Phase Curves Research Articles

The VSPEC Collection: A suite of utilities to model spectroscopic phase curves of 3D exoplanet atmospheres in the presence of stellar variability

We present the Variable Star PhasE Curve (VSPEC) Collection, a set of Python packages for simulating combined-light spectroscopic observations of 3-dimensional exoplanet atmospheres in the presence of stellar variability and inhomogeneity. VSPEC uses the Planetary Spectrum Generator’s Global Emission Spectra (PSG/GlobES) application along with a custom-built multi-component time-variable stellar model based on a user-defined grid of stellar photosphere models to produce spectroscopic light curves of the planet-host system. VSPEC can be a useful tool for modeling observations of exoplanets in transiting geometries (primary transit, secondary eclipse) as well as orbital phase curve measurements, and is built in a modular and flexible configuration for easy adaptability to new stellar and planetary model inputs. We additionally present a set of codes developed alongside the core VSPEC modules, including the stellar surface model generator vspec-vsm, the stellar spectral grid interpolation code GridPolator, and a Python interface for PSG, libpypsg.

Flows, circulations, and energy transport in the outer and deep atmospheres of synchronous and non-synchronous hot Jupiters

Aims. Recent studies have shown that vertical enthalpy transport can explain the inflated radii of highly irradiated gaseous exoplanets. Simultaneously, they have also shown that rotation can influence this transport, leading to highly irradiated, rapidly rotating objects that are uninflated. Here, we explore the flows that underpin this transport, including the impact of synchronous or non-synchronous rotation. Methods. We used DYNAMICO to run a series of long timescale HD209458b-like atmospheric models at various rotation rates. For models that are tidally locked, we considered rotation rates between 1/16th and 40 times the rotation rate of HD209458b, whilst for non-synchronous models, we considered the range one-eighth to four times HD209458b. Results. We find that our synchronous models fall into one of three Ω-dependent regimes. At low Ω, we find that the outer atmosphere dynamics are driven by a divergent day-night wind, which drives weak vertical transport and can lead to the formation of a night-side hot-spot. At intermediate Ω, we find classical hot Jupiter dynamics, whilst at high Ω we find a strong Coriolis effect that suppresses off-equator dynamics, including the jet-driving standing waves, thus also reducing vertical transport. As for non-synchronicity, when small, we find that it has little effect on the dynamics. However as it grows, we find that temporal variations prevent the formation of the persistent structures that drive large-scale dynamics and transport. Conclusions. We find that rotation can significantly impact the atmospheric dynamics of irradiated exoplanets, including vertical enthalpy advection, which may help explain the scatter in the hot Jupiter radius-irradiation relation. We have also identified a seemingly robust atmospheric feature at slow rotation: a night-side hot-spot. As this may have important implications for both the phase curve and atmospheric chemistry, we suggest that this study be followed up with next-generation global circulation models (GCMs) that robustly model radiation and chemistry.

An Absolute Mass, Precise Age, and Hints of Planetary Winds for WASP-121A and b from a JWST NIRSpec Phase Curve

We have conducted a planetary radial velocity measurement of the ultrahot Jupiter WASP-121b using JWST NIRSpec phase curve data. Our analysis reveals the Doppler shift of the planetary spectral lines across the full orbit, which shifts considerably across the detector (∼10 pixels). Using cross-correlation techniques, we have determined an overall planetary velocity amplitude of K p = 215.7 ± 1.1 km s−1, which is in good agreement with the expected value. We have also calculated the dynamical mass for both components of the system by treating it as an eclipsing double-line spectroscopic binary, with WASP-121A having a mass of M ⋆ = 1.330 ± 0.019 M ⊙, while WASP-121b has a mass of M p = 1.170 ± 0.043 M Jup. These dynamical measurements are ∼3× more precise than previous estimates and do not rely on any stellar modeling assumptions that have a ∼5% systematic floor mass uncertainty. Additionally, we used stellar evolution modeling constrained with a stellar density and parallax measurement to determine a precise age for the system, found to be 1.11 ± 0.14 Gyr. Finally, we observed potential velocity differences between the two NIRSpec detectors, with NRS1 lower by 5.5 ± 2.2 km s−1. We suggest that differences can arise from day/night asymmetries in the thermal emission, which can lead to a sensitivity bias favoring the illuminated side of the planet, with planetary rotation and winds both acting to lower a measured K P. The planet’s rotation can account for 1 km s−1 of the observed velocity difference, with 4.5 ± 2.2 km s−1 potentially attributable to vertical differences in wind speeds.

Out of the Darkness: High-resolution Detection of CO Absorption on the Nightside of WASP-33b

We observed the ultrahot Jupiter WASP-33b with the SpectroPolarimètre InfraRouge on the Canada–France–Hawaii Telescope. Previous observations of the dayside of WASP-33b show evidence of CO and Fe emission indicative of a thermal inversion. We observed its nightside over five Earth nights to search for spectral signatures of CO in the planet’s thermal emission. Our three pretransit observations and two posttransit observations are sensitive to regions near the morning or evening terminators, respectively. From spectral retrievals, we detect CO molecular absorption in the planet’s emission spectrum after transit at ∼6.6σ. This is the strongest ground-based detection of nightside thermal emission from an exoplanet and only the third ever. CO appearing in absorption suggests that the nightside near the evening terminator does not have a temperature inversion; this makes sense if the dayside inversion is driven by absorption of stellar radiation. On the contrary, we do not detect CO from the morning terminator. This may be consistent with heat advection by an eastward jet. Phase-resolved high-resolution spectroscopy offers an economical alternative to space-based full-orbit spectroscopic phase curves for studying the vertical and horizontal atmospheric temperature profiles of short-period exoplanets.

De-noising magnetotelluric data based on machine learning

The magnetotelluric (MT) sounding is a common geophysical exploration technique, but it is highly polluted by various types of cultural noise. In the realm of MT data processing, traditional techniques often rely on the quality of the measured MT data. Conventional MT time domain denoising methods tend to eliminate valuable signals, potentially leading to unreliable resistivity estimates. To address this concern, we propose employing machine learning to effectively suppress strong noise interference in MT data, thereby preventing the loss of valuable signals. We augment this approach with mathematical morphological filtering (MMF) to capture low-frequency signals, preserving their integrity. We constructed a signal sample library based on a substantial volume of signal samples. Through consistent training, we establish a support vector machine (SVM) classification model that distinguishes high-quality signal fragments from noisy signals. Subsequently, we use adaptive K-singular value decomposition (K-SVD) dictionary learning to extract noise profiles and suppress noisy signals. To validate the feasibility of our method, we apply machine learning to measured data from two distinct observation areas. The measured data were analyzed and processed, and the results were compared with the robust results. This method can effectively eliminate large-scale strong interference in time domain sequences and preserve more low-frequency slow change information and high-quality signals in the reconstructed signals. The apparent resistivity phase curve of synthetic data is smoother and more continuous, and the data quality in the low-frequency range is significantly improved. The results can more accurately and reliably reflect underground electrical structure information.

Vehicle noise characteristics in magnetotelluric data and vehicle noise removal using waveform fitting

Magnetic field fluctuations due to vehicle noise were observed in magnetotelluric (MT) time-series data measured near roads. The observed vehicle noise had magnitudes ranging from tens to thousands of μA/m, whereas the observed weak natural MT signal magnitudes were approximately tens of μA/m. A small signal-to-noise ratio made it difficult to apply robust processing for removing vehicle noise. In addition, vehicle noise severely distorts the MT response in the MT deadband from 0.01 Hz to 0.3 Hz, where the MT signal is very weak, and methods to remove it are required for deep structure imaging. In this study, magnetic field fluctuations due to moving vehicles were simulated with a magnetic dipole and attempted to be removed using a waveform fitting method. A total of 378 vehicle noises were extracted from the near-road MT data and synthesized with the remote MT data without vehicle noises to investigate the effect of vehicle noise on the MT response. Removal of vehicle noise from synthesized remote MT data resulted in substantial restoration of the apparent resistivity and phase curves around the MT deadband and below 0.001 Hz. In the MT field data, the vehicle noise was simulated and removed with two moving dipoles; the magnitude of the remaining vehicle noise was reduced by approximately half compared to a single dipole, and very stable apparent resistivity and phase curves were obtained. Although electromagnetic noise distortion remains after vehicle noise removal, the waveform fitting method significantly improves the apparent resistivity and phase curve response in the 0.01–0.3 Hz frequency band.

Rotation state, colors, and albedo of the mission-accessible tiny near-Earth asteroid 2001 QJ142

Context. Characterizing mission-accessible asteroids using telescopic observations is fundamental for target-selection and planning for spacecraft missions. Near-Earth asteroids on Earth-like orbits are of particular importance for applications such as asteroid mining. Aims. 2001 QJ142 is a tiny (D ≤ 100 m) near-Earth asteroid on an Earth-like orbit with a semimajor axis of 1.06 au, orbital eccentricity of 0.09, and orbital inclination of 3.10°. We aim to characterize 2001 QJ142 using ground-based observations with future spacecraft missions in mind. Methods. We performed visible multicolor photometry of 2001 QJ142 using the TriCCS on the Seimei 3.8 m telescope in February 2024. We also revisited the images taken with the Suprime-Cam on the Subaru 8.2 m telescope in August 2012. Results. Visible color indices of 2001 QJ142 indicate that 2001 QJ142 is a C- or X-complex asteroid. We detect a possible fast rotation with a period of about 10 min, which is consistent with a previous report. The geometric albedo of 2001 QJ142 is derived to be about 0.3 from a slope of its photometric phase curve, which is consistent with an albedo derived from thermal observations with updated physical quantities. A straightforward interpretation is that 2001 QJ142 is either an E- or M-type asteroid, although surface properties of such tiny fast-rotating asteroids are not well understood. Conclusions. We infer that 2001 QJ142 is a fast-rotating mission-accessible E- or M-type near-Earth asteroid. More characterizations of tiny asteroids are particularly important for a deeper understanding of their nature.

Warm Jupiters around M dwarfs are great opportunities for extensive chemical, cloud, and haze characterisation with JWST

Context. The known population of short-period giant exoplanets around M-dwarf stars is slowly growing. These planets present an extraordinary opportunity for atmospheric characterisation and defy our current understanding of planetary formation. Furthermore, clouds and hazes are ubiquitous in warm exoplanets, but their behaviour is still poorly understood. Aims. We studied the case of a standard warm Jupiter around an M-dwarf star to show the opportunity of this exoplanet population for atmospheric characterisation. We aimed to derive the cloud, haze, and chemical budget of such planets using JWST. Methods. We leveraged a 3D global climate model, the generic PCM, to simulate the cloudy and cloud-free atmosphere of warm Jupiters around an M dwarf. We then post-processed our simulations to produce spectral phase curves and transit spectra as would be seen with JWST. Results. We show that, using the amplitude and offset of the spectral phase curves, we can directly infer the presence of clouds and hazes in the atmosphere of such giant planets. Chemical characterisation of multiple species is possible with an unprecedented signal- to-noise ratio, using the transit spectrum in one single visit. In such atmospheres, NH3 could be detected for the first time in a giant exoplanet. We make the case that these planets are key to understanding the cloud and haze budget in warm giants. Finally, such planets are targets of great interest for Ariel.

Dual broadband phase curves of asteroid (3200) Phaethon

Dual broadband phase curves of asteroid (3200) Phaethon

JWST reveals the rapid and strong day-side variability of 55 Cancri e

Context. The nature of the close-in rocky planet 55 Cnce is puzzling, despite it having been observed extensively. Its optical and infrared occultation depths show temporal variability, in addition to a phase curve variability observed in the optical. Aims. We wish to explore the possibility that the variability originates from the planet being in a 3:2 spin–orbit resonance, and thus showing different sides during occultations. We proposed and were awarded Cycle 1 time at the James Webb Space Telescope (JWST) to test this hypothesis. Methods. JWST/NIRCam (Near Infrared Camera) observed five occultations (secondary eclipses) of the planet – of which four were observed within a week – simultaneously at 2.1 and 4.5 µm. While the former gives band-integrated photometry, the latter provides a spectrum between 3.9–5.0 µm. Results. We find that the occultation depths in both bandpasses are highly variable and change between a non-detection (−5 ± 6 ppm and 7 ± 9 ppm) to 96 ± 8 ppm and 119−19+34 ppm at 2.1 µm and 4.5 µm, respectively. Interestingly, the variations in both bandpasses are not correlated and do not support the 3:2 spin-orbit resonance explanation. The measured brightness temperature at 4.5 µm varies between 873–2256 K and is lower than the expected day-side temperature of bare rock with no heat redistribution (2500 K), which is indicative of an atmosphere. Our atmospheric retrieval analysis of occultation depth spectra at 4.5 µm finds that different visits statistically favour various atmospheric scenarios including a thin outgassed CO/CO2 atmosphere and a silicate rock vapour atmosphere. Some visits even support a flat line model. Conclusions. The observed variability could be explained by stochastic outgassing of CO/CO2, which is also hinted at by retrievals. Alternatively, the variability observed at both 2.1 and 4.5 µm could be the result of a circumstellar patchy dust torus generated by volcanism on the planet.

Measuring the Spot Variability of T Tauri Stars Using Near-infrared Atomic Fe and Molecular OH Lines

As part of the Young Exoplanets Spectroscopic Survey, this study explores the spot variability of 13 T Tauri Stars (TTSs) in the near-infrared H band, using spectra from the Immersion GRating INfrared Spectrometer. By analyzing effective temperature (T eff) sensitive lines of atomic Fe i at ∼1.56259 μm and ∼1.56362 μm, and molecular OH at ∼1.56310 and ∼1.56317 μm, we develop an empirical equivalent width ratio (EWR) relationship for T eff in the range of 3400–5000 K. This relationship allows for precise relative T eff estimates to within tens of Kelvin and demonstrates compatibility with solar metallicity target models. However, discrepancies between observational data and model predictions limit the extension of the T eff–EWR relationship to a broader parameter space. Our study reveals that both classical and weak-line TTSs can exhibit T eff variations exceeding 150 K over a span of 2 yr. The detection of a quarter-phase delay between the EWR and radial velocity phase curves in TTSs indicates spot-driven signals. A phase delay of 0.06 ± 0.13 for CI Tau, however, suggests additional dynamics, potentially caused by planetary interaction, inferred from a posited 1:1 commensurability between the rotation period and orbital period. Moreover, a positive correlation between T eff variation amplitude and stellar inclination angle supports the existence of high-latitude spots on TTSs, further enriching our understanding of stellar surface activity in young stars.

Distribution of cool starspots on the surface of the red dwarf V647 Her

Photometric observations of the star V647 Her (M3.5V) obtained in 2022 at the 1.25 m telescope of the Crimean Astrophysical Observatory are analyzed. The presence of a low-amplitude variability in brightness of the star with a period of 20.69 d, found from observations in 2019, is confirmed; it is shown that as the brightness decreases, the star becomes redder. The observed nature of photometric variability is due to the presence of cool spots on the surface of the star and manifestation of rotational brightness modulation with a full amplitude of no more than 0m.05. We have performed a comparison of the photometric results obtained in 2019, 2022 and 2004. The zones of starspot concentrations in different epochs were determined from the analysis of phase curves. The distribution of spots has been maintained for 40–100 days. Starspot parameters were estimated in the framework of the zonal model. The temperature of the spots is 2700–2800 K. The area they occupied in 2004 is 15% of the total surface area of the star. According to the 2019 and 2022 data, it increases to 30%. The difference between the spottedness of the hemispheres caused by their seasonal redistribution is less than 2%.

A discussion on estimating small bodies taxonomies using phase curves results

Upcoming large multiwavelength photometric surveys will provide a leap in our understanding of small body populations, among other fields of modern astrophysics. Serendipitous observations of small bodies in different orbital locations allow us to study diverse phenomena related to how their surfaces scatter solar light.In particular, multiple observations of the same object in different epochs permit us to construct their phase curves to obtain absolute magnitudes and phase coefficients. In this work, we tackle a series of long-used relationships associating these phase coefficients with the taxa of small bodies and suggest that some may need to be revised in the light of large-number statistics.

Artificial intelligence for assessing the planets' positions as a precursor to earthquake events

Questions about interconnection possibilities between planets’ positions and seismic events on the earth have emerged recently in TV channels, social media, etc. In this study, an Artificial Neural Network (ANN) and Random Forest Regression (RFR) are used to predict the number of earthquakes that can occur on Earth, depending on the Earth’s position relative to other planets and solar positions. Our new integration dataset contains 9809 observations and nine features firstly from the global earthquake archive, which is an authoritative layer by Esri, and secondly from the accurate data web portal “theskylive.com.”.The results obtained from RFR and ANN prove the partial influence of planets positions on sesimic activity on the earth. In other words, quantitatively through the ANN that gets an accuracy of 68.27 %, MAE of 5.36, MSE of 52.78, RMSE of 7.26, R-Squared of 0.65, and also through the RFR that gets an accuracy of 65.06 %, MAE of 5.60, MSE of 58.21, RMSE of 7.63, R-Squared of 0.67, prove the partial influence on one hand. Qualitatively through the curve of the training phase of the ANN, which is a decreasing and convex function, reinforces the aforementioned proof on the other hand. For these reasons, it can be deduced that there is a possible connection between tectonic stress triggers and the positions of the planets in the solar system. Our dataset was uploaded to the github(https://github.com/mouddentarik/Earthquake01.) as well as the code will be publicly available at the github(https://github.com/mouddentarik/PythonCode_Earthquakes-.) to share our results.

Ocean Circulation on Tide-locked Lava Worlds. I. An Idealized 2D Numerical Model

A magma ocean is expected to exist on the dayside of tide-locked planets if surface temperature exceeds the melting temperature of typical crust. As highly prioritized targets for the James Webb Space Telescope, more information about the surface and atmosphere of lava planets will soon be available. In most previous studies of lava planets, the system is typically assumed to be vigorously convecting and isentropic. This implies a magma ocean depth reaching O (104–105) m, determined by the adiabats and melting curves. In this study, we aim to simulate ocean circulation and ocean depth on tidally locked lava worlds using an idealized 2D (x–z) model developed by the authors. Our simulation results show that under zero or a small internal source, the maximum zonal current speed ranges from 0.1 to 1.0 m s−1 and the magma ocean depth remains O (100) m, being more than 100 times shallower than that predicted in a fully convecting system. We demonstrate that the ocean heat transport divergence is consistently smaller than the stellar insolation by 1–2 orders of magnitude. Consequently, the impact of ocean circulation on the thermal phase curve of tidally locked lava worlds is minimal in observations.

The potential role of breast MRI in evaluation of triple-negative breast cancer and fibroadenoma of less than 3 cm.

The majority of small-sized (<3 cm) triple-negative breast cancer (TNBC) exhibit smooth margins upon palpation and are often oval or rounded masses. Distinguishing these masses preoperatively from fibroadenomas (FAs) would be very meaningful for clinical practice. The aim of our study was to evaluate the magnetic resonance imaging (MRI) appearance of TNBC and differentiate it from FAs. In this retrospective single-center study, we included 37 patients with TNBCs and 36 patients with FAs who underwent breast MRI. We employed the χ2 test and t-test to compare the differences in morphological features, dynamic contrast-enhanced MRI (DCE-MRI) parameters, and apparent diffusion coefficient (ADC) values between the two groups. Additionally, we constructed non-parametric receiver operating characteristic (ROC) curves using ADC values, with pathological results serving as the gold standard. A total of 37 TNBC lesions and 39 FA lesions were included in the final analysis. TNBCs exhibited more frequent irregular shape, irregular margins, peritumoral edema, fast enhancement in the initial phase, rim enhancement, and time-signal intensity curve (TIC) type III compared to FAs (all P<0.05). Conversely, low-signal segregation in T2-weighted imaging (T2WI) and TIC type I were commonly found in FAs. The mean ADC value of TNBCs was significantly lower than that of FAs [(1.104±0.13)×10-3 vs. (1.613±0.16)×10-3 mm2/s, P<0.05]. The cutoff ADC for differentiating TNBCs from FAs was 1.239×10-3 mm2/s, yielding an area under the curve (AUC) of 0.997, a sensitivity of 94.6%, and a specificity of 100%. The morphological presentation of MRI, internal enhancement features of the mass, TIC curves, and ADC values provide valuable differential diagnostic information for TNBC and FA masses with a maximum diameter of less than 3 cm.

Nonlinear Vibrations of the Piezoelectric-Laminated Composite Cantilever Rectangular Plate Subjected to the Transverse and Parametric Excitation

The intelligent structure will be the key to the industrial manufacturing field in the future, piezoelectric materials are the most commonly used active materials in many mechatronic and vibration control systems. In this paper, we illustrated the nonlinear vibration behaviors of the piezoelectric-laminated composite cantilever rectangular plate subjected to transverse and parametric excitation. Two piezoelectric layers are attached to the upper and lower surfaces of graphite/epoxy composite laminated plate. The nonlinear dynamic equations are derived via the classical laminated plate theory, von Karman large deformation theory, the constitutive equation of the piezoelectric materials, and the Hamilton principle. Considering the Galerkin method, the nonlinear ordinary differential equations for the two-order vibration mode of the piezoelectric laminated composite cantilever rectangular plate are achieved. The multiple scale method is applied to obtain the average equations to study the nonlinear vibration characteristic of the stable motion. The primary resonance and the 1:1 internal resonance of the piezoelectric laminated composite cantilever rectangular plate are investigated. The amplitude-frequency response curves, force-amplitude response curves, time histories, phase curves, and bifurcation diagrams are given to investigate the nonlinear dynamic characteristic of the piezoelectric laminated composite cantilever rectangular plate. The detailed parametric analyses show that bubble response curves are separated from the amplitude-frequency response curves with the continuous increase of the external excitation due to the internal resonance. In addition, the results reveal the energy transform between the various order vibration modes of the system. This work is expected to provide theoretical guidance for the nonlinear vibration of the smart piezoelectric laminated composite structure.

Capillary blood parameters are gestational age, birthweight, delivery mode and gender dependent in healthy preterm and term infants.

The measurement of blood pH and gas analytes (BPGA), soon after birth, constitutes the first-line standard of care procedure in high-risk newborns. However, no data is available in capillary blood on perinatal bias such as gestational age (GA), weight at birth (BW), delivery mode, and gender. The aims of the present study were to investigate whether in a cohort of healthy preterm (PT) and term (T)infants BPGA were GA, BW, delivery mode and gender dependent, thus affecting BPGA reliability as diagnostic test. We performed a prospective case-control study in 560 healthy infants (PT: n=115, T: n=445). BPGA was measured within 24-h from birth. Perinatal characteristics, outcomes, and clinical examination were also recorded. PT infants showed higher (p<0.001) carbon dioxide partial pressure (pCO2), fraction of fetal hemoglobin (HbF), base excess (BE), bicarbonate (HCO3), and lower lactate (Lac) levels. When corrected for delivery mode, higher (p<0.001) HbF, BE, HCO3, and lower Lac levels were found. Similarly, higher (p<0.05, for all) pCO2, HbF, BE, HCO3 and lower Lac levels were found between female and male PT and T infants. Repeated multiple logistic regression analysis showed that BPGA was GA, BW, delivery mode and gender dependent. The present results showing that BPGA can be affected by a series of perinatal outcomes open the way to further investigations providing longitudinal BPGA reference curves in the transitional phase, thus empowering BPGA role as a reliable diagnostic and therapeutic strategies efficacy marker.

Novel Atmospheric Dynamics Shape the Inner Edge of the Habitable Zone around White Dwarfs

White dwarfs offer a unique opportunity to search nearby stellar systems for signs of life, but the habitable zone around these stars is still poorly understood. Since white dwarfs are compact stars with low luminosity, any planets in their habitable zone should be tidally locked, like planets around M dwarfs. Unlike planets around M dwarfs, however, habitable white dwarf planets have to rotate very rapidly, with orbital periods ranging from hours to several days. Here we use the ExoCAM global climate model to investigate the inner edge of the habitable zone around white dwarfs. Our simulations show habitable planets with ultrashort orbital periods (P ≲ 1 day) enter a “bat rotation” regime, which differs from typical atmospheric circulation regimes around M dwarfs. Bat rotators feature mean equatorial subrotation and a displacement of the surface’s hottest regions from the equator toward the midlatitudes. We qualitatively explain the onset of bat rotation using shallow water theory. The resulting circulation shifts increase the dayside cloud cover and decrease the stratospheric water vapor, expanding the white dwarf habitable zone by ∼50% compared to estimates based on 1D models. The James Webb Space Telescope should be able to quickly characterize bat rotators around nearby white dwarfs thanks to their distinct thermal phase curves. Our work underlines that tidally locked planets on ultrashort orbits may exhibit unique atmospheric dynamics, and guides future habitability studies of white dwarf systems.

Stress wave effects and their mechanisms on stress-strain curves in the elastic phase of SHPB tests

In Split Hopkinson Pressure Bar (SHPB) tests, the stress wave effects during the elastic phase of the stress-strain curve and their influence mechanisms are crucial. Due to the extremely short duration of the elastic deformation phase, the stress wave effects on the specimen during this stage cannot be ignored. This leads to significant errors in the obtained elastic stress-strain curves. However, the dynamic compressive elastic stress-strain relationship forms the basis for studying the viscoelastic behavior of materials. Accurate determination of elastic yield stress and yield strain is also essential for deriving accurate plastic stress-strain relationships. Quantitative research on the stress wave effects during the elastic compression phase of SHPB tests is fundamental for decoupling and obtaining accurate material elastic curves. This paper conducts a quantitative theoretical analysis of the structural effects caused by stress wave evolution during the elastic compression phase, based on the assumption of plane waves. It studies the deviation characteristics and main factors of the phenomenological engineering stress-strain curves of the specimen compared to the actual material stress-strain curves under different conditions, revealing the influence rules and mechanisms of this deviation. The maximum stress deviation value and its corresponding dimensionless time, as well as the variation trend of the maximum stress deviation value within different fluctuation intervals, are calculated. Additionally, the study investigates the cases where the incident wave is arc-shaped or a combination of arc and linear waves. The findings provide theoretical references for the precise design and accurate data processing of SHPB tests.