Context. The smoothed particle hydrodynamics (SPH) technique is a well-known numerical method that has been applied to simulate the evolution of a wide variety of systems. Modern astrophysical applications of the method rely on the Lagrangian formulation of fluid Euler equations, which is fully conservative. A different scheme, based on a matrix approach to the SPH equations is currently being used in computational fluid dynamics. These matrix formulations achieve better interpolations of the physical magnitudes but they are, in general, not fully conservative. The matrix approach to the Euler equations has never been used in astrophysics. Aims. We develop and test a fully conservative SPH scheme based on a tensor formulation that can be applied to simulate astrophysical systems. Methods. In the proposed scheme, derivatives are calculated from an integral expression that leads to a tensor (instead of a vectorial) estimation of gradients and reduces to the standard formulation in the continuum limit. The new formulation improves the interpolation of physical magnitudes, leading to a set of conservative equations that resembles those of standard SPH. The resulting scheme is verified using a variety of well-known tests, all of them simulated in two dimensions. We also discuss an application of the proposed tensor method to astrophysics by simulating the stability of a Sun-like polytrope calculated in three dimensions. Results. The proposed scheme is able to improve the results of standard SPH in the two-dimensional tests, especially in the simulation of subsonic hydrodynamic instabilities. Our results for the stability of the Sun-like polytrope suggest that the new method can be used in astrophysics to carry out three-dimensional calculations with a computational cost that is only slightly higher (i.e. ≤50% for a serial code) than that of a standard SPH formulation. Conclusions. A formalism based on a matrix approach to Euler SPH equations was developed and checked. The new scheme is more accurate because of the re-normalization imposed on the interpolations, which is fully conservative and probably less prone to undergo the tensile instability. The analysis of several test cases suggest that the method may improve the simulation of both subsonic and supersonic systems. An application of the tensor method to astrophysics is, for the first time, successfully carried out. These encouraging results indicates that more work should be invested in the applications of matrix SPH formulations to astrophysics.
Context. Even if the 12 C+ 12 C reaction plays a central role in the ignition of type Ia supernovae (SNIa), the experimental determination of its cross-section at astrophysically relevant energies (E 2 MeV) has never been made. The profusion of resonances throughout the measured energy range has led to speculation that there is an unknown resonance at E 0 ∼ 1.5 MeV possibly as strong as the one measured for the resonance at 2.14 MeV, i.e. (ωγ) R = 0.13 meV. Aims. We study the implications that such a resonance would have for our knowledge of the physics of SNIa, paying special attention to the phases that go from the crossing of the ignition curve to the dynamical event.Methods. We use one-dimensional hydrostatic and hydrodynamic codes to follow the evolution of accreting white dwarfs until they grow close to the Chandrasekhar mass and explode as SNIa. In our simulations, we account for a low-energy resonance by exploring the parameter space allowed by experimental data. Results. A change in the 12 C+ 12 C rate similar to the one explored here would have profound consequences for the physical conditions in the SNIa explosion, namely the central density, neutronization, thermal profile, mass of the convective core, location of the runaway hot spot, or time elapsed since crossing the ignition curve. For instance, with the largest resonance strength we use, the time elapsed since crossing the ignition curve to the supernova event is shorter by a factor ten than for models using the standard rate of 12 C+ 12 C, and the runaway temperature is reduced from ∼8.14 × 10 8 K to ∼4.26 × 10 8 K. On the other hand, a resonance at 1.5 MeV, with a strength ten thousand times smaller than the one measured at 2.14 MeV, but with an α/p yield ratio substantially different from 1 would have a sizeable impact on the degree of neutronization of matter during carbon simmering. Conclusions. A robust understanding of the links between SNIa properties and their progenitors will not be attained until the 12 C+ 12 C reaction rate is measured at energies ∼1.5 MeV.
Context. The smoothed particle hydrodynamics (SPH) technique is a well-known numerical method that has been applied to simulating the evolution of a wide variety of systems. Modern astrophysical applications of the method rely on the Lagrangian formulation of fluid Euler equations, which is fully conservative. A different scheme, based on a matrix approach to the SPH equations is currently being used in computational fluid dynamics. An original matrix formulation of SPH based on an integral approach to the derivatives, called IAD 0 , has been recently proposed and is fully conservative and well-suited to simulating astrophysical processes. Aims. The behavior of the IAD 0 scheme is analyzed in connection with several astrophysical scenarios, and compared to the same simulations carried out with the standard SPH technique. Methods. The proposed hydrodynamic scheme is validated using a variety of numerical tests that cover important topics in astrophysics, such as the evolution of supernova remnants, the stability of self-gravitating bodies, and the coalescence of compact objects.Results. The analysis of the hydrodynamical simulations of the above-mentioned astrophysical scenarios suggests that the SPH scheme built with the integral approach to the derivatives improves the results of the standard SPH technique. In particular, there is a better development of hydrodynamic instabilities, a good description of self-gravitating structures in equilibrium and a reasonable description of the process of coalescence of two white dwarfs. We also observed good conservations of energy and both linear and angular momenta that were generally better than those of standard SPH. In addition the new scheme is less susceptible to pairing instability. Conclusions. We present a formalism based on a tensor approach to Euler SPH equations that we checked using a variety of threedimensional tests of astrophysical interest. This new scheme is more accurate because of the re-normalization imposed on the interpolations, which is fully conservative and less prone to undergoing the pairing instability. The analysis of these test cases suggests that the method may improve the simulation of many astrophysical problems with only a moderate computational overload.
Context. The smoothed-particle hydrodynamics (SPH) technique is a numerical method for solving gas-dynamical problems. It has been applied to simulate the evolution of a wide variety of astrophysical systems. The method has a second-order accuracy, with a resolution that is usually much higher in the compressed regions than in the diluted zones of the fluid. Aims. We propose and check a method to balance and equalize the resolution of SPH between high-and low-density regions. This method relies on the versatility of a family of interpolators called sinc kernels, which allows increasing the interpolation quality by varying only a single parameter (the exponent of the sinc function). Methods. The proposed method was checked and validated through a number of numerical tests, from standard one-dimensional Riemann problems in shock tubes, to multidimensional simulations of explosions, hydrodynamic instabilities, and the collapse of a Sun-like polytrope.Results. The analysis of the hydrodynamical simulations suggests that the scheme devised to equalize the accuracy improves the treatment of the post-shock regions and, in general, of the rarefacted zones of fluids while causing no harm to the growth of hydrodynamic instabilities. The method is robust and easy to implement with a low computational overload. It conserves mass, energy, and momentum and reduces to the standard SPH scheme in regions of the fluid that have smooth density gradients.
Context. The accurate evaluation of gradients is a cornerstone of the smoothed particle hydrodynamics (SPH) technique. Using an integral approach to estimating gradients has been proven to substantially enhance its accuracy, retaining the Lagrangian structure of SPH equations and remaining fully conservative. However, in practice, it is difficult to ensure that the Lagrangian formulation is entirely consistent with regard to the exact partition of the unity. Aims. In this paper, we focus our study on the connection between the choice of the volume elements (VEs) in the SPH summations as well as the accuracy in the gradient estimation within the integral approach scheme (ISPH). We propose a new variant of VEs to improve the partition of the unity that is fully compatible with the Lagrangian formulation of SPH, including grad-h corrections. Methods. Using analytic considerations, simple static toy models in 1D, and a set of full 3D test cases, we show that any improvement in the partition of the unity also leads to a better calculation of gradients when the integral approach is used jointly. Additionally, we propose an easy-to-implement modification of the ISPH scheme, which makes it more flexible and better suited to handling sharp density contrasts. Results. The ISPH code that is built with the proposed scheme has been validated with a good number of standard tests, some of them involving contact discontinuities. The performance of the code was shown to be excellent in all of these tests, consistently demonstrating that an improvement in the partition of the unity is not detrimental to the optimal conservation of energy, momentum, and entropy that is typical of Lagrangian schemes. Conclusions. We successfully built a new ISPH scheme on a Lagrangian basis, which is fully conservative, and compatible with self-consistent grad-h terms and an improved partition of the unity. The ensuing code is able to successfully cope with the tensile instability and has been validated with a number of hydrodynamic tests with good results.
Context. The Euclid mission is expected to discover thousands of z > 6 galaxies in three Deep Fields, which together will cover a ∼40 deg 2 area. However, the limited number of Euclid bands and availability of ancillary data could make the identification of z > 6 galaxies challenging. Aims. In this work, we assess the degree of contamination by intermediate-redshift galaxies (z = 1-5.8) expected for z > 6 galaxies within the Euclid Deep Survey. Methods. This study is based on ∼176 000 real galaxies at z = 1-8 in a ∼0.7 deg 2 area selected from the UltraVISTA ultra-deep survey, and ∼96 000 mock galaxies with 25.3 ≤ H < 27.0, which altogether cover the range of magnitudes to be probed in the Euclid Deep Survey. We simulate Euclid and ancillary photometry from the fiducial, 28-band photometry, and fit spectral energy distributions (SEDs) to various combinations of these simulated data. Results. Our study demonstrates that identifying z > 6 with Euclid data alone will be very effective, with a z > 6 recovery of 91(88) % for bright (faint) galaxies. For the UltraVISTA-like bright sample, the percentage of z = 1-5.8 contaminants amongst apparent z > 6 galaxies as observed with Euclid alone is 18 %, which is reduced to 4(13) % by including ultra-deep Rubin (Spitzer) photometry. Conversely, for the faint mock sample, the contamination fraction with Euclid alone is considerably higher at 39 %, and minimized to 7 % when including ultra-deep Rubin data. For UltraVISTA-like bright galaxies, we find that Euclid (I E − Y E ) > 2.8 and (Y E − J E ) < 1.4 colour criteria can separate contaminants from true z > 6 galaxies, although these are applicable to only 54 % of the contaminants, as many have unconstrained (I E − Y E ) colours. In the most optimistic scenario, these cuts reduce the contamination fraction to 1 % whilst preserving 81 % of the fiducial z > 6 sample. For the faint mock sample, colour cuts are infeasible, but we find instead that a 5σ detection threshold requirement in at least one of the Euclid NIR bands reduces the contamination fraction to 25 %.
The various Euclid imaging surveys will become a reference for studies of galaxy morphology by delivering imaging over an unprecedented area of 15 000 square degrees with high spatial resolution. In order to understand the capabilities of measuring morphologies from Euclid-detected galaxies and to help implement measurements in the pipeline of the Organisational Unit MER of the Euclid Science Ground Segment, we have conducted the Euclid Morphology Challenge, which we present in two papers. While the companion paper focusses on the analysis of photometry, this paper assesses the accuracy of the parametric galaxy morphology measurements in imaging predicted from within the Euclid Wide Survey. We evaluate the performance of five state-of-the-art surface-brightness-fitting codes, DeepLeGATo, Galapagos-2, Morfometryka, ProFitand SourceXtractor++ , on a sample of about 1.5 million simulated galaxies (350 000 above 5σ) resembling reduced observations with the Euclid VIS and NIR instruments. The simulations include analytic Sérsic profiles with one and two components, as well as more realistic galaxies generated with neural networks. We find that, despite some code-specific differences, all methods tend to achieve reliable structural measurements (< 10% scatter on ideal Sérsic simulations) down to an apparent magnitude of about I E = 23 in one component and I E = 21 in two components, which correspond to a signal-to-noise ratio of approximately 1 and 5, respectively. We also show that when tested on non-analytic profiles, the results are typically degraded by a factor of 3, driven by systematics. We conclude that the official Euclid Data Releases will deliver robust structural parameters for at least 400 million galaxies in the Euclid Wide Survey by the end of the mission. We find that a key factor for explaining the different behaviour of the codes at the faint end is the set of adopted priors for the various structural parameters.
Euclid will be the first space mission to survey most of the extragalactic sky in the 0.95–2.02 µm range, to a 5 σ point-source median depth of 24.4 AB mag. This unique photometric dataset will find wide use beyond Euclid’s core science. In this paper, we present accurate computations of the Euclid YE, JE, and HE passbands used by the Near-Infrared Spectrometer and Photometer (NISP), and the associated photometric system. We pay particular attention to passband variations in the field of view, accounting for, among other factors, spatially variable filter transmission and variations in the angle of incidence on the filter substrate using optical ray tracing. The response curves’ cut-on and cut-off wavelengths – and their variation in the field of view – are determined with ~0.8 nm accuracy, essential for the photometric redshift accuracy required by Euclid. After computing the photometric zero points in the AB mag system, we present linear transformations from and to common ground-based near-infrared photometric systems, for normal stars, red and brown dwarfs, and galaxies separately. A Python tool to compute accurate magnitudes for arbitrary passbands and spectral energy distributions is provided. We discuss various factors, from space weathering to material outgassing, that may slowly alter Euclid’s spectral response. At the absolute flux scale, the Euclid in-flight calibration program connects the NISP photometric system to Hubble Space Telescope spectrophotometric white dwarf standards; at the relative flux scale, the chromatic evolution of the response is tracked at the milli-mag level. In this way, we establish an accurate photometric system that is fully controlled throughout Euclid’s lifetime.
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