Energy Star Research Articles

A simple model of magnetic universe without singularity associated with a quadratic equation of state

A model of magnetic universe based on nonlinear electrodynamics has been introduced by Kruglov (Phys Rev D 92:123523, 2015). This model describes an early inflation era followed by a radiation era. We show that this model is related to the model of universe based on a quadratic equation of state introduced in our previous paper (Chavanis in Universe 1:357, 2015). This correspondence may provide a more fundamental justification of our equation of state. It may arise from quantum corrections to linear electrodynamics when the electromagnetic field becomes very high. We discuss two quantitatively different models of early universe. In Model I, the primordial density of the universe is identified with the Planck density. At t=0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$t=0$$\\end{document}, the universe had the characteristics of a Planck black hole (“planckion” particle). During the inflation, which takes place on a Planck timescale, the size of the universe evolves from the Planck length to a size comparable to the Compton wavelength of the neutrino. If we interpret the radius of the universe at the end of the inflation (neutrino’s Compton wavelength) as a minimum length related to quantum gravity and use Zeldovich’s first formula of the vacuum energy, we obtain the correct value of the cosmological constant. In Model II, the primordial density of the universe is identified with the electron density as a consequence of nonlinear electrodynamics. At t=0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$t=0$$\\end{document}, the universe had the characteristics of an electron. This can be viewed as a refinement of the “primeval atom” of Lemaître. During the inflation, which takes place on a gravitoelectronic timescale, the size of the universe evolves from the electron’s classical radius to a size comparable to the size of a dark energy star of the stellar mass. If we interpret the radius of the universe at the beginning of the inflation (electron’s classical radius) as a minimum length related to quantum gravity and use Zeldovich’s second formula of the vacuum energy, we obtain the correct value of the cosmological constant. This provides an accurate form of Eddington’s relation between the cosmological constant and the mass of the electron. We use these arguments to show that the present universe contains about 1080\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$10^{80}$$\\end{document} protons (Eddington’s number). We also introduce a nonlinear electromagnetic Lagrangian that describes simultaneously the early inflation, the radiation era, and the dark energy era. It may account for a form of “generalized radiation” that is present from the beginning to the end of the cosmic evolution. Baryonic and dark matter are treated as independent noninteracting species. The dark energy era is due to the electromagnetic vacuum energy (zero-point radiation). In this approach, both the early inflation and the late acceleration of the universe (dark energy) arise as a consequence of nonlinear electrodynamics. This leads to a simple model of magnetic universe without singularity (aioniotic universe).

OPTIMIZING ENERGY EFFICIENCY: A COMPREHENSIVE ANALYSIS OF BUILDING DESIGN PARAMETERS

This study explores the critical role of financial incentives, energy performance certifications, government policies, and advanced technologies in driving the adoption of energy-efficient building practices. Financial incentives, such as tax credits, rebates, and grants, are shown to significantly reduce the upfront costs associated with energy-efficient technologies, making these innovations more accessible to developers and building owners. The research highlights the effectiveness of energy performance certifications, like LEED and Energy Star, in enhancing the market value and energy performance of buildings by providing a structured framework for evaluating sustainability. Government policies and building codes, including the International Energy Conservation Code (IECC) and ASHRAE standards, are identified as key drivers of energy efficiency, compelling developers to meet stringent performance standards. Additionally, the integration of renewable energy technologies, such as solar panels and geothermal heat pumps, alongside smart building automation systems, plays a vital role in reducing energy consumption and improving operational efficiency. However, regional disparities in the availability of financial incentives and enforcement of policies present challenges to widespread adoption. The study concludes that expanding financial support, strengthening policy enforcement, and increasing public and industry awareness of the long-term financial and environmental benefits of energy-efficient buildings are essential for accelerating the transition to sustainable building practices. By addressing these challenges, the construction industry can make significant strides toward reducing energy consumption, lowering greenhouse gas emissions, and achieving global sustainability goals.

Charged analog of anisotropic dark energy star in Rastall gravity

Dark energy is one of the potential strategies for preventing compact objects from gravitationally collapsing into singularities. Because it is the cause of the accelerated expansion of our universe, it has the greatest impact on the cosmos. Thus, it is plausible that dark energy will interact with any stellar object that is compact in the universe [Phys. Rev. D 103 (2021) 084042]. Our main goal in this work is to create a simplified model, in the Rastall gravitational framework, of a charged strange star coupled to anisotropic dark energy in Krori–Barua spacetime [J. Phys. A, Math. Gen. 8 (1975) 508]. Here, we consider a specific strange star object, Her [Formula: see text], with observed values of mass [Formula: see text] and radius [Formula: see text] km, so that we can develop our model. In this context, we began by modeling dark energy using the equation of state (EoS), in which the dark energy density is proportional to the isotropic perfect fluid matter-energy density. The Darmois–Israel condition has been used to calculate the unknown constants that are present in the metric. We perform a detailed analysis of the model’s physical properties, including the mass–radius relation, pressure, density, metric function, and dark energy parameters for different Rastall coupling parameter values. We also examine the stability and force equilibrium of our proposed stellar configuration. Following a comprehensive theoretical analysis, we discovered that our suggested model is both singularity-free and meets all stability requirements needed to be a stable, physically reasonable stellar model.

Institutional Conversion to Energy-Efficient Ultra-Low Freezers Decreases Carbon Footprint and Reduces Energy Costs.

Introduction: The storage of biospecimens is a substantial source of greenhouse gas emissions and institutional energy costs. Energy-intensive ultra-low temperature (ULT) freezers used for biospecimen storage are a significant source of carbon emissions. ENERGY STAR-certified ULT freezers have the potential to decrease the carbon footprint. Objective: Quantify the impact of an institutional-scale freezer conversion program on carbon emissions and energy costs. Methods: A ULT freezer energy use prediction model was developed to identify and replace the most inefficient freezers in the research building for this pilot, and eventually institution-wide. Multiple linear regression factors included the number of years of use, storage volume, and ENERGY STAR certification status. Electrical usage and carbon emissions were quantified before and after replacement with ENERGY STAR models. Logistical methods were developed to decrease the risks of exposure of frozen samples to ambient temperature during content transfers. Institution-wide energy costs were derived by converting electrical burden to electrical costs. Carbon footprint assessment from ULT freezer operation was computed using the U.S. EPA Greenhouse Gas Equivalencies Calculator. Results: The pilot project revealed an annual reduction of 310,493 kilowatt hours of electrical usage, equivalent to 134 metric tons of carbon emissions. Annual electrical costs were reduced by $55,889 resulting in an 8-year payback on the initial investment. Using the pilot results, we modeled the benefit of the freezer exchange across the entire institution. The modeling predicted that conversion of the institution's remaining 1119 conventional ULT freezers to ENERGY STAR models would lower annual electrical usage by 7,911,549 kilowatt hours (3423 metric tons of carbon emissions), resulting in savings of over $1.4 million annually. Conclusion: Our methods make a large-scale initiative to replace energy-inefficient ULT freezers logistically possible, reduce carbon footprint, and demonstrate an attractive return on investment while proactively protecting valuable research materials.

Not-so-little Red Dots: Two Massive and Dusty Starbursts at z ∼ 5–7 Pushing the Limits of Star Formation Discovered by JWST in the COSMOS-Web Survey

We present the properties of two candidate massive (M ⋆ ∼ 1011 M ⊙) and dusty (A v > 2.5 mag) galaxies at z = 5–7 in the first 0.28 deg2 of the COSMOS-Web survey. One object is spectroscopically confirmed at z spec = 5.051, while the other has a robust z phot = 6.7 ± 0.3. Thanks to their extremely red colors (F277W–F444W ∼ 1.7 mag), these galaxies satisfy the nominal color selection for the widely studied “little red dot” (LRD) population with the exception of their spatially resolved morphologies. The morphology of our targets allows us to conclude that their red continuum is dominated by highly obscured stellar emission and not by reddened nuclear activity. Using a variety of spectral energy distribution fitting tools and star formation histories, we estimate the stellar masses to be log(M⋆)=11.32−0.15+0.07M⊙ and log(M⋆)=11.2−0.2+0.1M⊙ , respectively, with a red continuum emission dominated by a recent episode of star formation. We then compare their number density to the halo mass function to infer stellar baryon fractions of ϵ ⋆ ∼ 0.25 and ϵ ⋆ ∼ 0.5. Both are significantly higher than what is commonly observed in lower-z galaxies or more dust-obscured galaxies at similar redshifts. With very bright ultra-high-z Lyman-Break Galaxies and some non-AGN-dominated LRDs, such “extended” LRDs represent another population that may require very efficient star formation at early times.

Causal effects of policy and occupant behavior on cooling energy

Rising energy consumption in buildings has prompted architectural engineers and policymakers to ask “what-if” questions in the pursuit of energy efficiency. Current simulation and machine learning methods rely primarily on correlations and associations necessitating causal inference techniques. In this research, a causal inferential approach combining double machine learning and domain knowledge using directed acyclic graphs is employed. The utility of this approach is demonstrated on the 2015 United States Residential energy consumption survey to evaluate the impact of energy policies and occupant behavior on cooling energy consumption. The results show that energy policies such as energy audits, proper insulation, access to interval data and Energy Star qualified windows significantly reduce energy use intensity (EUI). Additionally, air conditioning usage by occupants causally affects EUI. For instance, proper insulation reduces EUI by 5.603 kWh/m2 while changing static thermostat settings to automatic adjustments at certain times reduces EUI by 3.542 kWh/m2. This study suggests potential energy-saving policies for balanced building energy efficiency and functionality.

Modeling compact objects with quark matter and dark energy: A comparative study of the radial oscillation modes of HESS J1731-347 and PSR J0740+6620

We model the massive pulsar J0740+6620 and the light HESS J1731-347 compact object assuming (i) quark matter and (ii) dark energy stars. Within Einstein’s General Relativity, and assuming objects made of isotropic matter, we adopt analytic equations-of-state for both matter contents. Although the inner composition of the objects is very different in each case, both equations-of-state imply qualitatively very similar mass-to-radius relationships. We compute the spectra of radial equations for all four cases and the corresponding wave functions as well as the large frequency separations. A comparison between the different matter contents is made as well.

Anisotropic dark energy stars within vanishing complexity factor formalism: Hydrostatic equilibrium, radial oscillations, and observational implications

We investigate the structure and radial oscillations of anisotropic compact stars composed of dark energy, using the vanishing complexity factor formalism within general relativity. This novel approach establishes a direct link between the energy density and anisotropic factor, providing a robust framework for studying these exotic stellar objects. Employing an Extended Chaplygin Gas equation of state, we numerically compute interior solutions for both isotropic and anisotropic stars, revealing distinct differences in their properties. Additionally, we examine the oscillation modes and frequencies of these stars, highlighting the impact of anisotropy on their pulsational behaviour. Our results reveal distinct differences in the stellar properties, such as the metric potentials, pressure, speed of sound, and relativistic adiabatic index, between the two cases. Furthermore, we calculate the large frequency separation for the fundamental and first excited modes, offering insights relevant for future asteroseismology studies. Our findings shed light on the complex interplay of gravity, matter, and anisotropy in compact stars, providing a new perspective on dark energy's role in their structure and dynamics.

Comparative analysis of dark energy compact stars in f(T,T) and f(T) gravity theories via conformally flat condition

This manuscript is the first investigation of dark energy celestial phenomena in the modified gravity theory by examining dark energy compact stars within the context of modified f(T,T) gravity. In order to compare the outcomes of the f(T,T) and f(T) gravity theories, the model f(T,T)=αT(r)+βT(r)+ϕ is selected. This model is then simplified to f(T) gravity by setting β = 0. The f(T) gravity is torsion-based gravity, while in f(T,T ) gravity trace of energy-momentum tensor is coupled with torsion. Moreover, we note that we have more dense object formation in f(T,T) gravity as compared to f(T )-gravity. The spherically symmetric space-time inside the internal geometry is analyzed using a conformally flat condition, while the Schwarzschild geometry represents the outer space-time. Numerous characteristics of dark energy stars are examined, including equation of state components, energy conditions, and dark energy pressure components. Empirical evidence for the existence of dark energy in stellar configurations is presented by the results for pressure components in dark energy, which show a significant negative tendency in these stellar parameters. A complete analysis is performed by thoroughly investigating energy conditions, pressure profiles, sound speeds, gradients, adiabatic index, Tolman–Oppenheimer–Volkoff equation, mass function, compactness, and redshift function. The mass-radius relation is also discussed via M − R curves. This confirms that the studied star configuration is realistic and acceptable.

Finch-Skea dark energy star with anisotropy

Finch-Skea dark energy star with anisotropy

Quantifying the Enhanced Performance of Multifamily Residential Passive House over Conventional Buildings in Terms of Energy Use

In response to escalating energy demands and global warming concerns, the Passive House Standard has emerged as a solution in residential construction, aiming to drastically reduce energy consumption and operational costs primarily through high-performance building envelopes. While a considerable volume of the literature has focused on the Passivhaus Institute (PHI) standards, predominantly in European contexts, there is a gap in research on the Passive House Institute US (Phius) standards, particularly in North American climates. This study conducts a quantitative comparative analysis of two adjacent multifamily residential buildings in Central Pennsylvania, Climate Zone 5A—one built using conventional construction methods and the other following Passive House (PHIUS+ 2015) certification standards—to validate the energy efficiency improvements attributed to Passive House designs. A comparative analysis of the whole building energy use over two years reveals that the Passive House building consumes approximately 50% less energy than its conventional counterpart in terms of whole building energy use and the national median recommended benchmark metric defined by the Energy Star Portfolio Manager. These findings emphasize the potential for significant energy savings and greenhouse gas reductions in residential buildings, highlighting the necessity for policymakers and governments to incentivize the adoption of Passive House standards to achieve environmental sustainability and reduce energy costs for society.

Possible dark energy stars in Rastall gravity

Observational evidence revealed that in the composition of the Universe, the dark energy is in heap proportion which is mainly responsible for the accelerated expansion of the Universe. The astrophysicists hypothesized that every astrophysical object is likely interact with the dark energy Sakti and Sulaksono [Phys. Rev. D 103 (2021) 084042]. Therefore, researchers are intended to study the astrophysical objects with dark energy interaction. In this paper, we proposed a dark energy stars (composed of with dark matter and ordinary matter) model in the Rastall theory of gravity. The Rastall field equations are obtained in the Tolman–Kuchowicz-type metric. To solve the field equations, the arbitrary constants involved in the field equations (due to Tolman–Kuchowicz ansatz) are obtained by matching the interior geometry with the exterior Schwarzschild geometry. The obtained solution is tested physically by computing some analytical results and plotting graphs of different physical parameters like pressure, density for ordinary matter, density for dark matter, mass function, compactness and surface redshift. Stability of the model is also analyzed by different tests like velocity of sound, adiabatic index and TOV equations. The influence of the Rastall parameter on the model has been studied by plotting graphs and computing numerical values of model’s physical parameters for different values of the Rastall parameter. We infer that our propounded model fulfills all the necessary requirements for a physically plausible model.

Building benchmarking and energy performance: Analysis of social and affordable housing in British Columbia, Canada

This research assesses the energy performance of social and affordable housing by conducting quantitative analysis of 23 community housing buildings in British Columbia (BC) using ENERGY STAR Portfolio Manager. The study sampled community housing buildings, tracked utility bills from 2019 to 2022, and analyzed weather-normalized energy consumption. We find that high-rise buildings in our dataset performed worse compared to other buildings in the dataset and to market housing buildings in BC. We attribute these differences to variability in building characteristics, construction methods, and mechanical systems. Results also show that average energy consumption per dwelling unit in community housing buildings is lower than the BC average, indicating that residents in social and affordable housing use less energy. This could be linked to the lack of amenities in community housing like air conditioning as well as possible efforts taken by residents to reduce utility bills by using less energy. These results demonstrate that it is important to retrofit these buildings for the sake of building and environmental performance but also, and perhaps more critically, to improve the living conditions of those who live in social and affordable housing. Limited understanding of the influence of occupant behaviour on energy performance is a study limitation warranting further study.

Non-radial oscillations in anisotropic dark energy stars

We study the non-radial f-mode oscillations of both isotropic and anisotropic dark energy stars by using the modified Chaplygin prescription of dark energy to model the stellar matter. The anisotropic pressure in the system is modeled with Bowers–Liang prescription. By solving the stellar structure equations in presence of anisotropy, we study the global properties of the dark energy star and compare the mass-radius profiles with data from GW events and milli-second pulsars. The stellar radial and anisotropic pressure profiles have also been investigated. We proceed to determine the prominent non-radial l=2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$l=2$$\\end{document}f-mode frequencies of the anisotropic dark energy star by employing the Cowling approximation and analyse and quantify the spectra by varying the anisotropic parameter. We report that f-mode spectra of dark energy star have distinctly different behaviour compared to neutron star and quark star, and this may possibly help in its future identification. Further, the tidal deformability factors of the anisotropic dark energy stars have also been analyzed.

Dark energy stars in the context of black holes — The physical profiles

The dark energy star is a hypothetical model proposed as an alternative to address problems related to the structure of black holes (BHs), such as the presence of singularities. While dark energy star models have been previously explored, their application to BHs remains unexplored. This paper aims to investigate the concept of dark energy stars and compare their properties to BHs. The primary objective is to explore the physical profiles of dark energy stars and evaluate their similarity to the physical properties of BHs described by the Schwarzschild solution. To achieve this, specific properties of the dark energy star models need to be satisfied in the context of BHs, and their physical profiles are studied. The metric function [Formula: see text] proposed by M. R. Finch and J. E. F. Skea [Class. Quantum Grav. 6, 467 (1989)], as adopted by A. Banerjee, M. K. Jasim and A. Pradhan [Mod. Phys. Lett. A 35, 2050071 (2020), arXiv:1911.09546 [gr-qc]], is used and parametrized, making it close to BH spacetimes. The findings show that the model exhibits properties similar to BHs in terms of the stellar radius, compactness, surface redshift, and nature of gravity. Specifically, the dark energy star model behaves like BHs with a dark energy parameter [Formula: see text], satisfying all energy conditions. However, it should be noted that the investigation is limited to static spherically symmetric cases and further studies are required to explore the model in rotating cases. Overall, this study sheds light on the potential of dark energy star models in explaining BH properties and presents promising avenues for further research in understanding the nature of BHs and dark energy.

Decoding Energy Usage Predictions: An Application of XAI Techniques for Enhanced Model Interpretability

The growing complexity of machine learning models has heightened the need for interpretability, particularly in applications impacting resource management and sustainability. This study addresses the challenge of interpreting predictions from sophisticated machine learning models used for building energy consumption predictions. By leveraging Explainable AI (XAI) techniques, including Permutation Importance, SHapley Additive exPlanations (SHAP), and Local Interpretable Model-Agnostic Explanations (LIME), we have dissected the predictive features influencing building energy usage. Our research delves into a dataset consisting of various building characteristics and weather conditions, applying an XGBoost model to predict Site Energy Usage Intensity (Site EUI). The Permutation Importance method elucidated the global significance of features across the dataset, while SHAP provided a dual perspective, revealing both the global importance and local impact of features on individual predictions. Complementing these, LIME offered rapid, locally focused interpretations, showcasing its utility for instances where immediate insights are essential. The findings indicate that 'Energy Star Rating', 'Facility Type', and 'Floor Area' are among the top predictors of energy consumption, with environmental factors also contributing to the models' decisions. The application of XAI techniques yielded a nuanced understanding of the model's behavior, enhancing transparency and fostering trust in the predictions. This study contributes to the field of sustainable energy management by demonstrating the application of XAI for insightful model interpretation, reinforcing the significance of interpretable AI in the development of energy policies and efficiency strategies. Our approach exemplifies the balance between predictive accuracy and the necessity for model transparency, advocating for the continued integration of XAI in AI-driven decision-making processes.

The role of above-code labeling programs in reducing CO2e emissions in residential buildings

Residential buildings account for 15 % of total U.S. carbon dioxide (CO2) emissions. Voluntary, above-code labeling programs, such as the ENERGY STAR® and Zero Energy Ready Home™ programs, can play a crucial role in reducing the carbon footprint of the new construction residential building sector by encouraging adoption of more energy-efficient and lower emissions building practices and technologies. It’s important for the industry to understand the carbon dioxide equivalent (CO2e) and energy cost savings potential of these programs. To estimate the potential CO2e emissions savings for homes built to above-code labeling program levels, it is imperative to have reliable and accurate tools for estimating emissions from buildings. The open-source OpenStudio-ERI workflow employs detailed physics-based building energy modeling (BEM) to estimate energy usage and operational CO2e emissions. In this study we use the OpenStudio-ERI workflow and regional, time-varying emissions factors from the Cambium database to compare the CO2e emissions and energy costs of homes built to performance levels required by these above-code labeling programs relative to homes built to model energy codes. We present the results of our analysis and provide a range of emissions and annual energy cost savings for the above-code labeling programs.

Reducing the energy consumption of buildings by implementing insulation scenarios and using renewable energies

The reduction of fossil energy sources, the harmful environmental effects caused by high energy consumption, and the increase in the share of energy consumption in the building sector have increased the need to pay attention to building energy consumption. This study offers an intricate examination of a residential locality in Florida, with a particular emphasis on the architectural design of a building, issues related to the local environment and several possibilities for enhancing energy efficiency. It examines the influence of the environment in the area on architectural design and investigates two different possibilities for improving energy efficiency. The first scenario focuses on assessing thermal insulation and shading, while the second scenario envisions utilizing photovoltaic cells to achieve a zero-energy building. The proposed initiatives seek to optimize energy efficiency, save expenses, and foster environmental sustainability in the region. In this research, the total energy consumption of a building with residential use in the climate of the case study was validated by DesignBuilder® simulation software, and the results obtained from the software. Then, using the standard of energy consumption of the building, various strategies for optimizing energy consumption have been simulated. Using energy simulation software, solutions for using external horizontal awnings and installing a thermal insulation sheet on the external wall of the building were investigated, which resulted in a reduction of 200 kWh of energy consumption compared to the normal state. Then, the building’s energy consumption intensity was calculated for each of the proposed solutions, and the building’s energy classification was determined with energy star and LEED standards.

Symmetry energy and neutron star properties constrained by chiral effective field theory calculations

We investigate the nuclear symmetry energy and neutron star properties using a Bayesian analysis based on constraints from different chiral effective field theory calculations using new energy density functionals that allow for large variations at high densities. Constraints at high densities are included from observations of GW170817 and from NICER. In particular, we show that both NICER analyses lead to very similar posterior results for the symmetry energy and neutron star properties when folded into our equation-of-state framework. Using the posteriors, we provide results for the symmetry energy and the slope parameter, as well as for the proton fraction, the speed of sound, and the central density in neutron stars. Moreover, we explore correlations of neutron star radii with the pressure and the speed of sound in neutron stars. Our 95% credibility ranges for the symmetry energy Sv, the slope parameter L, and the radius of a 1.4M⊙ neutron star, R1.4, are Sv=(30.6–33.9)MeV, L=(43.7–70.0)MeV, and R1.4=(11.6–13.2)km. Our analysis for the proton fraction shows that larger and/or heavier neutron stars are more likely to cool rapidly via the direct Urca process. Within our equation-of-state framework a maximum mass of neutron stars Mmax>2.1M⊙ indicates that the speed of sound needs to exceed the conformal limit. Published by the American Physical Society 2024

A relativistic appearance of hotspots on an ultra-compact dark star

We depict the deflection of light near ultra-compact dark energy stars with a photon sphere, drawing inspiration from modern confirmations of general relativity. Utilizing the description of dark energy through a phantom scalar field, we model the spacetime outside the star using an exact dark energy solution metric. We provide a summary of the properties of photon orbits. Additionally, we illustrate the relativistic appearance of a hot spot on the surface of a dark energy star and investigate both the optical appearance of the surface and the star’s visual size on the screen of an asymptotic observer.