Analytic computation of the secular effects of encounters on a binary: features arising from second-order perturbation theory
Research output: Contribution to journal › Journal article › Research › peer-review
Standard
Analytic computation of the secular effects of encounters on a binary : features arising from second-order perturbation theory. / Hamers, Adrian S.; Samsing, Johan.
In: Monthly Notices of the Royal Astronomical Society, Vol. 487, No. 4, 25.06.2019, p. 5630-5648.Research output: Contribution to journal › Journal article › Research › peer-review
Harvard
APA
Vancouver
Author
Bibtex
}
RIS
TY - JOUR
T1 - Analytic computation of the secular effects of encounters on a binary
T2 - features arising from second-order perturbation theory
AU - Hamers, Adrian S.
AU - Samsing, Johan
PY - 2019/6/25
Y1 - 2019/6/25
N2 - Binary-single interactions play a crucial role in the evolution of dense stellar systems such as globular clusters. In addition, they are believed to drive black hole (BH) binary mergers in these systems. A subset of binary-single interactions are secular encounters, for which the third body approaches the binary on a relatively wide orbit, and such that it is justified to average the equations of motion over the binary's orbital phase. Previous works used first-order (FO) perturbation theory to compute the effects of such secular encounters on the binary. However, this approach can break down for highly eccentric binaries, which are important for BH binary mergers and gravitational wave sources. Here, we present an analytic computation using second-order perturbation techniques, valid to the quadrupole-order approximation. In our calculation, we take into account the instantaneous back reaction of the binary to the third body, and compute corrections to previous FO results. Using singly averaged and direct three-body integrations, we demonstrate the validity of our expressions. In particular, we show that the eccentricity change for highly eccentric binaries can reach a plateau, associated with a large inclination change, and can even reverse sign. These effects are not captured by previous FO results. We provide a simple script to conveniently evaluate our analytic expressions, including routines for numerical integration and verification.
AB - Binary-single interactions play a crucial role in the evolution of dense stellar systems such as globular clusters. In addition, they are believed to drive black hole (BH) binary mergers in these systems. A subset of binary-single interactions are secular encounters, for which the third body approaches the binary on a relatively wide orbit, and such that it is justified to average the equations of motion over the binary's orbital phase. Previous works used first-order (FO) perturbation theory to compute the effects of such secular encounters on the binary. However, this approach can break down for highly eccentric binaries, which are important for BH binary mergers and gravitational wave sources. Here, we present an analytic computation using second-order perturbation techniques, valid to the quadrupole-order approximation. In our calculation, we take into account the instantaneous back reaction of the binary to the third body, and compute corrections to previous FO results. Using singly averaged and direct three-body integrations, we demonstrate the validity of our expressions. In particular, we show that the eccentricity change for highly eccentric binaries can reach a plateau, associated with a large inclination change, and can even reverse sign. These effects are not captured by previous FO results. We provide a simple script to conveniently evaluate our analytic expressions, including routines for numerical integration and verification.
KW - celestial mechanics
KW - globular clusters: general
KW - gravitation
KW - stars: kinematics and dynamics
UR - http://www.scopus.com/inward/record.url?scp=85070105297&partnerID=8YFLogxK
U2 - 10.1093/mnras/stz1646
DO - 10.1093/mnras/stz1646
M3 - Journal article
AN - SCOPUS:85070105297
VL - 487
SP - 5630
EP - 5648
JO - Royal Astronomical Society. Monthly Notices
JF - Royal Astronomical Society. Monthly Notices
SN - 0035-8711
IS - 4
ER -
ID: 236270822