within the time step considered. After around ∼800 s (normalized time ∼0 . 84), the WD begins to experience more drag as it interacts with denser parts of the deformed MS star and starts to lose kinetic energy. This leads to the fast shock o v ertaking the WD (Fig. 2 , fourth row, right panel), and moving around it to eventually collide with the slow shock in which material is moving perpendicular to the initial trajectory of the WD when it entered the MS envelope. The deceleration of the WD and acceleration of the fast shock around the WD results in a more isotropic, circular flow of MS star material around the WD at later times. The o v erall dynamics is in good agreement with that found in previous studies, e.g. Soker et al. ( 1987 ) and Ruffert ( 1993 ). During the entire simulation ( ∼1 hour, normalized time ∼4) around E nuc = 2 . 62 ×10 47 erg was released via nuclear reactions, of which 94 per cent was released within the first 30 min (normalized time ∼2) of the WD entering the MS star envelope. This is almost an order of magnitude less than that calculated for head-on collisions (P1), due to the lower maximum temperature and densities reached in the off-centre interaction. In Table 3 , we present the mass fractions of various stable isotopes with respect to their solar values. Column 6 shows that there is an enrichment of 13 C, 15 N, 17 O and an depletion of 7 Li with respect to solar values. Since the time-scale of the collision is too short for any significant hydrogen burning to take place, and the maximum temperatures reached are too low to trigger triple-alpha processes, 1 H and 4 He remain unchanged. Comparing column 5 and 6, we see that these results are similar to that found for the head-on case (enrichment of 13 C, 15 N, 17 O), although the extent of the nuclear burning is now smaller, due to the lower temperature and densities reached in the off-centre collision. These results can also be seen in Table 4 , where we give various elements and isotopic ratios that may be useful in follow-up observations. As discussed in P1, the depletion of 7 Li is due to it being converted to 7 Be and 8 B via the 7 Li(p, γ) 8 B reaction. As the ejecta expands and cools sufficiently, the Downloaded from https://academic.oup.com/mnras/article/538/3/1384/8042563 by UPC Btca Rector G Ferrate user on 22 April 2025 1388 C. J. T. van der Merwe et al. MNRAS 538, 1384–1396 (2025) Figure 2. Model q1 dmin025 v elocity v ector plots (first and third rows), and density cross-sections in the xy-plane (second and fourth rows) for t = 383, 510, 638, 886, 1084, 1275 s. The contours in the rendered plots indicate the distribution of enriched 17 O. The three lines correspond to factors of 4, 10, and 100 times the solar mass fraction of 17 O. The red dots in the top panels are the position of the WD. Downloaded from https://academic.oup.com/mnras/article/538/3/1384/8042563 by UPC Btca Rector G Ferrate user on 22 April 2025 3D models of WD–MS star collisions in GCs 1389 MNRAS 538, 1384–1396 (2025) Table 2. Temperatures and densities reached by the MS star material for each model within ∼2 t norm where the most rapid nuclear burning takes place. Average temperature and density is estimated within 2 R WD of the WD surface. T max (10 8 K) T ave (10 8 K) ρmax (10 2 g cm −3 ) ρave (10 2 g cm −3 ) q1 dmin0 3 .72 1 .03 32 .3 1 .45 q1 dmin025 3 .67 0 .79 16 .8 0 .93 q1 dmin05 3 .18 0 .62 17 .1 0 .85 q05 dmin0 4 .61 1 .02 76 .6 4 .11 q05 dmin025 4 .30 0 .71 31 .1 2 .36 q05 dmin05 3 .16 0 .52 53 .8 1 .36 Figure 3. The average temperature (top), average density (middle) and the cumulative nuclear energy generated (bottom) as a function of normalized time for d min = 0; 0 . 25; 0 . 5, which are represented by the yellow, red, and blue lines, respectively. The solid lines show the estimates for the q = 1 scenario, and the dashed lines show that of the q = 0 . 5 scenario. Normalized time is the physical time of the simulation divided by the dynamical timescale of the MS star, i.e. ∼955 s for the 0.6 M and ∼478 s for the 0.3 M  MS star. Figure 4. The velocity of the WD (top), amount of MS star material bound to the WD (middle), and the total drag experienced by the WD as a function of normalized time (bottom) for d min = 0; 0 . 25; 0 . 5, which are represented by the yellow, red, and blue lines, respecti vely. The solid lines sho w the estimates for the q = 1 scenario, and the dashed lines show that of the q = 0 . 5 scenario. abundance of 7 Be will start to be transformed into 7 Li via electron captures, with half of the 7 Be being converted into 7 Li after two months ( ∼53.3 d, the half-life of 7 Be), leading to an o v erabundance of 7 Li compared to the solar value. Most of the nuclear burning takes place within the first 1000 s in the vicinity of the WD, and due to the Downloaded from https://academic.oup.com/mnras/article/538/3/1384/8042563 by UPC Btca Rector G Ferrate user on 22 April 2025 1390 C. J. T. van der Merwe et al. MNRAS 538, 1384–1396 (2025) Table 3. Nucleosynthetic yields of stable isotopes after 4 normalized times. Each column gives the mass fraction for each isotope for a given impact parameter. q = 0.5 q = 1 Species d min = 0 d min = 0 . 25 d min = 0 . 5 d min = 0 d min = 0 . 25 d min = 0 . 5 Solar 1 H 0.738 0.738 0.738 0.738 0.738 0.738 0.738 4 He 0.250 0.250 0.250 0.250 0.250 0.250 0.250 7 Li 1 . 35 ×10 −11 5 . 17 ×10 −11 4 . 18 ×10 −11 7 . 19 ×10 −13 1 . 20 ×10 −11 3 . 78 ×10 −11 5 . 27 ×10 −11 7 Be ∗1 . 67 ×10 −6 5 . 73 ×10 −7 6 . 40 ×10 −8 1 . 43 ×10 −6 9 . 03 ×10 −7 8 . 95 ×10 −8 7 . 00 ×10 −30 8 B ∗4 . 79 ×10 −10 7 . 25 ×10 −11 8 . 28 ×10 −12 8 . 41 ×10 −10 2 . 74 ×10 −7 2 . 28 ×10 −11 8 . 00 ×10 −30 12 C 1 . 93 ×10 −3 2 . 23 ×10 −3 2 . 33 ×10 −3 1 . 70 ×10 −3 2 . 15 ×10 −3 2 . 33 ×10 −3 2 . 34 ×10 −3 13 C 7 . 72 ×10 −5 4 . 37 ×10 −5 2 . 89 ×10 −5 1 . 22 ×10 −4 4 . 13 ×10 −5 2 . 82 ×10 −5 2 . 62 ×10 −5 14 N 8 . 89 ×10 −4 7 . 46 ×10 −4 6 . 95 ×10 −4 1 . 09 ×10 −4 7 . 66 ×10 −4 6 . 93 ×10 −4 6 . 92 ×10 −4 15 N 7 . 20 ×10 −4 2 . 05 ×10 −5 2 . 76 ×10 −6 1 . 94 ×10 −4 2 . 51 ×10 −5 2 . 46 ×10 −6 1 . 59 ×10 −6 16 O 5 . 29 ×10 −3 5 . 65 ×10 −3 5 . 73 ×10 −3 4 . 73 ×10 −3 5 . 56 ×10 −3 5 . 72 ×10 −3 5 . 73 ×10 −3 17 O 2 . 44 ×10 −4 4 . 56 ×10 −5 3 . 79 ×10 −6 3 . 38 ×10 −4 8 . 46 ×10 −5 4 . 10 ×10 −6 2 . 18 ×10 −6 18 O 8 . 02 ×10 −6 1 . 03 ×10 −5 1 . 13 ×10 −5 6 . 86 ×10 −6 9 . 51 ×10 −6 1 . 12 ×10 −5 1 . 15 ×10 −5 19 F 3 . 96 ×10 −7 4 . 78 ×10 −7 5 . 02 ×10 −7 3 . 42 ×10 −7 4 . 63 ×10 −7 5 . 01 ×10 −7 5 . 06 ×10 −7 20 Ne 1 . 15 ×10 −3 1 . 17 ×10 −3 1 . 17 ×10 −3 1 . 11 ×10 −3 1 . 17 ×10 −3 1 . 17 ×10 −3 1 . 17 ×10 −3 Note. ∗These isotopes are not stable, but are shown to give more insight into the potential conversion of 7 Be to 7 Li. Table 4. Mass fractions, ratios and isotopic ratios for different q’s at the end of the simulations. q = 0.5 q = 1 d min = 0 d min = 0 . 25 d min = 0 . 5 d min = 0 d min = 0 . 25 d min = 0 . 5 solar C 1.77 ×10 −3 2.20 ×10 −3 2.35 ×10 −3 2.08 ×10 −3 2.28 ×10 −3 2.37 ×10 −3 2.37 ×10 −3 N 1.21 ×10 −3 7.80 ×10 −4 6.95 ×10 −4 9.38 ×10 −4 7.57 ×10 −4 6.97 ×10 −4 6.94 ×10 −4 O 5.15 ×10 −3 5.66 ×10 −3 5.74 ×10 −3 5.58 ×10 −3 5.72 ×10 −3 5.74 ×10 −3 5.74 ×10 −3 N/C 0.685 0.355 0.295 0.452 0.333 0.295 0.293 C/O 0.343 0.388 0.410 0.372 0.398 0.411 0.413 N/O 0.235 0.138 0.121 0.168 0.132 0.121 0.121 12 C/ 13 C 18.63 59.94 84.70 37.11 64.19 82.17 89.34 14 N/ 15 N 4.96 29.42 285.7 8.390 34.65 253.7 435.7 16 O/ 17 O 14.0 65.57 1398 26.01 104.7 1514 2632 16 O/ 18 O 744.6 588.9 510.5 616.1 543.5 507.2 498.8 strong anisotropic flow, the nuclear burning products first get pushed against, and then transported along the fast shock as shown by the 17 O abundance contours in Fig. 2 . The consequence of this is that much of the evidence of nuclear burning gets swept up into a spiral arm that is formed as the WD, and the fast shock it generates, sweeps around the MS material and forms part of the ejected material. After 1 h, around 70 per cent of MS star material is still bound to the WD, which is within the range estimated by Ruffert ( 1993 ), i.e. 70 –74 per cent . This is greater than that in the head-on scenario ( ∼50 per cent ), which is expected since much of the initial orbital angular momentum is transferred to the MS star material that spins around the WD. The percentage of the enriched isotopes, i.e. the material that has X i /X i ,s olar > 1, that is still bound to the WD is: 17 O ∼53 per cent , 15 N ∼66 per cent , 13 C ∼57 per cent , 7 Be ∼62 per cent . Thus, we can expect signs of enrichment in these isotopes within the ejecta of the collision and potentially, depending on the mixing and settling processes in the envelope, the stellar remnant that forms at later times. 3.1.2 Off-centre: d min = 0 . 5 A more off-centre collision is considered for model q1 dmin05, where the WD and MS star are separated initially such that their periastron distance, modelled as point masses, would be d min = 0 . 5( R WD + R MS ). Again, we start our hydrodynamic simulation ( t = 0 s) when the stars are separated by a distance of ∼2( R WD + R MS ) with a relative velocity equal to that of the escape velocity of the system at that distance ∼700 km s −1 . As the WD starts to penetrate the MS star, a fast and slow shock develops as in model q1 dmin025. Due to the larger impact parameter, a larger fraction of the MS star is initially undisturbed by the shock fronts. The fraction of MS star material that initially remains undisturbed remains gravitationally bound to the WD. The undisturbed material slowly merges with the rest of the disrupted MS star material as it rotates around the WD, forming a clump of MS star material which will slowly spread more isotropically as it f alls tow ards the WD and continuously gets flung around the WD (see Fig. 5 ). Since the collision has a larger impact parameter, the WD passes through colder and less dense regions of the MS star than models q1 dmin0 and q1 dmin025. The drag experienced by the WD is thus considerably less than in the near head-on, and head-on scenarios (see Fig. 4 , bottom panel), and the WD as a result does not lose as much kinetic energy. This leads to lower average temperatures ( T ave ∼6 . 2 ×10 7 K) and densities ( ρave ∼96 g cm −3 ) during the first 30 min of the collision (see Fig. 3 ). These values again are similar, but slightly lower than those found by Ruffert ( 1993 ) for this impact parameter in the equal-mass scenario, i.e. T ave ∼6 . 6 ×10 7 K and ρave ∼10 2 g cm −3 , respectively near the WD surface. During the entire simulation ( ∼1 h) around E nuc = 2 . 63 × 10 46 erg was released via nuclear reactions. This is an order of magnitude less than the near head-on scenario, and almost two orders of magnitude less than that predicted for the head-on collision. Comparing column 7 of Table 3 with columns 5 and 6, the models Downloaded from https://academic.oup.com/mnras/article/538/3/1384/8042563 by UPC Btca Rector G Ferrate user on 22 April 2025 3D models of WD–MS star collisions in GCs 1391 MNRAS 538, 1384–1396 (2025) Figure 5. Cross-sections in the xy-plane showing the time evolution of the density (top) and temperature (bottom) for the q1 dmin05 model. Animations showcasing the time evolution of the models in this work are available here . Downloaded from https://academic.oup.com/mnras/article/538/3/1384/8042563 by UPC Btca Rector G Ferrate user on 22 April 2025 1392 C. J. T. van der Merwe et al. MNRAS 538, 1384–1396 (2025) Figure 6. Projection onto the xz-plane (top) and zy-plane (bottom) of the time evolution of enriched 17 O for the q1 dmin025 model. A movie showcasing the time evolution of this model is available here . predict significantly less enrichment of 13 C, 15 N, 17 O as well as a smaller underproduction of 7 Li when increasing the impact parameter. This is expected since the maximum temperatures and densities reached as the WD mo v es through the MS star are lower than the other cases considered in this work. Around ∼80 per cent of the MS star remains bound to the WD after the first hour of the simulation, which is again within the range predicted by Ruffert ( 1993 ). The percentage of the enriched isotopes that are still bound to the WD is: 17 O ∼12 per cent , 15 N ∼39 per cent , 13 C ∼16 per cent , and 7 Be ∼38 per cent . Since limited nuclear burning took place, and most of the enrichment is within the ejecta, the composition of the stellar remnant should be closer to solar. 3.2 Less massi v e MS stars: q = 0 . 5 The global dynamics of the collisions involving a less massive MS star is very similar to that of the equal-mass scenarios, except that they occur over a shorter timescale. Ho we ver, the stellar mass ratio does affect the detailed hydrodynamics, mass loss, energetics, and nuclear burning. The less massive 0 . 3 M MS star used in these models is smaller, and has steeper density and temperature gradients than the 0 . 6 M  MS star used in the equal-mass models (see Fig. 1 ). Although the maximum temperatures in the q = 0 . 5 models are not higher than those reached in the equal-mass cases, they do reach maximum Downloaded from https://academic.oup.com/mnras/article/538/3/1384/8042563 by UPC Btca Rector G Ferrate user on 22 April 2025