Holographic QCD models, particularly V-QCD (Veneziano-type QCD) models, provide an alternative perspective on quark matter by utilizing the gauge-gravity duality from string theory. These models treat strongly coupled QCD matter as a gravitational system in a higher-dimensional spacetime, offering insights into quark interactions that are difficult to capture using traditional field theory approaches. First, gauge-gravity duality provides an effective description of strongly coupled quark matter.Then, quark deconfinement occurs dynamically, leading to a possible stiffening of the EoS. Thirdly, strange quark matter could be absolutely stable, allowing for strange quark stars. Additionally, Holographic energy scales are used to determine effective QCD interactions at high densities. While no single model is definitively confirmed, overly soft EoSs are largely disfavored, whereas stiff EoSs and hybrid models with phase transitions remain promising.
Spaceborne Synthetic Aperture Radar Performance Prediction
First-order phase transitions can lead to mass twins—neutron stars with the same mass but different internal compositions depending on whether they contain a quark core. The presence of a phase transition can also affect gravitational wave signals from neutron star mergers, producing post-merger oscillations that may be detectable by next-generation gravitational wave observatories. First-order phase transition models predict distinct structural changes in neutron stars, particularly in the form of a quark core surrounded by a hadronic envelope.
Then, a sharp pressure discontinuity is present in the Maxwell construction, while the Gibbs construction allows a mixed phase. Hybrid models incorporate a transition from hadronic matter to deconfined quark matter at sufficiently high densities, providing a more complete description of neutron star interiors. These models bridge the gap between purely hadronic descriptions and full quark matter equations of state by allowing for the coexistence of nucleonic and quark phases within a neutron star core. The transition between hadronic and quark matter can occur in different ways, with some models predicting a first-order phase transition and others favoring a smooth crossover transition. The nature of this transition has profound implications for neutron star properties, including mass, radius, and trade99 review tidal deformability.
V-QCD models naturally predict a stiffer equation of state at high densities, making them compatible with observed neutron star mass constraints. Additionally, these models allow for the exploration of quark deconfinement mechanisms in a more controlled theoretical framework. The Skyrme models utilize effective density-dependent interactions that are calibrated using empirical nuclear matter properties. Another exotic feature that RMF models consider is meson condensation11, particularly pion (π𝜋\piitalic_π) and kaon (K𝐾Kitalic_K) condensation, which can occur at extremely high densities. The onset of meson condensation modifies the EoS by reducing the pressure at given energy densities, leading to additional phase transitions that impact neutron star cooling, thermal evolution, and structural stability. Kaon condensation, in particular, has been suggested as a potential mechanism for rapid neutron star cooling3 via enhanced neutrino emission, making it an important factor in astrophysical modeling.
In this section, we systematically discuss the major constraints imposed on the neutron star EoS and present the essential equations and relationships that reflect neutron star structure. One class of hybrid models is the Quark-Hadron Crossover (QHC) Model, which describes a gradual transition from hadronic matter to quark matter rather than a sharp phase boundary. These models are motivated by lattice QCD simulations, which suggest that at high densities, quark degrees of freedom emerge continuously rather than through a sudden phase transition.
Ostrogradsky’s theorem itself applies to a wide class of higher-derivative theories—from modified gravity models to extended-body dynamics and higher-spin interactions 10. Because of this, we are at liberty to select any convenient reference system from which to analyze our particle-field system’s evolution. The Larmor formula can only be used for non-relativistic particles, which limits its usefulness.
Consequently, self-force terms are excluded at the variational level, eliminating runaway solutions and cmc markets review non-causal behavior without regularization. Our framework further provides a first-principles derivation of minimal coupling and reveals gauge invariance as a necessary consequence of proper-time-based variational structure. The combination of gravitational wave signals, electromagnetic counterparts, and neutrino detections from neutron star mergers will provide unprecedented constraints on neutron star composition, particularly regarding the presence of quark matter. As observational techniques and theoretical modeling improve, the neutron star EoS will become one of the most precisely constrained aspects of dense matter physics. A technique closely related to SAR uses an array (referred to as a “phased array”) of real antenna elements spatially distributed over either one or two dimensions perpendicular to the radar-range dimension. These physical arrays are truly synthetic ones, indeed being created by synthesis of a collection of subsidiary physical antennas.
- The continued integration of astrophysical observations, nuclear experiments, and QCD theory is essential for advancing our understanding of dense matter and potential exotic phases inside neutron stars.
- Over time, individual transmit/receive cycles (PRT’s) are completed with the data from each cycle being stored electronically.
- Future studies must also consider magnetic fields, rotation, finite temperature, and potential dark matter interactions.
- Experimental progress from heavy-ion collisions not only from FAIR, NICA, J-PARC as mentioned above but also BEPCII in China30 and neutron skin measurements (e.g., PREX-II18) will continue to constrain the symmetry energy and stiffness of nuclear matter.
- The core of both the SAR and the phased array techniques is that the distances that radar waves travel to and back from each scene element consist of some integer number of wavelengths plus some fraction of a “final” wavelength.
- In the differential interferogram, each fringe is directly proportional to the SAR wavelength, which is about 5.6 cm for ERS and RADARSAT single phase cycle.
Those mirror images will appear within the shadow of the mirroring surface, sometimes filling the entire shadow, thus preventing recognition of the shadow. Returns from slopes steeper than perpendicular to slant range will be overlaid on those of lower-elevation terrain at a nearer ground-range, both being visible but intermingled. Another viewing inconvenience that arises when a surface is steeper than perpendicular to the slant range is that it is then illuminated on one face but “viewed” from the reverse face. Some return from the roof may overlay that from the front wall, and both of those may overlay return from terrain in front of the building. Long shadows may exhibit blurred edges due to the illuminating antenna’s movement during the “time exposure” needed to create the image.
In modern quantum field theory, physical particles often carry internal degrees of freedom—spin, polarization, or compositeness—that give rise to internal dynamics. However, these internal dynamics similarly produce bounded oscillatory behavior, and do not result in secular growth along the particle’s proper time. Observational constraints will benefit from coinbase exchange review next-generation facilities such as the Einstein Telescope, Cosmic Explorer, and SKA, enabling more precise mass-radius and tidal deformability measurements.
- These objects are the remnants of massive stellar explosions and contain densities exceeding nuclear saturation density, making their internal structure and composition a subject of significant interest in astrophysics and nuclear physics2.
- This process can reduce the pressure at a given energy density, leading to additional phase transitions that influence neutron star cooling and structural stability.
- Multimessenger astrophysics and potential detection of post-merger gravitational wave signatures or mass twins will offer critical insights into the existence of phase transitions and quark cores28.
- Notice that we do not specify the precise nature of this field or its internal symmetry structure, which makes the subsequent derivation entirely general.
- The dynamics of charged particles are significantly impacted by the existence of this force.
An additional safety factor of 5 is introduced for exposure of the public, giving an average whole-body SAR limit of 0.08 W/kg. As argued above, at any given moment, a particle cannot access any value of the field it emitted earlier; that field has already propagated away and is permanently out of reach. After rigorously mathematically proving the VKC and the VDC in the main body of the paper, here we provide intuitive arguments for both, suitable for pedagogical purposes.
Phase Shifter
The point at which the target leaves the view of the radar beam some time later, determines the length of the simulated or synthesized antenna. The synthesized expanding beamwidth, combined with the increased time a target is within the beam as ground range increases, balance each other, such that the resolution remains constant across the entire swath. The core of both the SAR and the phased array techniques is that the distances that radar waves travel to and back from each scene element consist of some integer number of wavelengths plus some fraction of a “final” wavelength.
V Appendix B: Intuitive Explanations of the VKC and VDC
Importantly, the transition from variationally structureless to internally reactive behavior can be probed experimentally. Earlier work on analytic pulse design 21, 22 demonstrated how tailored external fields can coherently activate internal degrees of freedom without full dynamical resolution. This suggests a route to test whether recoil emerges from such induced structure, offering a new perspective on radiation reaction beyond classical self-force models. This structural clarity could support extensions relevant to domains where LL begins to fail. Hybrid EoS models incorporating a phase transition can produce mass twins, neutron stars with the same mass but different internal compositions.
2.1 Nambu–Jona-Lasinio (NJL) Model
When variation is restricted to proper time along the worldline of a point particle, the only admissible interaction with a background field is a contraction of the particle’s four-velocity with a field’s potential evaluated at its current position. The resulting action is gauge invariant not by assumption, but as a structural consequence of the particle’s variational accessibility. Hybrid models incorporate both hadronic and quark matter components, allowing for a transition between them. The key difference among hybrid models is the nature of the transition—either a smooth crossover or a first-order phase transition.
Temporal frequencies being the variables commonly used by radar engineers, their analyses of SAR systems are usually (and very productively) couched in such terms. In particular, the variation of phase during flight over the length of the synthetic aperture is seen as a sequence of Doppler shifts of the received frequency from that of the transmitted frequency. Once the received data have been recorded and thus have become timeless, the SAR data-processing situation is also understandable as a special type of phased array, treatable as a completely geometric process. In comparison, a SAR’s (commonly) single physical antenna element gathers signals at different positions at different times. When the radar is carried by an aircraft or an orbiting vehicle, those positions are functions of a single variable, distance along the vehicle’s path, which is a single mathematical dimension (not necessarily the same as a linear geometric dimension).
Understanding the equation of state (EoS) of neutron stars is crucial for determining key properties such as their mass-radius relation, maximum mass, and tidal deformability, all of which have direct implications for both fundamental physics and astrophysical observations. Over the decades, numerous theoretical models have been proposed to describe the internal composition of neutron stars. In 1998, Akmal et al.4, 5 developed a variational approach to nuclear interactions, resulting in the widely adopted APR model, which remains a benchmark for nucleonic EOSs. Building on this, Read et al.20 in 2009 constructed the ALF1–ALF4 hybrid models by combining APR nuclear matter with color-flavor-locked quark matter, offering structured EOSs suitable for Bayesian inference. The equation of state (EoS) for neutron stars is a crucial topic in astrophysics, nuclear physics, and quantum chromodynamics (QCD), influencing their structure, stability, and observable properties. This review classifies EoS models into hadronic matter, hybrid, and quark matter models, analyzing their assumptions, predictions, and constraints.
4.1 MBPT Model
These constraints come from neutron skin thickness measurements, heavy-ion collisions, and nuclear symmetry energy studies17. This result ruled out overly soft equations of state that predict high tidal deformabilities. Future gravitational wave detections (e.g., Einstein Telescope, Cosmic Explorer14) will further refine these constraints. SAR radar is partnered by what is termed Inverse SAR (abbreviated to ISAR) technology which in the broadest terms, utilizes the movement of the target rather than the emitter to create the synthetic aperture.