Archival searches for stellar-mass binary black holes in LISA data

Stellar-mass binary black holes will sweep through the frequency band of the Laser Interferometer Space Antenna (LISA) for months to years before appearing in the audio-band of ground-based gravitational-wave detectors. One can expect several tens of these events up to a distance of 500 Mpc each year. The LISA signal-to-noise ratio for such sources even at these close distances will be too small for a blind search to confidently detect them. However, next generation ground-based gravitational-wave detectors, expected to be operational at the time of LISA, will observe them with signal-to-noise ratios of several thousands and measure their parameters very accurately. We show that such high fidelity observations of these sources by ground-based detectors help in archival searches to dig tens of signals out of LISA data each year.

Figure 1

The plot shows the distribution of the 181 $h\mathrm{BBHs}$ with a LISA SNR ${\rho }_{\mathrm{LISA}}\ge 4$, the two axes show the masses of the companions in both panels. In the left plot, color bar is the 3G SNR ${\rho }_{3\mathrm{G}}$ and the size of circles depict the LISA SNR ${\rho }_{\mathrm{LISA}}$; in the right plot, color bar is the luminosity distance $D_L$ and the size of the circles represent the effective spin parameter ${\chi }_{\mathrm{eff}}$.

Figure 2

The plot shows the probability and cumulative density functions of the measurement error for the nine parameters of interest for the 181 binary black hole mergers that can be detected in the archival search of LISA data after they are identified and measured in the 3G data. We simulated 100 realizations for the sky location and binary orientation angles to show the range of parameter errors to be expected from 3G networks.

Figure 3

Left: contour plot of the starting frequency for stellar mass binary black holes that last 5 years in the LISA band. The starting frequency scales with the mass ratio of each system and inversely with the total mass, as indicated by the colored contours, where the values of starting frequencies are shown in Hz. The grey dots mark the positions of the 181 $h\mathrm{BBHs}$ for which we performed Fisher analysis in a 3G network to obtain parameter error estimates. The size of the dots represents the corresponding LISA SNR, ${\rho }_{\mathrm{LISA}}$. Right: LISA’s amplitude noise spectral density (ASD) $\sqrt{S_h(f)}$ is plotted before (red solid line) and after (red dashed line) applying frequency scaling with $\alpha ={10}^4$. Also shown are the amplitude spectra $\sqrt{f}|\tilde{h}(f)|$ for GW150914-like (in orange) and GW190521-like (yellow) systems at a distance of 500 Mpc with signal-to-noise ratio of 4.8 and 16, respectively. The integration time is assumed to be 5 years in the LISA band which translates to $1.54\times {10}^5\mathrm{s}$ in the audio band.

Figure 4

Left: for a $h\mathrm{BBH}$ source with component masses constrained by 3G to $m_1=22.84892$ and $m_2=16.93702M_{\odot }$ the template (green) and injection (blue) component masses are shown for a 3.5 PN template bank. Chirp mass contours are indicated by the black lines. Right: for the same source, the injection component masses are shown with the one-dimensional Newtonian template component masses.

Figure 5

The number of templates from the stochastic placement algorithm is plotted against the LISA SNR, ${\rho }_{\mathrm{LISA}}$ for each source. The color bar indicates the CE SNR, ${\rho }_{\mathrm{CE}}$.

Figure 6

For 181 $h\mathrm{BBH}$ sources we plot the number of templates required for the minimal match condition, $M=0.98$ calculated using the metric approach for one-dimensional Newtonian template banks (horizontal axis) and the number of 3.5 PN templates found using the stochastic placement algorithm (vertical axis). The color bar indicates the lower frequency cutoff, after scaling to the audio band. For a linear fit, $N_{T,\text{stochastic}}=m\times N_{T,\text{metric}}$, we find $m=1.30$.

Figure 7

Top left: the plot shows the cumulative distribution of the 3.5 PN template bank sizes. The vertical lines indicate, from left to right, the 50th percentile, mean, and 90th percentile bank sizes. The bins are evenly spaced in log. Bottom left: the cumulative distribution of one-dimensional Newtonian template bank sizes. Top right: the plot shows the cumulative distribution of mismatches of 1000 injections with each 3.5 PN template bank. In the match calculation, we use the Newtonian approximation (green) and the 3.5 PN approximation (blue). The vertical lines indicate the mean 10th percentile match for both sets of template banks. The position of the mean 10th percentile match value for 3.5 PN approximation has been artificially shifted to the left by 0.0005 so that the two lines are distinguishable. Bottom right: the cumulative distribution of mismatches for one-dimensional Newtonian template banks.