## The space-based gravitational wave detector LISA

graphic (c) by NASA

The ESA/NASA collaborative space mission LISA (Laser Interferometer Space Antenna), which is planned to be launched 2018, aims to detect gravitational waves in the frequency range from 0.1 to 100 millihertz, a frequency band where the universe produce is richly populated in strong and periodic sources. This band is not accessible by ground-based gravitational wave detectors (e.g. LIGO Laser Interferometer Gravitational-wave Observatory or GEO600) utilizing laser interferometry due the gravity-gradient noise and arm-lengths limited to few kilometers. The main sources of gravitational radiation in the LISA frequency band are the galactic binaries and the massive black holes as shown in the figure below.

graphic (c) by LISA Science Case LISA-LIST-RP-436 Version 1.0

## Gravitational Waves

In Newton's theory of gravity there is no speed-limit for the gravitational interaction between two bodies. The gravity is a force that instantaneously interacts. In this theory gravitational waves do not exist.

Laplace predicts in 1805 that the angular momentum of a binary star system must slowly decrease with time if the gravitation propagates with finite speed.

100 years later in Einstein's Special Relativity the speed for all interactions is limited to the speed of light

*c*, and 1915/16 the General Relativity describes the gravitational acceleration by the curvature of the spacetime. Since then it's clear that the asymmetric motions of mass produce propagating vibrations, the gravitational waves, that travel through spacetime at speed of light. In the 1970's Hulse and Taylor measured the decreasing of the angular momentum of the binary pulsar PSR1913+16. This was the first indirect proof of the existence of gravitational waves and the both scientists were awarded the Nobel prize in 1993. Gravitational waves have never been directly detected up to this day.

_{0}## Laser Interferometer Space Antenna

Gravitational waves with the amplitude

*h*stretches and shrinks the proper distance between two free flying bodies by:

That means if a gravitational waves (

*h*~ 10

^{-22}) passes, the distance between earth and moon will change about approx 20 x 10

^{-15}m. This example explains why interferometric detectors should be made large.

graphic (c) by LISA Prephase A report (1998)

LISA comprises three identical satellites which form an equilateral triangle in space with an arm-length of approx 5 million km. The formation will fly in a heliocentric Earth-trailing orbit approximately 20° behind the Earth (cf. figure above). Any two arms of this triangle represent a Michelson-type interferometer. Gravitational waves deform spacetime and can be detected as a change in the length of the interferometer arms where in case of LISA a ~ 10 pm/Hz

^{1/2}sensitivity is needed. The current baseline design, the so-called "strap-down architecture", is shown in the figure below. Here, the displacement measurement between the distant spacecraft is split into three independent measurements: (i) one interferometer measuring changes in distance between a free flying proof mass and its associated optical bench on one spacecraft (cf.

*d*in figure below), (ii) one interferometer measuring changes in distance between two optical benches on two distant spacecraft (

_{1}*d*) and (iii) one interferometer measuring changes in distance between a free flying proof mass and its associated optical bench on the other spacecraft (

_{12}*d*). The main advantage is the technically and functionally decoupling of the proof mass assembly from the inter-spacecraft interferometry. In this concept, the distance between optical bench and its related proof mass has to be measured with the same sensitivity as in the interferometric measurements between the spacecraft: ~ 5 pm/Hz

_{2}^{1/2}for the translation measurement (for frequencies above 2.8 mHz with an f

^{-2}relaxation down to 0.03 mHz) and >20 nrad/Hz

^{1/2}for the tilt measurement (for frequencies above 0.1 mHz with an f

^{-1}relaxation down to 0.03 mHz).

graphic (c) by EADS-Astrium, LISA Mission Formulation