The ole o mass ans e e iciency in s abili y c i e ia:
A S udy wi h SEVN M. Eche es e1, G. J. Escoba 2,3, E. Pancino1,4
1 INAF – Osse a o io As o isico di A ce i, La go E. Fe mi 5, 50125 Fi enze, I aly. e-mail: mai e.eche es e@ina .i
2 Ins i u o de As o ísica de Cana ias, E-38205 La Laguna, Tene i e, Spain
3 Uni e sidad de La Laguna, Dp o. As o ísica, E-38206 La Laguna, Tene i e, Spain
4 Space Science Da a Cen e , Via del Poli ecnico SNC, I-00133 Roma, I aly
P ocedu e
He zsp ung-Russell diag am o BSS (seconda y) and hei companions (p ima y). Each
qua e e e s o a alue o β. The le column co esponds o he β dependen c i e ion
and he igh column o he Hu ley-Webbink one. The o ma ion o BSS is explo ed a wo
ages: 4 and 8 Gy .
1 Tou C. A., Aa se h S. J., Pols O. R., Eggle on P. P 1997, MNRAS, 291, 732
4 Io io, G., Mapelli, M., Cos a, G. e al. 2023, MNRAS, 524, 426
5 Leine E. & Gelle A., 2021, ApJ, 908,229
2 Spe a M., Mapelli M., B essan A. e al. 2015, MNRAS, 451, 4086
3 Spe a M., Mapelli M., Giacobbo N. e al., 2019, MNRAS, 485, 889
Mass ans e (MT) in in e ac ing bina y s a s plays a cen al ole in shaping a
wide ange o as ophysical phenomena. A key s ep in modeling MT is
de e mining whe he i p oceeds in a s able o uns able way, as his dis inc ion
p o oundly a ec s he ou come o he in e ac ion.
The s abili y o MT depends on how he dono s a adius esponds o mass
loss compa ed o he esponse o i s Roche lobe adius. These quan i ies a e
cha ac e ized by:
●The dono 's adiaba ic esponse, ξad = (d log Rad / d log M), which depends
on he s ella s uc u e, in pa icula , on he ene gy anspo mechanism
ha domina es in he en elope.
●The Roche lobe esponse, ξL = (d log RL / d log M), which depends on he
bina y's con igu a ion and on he o al mass and angula momen um
e olu ion.
ξL > ξad implies ins abili y and ξL ≤ ξad implies s abili y a he onse o a Roche
lobe o e low phase.
Con ex
Popula ion syn hesis codes o en use he exp ession o ξL de i ed by Tou e al.
(1997)1 unde conse a i e assump ions—i.e., nei he mass no angula
momen um a e los om he sys em. Howe e , his exp ession is s ill widely
applied in non-conse a i e cases.
He e, we de i e a gene alized exp ession o ξL ha includes non-conse a i e
MT and implemen i in he popula ion-syn hesis code SEVN (Spe a e al. 20152,
20193, Io io e al. 20234). We explo e i s implica ions in he o ma ion o blue
s aggle s a s (BSS) and bina y compac objec s (BCO).
We ollow he same s eps ha lead o Tou ’s exp ession o ξL , now d opping
he conse a ion assump ions and using
We ind he exp ession
whe e q = M1/M2 (i.e. he dono - o-acc e o mass- a io) and A, B, and c a e
cons an s. We implemen his exp ession in SEVN. He e, we assume he angula
momen um is los om he icini y o he acc e o . We explo e h ee alues o
he pa ame e β (0.1, 0.5, and 0.9). We compa e he numbe o BSS and BCO
o med wi h he Hu ley-Webbink s abili y c i e ion (named QCBSE in Io io e al.
2023) and wi h he new β-dependen one.
Resul s: bina y compac objec s
His og ams o he delay imes o bina ies composed by wo black holes (BBH), a black hole and a neu on s a (BHNS) and wo
neu on s a s (BNS). Each column e e s o a alue o β. The eal his og ams e e o he Hu ley-Webbink p esc ip ion while
whi e, diagonal-ha ched his og ams e e o he β-dependen one. The e ical b own line shows he alue o Hubble ime
employed in his wo k, 13.8 Gy .
Resul s: blue s aggle s
Al hough he dis ibu ion o BCO unde he β-dependen c i e ion is b oadly
consis en wi h ha ob ained using he Hu ley-Webbink p esc ip ion, a deepe
in es iga ion is wa an ed. In pa icula , i would be aluable o explo e whe he
he ela i e con ibu ion o di e en o ma ion channels changes depending on
he adop ed MT s abili y c i e ion. Such an analysis could p o ide new insigh s
in o he e olu iona y pa hways leading o BCO o ma ion and help e ine
cu en bina y e olu ion models.
On he o he hand, ou esul s show ha he β-dependen s abili y c i e ion
p oduces mo e BSS han he Hu ley-Webbink model. As no ed by Leine and
Gelle (2021)5, ‘popula ion syn hesis assump ions d ama ically unde -p oduce
he numbe o BSS in old open clus e s. This sugges s ha adop ing mo e
ealis ic physically mo i a ed s abili y c i e ia may help add ess his disc epancy.
Conclusions
HW
BD
