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At least 577 records · Page 32

Outflow from Outer-arm Starburst in a Grazing Collision between Galaxies

Gemini NIFS K-band spectra and Atacama Large Millimeter/submillimeter Array {sup 12}CO J=1→0, HCO{sup +}, and 100 GHz continuum observations are used to study a bright starburst clump on an outer arm of the interacting galaxy NGC 2207. This clump emits 23% of the total 24 μm flux of the galaxy pair and has an optically opaque dust cone extending out of its 170 pc core. The measured CO accounts for the dark cone extinction if almost all the gas and dust there are in front of the star clusters. An associated approaching CO outflow has v {sub z} ~ 16 km s{sup -1}, an estimated molecular mass 8 × 10{sup 6} M {sub ⊙}, and rises to heights ~0.9 kpc. A receding CO outflow on the far side with v {sub z} ~ 28 km s{sup -1} is less extensive. The observed star formation in the core over 10 Myr can supply the dark cone kinetic energy of roughly 2 × 10{sup 52} erg via supernovae and stellar winds. Other signs of intense activity are a variable radio continuum, suggesting an embedded supernova or other outburst; X-ray emission possibly from an X-ray binary or intermediate-mass black hole, depending on the extinction; and Brγ and He i lines with 82 km s{sup -1} line widths and fluxes consistent with excitation by embedded O-type stars. According to previous models, the retrograde encounter suffered by NGC 2207 caused the loss of angular momentum. This compressed its outer disk. We suggest that the resulting inward crashing stream hit a massive H i clump on the preexisting spiral arm and triggered the observed starburst.

79 ASTRONOMY AND ASTROPHYSICS↗

The Galactic Chemical Evolution of Chlorine

We measured {sup 35}Cl abundances in 52 M giants with metallicities in the range −0.5 < [Fe/H] < 0.12. Abundances and atmospheric parameters were derived using infrared spectra from CSHELL on the NASA Infrared Telescope Facility and from optical echelle spectra. We measured Cl abundances by fitting a H{sup 35}Cl molecular feature at 3.6985 μm with synthetic spectra. We also measured the abundances of O, Ca, Ti, and Fe using atomic absorption lines. We find that the [Cl/Fe] ratio for our stars agrees with chemical evolution models of Cl, and the [Cl/Ca] ratio is broadly consistent with the solar ratio over our metallicity range. Both indicate that Cl is primarily made in core-collapse supernovae with some contributions from Type Ia supernovae. We suggest that other potential nucleosynthesis processes, such as the ν-process, are not significant producers of Cl. Finally, we also find our Cl abundances are consistent with H ii and planetary nebular abundances at a given oxygen abundance, although there is scatter in the data.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Multiwavelength Observations of 2HWC J1928+177: Dark Accelerator or New TeV Gamma-Ray Binary?

2HWC J1928+177 is a Galactic TeV gamma-ray source detected by the High Altitude Water Cherenkov (HAWC) Observatory up to ~56 TeV. The HAWC source, later confirmed by the High Energy Stereoscopic System, still remains unidentified as a dark accelerator since there is no apparent supernova remnant or pulsar wind nebula detected in the lower-energy bands. The radio pulsar PSR J1928+1746, coinciding with the HAWC source position, has no X-ray counterpart. In this work, our SED modeling shows that inverse Compton scattering in the putative pulsar wind nebula can account for the TeV emission only if the unseen nebula is extended beyond $r\sim 4^{\prime} $. Alternatively, TeV gamma-rays may be produced by hadronic interactions between relativistic protons from an undetected supernova remnant associated with the radio pulsar and a nearby molecular cloud G52.9+0.1. NuSTAR and Chandra observations detected a variable X-ray point source within the HAWC error circle, potentially associated with a bright infrared (IR) source. The X-ray spectra can be fitted with an absorbed power-law model with N H = (9 ± 3) × 10 22 cm –2 and Γ X = 1.6 ± 0.3 and exhibit long-term X-ray flux variability over the last decade. If the X-ray source, possibly associated with the IR source (likely an O star), is the counterpart of the HAWC source, it may be a new TeV gamma-ray binary powered by collisions between the pulsar wind and stellar wind. Follow-up X-ray observations are warranted to search for diffuse X-ray emission and determine the nature of the HAWC source.

79 ASTRONOMY AND ASTROPHYSICS↗

Synthetic Absorption Lines from Simulations of Multiphase Gas in Galactic Winds

Supernova-driven galactic winds are multiphase streams of gas that are often observed flowing at a range of velocities out of star-forming regions in galaxies. In this study, we use high-resolution 3D simulations of multiphase galactic winds modeled with the hydrodynamics code Cholla to investigate the connection between numerical studies and observations. Using a simulated interaction between a hot $T$ ~ 10 4 K supernova-driven wind and a cool $T$ ~ 10 7 K cloud of interstellar material, we create mock observables, including the optical depth ($\tau$) and covering fraction ($C$ $f$ ) of six commonly observed ions (Si II , C II , Si IV , C IV , N V , and O VI ) as a function of gas velocity. We compare our mock observables to surveys of galactic winds in the literature, finding good agreement with velocities and profiles of the low ions. We then compute "empirical" values for the optical depth and covering fraction following observational techniques and compare them to the values calculated directly from the simulation data. We find that the empirically computed values tend to underestimate the "true" value of $\tau$ for ions with high optical depth and overestimate the "true" value of $\tau$ for ions with low optical depth relative to the simulated data. In conclusion, the empirically estimated covering fractions match our direct calculations very well for the low-ionization ions; for the high-ionization ions, the empirical covering fractions underestimate the directly computed values by up to ~40%.

79 ASTRONOMY AND ASTROPHYSICS↗

Investigating the Nature of the Luminous Ambiguous Nuclear Transient ASASSN-17jz

Abstract We present observations of the extremely luminous but ambiguous nuclear transient (ANT) ASASSN-17jz, spanning roughly 1200 days of the object’s evolution. ASASSN-17jz was discovered by the All-Sky Automated Survey for Supernovae (ASAS-SN) in the galaxy SDSS J171955.84+414049.4 on UT 2017 July 27 at a redshift of z = 0.1641. The transient peaked at an absolute B -band magnitude of M B ,peak = −22.81, corresponding to a bolometric luminosity of L bol,peak = 8.3 × 10 44 erg s −1 , and exhibited late-time ultraviolet emission that was still ongoing in our latest observations. Integrating the full light curve gives a total emitted energy of E tot = (1.36 ±0.08) × 10 52 erg, with (0.80 ± 0.02) × 10 52 erg of this emitted within 200 days of peak light. This late-time ultraviolet emission is accompanied by increasing X-ray emission that becomes softer as it brightens. ASASSN-17jz exhibited a large number of spectral emission lines most commonly seen in active galactic nuclei (AGNs) with little evidence of evolution. It also showed transient Balmer features, which became fainter and broader over time, and are still being detected >1000 days after peak brightness. We consider various physical scenarios for the origin of the transient, including supernovae (SNe), tidal disruption events, AGN outbursts, and ANTs. We find that the most likely explanation is that ASASSN-17jz was a SN IIn occurring in or near the disk of an existing AGN, and that the late-time emission is caused by the AGN transitioning to a more active state.

79 ASTRONOMY AND ASTROPHYSICS↗

Towards performance portability in the Spark astrophysical magnetohydrodynamics solver in the Flash-X simulation framework

Simulations of core-collapse supernovae, and other astrophysical phenomena, are quintessential extreme-scale computing challenges. For core-collapse supernova simulations to be carried out by the ExaStar project under the Exascale Computing Project umbrella, a robust, efficient, and state-of-the-art magnetohydrodynamics solver is a critical requirement. In Flash-X, the primary software instrument for ExaStar, a new magnetohydrodynamics solver has been designed and implemented from the ground up to achieve accuracy and efficiency for simulations of complex astrophysical flows. This new solver, dubbed Spark, uses high-order spatial reconstruction, Runge-Kutta time integration, and an efficient cell-centered approach to satisfying the divergence-free condition for the magnetic fields. Spark was written to be optimized for data locality in cache hierarchy of CPUs. Since data locality optimizations for cache hierarchy are not directly compatible with those of accelerators, we have taken the approach of using program synthesis to avoid massive amounts of code replication that would be necessary if we were to maintain two different versions of the solver. Our program synthesis relies on a simple key-dictionary approach, implemented in python, that enables us to assemble the version of the solver suitable for the target hardware from code fragments identified by specific keys. In this work, we describe the data locality optimizations of the solver for CPUs and accelerators and the program synthesis tools that enable this portability. We also detail the parallel performance of Spark for both CPUs and accelerators.

97 MATHEMATICS AND COMPUTING↗

Enhanced production of 60 Fe in massive stars

Massive stars are a major source of chemical elements in the cosmos, ejecting freshly produced nuclei through winds and core-collapse supernova explosions into the interstellar medium. Among the material ejected, long-lived radioisotopes, such as 60 Fe (iron) and 26 Al (aluminum), offer unique signs of active nucleosynthesis in our galaxy. There is a long-standing discrepancy between the observed 60 Fe/ 26 Al ratio by γ-ray telescopes and predictions from supernova models. This discrepancy has been attributed to uncertainties in the nuclear reaction networks producing 60 Fe, and one reaction in particular, the neutron-capture on 59 Fe. Here we present experimental results that provide a strong constraint on this reaction. We use these results to show that the production of 60 Fe in massive stars is higher than previously thought, further increasing the discrepancy between observed and predicted 60 Fe/ 26 Al ratios. The persisting discrepancy can therefore not be attributed to nuclear uncertainties, and points to issues in massive-star models.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Dynamical dark energy in light of the DESI DR2 baryonic acoustic oscillations measurements

Understanding whether cosmic acceleration arises from a cosmological constant or a dynamical component is a central goal of cosmology, and the Dark Energy Spectroscopic Instrument (DESI) enables stringent tests with high-precision distance measurements. Here we analyse measurements of baryon acoustic oscillations in DESI Data Release 1 and Data Release 2 and consider type Ia supernovae and a distance prior for the cosmic microwave background. With the larger statistical power and wider redshift coverage of Data Release 2, the preference for dynamical dark energy does not diminish relative to Data Release 1. Using both a shape-function reconstruction and non-parametric approaches with a Horndeski-motivated correlation prior, we find that the equation of state for dark energy w(z) varies with redshift. Baryon acoustic oscillation data alone yield modest constraints, but in combination with independent supernova compilations and the prior for the cosmic microwave background, they strengthen the evidence for dynamics. A Bayesian comparison of models shows moderate support for departures from Λ cold dark matter (ΛCDM) when several degrees of freedom in w(z) are allowed, corresponding to ~3σ tension with ΛCDM (and higher for some datasets). Despite methodological differences, our results are consistent with companion DESI papers, underscoring the complementarity of the approaches. Possible systematics remain under study; forthcoming DESI, Euclid and next-generation cosmic microwave background data will provide decisive tests.

cosmology↗

Dynamical dark energy in light of the DESI DR2 baryonic acoustic oscillations measurements

Understanding whether cosmic acceleration arises from a cosmological constant or a dynamical component is a central goal of cosmology, and the Dark Energy Spectroscopic Instrument (DESI) enables stringent tests with high-precision distance measurements. Here we analyse measurements of baryon acoustic oscillations in DESI Data Release 1 and Data Release 2 and consider type Ia supernovae and a distance prior for the cosmic microwave background. With the larger statistical power and wider redshift coverage of Data Release 2, the preference for dynamical dark energy does not diminish relative to Data Release 1. Using both a shape-function reconstruction and non-parametric approaches with a Horndeski-motivated correlation prior, we find that the equation of state for dark energy w(z) varies with redshift. Baryon acoustic oscillation data alone yield modest constraints, but in combination with independent supernova compilations and the prior for the cosmic microwave background, they strengthen the evidence for dynamics. A Bayesian comparison of models shows moderate support for departures from Λ cold dark matter (ΛCDM) when several degrees of freedom in w(z) are allowed, corresponding to ~3σ tension with ΛCDM (and higher for some datasets). Despite methodological differences, our results are consistent with companion DESI papers, underscoring the complementarity of the approaches. Possible systematics remain under study; forthcoming DESI, Euclid and next-generation cosmic microwave background data will provide decisive tests.

79 ASTRONOMY AND ASTROPHYSICS↗

Enrichment by the first stars in a relic dwarf galaxy

Stars that contain trace amounts of elements heavier than helium (that is, ‘metallicity’) preserve the chemical fingerprints of the first stars. In the Milky Way, nearly all of the lowest-metallicity stars show an extreme over-abundance of carbon. The origin of this signature has remained a mystery owing to the lack of observational constraints on the environments in which it originates. Here, in this work, we present observations of a star in the >10-billion-year-old ultrafaint dwarf galaxy Pictor II, showing the lowest iron and calcium abundances outside the Milky Way (<1/43,000th solar and ~1/160,000th solar), with >3,000× relative carbon enhancement. The star’s exceptional paucity in iron and calcium make it clearly preserve enrichment from the first stars in a relic dwarf galaxy; Pictor II is one of the smallest, most chemically primordial systems known. This star supports the hypothesis that extreme carbon enhancement results from low-energy supernovae from the first stars, as the yields of energetic supernovae are harder to retain in small-scale environments. This signature of enrichment by the first stars may trace a regime inaccessible to current high-redshift observations, which can hardly detect the initial enrichment of the smallest galaxies.

chemical evolution↗

Electron acceleration in laboratory-produced turbulent collisionless shocks

Astrophysical collisionless shocks are among the most powerful particle accelerators in the Universe. Generated by violent interactions of supersonic plasma flows with the interstellar medium, supernova remnant shocks are observed to amplify magnetic fields and accelerate electrons and protons to highly relativistic speeds. In the well-established model of diffusive shock acceleration, relativistic particles are accelerated by repeated shock crossings. However, this requires a separate mechanism that pre-accelerates particles to enable shock crossing. This is known as the ‘injection problem’, which is particularly relevant for electrons, and remains one of the most important puzzles in shock acceleration. In most astrophysical shocks, the details of the shock structure cannot be directly resolved, making it challenging to identify the injection mechanism. In this letter we report results from laser-driven plasma flow experiments, and related simulations, that probe the formation of turbulent collisionless shocks in conditions relevant to young supernova remnants. We show that electrons can be effectively accelerated in a first-order Fermi process by small-scale turbulence produced within the shock transition to relativistic non-thermal energies, helping overcome the injection problem. Our observations provide new insight into electron injection at shocks and open the way for controlled laboratory studies of the physics underlying cosmic accelerators.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Black hole–neutron star mergers: The first mass gap and kilonovae

Observations of X-ray binaries indicate a dearth of compact objects in the mass range from ~2 –5 M ⊙ . The existence of this (first mass) gap has been used to discriminate between proposed engines behind core-collapse supernovae. From LIGO/Virgo observations of binary compact remnant masses, several candidate first mass gap objects, either neutron stars (NSs) or black holes (BHs), were identified during the O3 science run. Motivated by these new observations, we study the formation of BH-NS mergers in the framework of isolated classical binary evolution, using population synthesis methods to evolve large populations of binary stars (Population I and II) across cosmic time. We present results on the NS to BH mass ratios (q = M NS /M BH ) in merging systems, showing that although systems with a mass ratio as low as q = 0.02 can exist, typically BH-NS systems form with moderate mass ratios q = 0.1 –0.2. If we adopt a delayed supernova engine, we conclude that ~30% of BH-NS mergers may host at least one compact object in the first mass gap (FMG). Even allowing for uncertainties in the processes behind compact object formation, we expect the fraction of BH-NS systems ejecting mass during the merger to be small (from ~0.6 –9%). In our reference model, we assume: (i) the formation of compact objects within the FMG, (ii) natal NS/BH kicks decreased by fallback, (iii) low BH spins due to Tayler-Spruit angular momentum transport in massive stars. We find that ≲1% of BH-NS mergers will have any mass ejection and about the same percentage will produce kilonova bright enough to have a chance of being detected with a large (Subaru-class) 8 m telescope. Interestingly, all these mergers will have both a BH and an NS in the FMG.

79 ASTRONOMY AND ASTROPHYSICS↗

Galactic chemical evolution with the short-lived isotopes 53 Mn, 60 Fe, 182 Hf, and 244 Pu

We run a three-dimensional Galactic chemical evolution (GCE) model to follow the propagation of 53 Mn from supernovae of type Ia (SNIa), 60 Fe from core-collapse supernovae (CCSNe), 182 Hf from intermediate mass stars (IMSs), and 244 Pu from neutron star mergers (NSMs) in the Galaxy. We compare the GCE of these short-lived radioactive isotopes (SLRs) to recent detections on the deep-sea floor. We find that although these SLRs originate from different sites, they often arrive conjointly on Earth.

79 ASTRONOMY AND ASTROPHYSICS↗

Theory and simulations of linear and nonlinear two-dimensional Rayleigh–Taylor dynamics with variable acceleration

Interfacial Rayleigh–Taylor mixing is crucial to describing important natural and engineering processes, such as exploding supernovae, laser micromachining, hot spots in inertial confinement fusion, and optical telecommunications. These require the characterization of the time dependence of the driving acceleration. We compare our theoretical formulation based on group theory foundations with interface-capturing numerical simulations for linear and nonlinear two-dimensional Rayleigh–Taylor instabilities in a finite-sized domain with time-varying acceleration over broad ranges of Atwood numbers and acceleration exponents. Detailed corroboration between theory and simulations is provided for this foundational case. Both demonstrate the strong interfacial nature of Rayleigh–Taylor instabilities, which suggests that practical flow fields can be reconstructed from the derived fluid potential using the proposed theory. A robust agreement is also obtained for the early and late-time evolution of the amplitudes of the bubble and spike, which demonstrate that the Rayleigh–Taylor flow can transition to the mixing regime even for a single-mode initial perturbation. Corroboration with experiments of high energy density plasmas motivated by studies of supernovae is also achieved. In addition, a long-standing puzzle in Rayleigh–Taylor dynamics on the interplay between the acceleration, the shear, and the interface morphology in the theory and simulations is resolved by accounting for finite viscosity of the fluids. The characterization of Rayleigh–Taylor instabilities as a highly interfacial phenomenon provides valuable insight into its multiscale nature, which enhances the design and understanding of numerous processes of practical interest.

42 ENGINEERING↗

Energy-dependent flavour ratios in neutrino telescopes from charm

Abstract The origin of the observed diffuse neutrino flux is not yet known. Studies of the relative flavour content of the neutrino flux detected at Earth can give information on the production mechanisms at the sources and on flavour mixing, complementary to measurements of the spectral index and normalization. Here we demonstrate the effects of neutrino fluxes with different spectral shapes and different initial flavour compositions dominating at different energies, and we study the sensitivity of future measurements with the IceCube Neutrino Observatory. Where one kind of flux gives way to another, this shows up as a non-trivial energy dependence in the flavour compositions. We explore this in the context of slow-jet supernovae and magnetar-driven supernovae — two examples of astrophysical sources where charm production may be effective. Using current best-fit neutrino mixing parameters and the projected 2040 IceCube uncertainties, we use event ratios of different event morphologies at IceCube to illustrate the possibilities of distinguishing the energy dependence of neutrino flavour ratios.

Astronomy & Astrophysics↗

DESI 2024 VI: cosmological constraints from the measurements of baryon acoustic oscillations

We present cosmological results from the measurement of baryon acoustic oscillations (BAO) in galaxy, quasar and Lyman-α forest tracers from the first year of observations from the Dark Energy Spectroscopic Instrument (DESI), to be released in the DESI Data Release 1. DESI BAO provide robust measurements of the transverse comoving distance and Hubble rate, or their combination, relative to the sound horizon, in seven redshift bins from over 6 million extragalactic objects in the redshift range 0.1 < z < 4.2. To mitigate confirmation bias, a blind analysis was implemented to measure the BAO scales. DESI BAO data alone are consistent with the standard flat ΛCDM cosmological model with a matter density Ω m =0.295±0.015. Paired with a baryon density prior from Big Bang Nucleosynthesis and the robustly measured acoustic angular scale from the cosmic microwave background (CMB), DESI requires H 0 =(68.52±0.62) km s -1 Mpc -1 . In conjunction with CMB anisotropies from Planck and CMB lensing data from Planck and ACT, we find Ω m =0.307± 0.005 and H 0 =(67.97±0.38) km s -1 Mpc -1 . Extending the baseline model with a constant dark energy equation of state parameter w, DESI BAO alone requirew=-0.99 +0.15 -0.13 . In models with a time-varying dark energy equation of state parametrised by w 0 and w a , combinations of DESI with CMB or with type Ia supernovae (SN Ia) individually prefer w 0 > -1 and w a < 0. This preference is 2.6σ for the DESI+CMB combination, and persists or grows when SN Ia are added in, giving results discrepant with the ΛCDM model at the 2.5σ, 3.5σ or 3.9σ levels for the addition of the Pantheon+, Union3, or DES-SN5YR supernova datasets respectively. For the flat ΛCDM model with the sum of neutrino mass ∑ m ν free, combining the DESI and CMB data yields an upper limit ∑ m ν < 0.072 (0.113) eV at 95% confidence for a ∑ m ν > 0 (∑ m ν > 0.059) eV prior. These neutrino-mass constraints are substantially relaxed if the background dynamics are allowed to deviate from flat ΛCDM.

79 ASTRONOMY AND ASTROPHYSICS↗

A sound horizon-free measurement of H 0 in DESI 2024

The physical size of the sound horizon at recombination is a powerful source of information for early-time measurements of the Hubble constant H 0 , and many proposed solutions to the Hubble tension therefore involve modifications to this scale. In light of this, there has been growing interest in measuring H 0 independently of the sound horizon. We present the first such measurement to use data from the Dark Energy Spectroscopic Instrument (DESI), jointly analyzing the full-shape galaxy power spectra of DESI luminous red galaxies, emission line galaxies, quasars, and the bright galaxy sample, in a total of six redshift bins. Information from the sound horizon scale is removed from our constraints via a rescaling procedure at the power spectrum level, with our sound horizon-marginalized measurement being driven instead primarily by the matter-radiation equality scale. This measurement is then combined with additional sound horizon-free information from Planck+ACT CMB lensing, uncalibrated type Ia supernovae, and the DESI Lyman-α forest. We agnostically combine with the DESY5, Pantheon+, and Union3 supernova datasets, with our tightest respective constraints being H 0 = 66.7 +1.7 -1.9 , 67.9 +1.9 -2.1 , and 67.8 +2.0 -2.2 km s -1 Mpc -1 . This corresponds to a sub-3% sound horizon-free constraint of the Hubble constant, and is the most precise measurement of its kind to date. Even without including information from the sound horizon, our measurement is still in 2.2-3.0σ tension with SH0ES. Additionally, the consistency between our result and other measurements that do rely on the sound horizon scale provides no evidence for new early-Universe physics (e.g. early dark energy). Future DESI data releases will allow unprecedented measurements of H 0 and place strong constraints on models that use beyond-ΛCDM physics to ameliorate the Hubble tension.

79 ASTRONOMY AND ASTROPHYSICS↗

Frequentist cosmological constraints from full-shape clustering measurements in DESI DR1

We present a frequentist analysis of clustering measurements from Data Release 1 of the Dark Energy Spectroscopic Instrument (DESI) using the standard profile likelihood method. While Bayesian inferences for effective field theory models of galaxy clustering can be highly sensitive to prior choices for extended cosmological models, frequentist inferences are not susceptible to such effects. We compare frequentist and Bayesian constraints for the parameter set {σ 8 , H 0 , Ω m , w 0 , w a } using the full-shape power spectrum multipoles, post-reconstruction baryon acoustic oscillation (BAO) measurements, and external datasets from the CMB and type Ia supernovae measurements. The frequentist confidence intervals are significantly shifted relative to the Bayesian credible intervals for the w 0 w a CDM model, unless supernovae data are included. When DESI full-shape and BAO data are fit jointly, we obtain the following 1σ frequentist confidence intervals for ΛCDM (w 0 w a CDM): σ 8 = 0.863 +0.048 -0.040 , H 0 = 68.96 +0.81 -0.80 km s -1 Mpc -1 , Ω m = 0.3034 ± 0.0110 (σ 8 = 0.782 +0.060 -0.036 , H 0 = 63.7 +4.2 -2.0 km s -1 Mpc -1 , Ω m = 0.378 +0.024 -0.047 , w 0 = -0.16 +0.10 -0.50 , w a = -3.0 +1.7 ), corresponding to 0.8σ, 0.3σ, 0.7σ (2.1σ, 4.1σ, 6.5σ, 6.3σ, 6.6σ) shifts between the maximum likelihood estimate and the Bayesian posterior mean for ΛCDM (w 0 w a CDM) respectively.

Bayesian reasoning↗