Doppler boosting the stochastic gravitational wave background

Abstract

One of the guaranteed features of the stochastic gravitational wave background (SGWB) is the presence of Doppler anisotropies induced by the motion of the detector with respect to the rest frame of the SGWB source. We point out that kinematic effects can be amplified if the SGWB is characterised by large tilts in its spectrum as a function of frequency, or by sizeable intrinsic anisotropies. Hence we examine the possibility to use Doppler effects as complementary probes of the SGWB frequency profile. For this purpose we work in multipole space, and we study the effect of kinematic modulation and aberration on the GW energy density parameter and on its angular power spectrum. We develop a Fisher forecast analysis and we discuss prospects for constraining parameters controlling kinematically induced anisotropies with future detector networks. As a case study, we apply our framework to a background component with constant slope in frequency, potentially detectable by a network of future ground-based interferometers. For this specific example, we show that a measurement of kinematic anisotropies with a network of Einstein Telescope and Cosmic Explorer will allow us to constrain the spectral shape with a precision of about 16%. We also show that, if a reconstruction of the spectral shape is done via other methods, e.g. frequency binning, a study of kinematic anisotropies can allow one to constrain our peculiar velocity with respect to the CMB frame with a precision of 30%. Finally, we identify cosmological and astrophysical scenarios where kinematic effects are enhanced in frequency ranges probed by current and future GW experiments.

The NANOGrav 15 yr Data Set: Evidence for a Gravitational-wave Background

“…A detection of pixel-scale anisotropy could provide the first indication of a single inspiraling SMBHB system which could then be subjected to targeted followup using both PTA GW and electromagnetic observatories. A detection of large scale anisotropy could indicate an over-density of SMBHB systems in a cluster environment, or might point to an extrinsic effect (Chung et al 2022), such as the kinematic dipole observed with the cosmic microwave background (Planck Collaboration et al 2020) and predicted to be detectable with a GWB (Bertacca et al 2020;Chung et al 2022;Cusin & Tasinato 2022;Valbusa Dall'Armi et al 2022). If we live in a Universe where both astrophysical (e.g., from SMBHBs) and cosmological (e.g., from cosmic strings) GWBs are present, we can leverage our knowledge of the different expected spatial (and spectral) distribution of these processes to disentangle them in the PTA datasets (Ungarelli & Vecchio 2001;Mandic et al 2012;Parida et al 2016;Biscoveanu et al 2020;Martinovic et al 2021;Suresh et al 2021;Kaiser et al 2022).…”

The NANOGrav 15 yr Data Set: Search for Anisotropy in the Gravitational-wave Background

“…A detection of pixel-scale anisotropy could provide the first indication of a single inspiraling SMBHB system that could then be subjected to targeted follow-up using both PTA GW and electromagnetic observatories. A detection of large-scale anisotropy could indicate an overdensity of SMBHB systems in a cluster environment, or might point to an extrinsic effect (Chung et al 2022), such as the kinematic dipole observed with the cosmic microwave background (Planck Collaboration et al 2020) and predicted to be detectable with a GWB (Bertacca et al 2020;Chung et al 2022;Cusin & Tasinato 2022;Valbusa Dall'Armi et al 2022). If we live in a Universe where both astrophysical (e.g., from SMBHBs) and cosmological (e.g., from cosmic strings) GWBs are present, we can leverage our knowledge of the different expected spatial (and spectral) distribution of these processes to disentangle them in the PTA data sets (Ungarelli & Vecchio 2001;Mandic et al 2012;Parida et al 2016;Biscoveanu et al 2020;Martinovic et al 2021;Suresh et al 2021;Kaiser et al 2022).…”

Targeted search for the kinematic dipole of the gravitational-wave background

“…3 (We have included only the linear-order term here, since v sol ∼ 10 −3 in relativistic units. See [33] for a recent discussion of higher-order kinematic effects in the GWB.) As a simple, specific example, consider the GWB generated by inspiraling compact binaries.…”

“…Aside from the intrinsic anisotropies, there are also extrinsic or kinematic anisotropies due to the peculiar motion of our GW detectors with respect to the rest frame of the GWB [20,23,[33][34][35]. Most notable of these is the Doppler enhancement of the GW intensity we observe from sources we are moving toward and the corresponding reduction in intensity from sources we are receding from.…”