Gravitational Wave Peep Contributions to Background Signal Confusion Noise for LISA

Abstract

Two-body gravitational interactions will occasionally lead to a stellar-mass compact object entering a very highly eccentric orbit around a massive black hole at the center of a galaxy. Gravitational radiation damping will subsequently result in an extreme mass ratio inspiral. Much of the inspiral time of these events is spent with the compact object on a long-period orbit, with a brief burst of gravitational wave emission at periapsis firmly in the mHz band. Burst orbits have been previously modeled as parabolic, with a focus on extreme examples that could be detectable by space-based gravitational wave detectors. This work focuses on the recurring bursts called ``peeps". Peeps are not likely to be individually resolvable; however, it is also important to consider them as possible sources of signal confusion noise because they do generate a signal within the LISA band with every pericenter passage. To account for peeps, we must utilize estimates for EMRI capture parameters along with tracking the massive black hole population out to a redshift of 3 using the Illustris Project. Then, this population is combined with an EMRI formation rate to estimate the number of EMRI events per unit volume for LISA. In this study, we model four different assumptions for the gravitational wave background produced by these highly eccentric peeps. We find that with our two most likely backgrounds, the signal may result in a slight rise of the LISA noise floor (SNR $\sim 0.3-2.4$); however, in two more abundant cases, the background generated by these sources would be detectable on their own and likely obscure many potentially detectable sources (SNR $\sim77-145$).

Figures (9)

• Figure 1: Calculated following Babak et al. (2017) babak_science_2017 using Eqs. 23-31, with a fixed plunge rate, a variable CO mass, and adjusted to be a rate $\Gamma$ given a $4$-year window for a given MBH mass. This rate is assuming that there are 10 plunges per formed EMRI, thus renormalizing the EMRI rate to account for sources that directly plunge after capture. The MBH mass limits were set based on our population model described in §\ref{['sec:massfunc']}, with the vertical black bar denoting the lower bound on MBH mass. We also include three separate rates based on different CO masses. In our study, we consider a uniform distribution of CO masses between these values (See Table \ref{['tab:Param_dist']}).
• Figure 2: (top): 2D histogram of mass function showing the count of MBHs versus redshift. (bottom): 2D histogram of mass function showing the count of MBHs versus $\log_{10}M$ in solar mass.
• Figure 3: Orbit of the first 4 months of an orbit of a peep with the same parameters as Figure \ref{['fig:test_wave_char']}. The orbit is shown in Cartesian coordinates with units of $M$. In this figure, the small body begins its orbit at periapsis. Here one can see the orbital precession due to the burst, which occurs after the small body completes its first orbit and passes periapsis again. This repeats with each pericenter passage forming the peep signal Oliver_2024.
• Figure 4: (top): Peep waveform with parameters $a=0.815535M$, $p_0=113.194144M$, $e_0=0.992424$, $\iota_0=2.363436^\circ$, $log_{10}\ M=5.2\ M_\odot$, $\mu=18.152765\ M_\odot$, $\theta_k=0.581082^\circ$, $\phi_k=14.558132^\circ$, $z=0.6$, and $dt=15 \mathrm{s}$ at a sky location of $\theta_s=0.980574^\circ$, $\phi_s=5.229798^\circ$ generated using the above methodology. The waveform depicts 4 years of a highly eccentric EMRI in the detector frame. On the y-axis is the strain amplitude of the gravitational wave signal. In purple dashed lines is the $h_+$ polarization, and in orange solid lines is the $h_\times$ polarization. The inset figure is zoomed in on the first burst in the repeated burst (peep) signal. (middle): The A and E channel outputs after passing the above waveform through fastlisaresponse. bottom: Characteristic strain for A and E channel plotted over the A1TDISens and E1TDISens sensitivity curves, respectively. The SNR for the A and E channels are $\sim 0.0012$ and the combined SNR is $\sim 0.0017$, which is undetectable on its own.
• Figure 5: Assumption 1 Background: 1,470 total peeps that were passed through the LISA response function from fastlisaresponselisaongpu1lisaongpu2 and then iteratively combined into a single background for each out the LISA TDI channels, A and E. We then took a FFT of each of the channels and plugged the values into Equation \ref{['eqn:char_strain']} to obtain the characteristic strain of the signal. The LISA sensitivity curve for each channel, A1TDISens and E1TDISens, (black) are then plotted over the background (orange). The amplitude of the background is just below the sensitivity curve and the total SNR in each channel is of order $\sim 0.2$ for the A and E channels, and a combined SNR of $0.33$.