Figure 2.4:The grav-itational wave spec-trum. Image from [27]
of approximately 36 and29 solar masses, with the final black hole having only a mass of approximately62solar masses. About3solar masses worth of energy were radiated in form of gravitational waves in this event, with a peak gravitational luminosity of 3.6×1049W.
The two aLIGO detectors are working in tandem with the European Virgo detector, with more gravitational wave observatories being planned to join in a global network of detectors [6], which promises an exciting future of ground based gravitational wave observations.
Indeed, within the first half year of observation, the LIGO-VIRGO collab-oration already detected three binary black hole mergers, followed by the detection of a binary neutron star merger and seven additional binary black hole mergers in the second observation run [7]. Including the latest catalogue of the first half of the third observation run [8], this collaboration reported a total of50individual detections.
2.4 gravitational wave spectrum
The Newtonian noiseis
caused by gravitational attraction of moving masses in the environment, for example due atmospheric variations.
growing network of ground based detectors are remarkable instruments, but they can only observe a limited part of the gravitational universe. In particular, they are severly limited at low frequencies, mainly due to the impact of seismic and newtonian noise.
However, it is exactly at these low frequencies were we expect a large catalogue of astrophysical GW sources [28]. This is not surprising, since the prime target for GW detection are binary systems of compact objects, most notably of black holes, neutron stars and white dwarfs. Due to the large mass and scale of
22 gravitational wave astronomy
these systems, they move comparatively slowly; consequently, their emitted GW radiation is also at low frequencies, especially while they are far away from their merger.
Figure2.4, provided by [27], shows an overview of the different sources we expect in different frequency ranges. We summarize here the main sources expected in some present and future GW observatories.
2.4.1 High frequency sources
Following [27], ground based interferometers such as aLIGO and Virgo cover only the very high part of the expected frequency spectrum, with GW periods of less than1second.
The main sources in that range are merging compact binaries, as those already observed by aLIGO and Virgo. The ground based observatories typically only see the very last few seconds of such a merger, when the two compact objects get close together, resulting in a large peak in amplitude as well as a shift to higher frequency.
Violent events such as supernovae also involve large mass redistributions, and could therefore also generate GW in this frequency range. As of the writing of this thesis, however, there have been no detections [4].
In addition to these transient signals, rapidly rotating neutron stars could gen-erate continous GW signals provided that they have some non-axisymmetric deformations. Even though the amplitude of these sources is expected to be much smaller than that of the transient signals, the fact that they are theorized to be stable over very long time scales allows statistical analysis of data from multiple observation runs. So far, no continous wave detection has been confirmed, but this might change when more data becomes available. See [31,80] for more information.
2.4.2 Mid frequency sources
Space-based observatories will be able to observe signals with GW periods ranging from seconds to hours. The most developed mission of this kind is LISA [10], planned to fly in the2030s, which aims to measure gravitational waves in the frequency band from 1×10−4Hz to 1 Hz.
Contrary to ground based detectors, which are mostly noise dominated with occasional loud transient sources, LISA will most likely be signal domi-nated.
Similar to ground based detectors, LISA will also be able to observe compact binaries such as those responsible for all direct detections up to date. However, we will be able to see them long before the merger, where the two components of the binary are still widely seperated on relatively stable orbits. This means that these sources will be present as quasi-monochromatic sources, which
2.4 gravitational wave spectrum 23 slowly increase in frequency as the binary radiates away its kinetic energy.
This could allow accurate predictions of the actual time and sky position of the merger, as described in [75], which both EM observatories and ground-based GW observatories could use as early warning to prepare for observation.
In addition to black hole and neutron star binaries, LISA will also be able to observe millions of white dwarf binaries in our own galaxy. EM observations already confirmed the existence of some of those white dwarf binary systems, which should produce continous GWs right in this frequency range. This will allow immediate verification of the measurement chain, since we know that these sources have to be in the data, with a predictable amplitude.
But not all of these will be resolvable as individual sources, such that we expect a stochastic gravitational wave background ever present in the signal.
This stochastic background might also have components which can be linked to a cosmological origin, and might give insight into the physics of the very young universe, shortly after the big bang.
Besides these stellar mass sources, LISA will also be able to observe merg-ers of supermassive black holes expected in the centmerg-ers of most galaxies, which are millions of times more massive than those visible in ground based observatories.
And a related class of signal are the so-called Extreme Mass Ratio Inspirals (EMRIs), which appear when a relatively small object, such as a stellar mass black hole, merges into a supermassive blackhole. These have a relatively complicated waveform, and allow a unique test of the predictions of GR.
In general, space based observatories such as LISA are projected to have some signals with very high signal to noise ratio. This will allow precision tests of the predictions made by GR, which could constrain the validity of alternative theories of gravity.
In addition, these GW observations can be used to get a completely indepen-dent estimate of the expansion rate of the universe.
2.4.3 Low frequency sources
We hinted in section2.3 that one of the primary challenges of constructing a light time GW detector is the requirement of having extremely stable clocks to measure fluctuations in the light travel time of the electromagnetic signals.
Pulsars are a special case of neutron stars from which we can observe peri-odical electromagnetic pulses with very high timing stability. Indeed, these pulses should be stable enough to in principle allow GW detection by ground based observation with radio telescopes. The actual measurement principle relies on measurements of the arrival time of pulses from multiple pulsars, which are then searched for correlations which can hint at the presence of a GW signal. Such a collection of observatories is called a Pulsar Timing Array (PTA), and is only sensitive to very low frequencies. Possible sources
24 gravitational wave astronomy
are for example super massive black hole binaries at the center of galax-ies, with orbital periods of months to years. See for example [13] for more information.
Finally, it is possible that GWs from the very early universe might have imprinted on the cosmic microwave background and could be discerned from EM observations of it. To date, this only lead to upper limits of such an effect, see e.g. [71] for more details.
T H E L A S E R I N T E R F E R O M E T E R S PA C E A N T E N N A
3
LISA is a large ESA mission, scheduled to fly in the mid2030s. It’s operating principle is similar to that of the ground based observatories, in that LISA also aims to detect gravitational waves using laser interferometry. However, there are some very significant design differences, and therefore unique technical challenges.
In this chapter, we give a brief overview of the LISA mission, with a particular emphasis on the technical details which are relevant to the research presented in this thesis.
In the following, we first describe the LISA constellation and orbits in sec-tion3.1. The orbital dynamics have important implications for the achievable laser noise reduction, which we discuss in section3.2. In addition, as we will discuss in section3.3, the large inter-spacecraft velocities require a heterodyne detection scheme, in which the on-board reference clocks become a significant performance limitation.
We then present an overview of the scientific payload in section3.4, describing the overall optical layout and the available interferometers on each satellite.
The main phase readout mechanism is then described in section3.5.
Finally, we describe further auxilliary functions related to the phasemeter and give an overview of the frequency distribution system in sections 3.6 and3.7.
3.1 the lisa constellation and orbits
LISA isn’t just a single Michelson interferometer, but consists of3 seperate spacecraft which all follow their individual orbits. The spacecraft exchange laser beams between them, tracking distance fluctuations to the level required for GW detection. The orbits are chosen in such a way that the overall constellation of the three spacecraft forms an almost equilateral triangle.
The iconic triangle configuration is achieved by positioning the three space-craft in a plane which is tilted by 60 degrees with respect to the ecliptic plane, with the center of mass of all3spacecraft trailing earth on its orbit by about20degrees, or roughly50million km [10], see fig.3.2. Each individual spacecraft is therefore on a slightly eccentric orbit, where it moves faster when close to the sun and slower when further away. The result is that the overall constellation performs a cartwheel motion around the sun, with the rotation direction of the spacecraft around their center of mass opposite to that of constellation as a whole, see fig.3.1.
25
26 the laser interferometer space antenna
Figure 3.1:The LISA orbits, from [10]. All three spacecraft fol-low their individual trajectory around the sun, such that the con-stellation as a whole performs a cart-wheel like motion.
Sun 1 AU
These kinds of orbits can be constructed for a wide range of spacecraft seperations [68]. As we saw in section 2.2, GWs create relative distance fluctuations, such that large armlengths are desirable, since they yield a stronger signal. However, this is only true up to a certain point: if the arms are too long with respect to the GW wavelength, multiple periods of the GW can partly cancel their effect during a single roundtrip time [10].
In addition, making the arms too long brings a number of technical challenges.
For example, even though the laser beams which leave the spacecraft are highly collimated, they will diverge during the propagation, such that only a fraction of the power will actually reach the far spacecraft. In the far field, the intensity of a gaussian laser beam in a given area evolves with the distance squared. Therefore, an increase in the arm length needs to be compensated by either larger telescopes, which would decrease the beam divergence while simultaneously increasing the reception area, or by using higher power lasers. Therefore, a tradeoff between technical challenges and ideal detector sensitivity must be found, balancing cost with scientific performance.
For LISA, the current baseline foresees arm lengths of 2.5×109m, which should allow fulfillment of all science objectives outlined in [10].