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1. Divergence beneath the Brillouin sphere and the phenomenology of prediction error in spherical harmonic series approximations of the gravitational field

   https://doi.org/10.1088/1361-6633/ad44d5  

   Bevis, M; Ogle, C; Costin, O; Jekeli, C; Costin, R D; Guo, J; Fowler, J; Dunne, G V; Shum, C K; Snow, K (June 2024, Reports on Progress in Physics)

   The Brillouin sphere is defined as the smallest sphere, centered at the origin of the geocentric coordinate system, that incorporates all the condensed matter composing the planet. The Brillouin sphere touches the Earth at a single point, and the radial line that begins at the origin and passes through that point is called the singular radial line. For about 60 years there has been a persistent anxiety about whether or not a spherical harmonic (SH) expansion of the external gravitational potential,V, will converge beneath the Brillouin sphere. Recently, it was proven that the probability of such convergence is zero. One of these proofs provided an asymptotic relation, called Costin’s formula, for the upper bound,E_N, on the absolute value of the prediction error,e_N, of a SH series model, $V_N(\theta ,\lambda ,r)$, truncated at some maximum degree, $N=n_{max}$. When the SH series is restricted to (or projected onto) a particular radial line, it reduces to a Taylor series (TS) in $1/r$. Costin’s formula is $E_N\simeq B{N}^{-b}(R/r{)}^N$, whereRis the radius of the Brillouin sphere. This formula depends on two positive parameters:b, which controls the decay of error amplitude as a function ofNwhenris fixed, and a scale factorB. We show here that Costin’s formula derives from a similar asymptotic relation for the upper bound,A_non the absolute value of the TS coefficients,a_n, for the same radial line. This formula, $A_n\simeq K{n}^{-k}$, depends on degree,n, and two positive parameters,kandK, that are analogous tobandB. We use synthetic planets, for which we can compute the potential,V, and also the radial component of gravitational acceleration, $g_r=\partial V/\partial r$, to hundreds of significant digits, to validate both of these asymptotic formulas. Let superscriptVrefer to asymptotic parameters associated with the coefficients and prediction errors for gravitational potential, and superscriptgto the coefficients and predictions errors associated withg_r. For polyhedral planets of uniform density we show that $b^V=k^V=7/2$and $b^g=k^g=5/2$almost everywhere. We show that the frequency of oscillation (around zero) of the TS coefficients and the series prediction errors, for a given radial line, is controlled by the geocentric angle,α, between that radial line and the singular radial line. We also derive useful identities connecting $K^V,B^V,K^g$, andB^g. These identities are expressed in terms of quotients of the various scale factors. The only other quantities involved in these identities areαandR. The phenomenology of ‘series divergence’ and prediction error (whenr < R) can be described as a function of the truncation degree,N, or the depth,d, beneath the Brillouin sphere. For a fixed $r\text{⩽}R$, asNincreases from very low values, the upper error boundE_Nshrinks until it reaches its minimum (best) value whenNreaches some particular or optimum value, $N_{\mathrm{opt}}$. When $N>N_{\mathrm{opt}}$, prediction error grows asNcontinues to increase. Eventually, when $N\gg N_{\mathrm{opt}}$, prediction errors increase exponentially with risingN. If we fix the value ofNand allow $R/r$to vary, then we find that prediction error in free space beneath the Brillouin sphere increases exponentially with depth,d, beneath the Brillouin sphere. Because $b^g=b^V-1$everywhere, divergence driven prediction error intensifies more rapidly forg_rthan forV, both in terms of its dependence onNandd. If we fix bothNandd, and focus on the ‘lateral’ variations in prediction error, we observe that divergence and prediction error tend to increase (as doesB) as we approach high-amplitude topography. 

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2. IGRINS Observations of WASP-127 b: H ₂ O, CO, and Super-solar Atmospheric Metallicity in the Inflated Sub-Saturn

   https://doi.org/10.3847/1538-3881/ad72f3  

   Kanumalla, Krishna; Line, Michael R; Weiner_Mansfield, Megan; Welbanks, Luis; Smith, Peter_C B; Bean, Jacob L; Pino, Lorenzo; Brogi, Matteo; Panwar, Vatsal (October 2024, The Astronomical Journal)

   Abstract High-resolution spectroscopy of exoplanet atmospheres provides insights into their composition and dynamics from the resolved line shape and depth of thousands of spectral lines. WASP-127 b is an extremely inflated sub-Saturn (R_p= 1.311R_Jup,M_p= 0.16M_Jup) with previously reported detections of H₂O and CO₂. However, the seeming absence of the primary carbon reservoir expected at WASP-127 b temperatures (T_eq∼1400 K) from chemical equilibrium, CO, posed a mystery. In this manuscript, we present the analysis of high-resolution observations of WASP-127 b with the Immersion Grating Infrared Spectrometer on Gemini South. We confirm the presence of H₂O (8.67σ) and report the detection of CO (4.34σ). Additionally, we conduct a suite of Bayesian retrieval analyses covering a hierarchy of model complexity and self-consistency. When freely fitting for the molecular gas volume mixing ratios, we obtain super-solar metal enrichment for H₂O abundance of log₁₀X ${}_{{\mathrm{H}}_2\mathrm{O}}$= −1.23 ${}_{-0.49}^{+0.29}$and a lower limit on the CO abundance of log₁₀X_CO≥–2.20 at 2σconfidence. We also report tentative evidence of photochemistry in WASP-127 b based upon the indicative depletion of H₂S. This is also supported by the data preferring models with photochemistry over free-chemistry and thermochemistry. The overall analysis implies a super-solar (∼39× Solar; [M/H] = ${1.59}_{-0.30}^{+0.30}$) metallicity for the atmosphere of WASP-127 b and an upper limit on its atmospheric C/O ratio as < 0.68. 

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3. The Cosmic Ultraviolet Baryon Survey (CUBS). VII. On the Warm-hot Circumgalactic Medium Probed by O vi and Ne viii at 0.4 ≲ z ≲ 0.7

   https://doi.org/10.3847/1538-4357/ad410b  

   Qu, Zhijie; Chen, Hsiao-Wen; Johnson, Sean D; Rudie, Gwen C; Zahedy, Fakhri S; DePalma, David; Schaye, Joop; Boettcher, Erin T; Cantalupo, Sebastiano; Chen, Mandy C; et al (June 2024, The Astrophysical Journal)

   Abstract This paper presents a newly established sample of 103 unique galaxies or galaxy groups at 0.4 ≲z≲ 0.7 from the Cosmic Ultraviolet Baryon Survey (CUBS) for studying the warm-hot circumgalactic medium (CGM) probed by both Oviand Neviiiabsorption. The galaxies and associated neighbors are identified at <1 physical Mpc from the sightlines toward 15 CUBS QSOs atz_QSO≳ 0.8. A total of 30 galaxies or galaxy groups exhibit associated Oviλλ1031, 1037 doublet absorption within a line-of-sight velocity interval of ±250 km s⁻¹, while the rest show no trace of Ovito a detection limit of $\log N_{\mathrm{OVI}}/{\mathrm{cm}}^{-2}\approx 13.7$. Meanwhile, only five galaxies or galaxy groups exhibit the Neviiiλλ770, 780 doublet absorption, down to a limiting column density of $\log N_{\mathrm{NeVIII}}/{\mathrm{cm}}^{-2}\approx 14.0$. These Ovi- and Neviii-bearing halos reside in different galaxy environments with stellar masses ranging from $\log M_{\mathrm{star}}/M_{\odot }\approx 8$to ≈11.5. The warm-hot CGM around galaxies of different stellar masses and star formation rates exhibits different spatial profiles and kinematics. In particular, star-forming galaxies with $\log M_{\mathrm{star}}/M_{\odot }\approx 9–11$show a significant concentration of metal-enriched warm-hot CGM within the virial radius, while massive quiescent galaxies exhibit flatter radial profiles of both column densities and covering fractions. In addition, the velocity dispersion of Oviabsorption is broad withσ_υ> 40 km s⁻¹for galaxies of $\log M_{\mathrm{star}}/M_{\odot }>9$within the virial radius, suggesting a more dynamic warm-hot halo around these galaxies. Finally, the warm-hot CGM probed by Oviand Neviiiis suggested to be the dominant phase in sub-L* galaxies with $\log M_{\mathrm{star}}/M_{\odot }\approx 9–10$based on their high ionization fractions in the CGM. 

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4. Theoretical Analysis of Critical Conditions for Crack Formation and Propagation, and Optimal Operation of SOECs

   https://doi.org/10.1149/1945-7111/ac5fee  

   Wang, Yudong; Virkar, Anil V.; Khonsari, M. M.; Zhou, Xiao-Dong (April 2022, Journal of The Electrochemical Society)

   A theoretical analysis on crack formation and propagation was performed based on the coupling between the electrochemical process, classical elasticity, and fracture mechanics. The chemical potential of oxygen, thus oxygen partial pressure, at the oxygen electrode-electrolyte interface ( ${\mu }_{O_2}^{\mathit{OE\mid El}}$) was investigated as a function of transport properties, electrolyte thickness and operating conditions (e.g., steam concentration, constant current, and constant voltage). Our analysis shows that: a lower ionic area specific resistance (ASR), $r_i^{OE},$and a higher electronic ASR ( $r_e^{OE}$) of the oxygen electrode/electrolyte interface are in favor of suppressing crack formation. The ${\mu }_{O_2}^{OE\mid El},$thus local pO₂, are sensitive towards the operating parameters under galvanostatic or potentiostatic electrolysis. Constant current density electrolysis provides better robustness, especially at a high current density with a high steam content. While constant voltage electrolysis leads to greater variations of ${\mu }_{O_2}^{OE\mid El}.$Constant current electrolysis, however, is not suitable for an unstable oxygen electrode because ${\mu }_{O_2}^{OE\mid El}$can reach a very high value with a gradually increased $r_i^{OE}.$A crack may only occur under certain conditions when $p_{O_2}^{TPB}>p_{cr}.$ 

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5. Atmospheric Characterization of the Super-Jupiter HIP 99770 b with KPIC

   https://doi.org/10.3847/1538-3881/ad6609  

   Zhang, Yapeng; Xuan, Jerry W; Mawet, Dimitri; Wang, Jason J; Hsu, Chih-Chun; Ruffio, Jean-Bapiste; Knutson, Heather A; Inglis, Julie; Blake, Geoffrey A; Chachan, Yayaati; et al (August 2024, The Astronomical Journal)

   Abstract Young, self-luminous super-Jovian companions discovered by direct imaging provide a challenging test for planet formation and evolution theories. By spectroscopically characterizing the atmospheric compositions of these super-Jupiters, we can constrain their formation histories. Here we present studies of the recently discovered HIP 99770 b, a 16M_Juphigh-contrast companion on a 17 au orbit, using the fiber-fed high-resolution spectrograph KPIC ( $\mathcal{R}$∼ 35,000) on the Keck II telescope. OurK-band observations led to detections of H₂O and CO in the atmosphere of HIP 99770 b. We carried out free retrieval analyses usingpetitRADTRANSto measure its chemical abundances, including the metallicity and C/O ratio, projected rotation velocity ( $v\sin i$), and radial velocity (RV). We found that the companion’s atmosphere has C/O $={0.55}_{-0.04}^{+0.06}$and [M/H] $={0.26}_{-0.23}^{+0.24}$(1σconfidence intervals), values consistent with those of the Sun and with a companion formation via gravitational instability or core accretion. The projected rotation velocity $v\sin \left(i\right)<7.8$km s⁻¹is small relative to other directly imaged companions with similar masses and ages. This may imply a nearly pole-on orientation or effective magnetic braking by a circumplanetary disk. In addition, we added the companion-to-primary relative RV measurement to the orbital fitting and obtained updated constraints on orbital parameters. Detailed characterization of super-Jovian companions within 20 au like HIP 99770 b is critical for understanding the formation histories of this population. 

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