Planned Laser Interferometer Space Antenna Research Articles

Multimessenger Picture of J1048+7143* *Released xxxx 2022.

We draw a multimessenger picture of J1048+7143, a flat-spectrum radio quasar known to show quasiperiodic oscillations in the γ-ray regime. We generate the adaptively binned Fermi Large Area Telescope light curve of this source above 168 MeV to find three major γ-ray flares of the source, such that each of the three flares consists of two sharp subflares. Based on radio interferometric imaging data taken with the Very Large Array, we find that the kiloparsec-scale jet is directed west, while our analysis of 8.6 GHz very long baseline interferometry data, mostly taken with the Very Long Baseline Array, revealed signatures of two parsec-scale jets, one pointing east, one pointing south. We suggest that the misalignment of the kiloparsec- and parsec-scale jets is a revealing signature of jet precession. We also analyze the 5 GHz total flux density curve of J1048+7143 taken with the Nanshan (Ur) and RATAN-600 single-dish radio telescopes and find two complete radio flares, lagging slightly behind the γ-ray flares. We model the timing of γ-ray flares as a signature of the spin–orbit precession in a supermassive black hole binary, and find that the binary could merge in the next ∼60–80 yr. We show that both pulsar timing arrays and the planned Laser Interferometer Space Antenna lack sensitivity and frequency coverage to detect the hypothetical supermassive black hole binary in J1048+7143. We argue that the identification of sources similar to J1048+7143 plays a key role in revealing periodic high-energy sources in the distant universe.

Polarization of gravitational waves from helical MHD turbulent sources

We use direct numerical simulations of decaying primordial hydromagnetic turbulence with helicity to compute the resulting gravitational wave (GW) production and its degree of circular polarization. The turbulence is sourced by magnetic fields that are either initially present or driven by an electromotive force applied for a short duration, given as a fraction of one Hubble time. In both types of simulations, we find a clear dependence of the polarization of the resulting GWs on the fractional helicity of the turbulent source. We find a low frequency tail below the spectral peak shallower than the f 3 scaling expected at super-horizon scales, in agreement with similar recent numerical simulations. This type of spectrum facilitates its observational detection with the planned Laser Interferometer Space Antenna (LISA). We show that driven magnetic fields produce GWs more efficiently than magnetic fields that are initially present, leading to larger spectral amplitudes, and to modifications of the spectral shape. In particular, we observe a sharp drop of GW energy above the spectral peak that is in agreement with the previously obtained results. The helicity does not have a huge impact on the maximum spectral amplitude in any of the two types of turbulence considered. However, the GW spectrum at wave numbers away from the peak becomes smaller for larger values of the magnetic fractional helicity. Such variations of the spectrum are most noticeable when magnetic fields are driven. The degree of circular polarization approaches zero at frequencies below the peak, and reaches its maximum at the peak. At higher frequencies, it stays finite if the magnetic field is initially present, and it approaches zero if it is driven. We predict that the spectral peak of the GW signal can be detected by LISA if the turbulent energy density is at least ∼3% of the radiation energy density, and the characteristic scale is a hundredth of the horizon at the electroweak scale. We show that the resulting GW polarization is unlikely to be detectable by the anisotropies induced by our proper motion in the dipole response function of LISA. Such signals can, however, be detectable by cross-correlating data from the LISA-Taiji network for turbulent energy densities of ∼5%, and fractional helicity of 0.5 to 1. Second-generation space-base GW detectors, such as BBO and DECIGO, would allow for the detection of a larger range of the GW spectrum and smaller amplitudes of the magnetic field.

Measuring the dark matter environments of black hole binaries with gravitational waves

Large dark matter overdensities can form around black holes of astrophysical and primordial origin as they form and grow. This "dark dress" inevitably affects the dynamical evolution of binary systems, and induces a dephasing in the gravitational waveform that can be probed with future interferometers. In this paper, we introduce a new analytical model to rapidly compute gravitational waveforms in presence of an evolving dark matter distribution. We then present a Bayesian analysis determining when dressed black hole binaries can be distinguished from GR-in-vacuum ones and how well their parameters can be measured, along with how close they must be to be detectable by the planned Laser Interferometer Space Antenna (LISA). We show that LISA can definitively distinguish dark dresses from standard binaries and characterize the dark matter environments around astrophysical and primordial black holes for a wide range of model parameters. Our approach can be generalized to assess the prospects for detecting, classifying, and characterizing other environmental effects in gravitational wave physics.

Numerical simulations of gravitational waves from early-universe turbulence

We perform direct numerical simulations of magnetohydrodynamic turbulence in the early universe and numerically compute the resulting stochastic background of gravitational waves and relic magnetic fields. These simulations do not make the simplifying assumptions of earlier analytic work. If the turbulence is assumed to have an energy-carrying scale that is about a hundredth of the Hubble radius at the time of generation, as expected in a first-order phase transition, the peak of gravitational wave power will be in the mHz frequency range for a signal produced at the electroweak scale. The efficiency of gravitational wave (GW) production varies significantly with how the turbulence is driven. Detectability of turbulence at the electroweak scale by the planned Laser Interferometer Space Antenna (LISA) requires anywhere from 0.1% to 10% of the thermal plasma energy density to be in plasma motions or magnetic fields, depending on the model of the driving process. Our results predict a new universal form below the spectral peak frequency that is shallower than previously thought. This implies larger values of the GW energy spectra in the low-frequency range. This extends the range where turbulence is detectable with LISA to lower frequencies, corresponding to higher energy scales than the assumed energy-carrying scale.

Gravitational-wave Detection and Parameter Estimation for Accreting Black-hole Binaries and Their Electromagnetic Counterpart

Abstract We study the impact of gas accretion on the orbital evolution of black-hole binaries initially at large separation in the band of the planned Laser Interferometer Space Antenna (LISA). We focus on two sources: (i) stellar-origin black-hole binaries (SOBHBs) that can migrate from the LISA band to the band of ground-based gravitational-wave (GW) observatories within weeks/months; and (ii) intermediate-mass black-hole binaries (IMBHBs) in the LISA band only. Because of the large number of observable GW cycles, the phase evolution of these systems needs to be modeled to great accuracy to avoid biasing the estimation of the source parameters. Accretion affects the GW phase at negative (−4) post-Newtonian order, being thus dominant for binaries at large separations. Accretion at the Eddington or at super-Eddington rate will leave a detectable imprint on the dynamics of SOBHBs. For super-Eddington rates and a 10 yr mission, a multiwavelength strategy with LISA and a ground-based interferometer can detect about 10 (a few) SOBHB events for which the accretion rate can be measured at 50% (10%) level. In all cases, the sky position can be identified within much less than 0.4 deg2 uncertainty. Likewise, accretion at ≳100% of the Eddington rate can be measured in IMBHBs up to redshift z ≈ 0.1, and the position of these sources can be identified within less than uncertainty. Altogether, a detection of SOBHBs or IMBHBs would allow for targeted searches of electromagnetic counterparts to black-hole mergers in gas-rich environments with future X-ray detectors (such as Athena) and/or radio observatories (such as SKA).

Discovery of an Outbursting 12.8 Minute Ultracompact X-Ray Binary∗

Abstract We report the discovery of OGLE-UCXB-01, a 12.8 minute variable object located in the central field of Galactic bulge globular cluster Djorg 2. The presence of frequent, short-duration brightenings at such an ultrashort period in long-term OGLE photometry together with the blue color of the object in Hubble Space Telescope images and the detection of moderately hard X-rays by Chandra observatory point to an ultracompact X-ray binary system. The observed fast period decrease makes the system a particularly interesting target for gravitational-wave detectors such as the planned Laser Interferometer Space Antenna.

Dynamical tides in compact white dwarf binaries: tidal synchronization and dissipation

In compact white dwarf (WD) binary systems (with periods ranging from minutes to hours), dynamical tides involving the excitation and dissipation of gravity waves play a dominant role in determining the physical conditions (such as rotation rate and temperature) of the WDs prior to mass transfer or binary merger. We calculate the amplitude of the tidally excited gravity waves as a function of the tidal forcing frequency ω= 2(Ω−Ωs) (where Ω is the orbital frequency and Ωs is the spin frequency) for several realistic carbon–oxygen WD models, under the assumption that the outgoing propagating waves are efficiently dissipated in the outer layer of the star by non-linear effects or radiative damping. Unlike main-sequence stars with distinct radiative and convection zones, the mechanism of wave excitation in WDs is more complex due to the sharp features associated with composition changes inside the WD. In our WD models, the gravity waves are launched just below the helium–carbon boundary and propagate outwards. We find that the tidal torque on the WD and the related tidal energy transfer rate, ⁠, depend on ω in an erratic way, with varying by orders of magnitude over small frequency ranges. On average, scales approximately as Ω5ω5 for a large range of tidal frequencies. We also study the effects of dynamical tides on the long-term evolution of WD binaries prior to mass transfer or merger. Above a critical orbital frequency Ωc, corresponding to an orbital period of the order of 1h (depending on WD models), dynamical tides efficiently drive Ωs towards Ω, although a small, almost constant degree of synchronization (Ω−Ωs∼ constant) is maintained even at the smallest binary periods. While the orbital decay is always dominated by gravitational radiation, the tidal energy transfer can induce a significant phase error in the low-frequency gravitational waveforms, detectable by the planned Laser Interferometer Space Antenna project. Tidal dissipation may also lead to significant heating of the WD envelope and brightening of the system long before binary merger.

Fast frequency-domain algorithm for gravitational self-force: Circular orbits in Schwarzschild spacetime

Fast, reliable orbital evolutions of compact objects around massive black holes will be needed as input for gravitational wave search algorithms in the data stream generated by the planned Laser Interferometer Space Antenna (LISA). Currently, the state of the art is a time-domain code by [Phys. Rev. D{\bf 81}, 084021, (2010)] that computes the gravitational self-force on a point-particle in an eccentric orbit around a Schwarzschild black hole. Currently, time-domain codes take up to a few days to compute just one point in parameter space. In a series of articles, we advocate the use of a frequency-domain approach to the problem of gravitational self-force (GSF) with the ultimate goal of orbital evolution in mind. Here, we compute the GSF for a particle in a circular orbit in Schwarzschild spacetime. We solve the linearized Einstein equations for the metric perturbation in Lorenz gauge. Our frequency-domain code reproduces the time-domain results for the GSF up to $\sim 1000$ times faster for small orbital radii. In forthcoming companion papers, we will generalize our frequency-domain methods to include bound (eccentric) orbits in Schwarzschild and (eventually) Kerr spacetimes for computing the GSF, where we will employ the method of extended homogeneous solutions [Phys. Rev. D {\bf 78}, 084021 (2008)].

SELF CONSISTENT MODEL FOR THE EVOLUTION OF ECCENTRIC MASSIVE BLACK HOLE BINARIES IN STELLAR ENVIRONMENTS: IMPLICATIONS FOR GRAVITATIONAL WAVE OBSERVATIONS

We construct evolutionary tracks for massive black hole binaries (MBHBs) embedded in a surrounding distribution of stars. The dynamics of the binary is evolved by taking into account the erosion of the central stellar cusp bound to the massive black holes, the scattering of unbound stars feeding the binary loss cone, and the emission of gravitational waves (GWs). Stellar dynamics is treated in a hybrid fashion by coupling the results of numerical 3-body scattering experiments of bound and unbound stars to an analytical framework for the evolution of the stellar density distribution and for the efficiency of the binary loss cone refilling. Our main focus is on the behaviour of the binary eccentricity, in the attempt of addressing its importance in the merger process and its possible impact for GW detection with the planned Laser Interferometer Space Antenna ({\it LISA}), and ongoing and forthcoming pulsar timing array (PTA) campaigns. We produce a family of evolutionary tracks extensively sampling the relevant parameters of the system which are the binary mass, mass ratio and initial eccentricity, the slope of the stellar density distribution, its normalization and the efficiency of loss cone refilling. We find that, in general, stellar dynamics causes a dramatic increase of the MBHB eccentricity, especially for initially already mildly eccentric and/or unequal mass binaries. When applied to standard MBHB population models, our results predict eccentricities in the ranges $10^{-3}-0.2$ and $0.03-0.3$ for sources detectable by {\it LISA} and PTA respectively. Such figures may have a significant impact on the signal modelling, on source detection, and on the development of parameter estimation algorithms.

GRAVITATIONAL WAVES FROM ECCENTRIC INTERMEDIATE-MASS BLACK HOLE BINARIES

If binary intermediate-mass black holes (IMBHs; with masses between 100 and 104 M☉) form in dense stellar clusters, their inspiral will be detectable with the planned Laser Interferometer Space Antenna (LISA) out to several Gpc. Here, we present a study of the dynamical evolution of such binaries using a combination of direct N-body techniques (when the binaries are well separated) and three-body relativistic scattering experiments (when the binaries are tight enough that interactions with stars occur one at a time). We find that for reasonable IMBH masses there is only a mild effect on the structure of the surrounding cluster even though the binary binding energy can exceed the binding energy of the cluster. We demonstrate that, contrary to standard assumptions, the eccentricity in the LISA band can be in some cases as large as ∼0.2–0.3 and that it induces a measurable phase difference from circular binaries in the last year before merger. We also show that, even though energy input from the binary decreases the density of the core and slows down interactions, the total time to coalescence is short enough (typically less than a 100 million years) that such mergers will be unique snapshots of clustered star formation.

Improved time–frequency analysis of extreme-mass-ratio inspiral signals in mock LISA data

The planned Laser Interferometer Space Antenna (LISA) is expected to detect gravitational wave signals from ∼100 extreme-mass-ratio inspirals (EMRIs) of stellar-mass compact objects into massive black holes. The long duration and large parameter space of EMRI signals make data analysis for these signals a challenging problem. One approach to EMRI data analysis is to use time–frequency methods. This consists of two steps: (i) searching for tracks from EMRI sources in a time–frequency spectrogram and (ii) extracting parameter estimates from the tracks. In this paper we discuss the results of applying these techniques to the latest round of the Mock LISA Data Challenge, Round 1B. This analysis included three new techniques not used in previous analyses: (i) a new chirp-based algorithm for track search for track detection; (ii) estimation of the inclination of the source to the line of sight; (iii) a Metropolis–Hastings Monte Carlo over the parameter space in order to find the best fit to the tracks.

LISA detections of massive black hole inspirals: Parameter extraction errors due to inaccurate template waveforms

The planned Laser Interferometer Space Antenna (LISA) is expected to detect the inspiral and merger of massive black hole binaries (MBHBs) at $z\ensuremath{\lesssim}5$ with signal-to-noise ratios (SNRs) of hundreds to thousands. Because of these high SNRs, and because these SNRs accrete over periods of weeks to months, it should be possible to extract the physical parameters of these systems with high accuracy; for instance, for a $\ensuremath{\sim}{10}^{6}{M}_{\ensuremath{\bigodot}}$ MBHBs at $z=1$ it should be possible to determine the two masses to $\ensuremath{\sim}0.1%$ and the sky location to $\ensuremath{\sim}1\ifmmode^\circ\else\textdegree\fi{}$. However, those are just the errors due to noise: there will be additional ``theoretical'' errors due to inaccuracies in our best model waveforms, which are still only approximate. The goal of this paper is to estimate the typical magnitude of these theoretical errors. We develop mathematical tools for this purpose, and apply them to a somewhat simplified version of the MBHB problem, in which we consider just the inspiral part of the waveform and neglect spin-induced precession, eccentricity, and PN amplitude corrections. For this simplified version, we estimate that theoretical uncertainties in sky position will typically be $\ensuremath{\sim}1\ifmmode^\circ\else\textdegree\fi{}$, i.e., comparable to the statistical uncertainty. For the mass and spin parameters, our results suggest that while theoretical errors will be rather small absolutely, they could still dominate over statistical errors (by roughly an order of magnitude) for the strongest sources. The tools developed here should be useful for estimating the magnitude of theoretical errors in many other problems in gravitational-wave astronomy.

Using LISA extreme-mass-ratio inspiral sources to test off-Kerr deviations in the geometry of massive black holes

Inspirals of stellar-mass compact objects (COs) into ~106M[sun] black holes are especially interesting sources of gravitational waves for the planned Laser Interferometer Space Antenna (LISA). The orbits of these extreme-mass-ratio inspirals (EMRIs) are highly relativistic, displaying extreme versions of both perihelion precession and Lense-Thirring precession of the orbital plane. We investigate the question of whether the emitted waveforms can be used to strongly constrain the geometry of the central massive object, and in essence check that it corresponds to a Kerr black hole (BH). For a Kerr BH, all multipole moments of the spacetime have a simple, unique relation to M and S, the BH mass, and spin; in particular, the spacetime's mass quadrupole moment Q is given by Q=-S2/M. Here we treat Q as an additional parameter, independent of S and M, and ask how well observation can constrain its difference from the Kerr value. This was already estimated by Ryan, but for the simplified case of circular, equatorial orbits, and Ryan also neglected the signal modulations arising from the motion of the LISA satellites. We consider generic orbits and include the modulations due to the satellite motions. For this analysis, we use a family of approximate (basically post-Newtonian) waveforms, which represent the full parameter space of EMRI sources, and which exhibit the main qualitative features of true, general relativistic waveforms. We extend this parameter space to include (in an approximate manner) an arbitrary value of Q, and then construct the Fisher information matrix for the extended parameter space. By inverting the Fisher matrix, we estimate how accurately Q could be extracted from LISA observations of EMRIs. For 1 yr of coherent data from the inspiral of a 10M[sun] black hole into rotating black holes of masses 105.5M[sun], 106M[sun], or 106.5M[sun], we find Delta(Q/M3)~10-4, 10-3, or 10-2, respectively (assuming total signal-to-noise ratio of 100, typical of the brightest detectable EMRIs). These results depend only weakly on the eccentricity of the inspiral orbit or the spin of the central object.

Interaction of Massive Black Hole Binaries with Their Stellar Environment. II. Loss Cone Depletion and Binary Orbital Decay

We study the long-term evolution of massive black hole binaries (MBHBs) at the centers of galaxies using detailed scattering experiments to solve the full three-body problem. Ambient stars drawn from a isotropic Maxwellian distribution unbound to the binary are ejected by the gravitational slingshot. We construct a minimal, hybrid model for the depletion of the loss cone and the orbital decay of the binary, and show that secondary slingshots - stars returning on small impact parameter orbits to have a second super-elastic scattering with the MBHB - may considerably help the shrinking of the pair in the case of large binary mass ratios. In the absence of loss-cone refilling by two-body relaxation or other processes, the mass ejected before the stalling of a MBHB is half the binary reduced mass. About 50% of the ejected stars are expelled ejected in a "burst" lasting ~1E4 yrs M_6^1/4, where M_6 is the binary mass in units of 1E6 Msun. The loss cone is completely emptied in a few bulge crossing timescales, 1E7 yrs M_6^1/4. Even in the absence of two-body relaxation or gas dynamical processes, unequal mass and/or eccentric binaries with M_6 >0.1 can shrink to the gravitational wave emission regime in less than a Hubble time, and are therefore "safe" targets for the planned Laser Interferometer Space Antenna (LISA).

Erratum: Semirelativistic approximation to gravitational radiation from encounters with nonspinning black holes [Phys. Rev. D72, 084009 (2005)

The capture of compact bodies by black holes in galactic nuclei is an important prospective source for low frequency gravitational wave detectors, such as the planned Laser Interferometer Space Antenna. This paper calculates, using a semirelativistic approximation, the total energy and angular momentum lost to gravitational radiation by compact bodies on very high eccentricity orbits passing close to a supermassive, nonspinning black hole; these quantities determine the characteristics of the orbital evolution necessary to estimate the capture rate. The semirelativistic approximation improves upon treatments which use orbits at Newtonian-order and quadrupolar radiation emission, and matches well onto accurate Teukolsky simulations for low eccentricity orbits. Formulae are presented for the semirelativistic energy and angular momentum fluxes as a function of general orbital parameters.

Gravitational Radiation Timescales for Extreme Mass Ratio Inspirals

The capture and inspiral of compact stellar masses into massive black holes is an important source of low-frequency gravitational waves (with frequencies of ~1-100mHz), such as those that might be detected by the planned Laser Interferometer Space Antenna (LISA). Simulations of stellar clusters designed to study this problem typically rely on simple treatments of the black hole encounter which neglect some important features of orbits around black holes, such as the minimum radii of stable, non-plunging orbits. Incorporating an accurate representation of the orbital dynamics near a black hole has been avoided due to the large computational overhead. This paper provides new, more accurate, expressions for the energy and angular momentum lost by a compact object during a parabolic encounter with a non-spinning black hole, and the subsequent inspiral lifetime. These results improve on the Keplerian expressions which are now commonly used and will allow efficient computational simulations to be performed that account for the relativistic nature of the spacetime around the central black hole in the system.

Semirelativistic approximation to gravitational radiation from encounters with nonspinning black holes

The capture of compact bodies by black holes in galactic nuclei is an important prospective source for low frequency gravitational wave detectors, such as the planned Laser Interferometer Space Antenna. This paper calculates, using a semirelativistic approximation, the total energy and angular momentum lost to gravitational radiation by compact bodies on very high eccentricity orbits passing close to a supermassive, nonspinning black hole; these quantities determine the characteristics of the orbital evolution necessary to estimate the capture rate. The semirelativistic approximation improves upon treatments which use orbits at Newtonian order and quadrupolar radiation emission, and matches well onto accurate Teukolsky simulations for low eccentricity orbits. Formulas are presented for the semirelativistic energy and angular momentum fluxes as a function of general orbital parameters.

Low-frequency gravitational radiation from coalescing massive black holes

We compute the expected low-frequency gravitational wave signal from coalescing massive black-hole (MBH) binaries at the centres of galaxies. We follow the merging history of halos and associated holes via cosmological Monte Carlo realizations of the merger hierarchy from early times to the present in a ΛCDM cosmology. MBHs get incorporated through a series of mergers into larger and larger halos, sink to the centre owing to dynamical friction, accrete a fraction of the gas in the merger remnant to become more massive, and form a binary system. Stellar dynamical processes dominate the orbital evolution of the binary at large separations, while gravitational wave emission takes over at small radii, causing the final coalescence of the system. We discuss the observability of inspiralling MBH binaries by a low-frequency gravitational wave experiment such as the planned Laser Interferometer Space Antenna (LISA), discriminating between resolvable sources and unresolved confusion noise. Over a three-year observing period LISA should resolve this GWB into discrete sources, detecting ≈90 individual events above a S/N = 5 confidence level, while expected confusion noise is well below planned LISA capabilities.

The Gravitational Wave Signal from Massive Black Hole Binaries and Its Contribution to theLISAData Stream

Massive black hole binaries, with masses in the range 103-108 M☉, are expected to be the most powerful sources of gravitational radiation at mHz frequencies, and hence are among the primary targets for the planned Laser Interferometer Space Antenna (LISA). We extend and refine our previous analysis, detailing the gravitational wave signal expected from a cosmological population of massive black hole binaries. As done in our previous paper, we follow the merger history of dark matter halos, the dynamics of the massive black holes they host, and their growth via gas accretion and binary coalescences in a ΛCDM cosmology. Stellar dynamical processes dominates the orbital evolution of black hole binaries at large separations, while gravitational wave emission takes over at small radii, causing the final coalescence of the pairs. We show that the GW signal from this population, in a 3 yr LISA observation, will be resolved into 90 discrete with S/N ≥ 5, among which 35 will be observed above threshold until coalescence. These merging events involve relatively massive binaries, M ~ 105 M☉, in the redshift range 2 z 6. The remaining 55 come from higher redshift, less massive binaries (M ~ 5 × 103 M☉ at z 6) and, although their S/N integrated over the duration of the observation can be substantial, the final coalescence phase is at too high a frequency to be directly observable by space-based interferometeres such as LISA. LISA will be able to detect a fraction 90% of all the coalescences of massive black hole binaries occurring at z 5. The residual confusion noise from unresolved massive black hole binaries is expected to be at least an order of magnitude below the estimated stochastic noise.

Probing anisotropies of gravitational-wave backgrounds with a space-based interferometer: Geometric properties of antenna patterns and their angular power

We discuss the sensitivity to anisotropies of stochastic gravitational-wave backgrounds (GWBs) observed via space-based interferometer. In addition to the unresolved galactic binaries as the most promising GWB source of the planned Laser Interferometer Space Antenna (LISA), the extragalactic sources for GWBs might be detected in the future space missions. The anisotropies of the GWBs thus play a crucial role to discriminate various components of the GWBs. We study general features of antenna pattern sensitivity to the anisotropies of GWBs beyond the low-frequency approximation. We show that the sensitivity of space-based interferometer to GWBs is severely restricted by the data combinations and the symmetries of the detector configuration. The spherical harmonic analysis of the antenna pattern functions reveals that the angular power of the detector response increases with frequency and the detectable multipole moments with effective sensitivity ${h}_{\mathrm{e}\mathrm{f}\mathrm{f}}\ensuremath{\sim}{10}^{\ensuremath{-}20}\text{ }\text{ }{\mathrm{H}\mathrm{z}}^{\ensuremath{-}1/2}$ may reach $\ensuremath{\ell}\ensuremath{\sim}8--10$ at $f\ensuremath{\sim}{f}_{*}=10\text{ }\text{ }\mathrm{m}\mathrm{H}\mathrm{z}$ in the case of the single LISA detector. However, the cross correlation of optimal interferometric variables is blind to the monopole ($\ensuremath{\ell}=0$) intensity anisotropy, and also to the dipole ($\ensuremath{\ell}=1$) in some case, irrespective of the frequency band. Besides, all the self-correlated signals are shown to be blind to the odd multipole moments ($\ensuremath{\ell}=\mathrm{o}\mathrm{d}\mathrm{d}$), independently of the frequency band.