**Inspiralling black-hole binaries**

Binary systems consisting of black holes can be produced in a variety of astrophysical scenarios. Such systems are strong sources of gravitational radiation. The binary loses energy and angular momentum through the emission of gravitational radiation and starts to spiral in. Binary black holes are among the most promising sources for the first detection of gravitational waves.

The movie on the left panel shows the orbital tracks of two black holes (each having a mass of 10 solar masses) during the last second of their inspiral. The movie on the right panel shows the “plus” polarization of the gravitational-wave signal observed by a detector placed at a distance of 1 million parsecs from the binary. The dynamics as well as the gravitational-wave signals have been computed using the “post-Newtonian” approximation to General Relativity. This approximation breaks down before the two black holes merge into each other. The movie has been artificially slowed down by a factor of 40.

Download the movies

In this movie, the black holes have unequal masses (one has 4 solar masses while the other has 16 solar masses). Note that the more massive black hole is closer to the center of mass (the origin of the coordinate system). The energy radiated by the binary (and hence the amplitude of the gravitational-wave signals) is lower than an equal-mass binary. Thus the binary spends takes more time to inspiral, starting from a given separation.

Astrophysical black holes can be have very high spins (rotation around a certain axis). According to General Relativity, any spinning object will drag the spacetime around it. In the case of rapidly spinning black holes this effect can be quite dramatic. The spin of a black hole can interact with the orbital angular momentum of the binary and also with the spin of its companion, hence affecting the dynamics of the binary and the emitted gravitational-wave signal.

In this movie, the spin vectors (shown by red/blue arrows) are aligned with the orbital angular momentum of the binary. (Orbital angular momentum points perpendicular to the plane of the binary). As a result, the black holes can inspiral to much closer separations, thus resulting in a significantly long (and stronger) gravitational-wave signal, as compared to a non-spinning binary. This effect is called the “orbital hang-up”.

In this movie, the spins are aligned opposite to the orbital angular momentum. As a result, the binary can not inspiral to very close separations (as compared to a non-spinning binary), thus resulting in a significantly short (and weaker) gravitational-wave signal, as compared to a non-spinning binary.

In this movie the spins are misaligned with the orbital angular momentum. If the spins are misaligned, then the interaction between the spins and orbital angular momentum (General Relativistic “spin-orbit” and “spin-spin” coupling) will cause the spins to precess, like a spinning top. This will cause the precession of the orbital angular momentum (or, the orbital plane) also. Since gravitational radiation is predominantly beamed along the direction of the orbital angular momentum, a fixed detector in space will see complicated modulations in the amplitude and phase of the arrived gravitational-wave signals. The amplitude of the observed gravitational-wave signal will be the maximum when the binary is “face-on” to the observer, while the amplitude is the minimum when the binary is “edge-on”.

The dynamics and the gravitational waves from the binary are calculated in the post-Newtonian approximation to General Relativity. The particular post-Newtonian approximant used for these calculations are described in the Sec. III of P. Ajith, Phys. Rev. D 84, 084037 (2011). For a review of the post-Newtonian approximation to General Relativity, see L. Blanchet, Living Rev. Relativity 9 (2006), 4.

# Non-spinning,equal-mass black holes

The movie on the left panel shows the orbital tracks of two black holes (each having a mass of 10 solar masses) during the last second of their inspiral. The movie on the right panel shows the “plus” polarization of the gravitational-wave signal observed by a detector placed at a distance of 1 million parsecs from the binary. The dynamics as well as the gravitational-wave signals have been computed using the “post-Newtonian” approximation to General Relativity. This approximation breaks down before the two black holes merge into each other. The movie has been artificially slowed down by a factor of 40.

Download the movies

# Non-spinning, unequal-mass black holes

In this movie, the black holes have unequal masses (one has 4 solar masses while the other has 16 solar masses). Note that the more massive black hole is closer to the center of mass (the origin of the coordinate system). The energy radiated by the binary (and hence the amplitude of the gravitational-wave signals) is lower than an equal-mass binary. Thus the binary spends takes more time to inspiral, starting from a given separation.

# Black holes with aligned-spins

Astrophysical black holes can be have very high spins (rotation around a certain axis). According to General Relativity, any spinning object will drag the spacetime around it. In the case of rapidly spinning black holes this effect can be quite dramatic. The spin of a black hole can interact with the orbital angular momentum of the binary and also with the spin of its companion, hence affecting the dynamics of the binary and the emitted gravitational-wave signal.

In this movie, the spin vectors (shown by red/blue arrows) are aligned with the orbital angular momentum of the binary. (Orbital angular momentum points perpendicular to the plane of the binary). As a result, the black holes can inspiral to much closer separations, thus resulting in a significantly long (and stronger) gravitational-wave signal, as compared to a non-spinning binary. This effect is called the “orbital hang-up”.

# Black holes with anti-aligned spins

In this movie, the spins are aligned opposite to the orbital angular momentum. As a result, the binary can not inspiral to very close separations (as compared to a non-spinning binary), thus resulting in a significantly short (and weaker) gravitational-wave signal, as compared to a non-spinning binary.

# Black holes with misaligned spins

In this movie the spins are misaligned with the orbital angular momentum. If the spins are misaligned, then the interaction between the spins and orbital angular momentum (General Relativistic “spin-orbit” and “spin-spin” coupling) will cause the spins to precess, like a spinning top. This will cause the precession of the orbital angular momentum (or, the orbital plane) also. Since gravitational radiation is predominantly beamed along the direction of the orbital angular momentum, a fixed detector in space will see complicated modulations in the amplitude and phase of the arrived gravitational-wave signals. The amplitude of the observed gravitational-wave signal will be the maximum when the binary is “face-on” to the observer, while the amplitude is the minimum when the binary is “edge-on”.

The dynamics and the gravitational waves from the binary are calculated in the post-Newtonian approximation to General Relativity. The particular post-Newtonian approximant used for these calculations are described in the Sec. III of P. Ajith, Phys. Rev. D 84, 084037 (2011). For a review of the post-Newtonian approximation to General Relativity, see L. Blanchet, Living Rev. Relativity 9 (2006), 4.

*Credits: Ankit Singh / P. Ajith / ICTS. This work was supported by a summer research fellowship from the Indian Academy of Sciences.*