Fakultäten » Mathematisch-naturwissenschaftliche Fakultät » Physik-Institut » Prof. Dr. Philippe Jetzer » Jetzer

Completed research project

Title / Titel Gravitational waves and LISA (2010)
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Summary / Zusammenfassung On the 1/c expansion of f(R) gravity (Ph. Jetzer, J. Naf) We studied f(R){theories, for which the Einstein{Hilbert action of GR is replaced by a nonlinear function f of the Ricci scalar R. We derived [5] for applications to isolated systems - on the scale of the Solar System - the rst relativistic terms in the 1=c expansion of the space time metric g for metric f(R) gravity theories, where f is assumed to be analytic at R = 0. For our purpose it suces to take into account up to quadratic terms in the expansion of f(R), thus we can approximate f(R) = R + aR2 with a positive dimensional parameter a. In the non-relativistic limit, we get an additional Yukawa correction with coupling strength G=3 and Compton wave length p 6a to the Newtonian potential. As an application, we derived to the same order the correction to the geodetic precession of a gyroscope in a gravitational eld and the precession of binary pulsars. The result of the Gravity Probe B experiment yields the limit a < 5  1011 m2, whereas for the pulsar B in the PSR J0737-3039 system we get a bound which is about 104 times larger. On the other hand the Eot-Wash experiment provides the best laboratory bound a < 10􀀀10 m2. Although the former bounds from geodesic precession are much larger than the laboratory ones, they are still meaningful in the case some type of chameleon e ect is present and thus the e ective values could be di erent at di erent length scales.

Gravitational radiation in f(R) gravity (Ph. Jetzer, J. Naf) 6 Since the discovery of the PSR 1913+16 system by Hulse and Taylor in 1974, binary pulsars have become an important laboratory for testing gravity theories. In particular the PSR J0737-3039 system detected in 2003 o ers unequaled opportunities to constrain extensions of GR. Among such theories we consider so{called f(R) theories, for which the Einstein{Hilbert action of GR is replaced by a nonlinear function f of the Ricci scalar R. For such theories, still an open problem is the calculation of the energy loss of a binary pulsar system by radiation of gravitational waves in the linearised theory. If we assume f to be analytic at R = 0, for this application it suces to consider functions of the form f(R) = R+aR2. We make use of the analogy of f(R) theories with scalar tensor theories, which in contrast to GR feature an additional scalar degree of freedom. Unlike GR, where the leading order gravitational radiation is produced by quadrupole moments, the presence of an additional degree of freedom implies gravitational radiation of all multipoles, in particular monopoles and dipoles. Whereas this is the case for almost every alternative gravity theory, in one point the theory described above considerably di ers from other theories, for which the gravitational radiation has already been evaluated. Since the scalar eld  is massive, it gives rise to a Yukawa correction in the non{relativistic limit, and for the same reason the dynamical part of  satis es a Klein{Gordon equation rather than a wave equation. Thus the computation of the gravitational radiation gets more involved.

Parameter estimation for coalescing massive binary black holes with LISA including e ects due to the eccentricity of the orbits (Ph. Jetzer, A. Klein, M. Sereno) Our paper on the parameter estimation for coalescing massive binary black holes with LISA using the full 2PN gravitational waveform and spin-orbit precession has appeared [6]. Its result have already been presented at two conferences on gravitational waves and LISA. Furthermore, we computed the spin-orbit and spin-spin couplings needed for an accurate computation of the phasing of gravitational waves emitted by comparable-mass binaries on eccentric orbits at the second post-Newtonian (PN) order. We used a quasi-Keplerian parametrization of the orbit free of divergences in the zero eccentricity limit. We found that spin-spin couplings induce a residual eccentricity for coalescing binaries at 2PN, of the order of 10􀀀4-10􀀀3 for supermassive black hole binaries in the LISA band. Spin-orbit precession also induces a non-trivial pattern in the evolution of the eccentricity, which could help to reduce the errors on the determination of the eccentricity and spins in a gravitational wave measurement. These results have been published in [7]. We are now working on implementing these results on the eccentricity in our code in order to estimate their in uence on the parameter estimation for coalescing massive black holes with LISA. We are also, in the framework of a master thesis (by C. Huwyler), studying the impact of alternative GR theories on the parameter estimation. 7

Lensing of gravitational waves (Ph. Jetzer, M. Sereno) We performed a preliminary study of strong gravitational lensing of gravitational waves from merging of massive black hole binaries in the context of the LISA mission. Even only one detection of a multiple event would provide invaluable information on competing theories of gravity, evolution and formation of structures and, should observations in optical (or other) bands be available, it would allow a direct determination of the Hubble constant and other cosmological parameters. The main bulk of the optical depth for lensing should be provided by intervening massive galactic halos, for which wave optics e ects are usually negligible in the LISA band. Lensing probabilities might be sizeable for the two main scenarios for black hole formation, namely, one where seeds are light (with at least a 30 􀀀 50% chance to observe one or more multiple events with a signal to noise ratio  8 in a 5-year mission) and one where seeds are heavy (20 􀀀 30%). For some hybrid formation models, up to 2􀀀4 events are expected. For a light seed scenario, some intrinsically too faint signals ( 3% of the total unlensed detections) are brought over threshold by lensing ampli cation, enhancing thus the total number of observations.

Gravitational waves from intermediate-mass black holes in young clus- ters (Ph. Jetzer) Massive young clusters (YCs) are expected to host intermediate-mass black holes (IMBHs) born via runaway collapse. These IMBHs are likely in binaries and can undergo mergers with other compact objects, such as stellar mass black holes (BHs) and neutron stars (NSs). We derived the frequency of such mergers starting from information available in the Local Universe. Mergers of IMBH-NS and IMBH-BH binaries are sources of gravitational waves (GWs), which might allow us to reveal the presence of IMBHs. We thus examined their detectability by current and future GW observatories, both ground- and space-based [8]. In particular, as representative of di erent classes of instruments we consider Initial and Advanced LIGO, the Einstein gravitational-wave Telescope (ET) and the Laser Interferometer Space Antenna (LISA). We nd that IMBH mergers are unlikely to be detected with instruments operating at the current sensitivity (Initial LIGO). LISA detections are disfavoured by the mass range of IMBH-NS and IMBH-BH binaries: less than one event per year is expected to be observed by such instrument. Advanced LIGO is expected to observe a few merger events involving IMBH binaries in a 1-year long observation. Advanced LIGO is particularly suited for mergers of relatively light IMBHs (100 M ) with stellar mass BHs. The number of mergers detectable with ET is much larger: tens (hundreds) of IMBH-NS (IMBH-BH) mergers might be observed per year, according to the runaway collapse scenario for the formation of IMBHs. We note that our 8 results are a ected by large uncertainties, produced by poor observational constraints on many of the physical processes involved in this study, such as the evolution of the YC density with redshift.

Small disturbances at low frequencies in the LISA band (Ph. Jetzer, M. Sereno) The analysis of non-radiative sources of static or time-dependent gravitational elds in the Solar System is crucial to accurately estimate the free-fall orbits of the LISA space mission. In particular, we take into account the gravitational e ects of Interplanetary Dust (ID) on the spacecraft trajectories. The perturbing gravitational eld has been calculated for some ID density distributions that t the observed zodiacal light. Then we integrated the Gauss planetary equations to get the deviations from the LISA keplerian orbits around the Sun. This analysis can be eventually extended to Local Dark Matter (LDM), as gravitational elds are expected to be similar for ID and LDM distributions. Under some strong assumptions on the displacement noise at very low frequency, the Doppler data collected during the whole LISA mission could provide upper limits on ID and LDM densities [9]. Further, we calculated the e ect of the Earth-Moon (EM) system on the free-fall motion of LISA test masses [10]. We showed that the periodic gravitational pulling of the EM system induces a resonance with fundamental frequency 1yr􀀀1 and a series of periodic perturbations with frequencies equal to integer harmonics of the synodic month (9:9210􀀀7Hz). We then evaluated the e ects of these perturbations (up to the 6th harmonics) on the relative motions between each test masses couple, nding that they range between 3mm and 10pm for the 2nd and 6th harmonic, respectively. If we take the LISA sensitivity curve, as extrapolated down to 10􀀀6Hz, we obtain that a few harmonics of the EM system can be detected in the Doppler data collected by the LISA space mission. This suggests that the EM system gravitational near eld could provide an absolute calibration for the LISA sensitivity at very low frequencies. B.7 Limits on decaying dark energy density models from the CMB temperature-redshift relation (Ph. Jetzer, C. Tortora) The nature of the dark energy is still a mystery and several models have been proposed to explain it. We considered a phenomenological model for dark energy decay into photons and particles as proposed in a paper by Lima (Phys. Rev. D 54, 2571, 1996). He studied the thermodynamic aspects of decaying dark energy models in particular in the case 9 of a continuous photon creation and/or disruption. Following his approach, we derived a temperature redshift relation for the CMB which depends on the e ective equation of state weff and on the \adiabatic index" [19]. Comparing our relation with the data on the CMB temperature as a function of the redshift obtained from Sunyaev- Zel'dovich observations and at higher redshift from quasar absorption line spectra, we nd weff = 􀀀0:97  0:034, adopting for the adiabatic index = 4=3, in good agreement with current estimates and still compatible with weff = 􀀀1 (this latter value implying that the dark energy content being constant in
Project leadership and contacts /
Projektleitung und Kontakte
Prof Philippe Jetzer (Project Leader)  
Antoine Klein  
Joachim Naef  
Dr Mauro Sereno  
Funding source(s) /
Unterstützt durch
Universität Zürich (position pursuing an academic career), SNF (Personen- und Projektförderung), Others
Duration of Project / Projektdauer Jan 2010 to Dec 2010