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Impact of the neutron star crust on the tidal polarizability

The first direct detection of a binary neutron star merger by the LIGO Scientific Collaboration and the Virgo Collaboration (LIGO-Virgo) has opened the brand new era of multimessenger astronomy. Here, this historic detection has been instrumental in providing initial constraints on the tidal polarizability (or deformability) of neutron stars. In turn, the tidal polarizability—an observable highly sensitive to stellar compactness—has been used to impose limits on stellar radii and ultimately on the underlying equation of state (EOS). Besides its strong dependence on the stellar compactness, the tidal polarizability is also sensitive to the second tidal Love number k 2 . It is the main purpose of this paper to perform a detailed study of k 2 which, for a given compactness parameter, encodes the entire sensitivity of the tidal polarizability to the underlying equation of state. In particular, we examine the important role that the crustal component of the EOS plays in the determination of k 2 . A set of realistic models of the equation of state that yield an accurate description of the properties of finite nuclei support neutron stars of two solar masses and provide a Lorentz covariant extrapolation to dense matter are used to solve both the Tolman-Oppenheimer-Volkoff and the differential equations for the induced quadrupole gravitational field from which k 2 is extracted. Given that the tidal polarizability scales as the fifth power of the compactness parameter, a universal relation exists among the tidal polarizability and the compactness parameter that is highly insensitive to the underlying equation of state. Thus, besides an extraction of the tidal polarizabilities, a measurement of the individual stellar masses is also required to impact the mass-radius relation. However, we observe a strong sensitivity of the second Love number to the underlying equation of state—particularly to the contribution from the inner crust. Although by itself the tidal polarizability cannot contribute to the determination of the mass-radius relation, future detections of binary neutron star mergers by the LIGO-Virgo Collaborations during the third observing run and beyond are poised to provide significant constraints on both the tidal polarizabilities and the masses of the individual stars, and thus ultimately on the mass-radius relation. Yet, subleading corrections to the tidal polarizability are encoded in the second Love number k 2 , which displays a large sensitivity to the entire—crust-plus-core—equation of state.

79 ASTRONOMY AND ASTROPHYSICS↗

Experimental Investigation of Pool Boiling Heat Transfer Enhancement in Microgravity in the Presence of Electric Fields

In boiling high heat fluxes are possible driven by relatively small temperature differences, which make its use increasingly attractive in aerospace applications. The objective of the research is to develop ways to overcome specific problems associated with boiling in the low gravity environment by substituting the buoyancy force with the electric force to enhance bubble removal from the heated surface. Previous studies indicate that in terrestrial applications nucleate boiling heat transfer can be increased by a factor of 50, as compared to values obtained for the same system without electric fields. The goal of our research is to experimentally explore the mechanisms responsible for EHD heat transfer enhancement in boiling in low gravity conditions, by visualizing the temperature distributions in the vicinity of the heated surface and around the bubble during boiling using real-time holographic interferometry (HI) combined with high-speed cinematography. In the first phase of the project the influence of the electric field on a single bubble is investigated. Pool boiling is simulated by injecting a single bubble through a nozzle into the subcooled liquid or into the thermal boundary layer developed along the flat heater surface. Since the exact location of bubble formation is known, the optical equipment can be aligned and focused accurately, which is an essential requirement for precision measurements of bubble shape, size and deformation, as well as the visualization of temperature fields by HI. The size of the bubble and the frequency of bubble departure can be controlled by suitable selection of nozzle diameter and mass flow rate of vapor. In this approach effects due to the presence of the electric field can be separated from effects caused by the temperature gradients in the thermal boundary layer. The influence of the thermal boundary layer can be investigated after activating the heater at a later stage of the research. For the visualization experiments a test cell was developed. All four vertical walls of the test cell are transparent, and they allow transillumination with laser light for visualization experiments by HI. The bottom electrode is a copper cylinder, which is electrically grounded. The copper block is heated with a resistive heater and it is equipped with 6 thermocouples that provide reference temperatures for the measurements with HI. The top electrode is a mesh electrode. Bubbles are injected with a syringe into the test cell through the bottom electrode. The working fluids presently used in the interferometric visualization experiments, water and PF 5052, satisfy requirements regarding thermophysical, optical and electrical properties. A 30kV power supply equipped with a voltmeter allows to apply the electric field to the electrodes during the experiments. The magnitude of the applied voltage can be adjusted either manually or through the LabVIEW data acquisition and control system connected to a PC. Temperatures of the heated block are recorded using type-T thermocouples, whose output is read by a data acquisition system. Images of the bubbles are recorded with 35mm photographic and 16mm high-speed cameras, scanned and analyzed using various software packages. Visualized temperature fields HI allows the visualization of temperature fields in the vicinity of bubbles during boiling in the form of fringes. Typical visualized temperature distributions around the air bubbles injected into the thermal boundary layer in PF5052 are shown. The temperature of the heated surface is 35 C. The temperature difference for a pair of fringes is approximately 0.05 C. The heat flux applied to the bottom surface is moderate, and the fringe patterns are regular. In the image a bubble penetrating the thermal boundary layer is visible. Because of the axial symmetry of the problem, simplified reconstruction techniques can be applied to recover the temperature field. The thermal plume developing above the heated surface for more intensive heating is shown. The temperature distribution in the liquid is clearly 3D, and tomographic techniques have to be applied to recover the temperature distribution in such a physical situation. A sequence of interferometric images showing the temperature distribution around the rising bubble, recorded with a high-speed camera is shown. Again, the temperature distribution is 3D, and a more complex approach to the evaluation, the tomographic reconstruction has to be taken. Measurement of the temperature distribution from the fringe pattern temperature distributions that yield important information regarding heat transfer are determined. Two algorithms that allow the quantitative evaluation of interferometric fringe patterns and the reconstruction of temperature fields during boiling have been developed at the Heat Transfer Laboratory of the Johns Hopkins University. In the first algorithm the bubble is assumed to be axially symmetrical, which significantly reduces the computational effort for quantifying the temperature distribution around the bubble. For this purpose the thermal boundary layer around the bubble is divided into equidistant concentric shells, and the refractive index is assumed to be constant in each of the shells. Since large temperature gradients are expected in the vicinity of the bubble during boiling, the deflection of the light beam cannot be neglected in boiling experiments. Since the exit angle of the light beam is known, this allows to account for the deflections and phase shifts outside the boundary layer (in the bulk fluid and in the windows of the test cell). Three dimensional temperature distributions in the vicinity of the bubble are reconstructed using tomographic techniques. In tomography, the measurement volume is sliced into 2D planes. In the present study these planes are parallel to the heated surface. The objective is to determine the values of the field parameter of interest in form of the field function in these 2D planes. The field parameter is the change of the refractive index of the liquid in the measurement volume caused by temperature changes. By superimposing data for many 2D planes recorded at the same time instant, the 3D temperature distribution in the measurement volume is recovered.

Herman, Cila↗