Characterizing the galactic gravitational wave background with LISA

We present a Monte Carlo simulation for the response of the Laser Interferometer Space Antenna (LISA) to the galactic gravitational wave background. The simulated data streams are used to estimate the number and type of binary systems that will be individually resolved in a 1-year power spectrum. We find that the background is highly non-Gaussian due to the presence of individual bright sources but, once these sources are identified and removed, the remaining signal is Gaussian. We also present a new estimate of the confusion noise caused by unresolved sources that improves on earlier estimates.

Figure 1

A comparison of our full Monte Carlo simulation (gray) and a running average of the simulation (white) to those of HBW (squares). For each binary type we are in agreement. To ease comparison, the final figure shows a background using the full realization of white dwarf binaries. However, our simulated background uses the 10% reduced white dwarf population.

Figure 2

A realization of the galactic background as observed in the barycenter frame. The dark line is the all-sky and polarization averaged LISA sensitivity curve [25]. The jump at ${10}^{-4.6}\mathrm{Hz}$ is due to sudden increase in the number of W UMa binaries. Had we included a realization of the unevolved binaries, the background levels would be roughly constant below ${10}^{-4.6}\mathrm{Hz}$ with a spectral amplitude of $h_f\approx {10}^{-17}{\mathrm{Hz}}^{-1/2}$.

Figure 3

Number of sources per frequency bin. Again the dip in the number of sources at ${10}^{-4.6}\mathrm{Hz}$ is associated with the neglected unevolved binaries.

Figure 4

A realization of the HBW 10% galactic background as measured in the detector’s frame. The dark line is the average Michelson noise associated with the detector. The galactic gravitational wave background is evident in the spiky structure between 0.1 and 10 mHz.

Figure 5

A realization of the HBW 10% galactic background as measured in the detector’s frame shown in the time domain (with no instrument noise). The annual modulation of the signal due to the detector motion is apparent by the two large lobes.

Figure 6

The Kolmogorov-Smirnov Gaussianity test applied to the real Fourier coefficients for the detector output shown in Fig. 4. The presence of the galactic background is apparent by the low $p$ values about $f={10}^{-3}\mathrm{Hz}$. Similar results are found for the imaginary coefficients, for the other data channels, and when using a ${\chi }^2$ test.

Figure 7

Effective noise levels for the HBW 100% ($\mathrm{SNR}>10$) and HBW 10% ($\mathrm{SNR}>5$) models with (solid) and without (dotted) a source density cutoff of one resolved source per four frequency bins.

Figure 8

The same Michelson signal from before, but after the $\sim {10}^4$ bright sources have been removed from the data streams.

Figure 9

A running Gauss test applied to the detector output after the bright sources have been removed. Unlike before, all returned $p$ values are consistent with a Gaussian distribution.

Figure 10

Our estimates for the HBW 10% barycenter (solid line) and detector frame (dot-dashed line) confusion noise levels compared to the Ref. 4 estimate (dotted line). Our detector frame confusion noise has been multiplied by a factor of $\sqrt{20/3}$ to account for the average detector efficiency.

Figure 11

Estimates of the effective noise level for the HBW 10% model (dotted line), and the NYZ model (solid line). The effective noise curve used by Barack-Cutler Curve (dashed line) is also shown.

Figure 12

The accumulated number of bright sources per frequency bin using a 100 bin average, both with (black) and without ( gray) a bright source density cutoff. Starting in the upper left and going clockwise we have: HBW 10% with $\mathrm{SNR}\ge 10$, HBW 10% with $\mathrm{SNR}\ge 5$, HBW 100% with $\mathrm{SNR}\ge 10$, and NYZ with $\mathrm{SNR}\ge 10$.

Figure 13

Distribution of outlier distances as a function of their frequency. Filled squares are white dwarf binaries, open circles are black hole–neutron star binaries, asterisks are neutron star binaries, and open squares are cataclysmic binaries.

Figure 14

The correlation between the Extended Low Frequency Approximation and the Rigid Adiabatic Approximation.