Search for nonlinear memory from subsolar mass compact binary mergers

We present the first results of the search for nonlinear memory from subsolar mass binary black hole (BBH) mergers during the second observing run (O2) of the LIGO and Virgo detectors. The oscillatory chirp signal from the inspiral and merger of low mass BBHs ($M_{\mathrm{Tot}}\le 0.4M_{\odot }$) are at very high frequencies and fall outside the sensitivity band of the current ground-based detectors. However, the nonoscillatory memory signal during the merger saturates toward the lower frequencies and can be detected for those proposed BBHs. We show in this work that the morphology of the memory signal depends minimally upon the source parameters of the binary, thus only the overall amplitude of the signal changes and hence the result can be interpolated for extremely low mass BBH mergers. We did not find any signal which can be interpreted as a memory signal, and we place upper limits on the rate of BBH mergers with $M_{\mathrm{Tot}}\le 0.4M_{\odot }$ for the first time.

Figure 1

The time-domain memory waveform of an edge-on binary black hole merger of $2M_{\odot }$ total mass at 10 kpc. The black holes are of the same mass and nonspinning. Note that we neglect any memory from the inspiral and only consider the memory generated from about −0.04 s until the merger.

Figure 2

Whitened spectrogram with O2 noise power spectral density of the GW signal of an equal mass binary black hole merger at $\mathrm{SNR}\approx 100$. One can clearly distinguish the chirp signal from the memory burst saturating toward lower-frequency cutoff of the analysis at the time of the merger. This signal is from a $5-5M_{\odot }$ system; the oscillatory part is shown above 100 Hz, and the memory contribution is slightly exaggerated. For lower mass binaries, the chirp signal will rise in frequency, whereas the memory signal will always look the same in a time-frequency representation and only change in amplitude.

Figure 3

The maximum of the bandpassed (10 Hz) memory amplitude as a function of the total mass for an edge-on binary at 10 kpc. In the aligned spin case, both black holes are spinning with spin magnitude of 0.8, and the unequal mass system has a mass ratio of $m_1/m_2=3$. The amplitude scales linearly well below $1M_{\odot }$.

Figure 4

Histogram of the central frequency of recovered memory injections for a $0.02M_{\odot }$ system. In fact, the memory from low mass systems always saturates around the detectors’ most sensitive region, which is around 100 Hz.

Figure 5

Range of the cWB analysis to recover a memory signal from subsolar mass BBH mergers at an $\mathrm{iFAR}\ge 1\mathrm{yr}$ as a function of total mass. Only equal mass coalescences are considered. The result from the injections can be extrapolated to very small masses because the search sensitivity depends only on the amplitude of the memory signal. The shaded regions show the $1\sigma$ uncertainties.

Figure 6

The constraint on the merger rate density for equal mass binaries. Shaded regions represent excluded values. We can compare the constraint on nonspinning subsolar mass black hole mergers to the results obtainted by LIGO using a matched-filtering search in the O2 subsolar mass paper [8]. For completeness, we also show the constraint on an aligned spin population.