BBH Spectrocopy

Slide1: 

An inspiralling binary emits most of its radiation at twice the orbital frequency, producing a spectrum as shown in the diagram below at the left. However, the radiation comes off at other frequencies too giving a very rich structure to the emitted spectrum of the signal as shown in the diagram below on the right. Binary black hole spectrum A black hole disturbed from its equilibrium will ring like a bell that is struck with a hammer. A vibrating black hole would emit gravitational waves in the form of a family of normal modes. These normal modes are damped sinusoids whose frequencies and decay times depend on the mass and spin of the black hole. Observing black hole normal modes will make it possible to test Einstein’s gravity and its alternatives. The space based LISA detector will enable some of the most stringent tests ever. Black hole normal modes The presence of harmonics has two implications: 1. Higher harmonics can help observe more massive binaries than was possible before (below left). 2. The rich signal structure due to the presence of harmonics will enable a very accurate measurement of the source’s parameters – masses, spins, coalescence time, etc. (below middle and right). By measuring the parameters more accurately it will be possible to put Einstein’s gravity to more stringent tests than was thought possible before. Binary black hole spectroscopy Higher signal harmonics will help LISA to observe the more commonly found super-massive black hole binaries of 100’s of million solar masses. They will also help to pin point the position of a super-massive black hole binary to a good enough accuracy so as to uniquely identify the host galaxy or galaxy cluster and measure its red-shift. Cosmology and fundamental physics with LISA Since black hole binaries are standard candles, knowing their red-shift means that we will be able to establish a new cosmic distance scale avoiding all the lower rungs of the cosmic distance ladder and thereby learn about the nature of dark energy and dark matter. In the diagram above, blue and black curves are for higher harmonics while red and pink curves are for a signal using only the dominant harmonic. The increase in mass range is clearly demonstrated. The diagram on the left shows the spectrum (power as a function of frequency) of an inspiral signal consisting only of the dominant harmonic at twice the orbital frequency. In this case the signal at any one time contains only one frequency and hence the spectrum is more or less smooth. On the right is the spectrum of a signal that contains up to seven harmonics. Constructive and destructive interferences between the various terms is responsible for the rich structure seen in the spectrum on the right.