Talk given at the European Week of Astronomy and Space Science (EWASS) 2018 The LIGO/Virgo observatories recently detected gravitational waves (GWs) from black hole (BH) mergers. Although BH binaries seem to be abundant in the Universe, it is still in debate how to form binaries that can merge in less than the age of the Universe. We discuss a new formation mechanism of BH mergers. The tidal disruption of stellar binaries by a massive BH is well known to produce hypervelocity stars. However, such tidal encounter with a massive BH does not always lead to the break-up of binaries. Numerical simulations show that 10 percent of binaries survive even for very close encounters. We show that they tend to become hard and eccentric. Since the GW merger time of binaries is sensitive to the semi-major axis length and eccentricity, we find that this leads to a reduction of the merger time by several orders of magnitude in some cases. Therefore, tidal encounters of stellar mass BH binaries with a massive BH at the centre of galaxies or in dense star clusters can provide a new formation channel of BH mergers. We have evaluated how the effective spin parameter of BH binaries changes at the tidal encounter, and we found that post-encounter binaries could rotate in opposite direction in some cases (i.e. negative effective spin parameters). The distribution of the effective spin parameter is evaluated by using Monte Carlo calculations, and the results are compared with the LIGO/Virgo observations and the distributions expected from other models.

1. Black Hole Mergers induced by tidal encounters
with a Galactic Centre Black Hole
Joseph Fernandez & Shiho Kobayashi

2. -Where do they come from?
-Need more observations!
-Dynamical vs isolated evolution
Image credit: LIGO/Caltech/Sonoma State (Aurore Simonnet)

3. Galaxies present dense environments:
Globular clusters Galactic centre
How do we make black hole binaries merge?
Globular clusters
- Make them hard → tighter orbits
- Make them eccentric
Images credit: ESA/Hubble & NASA; NASA/CXC/Univ. of Wisconsin/Y.Bai, et al.

4. Galactic centre:
tidal encounters
- Massive black hole → deep potential well,
extreme physics

5. Galactic centre:
tidal encounters
- Massive black hole → deep potential well,
extreme physics
What if a compact binary has a close encounter with
the MBH?
Disruption Survival: modified orbital
parameters
10% survive even for very close encounters

6. Galactic centre:
tidal encounters
- Massive black hole → deep potential well,
extreme physics
Survival: modified orbital
parameters
- Can tidal encounters of binaries with the MBH
lead to GW mergers?
- What are the peculiar features of this mechanism?

7. Survival → modified orbital parameters
Tidal encounter dynamics: restricted parabolic three-body problem
· Key assumption: M >> m → simplify EoM
· Initially circular binaries
· Monte Carlo simulations:
- Uniformly distributed orientation and phase
- Two D-distributions, uniform and p(D)~ D
· Non-relativistic calculations: BH spins constant
Penetration factor → Orientation →

8. Survival → modified orbital parameters
Tidal encounter dynamics: restricted parabolic three-body problem
· Key assumption: M >> m → simplify EoM
· Initially circular binaries
· Monte Carlo simulations:
- Uniformly distributed orientation and phase
- Two D-distributions, uniform and p(D)~ D
· Non-relativistic calculations: BH spins constant
We need to recover post-encounter semi-major
axes, eccentricities and effective spins.
Penetration factor → Orientation →

9. Survival → modified orbital parameters
Tidal encounter dynamics: restricted parabolic three-body problem

10. Can tidal encounters of binaries with the MBH lead to GW mergers?

11. Factor of >10² faster!
Factor of >10 faster!⁵
Can tidal encounters of binaries with the MBH lead to GW mergers?

12. How can we distinguish this mechanism from others?

13. How can we distinguish this mechanism from others?
5 -9 % with χeff
< 0
> 10 % with 0< χeff
< 0.5

14. Rs
→ event horizon scale of MBH (~ 10 Pc)⁻⁷
1.7 % merge
within 10 R⁶ s
There is more:
- Some of the binaries will merge close to the MBH
~ 5 % merge within 1 pc

15. There is more:
- These are very eccentric → follow multi-waveband
gravitational wave astronomy
1.69 % merge
within 10 R⁶ s

16. There is more:
- These are very eccentric → follow multi-waveband
gravitational wave astronomy
1.69 % merge
within 10 R⁶ s

17. Conclusions:
- Tidal encounters of black hole binaries with massive black holes
can induce BH merger events.
- The process can yield χeff
< 0 in ~10% of cases→ tell-tale sign
- Multi-waveband gravitational wave astronomy (>90% with
eccentricities detectable by LISA, ~7% by LIGO)!!
-We still do not know
where they come
from!

18. Conclusions:
The galactic centre should be very noisy
in GWs! → a gravitational brass band!
More detailed modeling required!