MNRAS 538, 1384–1396 (2025) h ps://doi.o g/10.1093/mn as/s a 328
Ad ance Access publica ion 2025 Feb ua y 25
3D hyd odynamic simula ions o whi e dwa -main-sequence s a
collisions – II. O -cen e collisions
C. J. T. an de Me we ,
1 , 2 ‹S. S. Mohamed,
1 , 2 , 3 , 4 , 5
J. Jos
´
e,
6 , 7 M. M. Sha a
8 and T. Kami
´
nski
9
1
Depa men o As onomy, Uni e si y o Cape Town, P i a e Bag X3, Rondebosch, 7701, Cape Town, Sou h A ica
2
Sou h A ican As onomical Obse a o y, P. O Box 9, Obse a o y, 7935, Cape Town, Sou h A ica
3
Depa men o As onomy, Uni e si y o Vi ginia, Cha lo es ille, VA 22904, USA
4
NITheCS Na ional Ins i u e o Theo e ical and Compu a ional Sciences, Sou h A ica
5
Vi ginia Ins i u e o Theo e ical As onomy, Uni e si y o Vi ginia, Cha lo es ille, VA 22904, USA
6
Depa amen de F
´
ısica, EEBE, Uni e si a Poli
`
ecnica de Ca alunya, c/Edua d Ma is any 16, E-08019 Ba celona, Spain
7
Ins i u d’Es udis Espacials de Ca alunya, c/Es e e Te adas 1, E-08860 Cas ellde els, Spain
8
Depa men o As ophysics, Ame ican Museum o Na u al His o y, Cen al Pa k Wes a 79 h S ee , New Yo k, NY 10024, USA
9
Nicolaus Cope nicus As onomical Cen e , Polish Academy o Sciences, Rabia
´
nska 8, PL-87-100 To u
´
n, Poland
Accep ed 2025 Feb ua y 17. Recei ed 2025 Feb ua y 4; in o iginal o m 2024 No embe 20
A B S T R A C T
S ella collisions ha e ga ne ed enewed a en ion o hei ole in he o ma ion o peculia objec s, such as blue s aggle s,
and hei po en ial o explain ansien s wi h a ypical obse a ional and spec oscopic signa u es. Among hese, whi e dwa –
main sequence (WD–MS) collisions a e pa icula ly in iguing due o he di e se e olu iona y pa hways hey can p oduce
– such as peculia ed gian s, no ae, o sub-Chand asekha supe no ae. We p esen 3D smoo hed pa icle hyd odynamics
(SPH) simula ions o WD–MS collisions, explo ing a ange o mass a ios and impac pa ame e s. We analyze he dynamics,
ene ge ics, gas mo phology, and mass-loss om hese in e ac ions. Using a 34-iso ope nuclea ne wo k, we u he p edic he
nucleosyn hesis p oduc s gene a ed du ing hese collisions. Ou models sugges ha a ea ly imes he ejec a ha e a bipola
s uc u e and, along wi h he s ella emnan , may be en iched in iso opes such as
13
C,
15
N, and
17
O. In he case o nea head-on
collisions, he ejec a may also show an o e abundance o
7
Li ela i e o sola alues.
Key wo ds: hyd odynamics – nuclea eac ions, nucleosyn hesis, abundances – bina ies: gene al – s a s: mass-loss – globula
clus e s: gene al.
1 INTRODUCTION
The de ec ion o peculia s ella popula ions (e.g. blue s aggle s and
li hium- ich gian s) and ansien s wi h obse a ional and spec o-
scopic cha ac e is ics ha di e om he mo e well-known ansien
subclasses (Tylenda & Soke 2006 ; Ka ambelka e al. 2023 ; Cas o-
Tapia, Aguile a-G
´
omez & Chanam
´
e 2024 ) has enewed in e es in
s ella collisions as a possible o ma ion pa hway o hese objec s
wi hin dense s ella en i onmen s such as he co es o globula
clus e s (GCs) (e.g. Cha e jee e al. 2013b ; Rozne & Pe e s 2022 ).
Popula ion syn hesis models sugges ha he mos common
in e ac ions ha occu in GCs a e main-sequence-main-sequence
(MS–MS) s a and whi e-dwa -main-sequence s a (WD–MS) in e -
ac ions (Cha e jee e al. 2013a ; K eme e al. 2020 , 2021 , 2022 ; Rui
e al. 2021 ). The eason o his is he la ge abundance o WDs in hese
en i onmen s and also he la ge MS s a geome ical c oss-sec ions.
Addi ionally, he low dispe sion eloci y wi hin GCs ampli y he
e ec o g a i a ional ocusing be ween s a s, leading o la ge colli-
sional c oss-sec ions and a highe p obabili y o in e ac ions (F ei ag
& Benz 2005 ; K eme e al. 2021 ). The WD–MS s a in e ac ions
a e pa icula ly in e es ing as hey can lead o a a ie y o ene ge ic
E-mail:
ch is ian[email p o ec ed]
phenomena ha may be de ec able wi h he upcoming ime-domain
ansien su e ys such as he Rubin Obse a o y Le gac y Su e y o
Space and Time
1
(RO–LSST) and Squa e Kilome e A ay
2
(SKA).
These ins umen s and su e ys will de ec up o 10 million ansien s
e e y day, and p edic ions owa ds he ene ge ics and obse a ional
signa u es o hese a ious in e ac ions will be needed in o de o
success ully dis inguish hem among he la ge in lux o de ec ions. I
is hus impo an and ad an ageous o model dynamic WD–MS s a
collisions wi hin hese dense s ella en i onmen s o make heo e ical
p edic ions owa ds hei expec ed obse a ional signa u es.
A ecen example o a success ul iden i ica ion o a ansien
caused by a s ella collision in ol ing a WD is he case o CK Vul
o No a 1670. Ini ially p oposed o be a WD-b own dwa collision
(Ey es e al. 2018 ), based on he composi ion o he ejec a and he
ene ge ics, i is now hough o esul om a WD– ed gian in e ac ion
(Tylenda, Kami
´
nski & Smolec 2024 ). I had been sugges ed ha
me ge s o helium WDs wi h ed gian b anch (RGB) s a s a e
ela i ely common and can explain he popula ion o ea ly R- ype
s a s, which a e li hium- ich ca bon s a s wi h e y speci ic a ios
o ca bon and ni ogen iso opes, bu do no ha e enhancemen o
1
h ps:// www.lss .o g/
2
h ps:// www.skao.in /
© 2025 The Au ho (s).
Published by Ox o d Uni e si y P ess on behal o Royal As onomical Socie y. This is an Open Access a icle dis ibu ed unde he e ms o he C ea i e
Commons A ibu ion License ( h ps:// c ea i ecommons.o g/ licenses/ by/ 4.0/ ), which pe mi s un es ic ed euse, dis ibu ion, and ep oduc ion in any medium,
p o ided he o iginal wo k is p ope ly ci ed.
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3D models o WD–MS s a collisions in GCs 1385
MNRAS 538, 1384–1396 (2025)
s-p ocess elemen s. The link o me ge s was based on popula ion
syn hesis s udies o collisions and coalescence p oduc s (e.g. Izza d,
Je e y & La anzio 2007 ; Zhang e al. 2020 ). These heo e ical
models sugges ed ha some o he me ge s ac i a e helium bu ning.
I was a a he su p ising no ion ha he emnan o he ancien e en
No a 1670, kno wn as CK Vul and classi ied oday as a ed no a, is
su ounded by ci cums ella ma e ial ha can only be explained by a
WD–RGB me ge ha ac i a ed pa ial helium bu ning and dispe sed
26
Al in o he su ounding medium, as expec ed by some o he models
(Tylenda e al. 2024 ). This example demons a es ha , beyond he
WD–WD collisions ha a e he ocus o Type Ia supe no ae s udies,
he e may be ansien s p oduced by WD collisions ha a e ye o be
iden i ied.
Hyd odynamic simula ions in es iga ing head-on WD–MS colli-
sions (Sha a & Sha i 1977 , 1978 ; Sha a & Rege 1986 ; Rozyczka
e al. 1989 ; Ru e & Muelle 1990 ; Ru e 1992 , 1993 ) showed
ha he MS s a is comple ely dis up ed du ing hese collisions,
leading o la ge amoun s o ma e ial being ejec ed ( ∼50 pe cen o
he MS s a ). As he WD mo es h ough he cen al egions o he
MS s a , he MS s a ma e ial closes o i eached empe a u es and
densi ies o ∼10
8 K and ∼10
3
g cm
−3
, espec i ely. Unde hese
condi ions, i was p oposed ha signi ican nuclea bu ning can occu
(Sha a & Sha i 1977 , 1978 ; Michaely & Sha a 2021 ). Howe e , he
impo ance o nuclea eac ions was hough o be negligible, i.e. he
nuclea ene gy eleased is insu icien o ha e a dynamical e ec ,
and he e o e need no be conside ed in head-on WD–MS collisions
(Rozyczka e al. 1989 ). Ou own esul s ( an de Me we e al. 2024 ,
he ea e P1), which explici ly included a nuclea eac ion ne wo k
o WD-MS collisions o he i s ime, showed conclusi ely ha
he ene gy con ibu ion om nuclea eac ions is a om negligible.
On he con a y, i is compa able o he 3 ×10
47
e g kine ic ene gy
o each s a ela i e o he o he , and o he MS s a binding ene gy.
The la ge amoun o ma e ial ha emained bound o he WD
a e he collision led o sugges ions ha he s ella emnan will
e en ually e ol e in o a ed gian . I nuclea eac ions we e shown
o be signi ican in hese in e ac ions, hese collisions may lead o
he o ma ion o peculia ed gian popula ions ha ha e unusual
spec oscopic signa u es. Fu he in es iga ion in o hese ques ions
has ecen ly been done in P1, whe e he impo ance o nuclea
bu ning o di e en s ella mass- a ios was s udied using high
esolu ion, 3D models.
In P1, ou simula ions showed ha MS s a ma e ial can each em-
pe a u es and densi ies o T > 1 ×10
8
K and ρ∼1 ×10
3
g cm
−3
,
espec i ely. Unde hese condi ions, ho CNO-cycles con ibu e
signi ican ly owa ds he o al ene gy eleased du ing he collision,
becoming e en mo e signi ican o lowe mass a ios ( q ≤0 . 5)
whe e he amoun o nuclea ene gy gene a ed du ing he collision
was simila o he binding ene gy o he MS s a ( ∼10
47
e g).
Fu he mo e, signs o incomple e CNO bu ning a e p edic ed o be
e iden in he ejec a and s ella emnan wi h en iched alues o
13
C,
15
N, and
17
O iso opes compa ed o sola alues. Using simple
analy ical es ima es, i is p edic ed ha hese head-on collisions
could each bolome ic luminosi ies simila o o highe han ha
o classical no ae ( ∼10
5
–10
7
L
). Howe e , head-on collisions a e
no expec ed o occu equen ly; we hus need o look in o o -axis
collisions which a e mo e p obable, and likely o be less ene ge ic.
P e ious models o pa abolic WD–MS s a collisions ha e shown
ha hese collisions a e less dis up i e han head-on collisions and
may lead o he o ma ion o massi e disks a ound he WD (Soke
e al. 1987 ; Ru e & Muelle 1990 ; Ru e 1992 ). These s udies,
which we e p ima ily conduc ed a low esolu ion and implemen ed
poin -mass app oxima ions o he WD, sugges ha empe a u es
and densi ies eached in o -axis collisions a e oo low ( T ≤10
7
K)
o any signi ican nuclea ene gy o be gene a ed du ing he collision
(Soke e al. 1987 ; Ru e 1992 ). Ho we e , implemen ing a ini e
adius o he WD su ace and inc easing he esolu ion close o
he WD in hese models led o highe empe a u e ( T ∼10
8
K) and
densi y ( ρ∼10
2
–10
3
g cm
−3
) es ima es in he icini y o he WD
ha may lead o non-negligible con ibu ions om nuclea eac ions
du ing he collision (Ru e 1993 ).
In his wo k, we u ilize he smoo hed pa icle hyd odynamics
(SPH) me hod (Lucy 1977 ; Monaghan 1992 ), speci ically a modi ied
e sion o he GADGET-4 code (Sp ingel e al. 2021 ), o u he ou
in es iga ion in o he ene ge ics and hyd odynamics o WD-MS
collisions in GCs, speci ically ocusing on o -axis collisions. We
will imp o e on he p e ious wo k by simula ing hese collisions a
highe esolu ion and in 3D o in es iga e he dynamics, ene ge ics,
mass loss, and mo phology o he s ella emnan o di e en s ella
mass a ios and impac angles. We implemen a simpli ied nuclea
ne wo k, wi h 34-iso opes anging om
1
H o
56
Ni, o assess he
impac o nuclea bu ning du ing hese collisions, and o also es ima e
he elemen al abundances and po en ially obse able iso opic a ios.
The pape is s uc u ed as ollows: in Sec ion 2 , we gi e a
desc ip ion o he code se -up, as well as he ini ial condi ions o
ou models. In Sec ion 3 , we p esen ou esul s o he di e en
s ella mass a ios and impac pa ame e s conside ed. We discuss
obse a ional p edic ions in Sec ion 4 , ollowed by an in es iga ion
in o angula momen um and possible disk o ma ion du ing hese
collisions in Sec ion 5 . We p esen ou conclusions in Sec ion 6 .
2 NUMERICAL METHODS AND SET-UP
2.1 The Code
In his wo k, we use a modi ied e sion o he GADGET-4 code. We
adop he en opy-densi y o mula ion, oge he wi h he Wendland
C4 ke nel wi h N
ngb
= 137 neighbou s, ime-dependen a i icial
iscosi y (AV), and as mul ipole me hod (FMM), and include an
upda ed equa ion o s a e (EOS) wi h adia ion p essu e. We u he
include a i icial conduc i i y (AC) which p o ides be e es ima es
o hyd odynamic quan i ies o e s eep g adien s ha exis be ween
he WD su ace and su ounding MS s a ma e ial (see Me we e al.
2024 , and e e ences he ein o de ails).
Addi ionally, we ha e coupled a 34-iso ope nuclea eac ion
ne wo k
3 (Timmes 1999 ) ha includes 125 eac ions; his ne wo k
includes pp-chains, cold and ho CNO-cycles, as well as he iple-
alpha p ocess. We es ed and compa ed a ious ne wo ks and ound
ha his ne wo k is su icien o es ima e he ene gy elease due o
nuclea bu ning du ing he condi ions ound in hese collisions, i.e.
T
max
∼10
8
K and ρmax
∼10
3
g cm
−3
. We e e he eade o P1 and
Sp ingel e al. ( 2021 ) o mo e de ails o ou nume ical app oach and
GADGET-4 code modi ica ions.
2.2 Ini ial condi ions
The s a s a e modelled as n = 1 . 5 poly opes o sola composi ion
(Sha a & Sha i 1977 , 1978 ; Soke e al. 1987 ; Rozyczka e al.
1989 ; Ru e 1993 ; Lodde s 2021 ). As men ioned in P1, he use o
poly opic models is no ideal when modelling s ella in e ac ions.
Using ealis ic s ella p o iles de i ed om s ella e olu ion codes has
been shown o signi ican ly a ec he s uc u e o he s ella emnan
3
h ps:// cococubed.com/ code pages/ bu n helium.sh ml
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1386 C. J. T. an de Me we e al.
MNRAS 538, 1384–1396 (2025)
Figu e 1. Densi y ( op) and empe a u e (bo om) p o iles o he 0 . 3 M
( ed) and 0 . 6 M
(blue) MS s a , espec i ely.
o e long ime-scales (Sills & Lomba di J
1997 ). The simula ions
in his wo k ho we e co e he i s ew hou s o he in e ac ion,
ocusing on he ene ge ics o he collision and no he long- e m
e olu ion o he s ella emnan . Thus, we implemen ed poly opic
p o iles o he s a s wi h sola me allici y as his also enabled be e
compa ison wi h p e ious wo ks o mo e clea ly iden i y he e ec s
o he addi ional physics in ou models. To se up hese poly opes, we
used he weigh ed Vo onoi essella ion ini ial con igu a ion ( WVTIC )
code (A h e al. 2019 ) o gene a e a cons an densi y sphe e wi h
he desi ed adius o he s a . This cons an densi y sphe e is hen
e ol ed wi h a cons an speci ic en opy p o ile, which a e a ew
dynamical imes elaxes in o hyd os a ic equilib ium wi h he desi ed
densi y and empe a u e p o iles (see P1 o mo e de ails). We use
N = 2 . 5 –5 ×10
5 equal-mass pa icles o ep esen each poly ope
in he a ious models, as i was shown in P1 o esul in su icien
con e gence o ou esul s.
Follo wing p e ious wo ks and ecen popula ion syn hesis models
o GCs (Sha a & Rege 1986 ; Soke e al. 1987 ; Rozyczka e al.
1989 ; Ru e & Muelle 1990 ; K eme e al. 2022 ) ou models
comp ise o MS s a s wi h masses, M
MS
= 0 . 3 M
and 0 . 6 M
, and
adii, R
MS
= 0 . 28 R
and 0 . 56 R
, espec i ely, and a WD wi h
mass, M
WD
= 0 . 6 M
, and adius, R
WD
= 0 . 01 R
(see Fig. 1 o
he s ella p o iles). We de ine he mass- a io as q = M
MS
/M
WD
.
The ini ial posi ion and eloci y o he s a s in ou models a e
de e mined as ollows: we use a simpli ied N -body code
4
o simula e
he ini ial pa abolic o bi o he s a s, which is only in luenced by he
g a i a ional o ces be ween he s a s, app oxima ed as poin -masses.
We choose he collision axis o be in he xy-plane and he e o e place
he s a s d
x
∼4 ( R
MS
+ R
WD
) apa in he x -axis, and sepa a e he
s a s in he y -axis by a alue b, he impac pa ame e . The ini ial
4
h ps:// gi hub.com/ pmocz/ nbody-py hon
eloci y o he s a s a he ini ial sepa a ion ( d
0
) is equal o
esc
∼
2 G ( M
WD
+ M
MS
)
d
0
, (1)
whe e G is he g a i a ional cons an , and d
0
=
d
2
x
+ b
2
. We
choose b such ha he pe ias on dis ance be ween he co es o he
s a s a e d
min
= 0 . 25 , 0 . 5 ( R
MS
+ R
WD
). We selec hese alues as
we a e in e es ed in he mos ene ge ic o -axis scena ios; in ui i ely
la ge d
min alues will lead o less ene ge ic in e ac ions. Once he
poin -masses (s a s) a e d
min
= 2 ( R
MS
+ R
WD
) apa , we ex ac hei
posi ion and eloci ies and assign hem o he poly opes used in ou
hyd odynamic models as he s a ing condi ions. This dis ance is
chosen o ensu e ha we can ully model he idal dis o ion o he
MS s a expec ed du ing he ini ial in e ac ion.
The model pa ame e s a e gi en in Table 1 . Column (2) indica es
he minimum sepa a ion, d
min
, o he cen e o he s a s du ing he
collision. Columns (3)–(6) show he MS/WD mass and adii used
in he di e en models. Columns (7) and (8) gi e he numbe o
pa icles used o model each s a in he collision. Ene gy conse a ion
is wi hin < 1 pe cen o all models in his wo k. Las ly, in many
o he igu es below, we e e o no malized ime (
no m
), which
is simply he a io o he physical ime o he simula ion and he
dynamical ime-scale o he MS s a o each model. The dynamical
ime-scales o he MS s a s used in his wo k a e:
dyn , 0 . 3 M
∼478 s
and
dyn , 0 . 6 M
∼955 s.
The ollowing assump ions a e implemen ed in ou models:
(i) We assume he s a s a e on pa abolic o bi s.
(ii) We do no include he e ec o magne ic ields.
(iii) The s a s a e non- o a ing.
(i ) Only MS s a pa icles en e he nuclea eac ion ne wo k.
( ) We neglec ela i is ic e ec s, since he eloci ies eached a e
small compa ed o he eloci y o ligh (
max
∼10
3
km/s).
2.3 Bound mass calcula ion
As in P1, we implemen an i e a i e me hod o es ima e he mass
bound o he WD du ing he in e ac ion. An ini ial guess o he
bound ma e ial is es ima ed as ollows: We de ine pa icle j o be
bound o he WD i
1
2
m
j
(
j
−
WD
)
2
+ U
j
−G
m
j
( M
WD
+ M
bound
)
d
< 0 , (2)
whe e d is he dis ance be ween he pa icle o in e es and he WD’s
cen e o mass, U
j
is he pa icle’s in e nal ene gy,
j
is he eloci y
o pa icle j,
WD
is he WD cen e-o -mass (COM) eloci y, G is
he g a i a ional cons an , and M
bound
is he mass o bound MS s a
ma e ial which is se o ze o in he ini ial guess; he i s e m is
he kine ic ene gy o he pa icle and he inal e m ep esen s he
pa icle’s g a i a ional po en ial ene gy.
We hen se M
bound
equal o he amoun o MS s a ma e ial ha
is calcula ed o be bound o he WD in he ini ial es ima e. Thus,
he subsequen i e a ions o he equa ion now also ake in o accoun
he g a i a ional in luence o bound ma e ial in addi ion o M
WD
.
This s ep is epea ed (upda ing M
bound
) un il he bound mass ac ion
con e ges o wi hin 0.01 pe cen .
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3D models o WD–MS s a collisions in GCs 1387
MNRAS 538, 1384–1396 (2025)
Table 1. P ope ies o he s a s in his wo k modelled as n = 1 . 5 poly opes.
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 s a s: q = 1
3.1.1 Nea head-on collision: d
min
= 0 . 25
The dynamics o he in e ac ions be ween he WD and MS s a
men ioned in P1 (head-on collisions) change signi ican ly when
in oducing a non-ze o impac pa ame e as in model q1 dmin025.
In his scena io, he WD and MS s a a e sepa a ed ini ially such ha
hei pe ias on dis ance would be equal o d
min
= 0 . 25( R
WD
+ R
MS
)
i he s a s we e ep esen ed by poin masses as desc ibed in
Sec ion 2.2 . A = 0 s he s a s a e sepa a ed by a dis ance o
∼2( R
WD
+ R
MS
) wi h a ela i e eloci y equal o ha o he escape
eloci y o he s a s a ha dis ance, i.e. ∼700 km s
−1
. As he s a s
accele a e owa ds each o he , ma e ial om he MS s a ’s ou e
en elope is ocused owa ds he WD.
As he WD s a s o pene a e he MS s a en elope (no mal-
ized ime ∼0 . 73), MS s a ma e ial is ejec ed a eloci ies o
∼10
3
km s
−1
, p e e en ially along he ne ga i e p essu e g adien
behind he WD as i en e s he MS s a (Fig. 2 , le panels).
Some o he shocked ma e ial is lung a ound he WD o he
ex en ha i collides wi h undis u bed MS s a ma e ial in he
ou e en elope on he o he side o he WD. This la e in e ac ion
esul s in a shock on ha uns apidly along he ou e edges o
he MS s a (le -hand side o he WD in Fig. 2 ). The low o he
ma e ial in on o he as e shock is owa ds he WD, whe eas
he ma e ial behind he as shock lows away om he WD. This
is a esul o he s ong aniso opic, coun e -clockwise low o MS
s a ma e ial ha was se up as he WD en e ed he MS s a . The
ma e ial in on o he slow shock, which p opaga es pe pendicula
o he en y di ec ion o he WD, lows away om he WD along
he shock, while he ma e ial behind he slow shock ei he ge s lung
a ound he WD o ge s ejec ed downs eam ia he ne ga i e p essu e
g adien .
The low di e s om ha in head-on collisions (see P1) whe e he
shock is symme ic abou he collision axis, and emains wi hin he
MS s a o mos o he collision. Thus, whe eas head-on collisions
may exhibi a so X- ay/UV lash when he, ini ially hidden, shock
b eaks h ough he ou e su ace o he MS s a (Rozyczka e al.
1989 ), we do no expec such a lash o o -cen e in e ac ions. The
a e aged maximum empe a u e and densi y eached wi hin 2 R
WD
o
he WD su ace du ing he o -cen e collision a e T
a e
∼8 ×10
7
K
and ρa e
∼130 g cm
−3
, espec i ely. The maximum empe a u es
and densi ies eached du ing he un o each model can be ound
in Table 2 . As expec ed, hese alues a e lowe compa ed o he
head-on case ( T
a e
∼1 . 03 ×10
8
K and ρa e
∼230 g cm
−3
, model
q1 dmin0) since he WD passes h ough egions wi h lowe densi ies
and empe a u es as hey a e a he om he cen al pa o he MS
s a (see Fig. 3 ). Ou empe a u e and densi y es ima es a e simila
o he T ∼8 . 3 ×10
7
K and ρ∼10
2
g cm
−3
p edic ed nea he WD
su ace in Ru e ( 1993 ). De ia ions a e due in pa o di e ing
ini ial condi ions, e.g. sligh ly smalle and less massi e s a s, highe
esolu ion, and also he ac ha we selec ed a la ge adius o e
which o calcula e he a e age empe a u e and densi ies nea he
WD su ace compa ed o Ru e ( 1993 ).
In o -axis collisions, he WD mo es h ough egions wi h lowe
densi y, which leads o less kine ic ene gy being con e ed in o hea
due o hyd odynamical and g a i a ional d ag compa ed o he head-
on case, as shown in he op and bo om panels o Fig. 4 . An o de
o magni ude calcula ion o he o al d ag expe ienced by he WD
in he ime in e al , is es ima ed by combining he hyd odynamic
and g a i a ional d ag as
E
hyd o , d ag
= πR
2
WD
ρa e
2
el
D, (3)
E
g a , d ag
= G
2
M
2
WD
ρa e
D /
2
el
, (4)
espec i ely, whe e ρa e is he a e age densi y wi hin 3 R
WD o he
WD,
el is he maximum ela i e eloci y be ween he MS s a
ma e ial nea he WD and he WD’s COM eloci y, and D =
WD
×
is he dis ance he WD a elled wi hin he ime s ep conside ed.
A e a ound ∼800 s (no malized ime ∼0 . 84), he WD begins
o expe ience mo e d ag as i in e ac s wi h dense pa s o he
de o med MS s a and s a s o lose kine ic ene gy. This leads o
he as shock o e aking he WD (Fig. 2 , ou h ow, igh panel),
and mo ing a ound i o e en ually collide wi h he slow shock in
which ma e ial is mo ing pe pendicula o he ini ial ajec o y o he
WD when i en e ed he MS en elope. The decele a ion o he WD
and accele a ion o he as shock a ound he WD esul s in a mo e
iso opic, ci cula low o MS s a ma e ial a ound he WD a la e
imes. The o e all dynamics is in good ag eemen wi h ha ound in
p e ious s udies, e.g. Soke e al. ( 1987 ) and Ru e ( 1993 ).
Du ing he en i e simula ion ( ∼1 hou , no malized ime ∼4)
a ound E
nuc
= 2 . 62 ×10
47
e g was eleased ia nuclea eac ions, o
which 94 pe cen was eleased wi hin he i s 30 min (no malized
ime ∼2) o he WD en e ing he MS s a en elope. This is almos
an o de o magni ude less han ha calcula ed o head-on collisions
(P1), due o he lowe maximum empe a u e and densi ies eached
in he o -cen e in e ac ion. In Table 3 , we p esen he mass ac ions
o a ious s able iso opes wi h espec o hei sola alues. Column 6
shows ha he e is an en ichmen o
13
C,
15
N,
17
O and an deple ion o
7
Li wi h espec o sola alues. Since he ime-scale o he collision
is oo sho o any signi ican hyd ogen bu ning o ake place, and he
maximum empe a u es eached a e oo low o igge iple-alpha
p ocesses,
1
H and
4
He emain unchanged. Compa ing column 5 and
6, we see ha hese esul s a e simila o ha ound o he head-on
case (en ichmen o
13
C,
15
N,
17
O), al hough he ex en o he nuclea
bu ning is now smalle , due o he lowe empe a u e and densi ies
eached in he o -cen e collision. These esul s can also be seen
in Table 4 , whe e we gi e a ious elemen s and iso opic a ios ha
may be use ul in ollow-up obse a ions. As discussed in P1, he
deple ion o
7
Li is due o i being con e ed o
7
Be and
8
B ia he
7
Li(p, γ)
8
B eac ion. As he ejec a expands and cools su icien ly, he
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1388 C. J. T. an de Me we e al.
MNRAS 538, 1384–1396 (2025)
Figu e 2. Model q1 dmin025 eloci y ec o plo s ( i s and hi d ows), and densi y c oss-sec ions in he xy-plane (second and ou h ows) o = 383, 510,
638, 886, 1084, 1275 s. The con ou s in he ende ed plo s indica e he dis ibu ion o en iched
17
O. The h ee lines co espond o ac o s o 4, 10, and 100 imes
he sola mass ac ion o
17
O. The ed do s in he op panels a e he posi ion o he WD.
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3D models o WD–MS s a collisions in GCs 1389
MNRAS 538, 1384–1396 (2025)
Table 2. Tempe a u es and densi ies eached by he MS s a ma e ial o each model wi hin ∼2
no m
whe e he mos
apid nuclea bu ning akes place. A e age empe a u e and densi y is es ima ed wi hin 2 R
WD
o he WD su ace.
T
max
(10
8
K) T
a e
(10
8
K) ρmax
(10
2
g cm
−3
) ρa e
(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
Figu e 3. The a e age empe a u e ( op), a e age densi y (middle) and he
cumula i e nuclea ene gy gene a ed (bo om) as a unc ion o no malized
ime o d
min
= 0; 0 . 25; 0 . 5, which a e ep esen ed by he yellow, ed, and
blue lines, espec i ely. The solid lines show he es ima es o he q = 1
scena io, and he dashed lines show ha o he q = 0 . 5 scena io. No malized
ime is he physical ime o he simula ion di ided by he dynamical ime-
scale o he MS s a , i.e. ∼955 s o he 0.6 M
and ∼478 s o he 0.3 M
MS s a .
Figu e 4. The eloci y o he WD ( op), amoun o MS s a ma e ial bound
o he WD (middle), and he o al d ag expe ienced by he WD as a unc ion o
no malized ime (bo om) o d
min
= 0; 0 . 25; 0 . 5, which a e ep esen ed by
he yellow, ed, and blue lines, espec i ely. The solid lines sho w he es ima es
o he q = 1 scena io, and he dashed lines show ha o he q = 0 . 5 scena io.
abundance o
7
Be will s a o be ans o med in o
7
Li ia elec on
cap u es, wi h hal o he
7
Be being con e ed in o
7
Li a e wo
mon hs ( ∼53.3 d, he hal -li e o
7
Be), leading o an o e abundance
o
7
Li compa ed o he sola alue. Mos o he nuclea bu ning akes
place wi hin he i s 1000 s in he icini y o he WD, and due o he
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1390 C. J. T. an de Me we e al.
MNRAS 538, 1384–1396 (2025)
Table 3. Nucleosyn he ic yields o s able iso opes a e 4 no malized imes. Each column gi es he mass ac ion o each iso ope o a
gi en impac pa ame e .
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 Sola
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
No e.
∗These iso opes a e no s able, bu a e shown o gi e mo e insigh in o he po en ial con e sion o
7
Be o
7
Li.
Table 4. Mass ac ions, a ios and iso opic a ios o di e en q’s a he end o he simula ions.
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 sola
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
s ong aniso opic low, he nuclea bu ning p oduc s i s ge pushed
agains , and hen anspo ed along he as shock as shown by he
17
O abundance con ou s in Fig. 2 . The consequence o his is ha
much o he e idence o nuclea bu ning ge s swep up in o a spi al
a m ha is o med as he WD, and he as shock i gene a es, sweeps
a ound he MS ma e ial and o ms pa o he ejec ed ma e ial.
A e 1 h, a ound 70 pe cen o MS s a ma e ial is s ill bound
o he WD, which is wi hin he ange es ima ed by Ru e ( 1993 ),
i.e. 70 –74 pe cen . This is g ea e han ha in he head-on scena io
( ∼50 pe cen ), which is expec ed since much o he ini ial o bi al
angula momen um is ans e ed o he MS s a ma e ial ha spins
a ound he WD. The pe cen age o he en iched iso opes, i.e. he
ma e ial ha has X
i
/X
i ,s ola > 1, ha is s ill bound o he WD is:
17
O ∼53 pe cen ,
15
N ∼66 pe cen ,
13
C ∼57 pe cen ,
7
Be
∼62 pe cen . Thus, we can expec signs o en ichmen in hese
iso opes wi hin he ejec a o he collision and po en ially, depending
on he mixing and se ling p ocesses in he en elope, he s ella
emnan ha o ms a la e imes.
3.1.2 O -cen e: d
min
= 0 . 5
A mo e o -cen e collision is conside ed o model q1 dmin05,
whe e he WD and MS s a a e sepa a ed ini ially such ha hei
pe ias on dis ance, modelled as poin masses, would be d
min
=
0 . 5( R
WD
+ R
MS
). Again, we s a ou hyd odynamic simula ion ( =
0 s) when he s a s a e sepa a ed by a dis ance o ∼2( R
WD
+ R
MS
)
wi h a ela i e eloci y equal o ha o he escape eloci y o he
sys em a ha dis ance ∼700 km s
−1
.
As he WD s a s o pene a e he MS s a , a as and slow shock de-
elops as in model q1 dmin025. Due o he la ge impac pa ame e ,
a la ge ac ion o he MS s a is ini ially undis u bed by he shock
on s. The ac ion o MS s a ma e ial ha ini ially emains undis-
u bed emains g a i a ionally bound o he WD. The undis u bed
ma e ial slowly me ges wi h he es o he dis up ed MS s a ma e ial
as i o a es a ound he WD, o ming a clump o MS s a ma e ial
which will slowly sp ead mo e iso opically as i alls ow a ds he
WD and con inuously ge s lung a ound he WD (see Fig. 5 ).
Since he collision has a la ge impac pa ame e , he WD passes
h ough colde and less dense egions o he MS s a han models
q1 dmin0 and q1 dmin025. The d ag expe ienced by he WD is hus
conside ably less han in he nea head-on, and head-on scena ios
(see Fig. 4 , bo om panel), and he WD as a esul does no lose
as much kine ic ene gy. This leads o lowe a e age empe a u es
( T
a e
∼6 . 2 ×10
7
K) and densi ies ( ρa e
∼96 g cm
−3
) du ing he i s
30 min o he collision (see Fig. 3 ). These alues again a e simila ,
bu sligh ly lowe han hose ound by Ru e ( 1993 ) o his impac
pa ame e in he equal-mass scena io, i.e. T
a e
∼6 . 6 ×10
7
K and
ρa e
∼10
2
g cm
−3
, espec i ely nea he WD su ace.
Du ing he en i e simula ion ( ∼1 h) a ound E
nuc
= 2 . 63 ×
10
46
e g was eleased ia nuclea eac ions. This is an o de o
magni ude less han he nea head-on scena io, and almos wo
o de s o magni ude less han ha p edic ed o he head-on collision.
Compa ing column 7 o Table 3 wi h columns 5 and 6, he models
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3D models o WD–MS s a collisions in GCs 1391
MNRAS 538, 1384–1396 (2025)
Figu e 5. C oss-sec ions in he xy-plane showing he ime e olu ion o he densi y ( op) and empe a u e (bo om) o he q1 dmin05 model. Anima ions
showcasing he ime e olu ion o he models in his wo k a e a ailable he e .
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1392 C. J. T. an de Me we e al.
MNRAS 538, 1384–1396 (2025)
Figu e 6. P ojec ion on o he xz-plane ( op) and zy-plane (bo om) o he ime e olu ion o en iched
17
O o he q1 dmin025 model. A mo ie showcasing he
ime e olu ion o his model is a ailable he e .
p edic signi ican ly less en ichmen o
13
C,
15
N,
17
O as well
as a smalle unde p oduc ion o
7
Li when inc easing he impac
pa ame e . This is expec ed since he maximum empe a u es and
densi ies eached as he WD mo es h ough he MS s a a e lowe
han he o he cases conside ed in his wo k. A ound ∼80 pe cen
o he MS s a emains bound o he WD a e he i s hou o
he simula ion, which is again wi hin he ange p edic ed by Ru e
( 1993 ). The pe cen age o he en iched iso opes ha a e s ill bound o
he WD is:
17
O ∼12 pe cen ,
15
N ∼39 pe cen ,
13
C ∼16 pe cen ,
and
7
Be ∼38 pe cen . Since limi ed nuclea bu ning ook place, and
mos o he en ichmen is wi hin he ejec a, he composi ion o he
s ella emnan should be close o sola .
3.2 Less massi e MS s a s: q = 0 . 5
The global dynamics o he collisions in ol ing a less massi e MS
s a is e y simila o ha o he equal-mass scena ios, excep ha
hey occu o e a sho e imescale. Ho we e , he s ella mass a io
does a ec he de ailed hyd odynamics, mass loss, ene ge ics, and
nuclea bu ning.
The less massi e 0 . 3 M
MS s a used in hese models is smalle ,
and has s eepe densi y and empe a u e g adien s han he 0 . 6 M
MS s a used in he equal-mass models (see Fig. 1 ). Al hough he
maximum empe a u es in he q = 0 . 5 models a e no highe han
hose eached in he equal-mass cases, hey do each maximum
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