Survey of LISA Science

    Table of Contents

    In the following a brief survey of the key scientific measurements that LISA will perform is given. These measurements address the basic scientific goals of the LISA mission, which are captured formally in the LISA Science Objectives. The scientific background for the LISA science measurements and objectives is discussed extensively in the Science Case Document, from which this text is adapted.

    LISA records the inspirals and mergers of binary black holes, the most powerful transformations of energy in the Universe, allowing precision measurements of systems composed only of pure dynamical spacetime.

    The strongest gravitational waves are generated by systems with the largest gravitational fields GM/R, hence large masses and small sizes. The strongest of all are generated by interactions of black holes, dense knots of pure spacetime energy with GM/(Rc2)≈1. At LISA frequencies the strongest sources are massive black hole binaries with about 104 to 107 times the mass of the Sun. Two black holes orbit each other, spiral together as they lose energy by radiation, and finally merge. The waves from these events — many cycles over a long inspiral, climaxing in a brief series of powerful waves during a violent merger, and a final ringdown to a quiescent single black hole — record dynamical general relativity not only in its purest form but also in its most violent, nonlinear behavior: a maximally warped vacuum spacetime interacting with itself.

    The black hole binaries start with wide orbits at low frequencies. As they lose energy their frequency increases and their radiation strengthens. A typical source enters the LISA band a year or more before the final merger so many orbits are recorded, encoding details of the system properties and behavior, position on the sky, and absolute distance. The coherent phase and polarization information obtained over LISA's solar-orbit baseline (and variable inclination) can often pinpoint where a source is in the sky to better than a degree. In the last hours or minutes the signal-to-noise ratio grows very high, often into the hundreds to thousands depending on distance. At its peak luminosity, around the moment of merger, a black hole binary is the most extreme transformation of mass-energy of any kind in the Universe, radiating a power 10-3c5/G (or ~1049 watts), in a few wave cycles, for a time of about 100 GM/c3. This peak radiated power is about 1000 times more than all the stars in the visible Universe. The merger throes of a million solar mass binary black hole merger last about 500 seconds. Massive black hole binary inspiral and merger events are such powerful radiators that LISA can detect them anywhere, out to the largest redshifts where galaxies might exist.

    The detailed study of waveforms from black hole binaries provides a rich testbed for general relativity. Recent breakthroughs now allow numerical computation of Einstein's field equations throughout the entire inspiral and merger event, yielding a detailed map of the predicted gravitational waveform that will be the first detailed test of dynamical, strong-field general relativity. Waveforms coherently correlated over many orbits (from approximately 10 to about 1000 depending on mass and redshift) recorded in the LISA signal stream, and detection of events with a signal to noise of a thousand or more, allow precise tests of the theory as well as precise measurements of system parameters to a precision of order 10-2 to 10-3. Comparison with the computed details of the inspiral and merger waveform will provide a powerful test of the binary black hole model assumed for these systems.

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    LISA will map isolated black holes with high precision, verifying whether they are the stationary "no hair" spacetime configurations described by the Kerr metric, completely specified by four numbers: the mass and three components of spin.

    In general relativity the final isolated spinning black hole is described mathematically as a particular, precisely specified spacetime shape called a Kerr metric, that depends only on the physics of gravity and not at all on the history or environment of the black hole. Comparison of the ringdown waveform with theory can verify that the final black hole which arises from a merger is indeed described by the Kerr solution, and satisfies the "no hair" theorem of general relativity that states that an isolated, stationary black hole is completely specified by its mass, charge and angular momentum. The LISA signals during the merger phase are so strong that the signal-to-noise ratio is often greater than 100 even in one oscillation cycle: signal waveforms are visible on an oscilloscope type display of raw data even to the naked eye, so even if general relativity were to be wrong at the levels allowed by our existing tests (e.g. the double binary pulsar J07037-3039) we would be able to use LISA data to make sense of what is happening.

    LISA also uses a second type of source to explore the spacetime near a massive black hole. Driven by chance encounters, a much smaller mass compact objects — such as a degenerate dwarf, neutron star or stellar-mass black hole — sometimes finds itself captured by the massive black hole, after which it orbits many times until it finally plunges into the horizon and disappears. The gravitational waves from these extreme mass ratio inspirals (EMRIs) encode a detailed map of a relatively unperturbed massive black hole, predicted to be a pure Kerr knot of highly curved, spinning spacetime. About 105 wave cycles are measured for each source, emitted from orbital paths exploring deep into different parts of the relativistic region near the massive black hole. The specific mass quadrupole and higher moments predicted by the Kerr solution are measured with a precision of about 10-4, and precision tests of small variations about the equilibrium Kerr solution — the small amounts of "hair" added by the perturbing object — are measured at the one percent level. Gravitational waves from these events map in exquisite detail the cleanest and most accurately predicted structures in all of astrophysics, whose mathematical elegance Chandrasekhar once likened to that of atoms.

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    LISA directly observes how massive black holes form, grow, and interact over the entire history of galaxy formation.

    Optical, radio and x-ray astronomy have produced abundant evidence that nearly all galaxies have massive black holes in their central nuclei (and indeed that some recently merged galaxies even have two black holes). These nuclear black holes have a profound effect on galaxy formation; the influence of black hole powered jets on the intergalactic gas out of which galaxies form is in some cases directly observed. There is a circumstantial case, but no direct evidence, that the formation of this population of black holes was associated with a multistage process of binary inspiral and merger, together with accretion. LISA will obtain direct and conclusive evidence and study details of this process via gravitational radiation.

    In standard concordance cosmology, the first massive black holes naturally arise from the very first, supermassive stars. In this scenario, black hole binaries begin to form from a high redshift, z ≈ 20, when galaxies start to assemble by a series of (hundreds to thousands of) hierarchical mergers of smaller protogalaxies. When two galaxies merge into one, their central black holes sink to the center of the new galaxy, find each other, inspiral and merge. There are so many galaxies forming in the Universe observed by LISA that mergers happen quite frequently: estimates based on standard galaxy formation theory suggest that if black holes indeed grew by hierarchical merging, LISA detects a merger event about once or twice every week on average, from a wide range of redshifts extending back to massive binaries in early protogalaxies at z ≈ 15. At any given time, in addition to the actual mergers, these models predict that LISA observes inspiral signals from hundreds of binaries in the final years before their merger. LISA digs directly and intimately into the detailed evolution of galactic nuclei: the large sample of binaries provides a direct record of the whole history of galaxy formation in the observable Universe, and of the processes that grew their central black holes and shaped their nuclei.

    In addition to mergers of massive black holes, LISA will also observe the inspiral of stellar mass black holes into the massive black holes in the centers of normal galaxies. These are the extreme mass ratio inspiral events (EMRIs) mentioned earlier. The parameters measured from extreme mass ratio events yield a census of isolated massive black hole spins and masses in many galaxies today, a revealing relic of black hole history. The local universe also produces observable inspirals of less compact stars and stellar remnants that probe the rich astrophysics near the massive central black holes as they consume piecemeal the various stellar populations in their vicinity.

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    LISA measures precise, gravitationally-calibrated absolute luminosity distances to high redshift, with the potential of contributing uniquely to measurement of the Hubble constant and dark energy.

    Because the inspiral leading up to the merger is a clean, pure vacuum spacetime system of two black holes, properties of the radiation can be computed exactly in general relativity, so that the black hole masses, spins, orientations and even the exact distance can be reconstructed from LISA data. (Roughly speaking, the final wave cycle period tells the final absolute Schwarzschild radius, and the ratio of that length to the distance is the metric strain, h.) These inspiral distances are both individually precise and absolutely calibrated, using only pure gravitational physics, and they cover a wide range of redshift. In the absence of lensing effects the absolute physical luminosity distance to a single LISA inspiral event is typically estimated from the waveform alone with on the order of one percent precision, and in some cases with as good as 0.1% precision. If identification of the host galaxy1 allows an independent redshift determination, the redshift-distance relation is also measured with high precision. Black hole binaries thus represent a unique and independent new capability for precision cosmology that complements other techniques. Even a small number of sources at moderate redshift calibrates the distance scale and Hubble constant an order of magnitude better than any current method — a powerful constraint on dark energy models in combination with microwave background data. The expected large sample of high redshift inspiral events may lead to measurements of dark energy parameters comparable in precision to other methods, but with independent calibration and completely different systematic errors. The main source of error, especially at high redshift, is the noise induced by cosmic weak gravitational lensing along the line of sight, but in a statistical sample this is controllable, and indeed provides unique new information about the nature and clustering of dark matter over time.

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    LISA studies in detail thousands of compact binary stars in the Galaxy, providing a new window into matter at the extreme endpoints of stellar evolution.

    In addition to mergers and meals of distant black holes, LISA detects many lower mass binary systems in our galaxy, mostly very compact remnants of normal stars, called white dwarfs. Very soon after turning on, LISA will quickly detect a handful of nearby binary compact stars already studied and named. These "verification binaries" provide sources with known positions and periods ensuring particular, predictable LISA signals. Signals are also certain to appear from populations in our galaxy of numerous and various remnants, including white dwarfs and neutron stars, which are known to exist from some that emit electro- magnetically. Simple extrapolation of known nearby samples to the whole Galaxy predicts that LISA will detect thousands of binaries. The most compact binaries (those at high frequency) will be measured in detail as individual sources from across the Galaxy, while at lower frequencies only the nearby ones will be indi- vidually distinguished; millions of others from across the Galaxy will blend together into a confusion background. LISA provides distances and detailed orbital and mass parameters for hundreds of the most compact binaries, a rich trove of information for detailed mapping and reconstruction of the history of stars in our galaxy, and a source of information about tidal and other non-gravitational influences on orbits associated with the internal physics of the compact remnants themselves. LISA may also detect at high frequencies the background signal from compact binaries in all the other galaxies.

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    LISA may find entirely new phenomena of nature not detected using light or other particles.

    Given that all forms of mass and energy couple to gravity, other sources of gravitational waves may exist that are not known from extrapolating current electromagnetic observations. LISA's frequency band can indeed be extrapolated to very high redshift where we do not yet have any direct observations, and to a regime where LISA itself will be our first information of any kind about the nonlinear behavior and motion of matter. For example, the LISA frequency band in the relativistic early Universe corresponds to horizon scales at the Terascale frontier, where phase transitions of new forces of nature or extra dimensions of space may have caused catastrophic, explosive bubble growth and efficient gravitational wave production. LISA is capable of detecting a stochastic background from such events from about 100 GeV to about 1000 TeV, if gravitational waves in the LISA band were produced with an overall efficiency more than about 10-7, a typical estimate from a moderately strong relativistic first-order phase transition. This corresponds to times about 3×10-18 to 3×10-10 seconds after the start of the Big Bang, a period not directly accessible with any other technique. Reaching much further still beyond the range of any particle accelerator, LISA also deeply probes possible new forms of energy such as cosmic superstrings, relics of the early Universe predicted in some versions of string theory, that are invisible in all ways except by the gravitational waves they emit. In principle, their signature could provide direct evidence for new ideas unifying all forms of mass and energy, and possibly even spacetime itself.

    Footnotes

    1 LISA's waveform fitting can often pinpoint the direction of a source to much better than a degree, and the distance estimate also narrows the redshift range considerably; nevertheless there may be many thousands of galaxies in the LISA "error box" for a given source. Models suggest that the host may be identified from a telltale nuclear starburst associated with the merger, or from variability associated with the disrupted disks around the merging holes, but galaxy nuclei are too little understood to make a firm prediction. Study of LISA electromagnetic counterparts may provide an exploratory bonanza for wide field synoptic imaging and spectroscopy across the electromagnetic spectrum, but it is also possible that identification of hosts will prove elusive. Back

    Oliver Jennrich, 06 Feb 2007