Tidal Excitation of Modes in Binary Systems with Applications to Binary Pulsars

We consider the tidal excitation of modes in a binary system of arbitrary eccentricity. For a circular orbit, the modes generally undergo forced oscillation with a period equal to the orbital period ($T$). For an eccentric orbit, the amplitude of each tidally excited mode can be written approximately as the sum of an oscillatory term that varies sinusoidally with the mode frequency and a `static' term that follows the time dependence of the tidal forcing function. The oscillatory term falls off exponentially with increasing \b (defined as the ratio of the periastron passage time to the mode period), whereas the `static' term is independent of \b. For small \b modes (\b \approx 1), the two terms are comparable, and the magnitude of the mode amplitude is nearly constant over the orbit. For large \b modes (\b \gta a few), the oscillatory term is very small compared to the `static' term, in which case the mode amplitude, like the tidal force, varies as the distance cubed. For main sequence stars, $p$, $f$, and low order $g$-modes generally have large \b and hence small amplitudes of oscillation. High overtone $g$-modes, however, have small overlap with the tidal forcing function. Thus, we expect an intermediate overtone $g$-mode with \b \sim 1 to have the largest oscillation amplitude. The dependence on mode damping and the stellar rotation rate is considered, as well as the effects of orbital evolution. We apply our work to the two binary pulsar system: PSR J0045-7319 and PSR B1259-63.Comment: 28 pages of uuencoded compressed postscript. 9 postscript figures available by anonymous ftp from ftp://brmha.mit.edu/ To be published in ApJ

On the Validity of the Classical Apsidal Motion Formula for Tidal Distortion

We check the validity of the widely used classical apsidal motion formula as a function of orbital parameters, stellar structure, and stellar rotation rate by comparing dynamical calculations of the periastron advance with the static tidal formula. We find that the classical formula gives very accurate results when the periods of the low order quadrupole g, f and p modes are smaller than the periastron passage time by a factor of about 7 or more. However, when this condition is not satisfied, the difference between the classical formula and the exact result can be quite large, and even periastron recession can result. The largest difference arises when one of the low order modes of the star is nearly resonant with an integer multiple of the orbital frequency minus twice the rotation rate of the star. The resonance of higher order g-modes (number of radial nodes \gta 4) with the orbit is very unlikely to cause significant deviation from the classical result because of their weak coupling to the tidal force and thus their small contribution to the apsidal motion. Resonances involving rotational modes of the star are also unlikely to make much contribution to the apsidal motion because of their small overlap with the tidal force, even though they have periods comparable to the periastron passage time. We apply our work to two famous binary systems (AS Cam and DI Her) which show abnormally small apsidal motion, and conclude that dynamical effects are unimportant for these systems, i.e. the static tide assumption is an excellent approximation.Comment: paper is in uuencoded, compressed post-script file: 6 post-script figures available via anonymous ftp at ftp://brmha.mit.edu/papers/ftp

Electromagnetic wave scattering by discrete random media with remote sensing applications

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 2001.Includes bibliographical references (p. 171-182).This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.The scattering of electromagnetic waves in medium with randomly distributed discrete scatterers is studied. Analytical and numerical solutions to several problems with implications for the active and passive remote sensing of the Earth environment are obtained. The quasi-magnetostatic (QMS) solution for a conducting and permeable spheroid under arbitrary excitation is presented. The spheroid is surrounded by a weakly conducting background medium. The magnetic field inside the spheroid satisfies the vector wave equation, while the magnetic field outside can be expressed as the gradient of the Laplace solution. We solve this problem exactly using the separation of variables method in spheroidal coordinates by expanding the internal field in terms of vector spheroidal wavefunctions. The exact formulation works well for low to moderate frequencies; however, the solution breaks down at high frequency due to numerical difficulty in computing the spheroidal wavefunctions. To circumvent this difficulty, an approximate theory known as the small penetration-depth approximation (SPA) is developed. The SPA relates the internal field in terms of the external field by making use of the fact that at high frequency, the external field can only penetrate slightly into a thin skin layer below the surface of the spheroid. For spheroids with general permeability, the SPA works well at high frequency and complements the exact formulation. However, for high permeability, the SPA is found to give accurate broadband results. By neglecting mutual interactions, the QMS frequency response from a collection of conducting and permeable spheroids is also studied.(cont.) In a dense medium, the failure to properly take into account of multiple scattering effects could lead to significant errors. This has been demonstrated in the past from extensive theoretical, numerical, and experimental studies of electromagnetic wave scattering by densely packed dielectric spheres. Here, electromagnetic wave scattering by dense packed dielectric spheroids is studied both numerically through Monte Carlo simulations and analytically through the quasi-crystalline approximation (QCA) and QCA with coherent potential (QCA-CP). We assume that the spheroids are electrically small so that single-particle scattering is simple. In the numerical simulations, the Metropolis shuffling method is used to generate realizations of configurations for non-interpenetrable spheroids. The multiple scattering problem is formulated with the volume integral equation and solved using the method of moments with electrostatic basis functions. General expressions for the self-interaction elements are obtained using the low-frequency expansion of the dyadic Green's function, and radiative correction terms are included. Results of scattering coefficient, absorption coefficient, and scattering matrix for spheroids in random and aligned orientation configurations are presented. It is shown that independent scattering approximation can give grossly incorrect results when the fractional volume of the spheroids is appreciable.(cont.) In the analytical approach, only spheroids in the aligned configuration are solved. Low-frequency QCA and QCA-CP solutions are obtained for the average Green's function and the effective permittivity tensor. For QCA-CP, the low-frequency expansion of the uniaxial dyadic Green's function is required. The real parts of the effective permittivities from QCA and QCA-CP are compared with the Maxwell-Garnett mixing formula. ...by Chi On Ao.Ph.D

The ROHP-PAZ Polarimetric Radio Occultation research dataset and its applications

Trabajo presentado al 7th International Workshop on Occultations for Probing Atmosphere and Climate y al 9th Workshop of the International Radio Occultation Working Group (OPAC-IROWG), celebrados del 8 al 14 de septiembre de 2022 en Leibnitz, Austria.After more than 4 years on orbit, the Radio Occultations and Heavy Precipitation aboard PAZ satellite (ROHP-PAZ) experiment has already demonstrated the ability of polarimetric radio occultations (PRO) to detect precipitation. In fact, PRO have shown potential not only in rain detection, but also in precipitation characterization and in sensing the associated vertical cloud structures. PAZ PRO Δϕ observable profiles were made available in 2020 trough the ICE servers (https://paz.ice.csic.es), (https://genesis.jpl.nasa.gov). and more recently through the JPL A new re-processing of the PRO observations is being carried out with the aim to make it public during the second half of 2022. In addition to a better treatment of the rainy observations, the new re-processed profiles will come with an extensive collocation dataset that will allow the users to address scientific studies much more easily. These will take into account the limb-sounding geometry of the observations, performing the collocations directly into the RO rays obtained through a ray-tracer. These collocations include observations like the 30-minute geostationary 10.8 µm brightness temperature, GPM IMERG surface precipitation, microwave brightness temperatures from the numerous overpasses by the satellites in the GPM constellation, radar reflectivities from the GPM core satellite and the NEXRAD ground based weather radars, among others. Furthermore, the collocation algorithms are designed so that more external observations can be easily included. In addition to the exact collocations as described above, external databases are also checked so that coincidences with Tropical Cyclones, Mesoscale Convective Systems and other relevant precipitating systems are identified nearby PAZ observations. In this presentation, we will show a brief overview of the re-processing of the ROHP-PAZ data, with emphasis in the differences between the Δϕ profiles obtained from UCAR’s CDAAC excess phases and from those obtained from JPL excess phases. After that, examples of the coincident datasets will be presented. Results will include statistics gathered from the differentiation of different precipitation regimes (e.g. stratiform vs convective), identification and validation of cloud top height determination, and comparison with other relevant parameters obtained from the collocated observations.The ROHP-PAZ project is part of the Grant RTI2018-099008-B-C22 funded by the Spanish Ministry of Science and Innovation MCIN/AEI/10.13039/501100011033 and by “ERDF A way of making Europe” of the “European Union”. Part of the investigations are done under the EUMETSAT ROM SAF CDOP4. This work was partially supported by the program Unidad de Excelencia María de Maeztu CEX2020-001058-M. Part of this research has received funding from the postdoctoral fellowships program Beatriu de Pinós, funded by the Secretary of Universities and Research (Government of Catalonia) and by the Horizon 2020 program of research and innovation of the European Union under the Marie Sklodowska-Curie grant agreement No 801370.Peer reviewe

A Multi-center exercise on the sensitivity of PAZ GNSS Polarimetric RO for NWP modelling

Trabajo presentado al 7th International Workshop on Occultations for Probing Atmosphere and Climate y al 9th Workshop of the International Radio Occultation Working Group (OPAC-IROWG), celebrados del 8 al 14 de septiembre de 2022 en Leibnitz, Austria.A better understanding of the thermodynamics of heavy precipitation events is necessary towards improving weather and climate models and quantifying the impact of climate variability on precipitation. However, there are limited observations available to assess the model structure within heavy precipitation conditions. Recently, it has also been shown that the Radio Occultations Through Heavy Precipitation (ROHP) GNSS polarimetric radio occultation (GNSS PRO) observations are highly sensitive to hydrometeors above the freezing layer, which expands the potential uses of the GNSS PRO dataset for weather-related science and applications. An exercise is presented to analyze the sensitivity of PRO observations for NWP modeling applications. The ROHP experiment now provides over four years of coincident thermodynamic and precipitation information with high vertical resolution within regions with thick clouds. Murphy et al. (2019) simulated GNSS airborne polarimetric RO (GNSS PRO) events along an atmospheric river. These were modeled by the community WRF mesoscale model using two different microphysical parameterization schemes. The GNSS PRO observables simulated with the two schemes differed significantly, more than the actual GNSS PRO precision. The new exercise presented here reproduces this methodology for spaceborne data, using different global and regional NWP models, and it analyzes the results and divergences with the help of actual GNSS PRO data acquired aboard the PAZ satellite. The objectives of the activity are: (1) To compare simulated GNSS PRO observables, generated with models from different centers and different microphysics schemes, against actual PAZ GNSS PRO observables. Can the models reproduce the main features of the actual data? (2) To assess whether different models/schemes result in different GNSS PRO observables, and whether these differences are larger than the measurement uncertainty. This effort provides insight on future methods to assimilate the PRO profile alongside other conventional (non-polarimetric) RO data. (3) To examine the utility of PAZ GNSS PRO observations for model validation and diagnosis. The exercise includes comparisons with ECWMF reanalysis ERA-5 model, the operational NWP at the Japan Meteorological Agency, and a near-real-time implementation of the WRF regional model over the northeastern Pacific produced at the Center for Western Weather and Water Extremes (CW3E) called West WRF, among others.The ROHP-PAZ project is part of the Grant RTI2018-099008-B-C22 funded by the Spanish Ministry of Science and Innovation MCIN/AEI/10.13039/501100011033 and by “ERDF A way of making Europe” of the “European Union”. Part of the investigations are done under the EUMETSAT ROM SAF CDOP4. This work was partially supported by the program Unidad de Excelencia María de Maeztu CEX2020-001058-M. Part of this research has received funding from the postdoctoral fellowships program Beatriu de Pinós, funded by the Secretary of Universities and Research (Government of Catalonia) and by the Horizon 2020 program of research and innovation of the European Union under the Marie Sklodowska-Curie grant agreement No 801370.Peer reviewe

Evaluation of Refractivity Profiles from CHAMP and SAC-C GPS Radio Occultation

The GeoForschungsZentrum's Challenging Minisatellite Payload for Geophysical Research and Application (CHAMP, Germany-US) and the Comision Nacional de Actividades Especiales' Satelite de Aplicaciones Cientificas-C (SAC-C, Argentina-US) missions are the first missions to carry a second-generation Blackjack Global Positioning System (GPS) receiver. One of the new features of this receiver is its ability to sense the lower troposphere closer to the surface than the proof-of-concept GPS Meteorology experiment (GPS/MET). Since their launch, CHAMP and SAC-C have collected thousands of GPS radio occultations, representing a wealth of measurements available for data assimilation and Numerical Weather Prediction (NWP). In order to evaluate the refractivity data derived by the Jet Propulsion Laboratory (JPL) from raw radio occultation measurements, we use Data Assimilation Office (DAO) 6-hour forecasts as an independent state of the atmosphere. We compare CHAMP and SAC-C refractivity (processed by JPL) with refractivity calculated from the DAO global fields of temperature, water vapor content and humidity. We show statistics of the differences as well as histograms of the differences

Calibration and validation of the Polarimetric Radio Occultation and Heavy Precipitation experiment aboard the PAZ satellite

This paper presents the calibration and validation studies for the Radio Occultation and Heavy Precipitation experiment aboard the PAZ satellite. These studies, necessary to assess and characterize the noise level and robustness of the differential phase shift (ΔΦ18) observable of polarimetric radio occultations (PROs), confirm the good performance of the experiment and the capability of this technique in sensing precipitation. It is shown how all the predicted effects that could have an impact into the PRO observables (e.g., effect of metallic structures nearby the antenna, the Faraday rotation at the ionosphere, signal impurities in the transmission, and altered cross-polarization isolation) are effectively calibrated and corrected, and they have a negligible effect on the final observable. The on-orbit calibration, performed using an extensive dataset of free-of-rain and low-ionospheric activity observations, is successfully used to correct all the collected observations, which are further validated against independent precipitation observations confirming the sensitivity of the observables to the presence of hydrometeors. The validation results also show how vertically averaged 18 can be used as a proxy for precipitation.This research has been supported by NASA ROSES Earth Science U.S. Participating Investigator grant no. 14- ESUSPI14-0014; Spanish Ministry of Science, Innovation and Universities (RTI2018-099008-B-C22); and EUMETSAT (ROM SAF CDOP3)

Tutorial on GNSS Polarimetric Radio Occultations (GNSS PRO)

Talk delivered in 1st Paz Polarimetric Radio Occultations User Workshop, 23 April 202045 minute tutorial to explain the basics of the GNSS polarimetric radio occultation

The Effects of Heavy Precipitation on Polarimetric Radio Occultation (PRO) Bending Angle Observations

Following the successful launch of the Spanish PAZ mission the proof of concept experiment ¿Radio Occultation and Heavy Precipitation with PAZ¿ (ROHP-PAZ) started operating in May 2018. The ROHP-PAZ observations demonstrated that precise measurements of the phase shift between horizontal and vertical polarizations from Global Navigation Satellite System (GNSS) L-band signals are sensitive to oriented hydrometeors along the ray paths. While this differential phase shift measurement as a function of time has proven very useful, the regular radio occultation (RO) intermediate products from different polarized channels, such as bending angle and phase retrievals on the domain of impact parameter, have never been exploited. In this research, we studied the characteristics of polarimetric phase and bending angle difference retrieved by the radio-holographic (RH) method to mitigate atmospheric multipath effect and to explore their use in data assimilation. To validate RH approach in polarimetric retrievals, we performed end-to-end simulations where the hydrometeors are modeled by the effective refractivity with different horizontal extents. The simulation results demonstrate that the strong precipitation (>15 mm h^-1) with 40-km horizontal extent can be detected with the retrieved bending angle shift. The calibration process on the impact parameter domain has also been developed to extract the differential phase and bending angle shift from the actual polarimetric RO data. Statistics from the PAZ data shows that the mean retrieved RH polarimetric phase shift with various horizontal extent is approximately proportional to the tangent point location rain rate at a ratio of 0.02 rad (mm h^-1)^-1It is supported by NASA ROSES Earth Science U.S. Participating Investigator Program 14-ESUSPI14-0014. The GNSS PRO experiment aboard PAZ is funded by the Spanish Grant MCI RTI2018-099008-B-C21/AEI/10.13039/501100011033/ERDF. E.C. is member of the EUMETSAT ROM SAF

Calibration, Validation, and Science Results from PAZ Polarimetric Radio Occultations

Talk delivered in 100th American Meteorological Society in Boston, USA, 14 January 2020The Radio Occultations and Heavy Precipitation (ROHP) experiment on board the Spanish satellite PAZ was launched in February 2018 to demonstrate the concept of polarimetric radio occultation (PRO) in detecting heavy precipitation. Soon after its activation, it became clear that the signals exhibited signatures of precipitation structures, therefore confirming the hypothesis and its main science goal. Since high vertical-resolution tropospheric water vapor profiles can be retrieved simultaneously through clouds and precipitation, the PAZ data offers a unique view of water vapor in extreme weather conditions that pose significant difficulties to passive infrared and microwave sounder retrievals. The PRO technique consists in measuring the phase difference between the horizontal (H) and vertical (V) components of the electromagnetic field coming from GPS satellites in an occulting geometry. H and V components are measured independently, yet synchronously, with a dual linear polarized antenna placed on a Low Earth Orbiter and pointing towards the limb of the Earth in the satellite¿s anti-velocity direction. In the presence of asymmetric hydrometeors (flattened during their fall by air drag), the phase delay in the H component is larger than for the V component. PAZ data confirm that this phase delay difference can be measured. In this talk, I will describe the calibration and validation of the PAZ PRO data. Unlike standard RO processing, PRO measurements must be carefully calibrated to remove non-hydrometeor contributions (e.g., antenna cross-polarization, ionospheric effects) to the H-V phase difference observable. Validation of the PAZ polarimetric phase difference relies on global precipitation products such as IMERG and collocated GPM precipitation radar measurements. Forward simulations of PAZ observables in convective environments based on TRMM/GPM and CloudSat retrievals show that PAZ measurements are sensitive not only to heavy precipitation but also to frozen hydrometeors in the tropical mid-troposphere. We will discuss implications of these results and our ongoing retrieval efforts