Millihertz Band Research Articles

Gravitational wave peeps from EMRIs and their implication for LISA signal confusion noise

Scattering events around the center of massive galaxies will occasionally toss a stellar-mass compact object into an orbit around the massive black hole (MBH) at the center, beginning an extreme mass ratio inspiral (EMRI). The early stages of such a highly eccentric orbit are not likely to produce detectable gravitational waves (GWs), as the source will only be in a suitable frequency band briefly when it is close to periapsis during each long-period orbit. This repeated burst of emission, firmly in the millihertz band, is the GW peep. While a single peep is not likely to be detectable, if we consider an ensemble of such subthreshold sources, spread across the Universe, together they may produce an unresolvable background noise that could obscure sources otherwise detectable by the Laser Interferometer Space Antenna. Previous studies of the extreme mass ratio signal confusion background focused either on parabolic orbits near the MBH or events closer to merger. We seek to improve this characterization by implementing numerical kludge waveforms that can calculate highly eccentric orbits with relativistic effects. Our focus is on orbits at the point of capture that are farther away from the MBH. Here we present the waveforms and spectra of peeps generated from recent calculations of EMRIs/extreme mass ratio bursts capture parameters and discuss how these can be used to estimate the signal confusion noise generated by such events. We demonstrate the effects of changing the orbital parameters on the resulting spectra as well as showing direct comparisons to parabolic orbits and why the GW ‘peep’ needs to be studied further. The results of this study will be expanded upon in a further paper that aims to provide an update on the EMRI signal confusion noise problem.

LitePIG: a lite parameter inference system for the gravitational wave in the millihertz band

We present a Python based parameter inference system for the gravitational wave (GW) measured in the millihertz band. This system includes the following features: the GW waveform originated from the massive black hole binaries (MBHB), the stationary instrumental Gaussian noise, the higher-order harmonic modes, the full response function from the time delay interferometry and the Gaussian likelihood function with the dynamic nested parameter sampler. In particular, we highlight the role of higher-order modes. By including these modes, the luminosity distance estimation precision can be improved roughly by a factor of 50, compared with the case with only the leading order (ℓ = 2, ∣m∣ = 2) mode. This is due to the response functions of different harmonic modes on the inclination angle are different. Hence, it can help to break the distance-inclination degeneracy. Furthermore, we show the robustness of testing general relativity (GR) by using higher-order harmonics. Our results show that the GW from MBHB can simultaneously constrain four of the higher harmonic amplitudes (deviation from GR) with 95% confidence level of , , and , respectively.

Imaging the Milky Way with Millihertz Gravitational Waves

Modern astronomers enjoy access to all-sky images across a wide range of the electromagnetic spectrum from long-wavelength radio to high-energy gamma rays. The most prominent feature in many of these images is our own Galaxy, with different features revealed in each wave band. Gravitational waves (GWs) have recently been added to the astronomers’ toolkit as a nonelectromagnetic messenger. To date, all identified GW sources have been extra-Galactic and transient. However, the Milky Way hosts a population of ultracompact binaries (UCBs), which radiate persistent GWs in the milliHertz band that is not observable with today’s terrestrial gravitational-wave detectors. Space-based detectors such as the Laser Interferometer Space Antenna will measure this population and provide a census of their location, masses, and orbital properties. In this work, we will show how this data can be used to form a false-color image of the Galaxy that represents the intensity and frequency of the gravitational waves produced by the UCB population. Such images can be used to study the morphology of the Galaxy, identify interesting multimessenger sources through cross-matching, and for educational and outreach purposes.

Confusion noise from Galactic binaries for Taiji

Gravitational waves (GWs) from tens of millions of compact binaries in our Milky Way enter the milli-Hertz band of space-based detection. The majority of them cannot be resolved individually, resulting in a foreground confusion noise for Laser Interferometer Space Antenna (LISA). The concept of Taiji mission is similar to LISA's with slightly better sensitivity, which means that the galactic GW signals will also affect the detection with Taiji. Here we generate the GW signals from 29.8 million galactic binaries for Taiji and subtract the `resolvable' sources. The confusion noise is estimated and fitted in an analytic form with 6-month, 1-year, 2-year and 4-year observation time. We find that the full sensitivity curve is slightly lower for Taiji than for LISA at frequencies of $\leq 0.8$ mHz and around 2~mHz. For a 4-year lifetime, more than 29 thousand sources are resolvable with Taiji. Compared to LISA, Taiji can subtract $\sim 20 \%$ more sources and the distribution of them in our Milky Way is consistent with that of the resolvable sources with LISA. At frequencies around 2~mHz or with the chirp masses ranging from $0.2 M_\odot$ to $0.4 M_\odot$, more sources become resolvable with Taiji.

Calculating the precision of tilt-to-length coupling estimation and noise subtraction in LISA using Fisher information

Tilt-to-length (TTL) noise from angular jitter in LISA is projected to be the dominant noise source in the milli-Hertz band unless corrected in post-processing. The correction is only possible after removing the overwhelming laser phase noise using time-delay interferometry (TDI). We present here a frequency domain model that describes the effect of angular motion of all three spacecraft on the interferometric signals after propagating through TDI. We then apply a Fisher information matrix analysis to this model to calculate the minimum uncertainty with which TTL coupling coefficients may be estimated. Furthermore, we show the impact of these uncertainties on the residual TTL noise in the gravitational wave readout channel, and compare it to the impact of the angular witness sensors' readout noise. We show that the residual TTL noise post-subtraction in the TDI variables for a case using the LISA angular jitter requirement and integration time of one day is limited to the $8\text{ }\text{ }\mathrm{pm}/\sqrt{\mathrm{Hz}}$ level by angular sensing noise. However, using a more realistic model for the angular jitter we find that the TTL coupling uncertainties are 70 times larger, and the noise subtraction is limited by these uncertainties to the $14\text{ }\text{ }\mathrm{pm}/\sqrt{\mathrm{Hz}}$ level.

Millihertz band low-intensity-noise single-frequency laser for space gravitational wave detection

A low-noise single-frequency laser is a key component of the space-based gravitational wave detector, and the intensity noise of the laser directly affects the sensitivity of the space-based GW detector. In this work, we report a low-noise single-frequency laser designed for space-based gravitational wave detector. The laser is based on a master oscillator power amplifier (MOPA), which is designed to possess a low-power, narrow-linewidth seed laser acting as master oscillator (MO) and an all polarization-maintaining fiber amplifier acting as power amplifier (PA). The amplifier that uses a robust mechanical design consists of an Yb-doped double-clad fiber forward pumped by wavelength-locked 976 nm pump laser diode (LD) to achieve 2.13 W of output power and 70 dB of signal-noise ratio (SNR). To suppress the relative intensity noise (RIN) in a millhertz regime (1 mHz–1 Hz), we characterize the power stabilization of a pump diode laser based on a proportional-integral-derivative (PID) feedback control loop where an in-loop photodetector is used. The power fluctuation can be converted into the fluctuation of the current signal by the photodiode, the current signal is converted into the voltage signal and amplified by a transimpedance circuit. Then, the voltage signal is compared with the voltage reference signal, and the error signal is achieved to adjust real-timely the drive current of the pump laser diode. This is a good way to significantly suppress the RIN of a laser at low frequencies, but the measured RIN below 4 mHz is still higher than –60 dBc/Hz. In order to further suppress the RIN to lower than 4 mHz, an active precise temperature control technology is used to suppress the thermal noise from pump LD and fiber coupler. To assess the RIN milliertz regime, we design an RIN measurement system consisting of a high-precision signal acquisition card (24 bit) and a computer program based on LabVIEW. The measurement range of the system is 2 μHz–102.4 kHz and the frequency resolution up to 2 µHz, much better than the counterparts of commercial instruments. By stabilizing the fiber amplifier pump LD current and the temperature of pump LD and the temperature of fiber coupler, the out-of-loop RINs are measured to be –63.4 dBc/Hz@1 mHz and –105.8 dBc/Hz@1 Hz , and in a milliertz regime of 1 mHz–1 Hz, the RIN is below –60 dBc/Hz. The results show that the feedback control of the fiber amplifier pump LD current and the temperature control of the key devices can effectively suppress the RIN in the millihertz frequency band, which lays a foundation for further improving the intensity noise performance in the low frequency band.

Milli-Hertz Gravitational-wave Background Produced by Quasiperiodic Eruptions

Extreme-mass-ratio inspirals (EMRIs) are important targets for future space-borne gravitational-wave (GW) detectors, such as the Laser Interferometer Space Antenna (LISA). Recent works suggest that EMRIs may reside in a population of newly discovered X-ray transients called “quasiperiodic eruptions” (QPEs). Here, we follow this scenario and investigate whether LISA could in the future detect the QPEs. We consider two specific models, in which the QPEs are made of either stellar-mass objects moving on circular orbits around massive black holes (MBHs) or white dwarfs (WDs) on eccentric orbits around MBHs. We find that in either case the five QPEs detected so far are too weak to be resolvable by LISA. However, if QPEs are made of eccentric WD–MBH binaries, they radiate GWs over a wide range of frequencies. The broad spectra overlap to form a background that peaks in the milli-Hertz band and has a signal-to-noise ratio of 9–17 even in the most pessimistic scenario. The presence of this GW background in the LISA band could impact future searches for seed black holes at high redshift as well as stellar-mass binary black holes in the local universe.

Analysis of beam currents under an oscillating cone-jet mode for developing high-precision electrospray thrusters

As an application of electrospray, electrospray thrusters are preferred to work in a steady electrohydrodynamic mode to output high-precision and adjustable thrust through controlling voltages and flow rates. However, voltages and flow rates can only be modified in a small range to avoid mode transiting, thereby limiting the thrust range. To increase the thrust, adding the number of emitters or more grids for beam acceleration is considered, but it inevitably increases mechanical complexities and risks of component failure. In this paper, electrosprays are investigated by analyzing the beam current over the time and frequency domains. Results suggest that the steady cone-jet transfers into an oscillating cone-jet with a frequency of several kHz as the flow rate increases. In the oscillating cone-jet mode, beam currents and flow rates still follow the power-law relation, which is derived for the steady cone-jet. The finding suggests that setting a desired thrust over the oscillating cone-jet mode is feasible, whose maximum thrust allowed is 2.3 times the one in the steady cone-jet mode. The calculated thrust noises of the oscillating cone-jet mode are lower than 0.1 μN/Hz0.5 in the millihertz band, which meets the requirement of most drag-free satellites. The oscillation frequency is also adjustable by changing voltages or flow rates, offering another control parameter for electrospray devices. Compared to other instable modes, the oscillating cone-jet mode demonstrates superior low-noise output and controllability, thereby making it another suitable operational mode for high-precision electrospray thrusters in addition to the steady cone-jet mode.

Constraining the Hubble constant to a precision of about 1% using multi-band dark standard siren detections

Gravitational wave signal from the inspirai of stellar-mass binary black hole can be used as standard sirens to perform cosmological inference. This inspirai covers a wide range of frequency bands, from the millihertz band to the audio-band, allowing for detections by both space-borne and ground-based gravitational wave detectors. In this work, we conduct a comprehensive study on the ability to constrain the Hubble constant using the dark standard sirens, or gravitational wave events that lack electromagnetic counterparts. To acquire the redshift information, we weight the galaxies within the localization error box with photometric information from several bands and use them as a proxy for the binary black hole redshift. We discover that TianQin is expected to constrain the Hubble constant to a precision of roughly 30% through detections of 10 gravitational wave events; in the most optimistic case, the Hubble constant can be constrained to a precision of <10%, assuming TianQin I+II. In the optimistic case, the multi-detector network of TianQin and LISA is capable of constraining the Hubble constant to within 5% precision. It is worth highlighting that the multi-band network of TianQin and Einstein Telescope is capable of constraining the Hubble constant to a precision of about 1%. We conclude that inferring the Hubble constant without bias from photo-z galaxy catalog is achievable, and we also demonstrate self-consistency using the P-P plot. On the other hand, high-quality spectroscopic redshift information is crucial for improving the estimation precision of Hubble constant.

Characterization of the stochastic signal originating from compact binary populations as measured by LISA

The Laser Interferometer Space Antenna (LISA) mission, scheduled for launch in the early 2030s, is a gravitational wave observatory in space designed to detect sources emitting in the milli-Hertz band. In contrast to the present ground based detectors, the LISA data are expected to be a signaldominated, with strong and weak gravitational wave signals overlapping in time and in frequency. Astrophysical population models predict a sufficient number of signals in the LISA band to blend together and form an irresolvable foreground noise. In this work, we present a generic method for characterizing the foreground signals originating from a given astrophysical population of coalescing compact binaries. Assuming idealized detector conditions and perfect data analysis technique capable of identifying and removing the bright sources, we apply an iterative procedure which allows us to predict the different levels of foreground noise.

Degeneracy between mass and peculiar acceleration for the double white dwarfs in the LISA band

ABSTRACT Mass and distance are fundamental quantities to measure in gravitational wave (GW) astronomy. However, recent studies suggest that the measurement may be biased due to the acceleration of GW source. Here, we develop an analytical method to quantify such a bias induced by a tertiary star on a double white dwarf (DWD), since DWDs are the most common GW sources in the milli-Hertz band. We show that in a large parameter space the mass is degenerate with the peculiar acceleration, so that from the waveform we can only retrieve a mass of ${\cal M}(1+\Gamma)^{3/5}$, where ${\cal M}$ is the real chirp mass of the DWD and Γ is a dimensionless factor proportional to the peculiar acceleration. Based on our analytical method, we conduct mock observation of DWDs by the Laser Interferometer Space Antenna. We find that in about $9{{\ \rm per\ cent}}$ of the cases the measured chirp mass is biased by $(5-30){{\ \rm per\ cent}}$ due to the presence of a tertiary. Even more extreme biases are found in about a dozen DWDs and they may be misclassified as double neutron stars, binary black holes, DWDs undergoing mass transfer, or even binaries containing lower-mass-gap objects and primordial black holes. The bias in mass also affects the measured distance, resulting in a seemingly overdensity of DWDs within a heliocentric distance of 1 kpc as well as beyond 100 kpc. Our result highlights the necessity of modelling the astrophysical environments of GW sources to retrieve their correct physical parameters.

Fake Massive Black Holes in the Milli-Hertz Gravitational-wave Band

Abstract In gravitational-wave (GW) astronomy accurate measurement of the source parameters, such as mass, relies on accurate waveform templates. Currently, templates are developed assuming that a source, such as a stellar-mass binary black hole (BBH), is residing in a vacuum. However, astrophysical models predict that BBHs could form in gaseous environments, such as common envelopes, stellar cores, and accretion disks of active galactic nuclei. Here we revisit the impact of gas on the GW waveforms of BBHs with a focus on the early inspiral phase when the GW frequency is around milli-Hertz. We show that for these BBHs, gas friction could dominate the dynamical evolution and hence duplicate chirp signals. The relevant hydrodynamical timescale, τ gas, could be much shorter than the GW radiation timescale, τ gw, in the above astrophysical scenarios. As a result, the observed chirp mass is higher than the real one by a factor of if the gas effect is ignored in the data analysis. This kind of error also results in an overestimation of the source distance by a factor of . By performing matched-filtering analysis in the milli-Hertz band, we prove that the gas-dominated signals are practically indistinguishable from the chirp signals of those more massive BBHs residing in a vacuum environment. Such fake massive objects in the milli-Hertz band, if not appropriately accounted for in the future, may alter our understanding of the formation, evolution, and detection of BBHs.

Ultrarelativistic astrophysics using multimessenger observations of double neutron stars with LISA and the SKA

ABSTRACTRecent work highlights that tens of Galactic double neutron stars are likely to be detectable in the millihertz band of the space-based gravitational-wave observatory, LISA, some of which might be detectable as radio pulsars using the Square Kilometer Array (SKA). We point out that the joint LISA + SKA detection of a fgw ≳ 1 mHz binary, corresponding to a binary period of ≲400 s, would enable precision measurements of ultrarelativistic phenomena. We show that, given plausible assumptions, multimessenger observations of ultrarelativistic binaries can be used to constrain the neutron star equation of state with remarkable fidelity. It may be possible to measure the mass–radius relation with a precision of ≈0.2 per cent after 10 yr of observations with the SKA. Such a measurement would be roughly an order of magnitude more precise than possible with other proposed observations. We summarize some of the other remarkable science made possible with multimessenger observations of millihertz binaries, and discuss the prospects for the detection of such objects.

TianQin project and international collaboration

The proposed TianQin gravitational wave observatory is aiming to detect gravitational wave signals in the millihertz frequency band, through the method of space-borne laser interferometry. In total, three satellites will be launched, each following a geocentric orbit, with an orbital altitude of about one hundred thousand kilometers. They form into an equilateral triangle formation, with an orbital period of <sc>3.6 d.</sc> The orbital plane of TianQin is fixed almost constant, towards one specific gravitational wave source, RXJ0806.3+1527, so that TianQins response to this source is maximized, and this source can be used to calibrate and assess the facilities performance. It is widely anticipated that in the millihertz frequency band, there lurks a wide variety of gravitational wave sources, ranging from massive black hole binary mergers, extreme mass ratio inspirals, Galactic binary white dwarves, stellar mass binary compact objects inspirals, as well as stochastic gravitational wave background. Meanwhile, the expected source number in such frequency band would also be huge. The successful implementation of the TianQin project would pave the way towards exciting prospects of future gravitational wave research. By successfully performing gravitational wave observation, the TianQin gravitational wave observatory can open a new window for the study of gravitational wave astronomy, gravitational wave cosmology as well as gravitational wave physics. The science prospect of TianQin gravitational wave observation can be further enhanced through a combination with multi-band gravitational wave detection and multi-messenger astronomical observations, by collaboration with gravitational wave detectors operating in different frequency bands as well as with other probes focusing on different messengers like electro-magnetic signals, neutrinos or cosmic rays. The TianQin project will also greatly promote the construction of a high-precision space-time reference system, ultra-long-range laser interferometry, high-precision satellite platform, etc. The development of cutting-edge space technologies has important applications in the national economy as well as the national strategic needs. Currently, the TianQin project has made important progress in the precision gravity measurement facility, the payload research base, the laser ranging station, the simulation facility for space-borne gravitation wave detection on ground, and the series test satellite for the TianQin project. Based on the long-term accumulation of relevant technology, the TianQin project team proposed the goal of achieving gravitational wave detection in the 2030s, and a 0123 plan roadmap is formulated, aiming to perform, step by step, lunar or relay satellite laser ranging, testing key technology like space-borne laser interferometry and drag-free control, verifying high precision space-borne laser interferometry technology, and ultimately detecting gravitational wave. By the 2030s, the scientific cooperation between scientists from all over the world and the use of various means to jointly conduct exploration and research on the Universe will face great development. So far, the TianQin project has held many international seminars and received extensive international attention and active participation. Currently, the TianQin Collaboration Group has been formally established, with a collaboration group advisory committee also established, consisting of scientists with significant influence in the field of gravitational wave detection all over the world. The TianQin project will establish a collaborative research or comprehensive cooperation agreement with foreign universities or research organizations, and vigorously promote the China-led space-borne gravitational wave detection business. Through extensive international cooperation, the TianQin project will unite domestic and foreign strengths and strive to take the lead in realizing the gravitational wave detection in the window of millihertz band.

Experimental results from the ST7 mission on LISA Pathfinder

The Space Technology 7 Disturbance Reduction System (ST7-DRS) is a NASA technology demonstration payload that operated from January 2016 through July of 2017 on the European Space Agency's LISA Pathfinder spacecraft. The joint goal of the NASA and ESA missions was to validate key technologies for a future space-based gravitational wave observatory targeting the source-rich milliHertz band. The two primary components of ST7-DRS are a micropropulsion system based on colloidal micro-Newton thrusters (CMNTs) and a control system that simultaneously controls the attitude and position of the spacecraft and the two free-flying test masses (TMs). This paper presents our main experimental results and summarizes the overall the performance of the CMNTs and control laws. We find that the CMNT performance to be consistent with pre-flight predictions, with a measured system thrust noise on the order of $100\,\textrm{nN}/\sqrt{\textrm{Hz}}$ in the $1\,\textrm{mHz}\leq f \leq 30\,\textrm{mHz}$ band. The control system maintained the TM-spacecraft separation with an RMS error of less than 2$\,$nm and a noise spectral density of less than $3\,\textrm{nm}/\sqrt{\textrm{Hz}}$ in the same band. Thruster calibration measurements yield thrust values consistent with the performance model and ground-based thrust-stand measurements, to within a few percent. We also report a differential acceleration noise between the two test masses with a spectral density of roughly $3\,\textrm{fm}/\textrm{s}^2/\sqrt{\textrm{Hz}}$ in the $1\,\textrm{mHz}\leq f \leq 30\,\textrm{mHz}$ band, slightly less than twice as large as the best performance reported with the baseline LISA Pathfinder configuration and below the current requirements for the Laser Interferometer Space Antenna (LISA) mission.

Impact of galactic foreground characterization on a global analysis for the LISA gravitational wave observatory

The Laser Interferometer Space Antenna (LISA) will explore the source-rich milli-Hertz band of the gravitational wave spectrum. In contrast to ground based detectors, where typical signals are short-lived and discrete, LISA signals are typically long-lived and over-lapping, thus requiring a global data analysis solution that is very different to the source-by-source analysis that has been developed for ground based gravitational wave astronomy. Across the LISA band, gravitational waves are both signals and noise. The dominant contribution to this so-called confusion noise (better termed unresolved signal noise) is expected to come from short period galactic white dwarf binaries, but all sources, including massive black hole binaries and extreme mass ratio captures will also contribute. Previous estimates for the galactic confusion noise have assumed perfect signal subtraction. Here we provide analytic estimates for the signal subtraction residuals and the impact they have on parameter estimation while for the first time incorporating the effects of noise modeling. The analytic estimates are found using a maximum likelihood approximation to the full global Bayesian analysis. We find that while the confusion noise is lowered in the global analysis, the waveform errors for individual sources are increased relative to estimates for isolated signals. We provide estimates for how parameter estimation errors are inflated from various parts of a global analysis.

The local nanohertz gravitational-wave landscape from supermassive black hole binaries

Supermassive black hole binaries (SMBHBs) in the 10 million to 10 billion $M_\odot$ range form in galaxy mergers, and live in galactic nuclei with large and poorly constrained concentrations of gas and stars. There are currently no observations of merging SMBHBs--- it is in fact possible that they stall at their final parsec of separation and never merge. While LIGO has detected high frequency GWs, SMBHBs emit GWs in the nanohertz to millihertz band. This is inaccessible to ground-based interferometers, but possible with Pulsar Timing Arrays (PTAs). Using data from local galaxies in the 2 Micron All-Sky Survey, together with galaxy merger rates from Illustris, we find that there are on average $91\pm7$ sources emitting GWs in the PTA band, and $7\pm2$ binaries which will never merge. Local unresolved SMBHBs can contribute to GW background anisotropy at a level of $\sim20\%$, and if the GW background can be successfully isolated, GWs from at least one local SMBHB can be detected in 10 years.

Transition of EMRIs through resonance: Corrections to higher order in the on-resonance flux modification

Extreme-mass-ratio inspirals are candidate events for gravitational wave detection in the millihertz band (by detectors like Laser Interferometer Space Antenna (lisa)). These events involve a stellar-mass black hole, or a similar compact object, descending in the gravitational field of a supermassive black hole, eventually merging with it. Properties of the inspiralling trajectory away from resonance are well known and have been studied extensively; however, little is known about the behaviour of these binary systems at resonance, when the radial and lateral frequencies of the orbit become commensurate. We describe the two existing models: the instantaneous frequency approach used by Gair, Bender, and Yunes and the standard two-time scale approach implemented by Flanagan and Hinderer. In both cases, the exact treatment depends on the modeling of the gravitational self-force, which is currently not available. We extend the results from the work of Gair, Bender, and Yunes to higher order in the on-resonance flux modification and argue that the instantaneous frequency approach is also a valid treatment of the resonance problem. The non-linear differential equations which arise in treating resonances are interesting from a mathematical view point. We present our algorithm for perturbative solutions and the results to third order in the infinitesimal parameter and discuss the scope of this approach.

Enhanced Gravitational Wave Science with LISA and gLISA.

The geosynchronous Laser Interferometer Space Antenna (gLISA) is a space-based gravitational wave (GW) mission that, for the past five years, has been under joint study at the Jet Propulsion Laboratory, Stanford University, the National Institute for Space Research (I.N.P.E., Brazil), and Space Systems Loral. With an arm length of 73,000 km, gLISA will display optimal sensitivity over a frequency region that is exactly in between those accessible by LISA and LIGO. Such a GW frequency band is characterized by the presence of a very large ensemble of coalescing black-hole binaries (BHBs) similar to those first observed by LIGO and with masses that are 10 to 100 times the mass of the Sun. gLISA will detect thousands of such signals with good signal-to-noise ratio (SNR) and enhance the LIGO science by measuring with high precision the parameters characterizing such signals (source direction, chirp parameter, time to coalescence, etc.) well before they will enter the LIGO band. This valuable information will improve LIGO’s ability to detect these signals and facilitate its study of the merger and ring-down phases not observable by space-based detectors. If flown at the same time as the LISA mission, the two arrays will deliver a joint sensitivity that accounts for the best performance of both missions in their respective parts of the milliHertz band. This simultaneous operation will result in an optimally combined sensitivity curve that is “white” from about 3 × 10−3 Hz to 1 Hz, making the two antennas capable of detecting, with high signal-to-noise ratios (SNRs), BHBs with masses in the range (10 − 107)M⊙. Their ability of jointly tracking, with enhanced SNR, signals similar to that observed by the Advanced Laser Interferometer Gravitational Wave Observatory (aLIGO) on September 14, 2015 (the GW150914 event) will result in a larger number of observable small-mass binary black-holes and an improved precision of the parameters characterizing these sources. Together, LISA, gLISA and aLIGO will cover, with good sensitivity, the (10−4 − 103) Hz frequency band.

Background Lamb waves in the Earth's atmosphere

Abstract Lamb waves of the Earth's atmosphere in the millihertz band have been considered as transient phenomena excited only by large events. Here, we show the first evidence of background Lamb waves in the Earth's atmosphere from 0.2 to 10 mHz, based on the array analysis of microbarometer data from the USArray in 2012. The observations suggest that the probable excitation source is atmospheric turbulence in the troposphere. Theoretically, their energy in the troposphere tunnels into the thermosphere at a resonant frequency via thermospheric gravity wave, where the observed amplitudes indeed take a local minimum. The energy leak through the frequency window could partly contribute to thermospheric wave activity.