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1. Resolving the Peak of the Black Hole Mass Spectrum

   https://doi.org/10.3847/1538-4357/ac8b83  

   Farag, Ebraheem; Renzo, Mathieu; Farmer, Robert; Chidester, Morgan_T; Timmes, F_X (October 2022, The Astrophysical Journal)

   Abstract Gravitational-wave (GW) detections of binary black hole (BH) mergers have begun to sample the cosmic BH mass distribution. The evolution of single stellar cores predicts a gap in the BH mass distribution due to pair-instability supernovae (PISNe). Determining the upper and lower edges of the BH mass gap can be useful for interpreting GW detections of merging BHs. We useMESAto evolve single, nonrotating, massive helium cores with a metallicity ofZ= 10⁻⁵, until they either collapse to form a BH or explode as a PISN, without leaving a compact remnant. We calculate the boundaries of the lower BH mass gap for S-factors in the range S(300 keV) = (77,203) keV b, corresponding to the ±3σuncertainty in our high-resolution tabulated¹²C(α,γ)¹⁶O reaction rate probability distribution function. We extensively test temporal and spatial resolutions for resolving the theoretical peak of the BH mass spectrum across the BH mass gap. We explore the convergence with respect to convective mixing and nuclear burning, finding that significant time resolution is needed to achieve convergence. We also test adopting a minimum diffusion coefficient to help lower-resolution models reach convergence. We establish a new lower edge of the upper mass gap asM_lower≃ ${60}_{-14}^{+32}$M_⊙from the ±3σuncertainty in the¹²C(α,γ)¹⁶O rate. We explore the effect of a larger 3αrate on the lower edge of the upper mass gap, findingM_lower≃ ${69}_{-18}^{+34}$M_⊙. We compare our results with BHs reported in the Gravitational-Wave Transient Catalog. 

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2. On Trapped Modes in Variable White Dwarfs as Probes of the ¹² C(α, γ) ¹⁶ O Reaction Rate

   https://doi.org/10.3847/1538-4357/ac7ec3  

   Chidester, Morgan T.; Farag, Ebraheem; Timmes, F. X. (August 2022, The Astrophysical Journal)

   Abstract We seek signatures of the current experimental 12 C α , γ 16 O reaction rate probability distribution function in the pulsation periods of carbon–oxygen white dwarf (WD) models. We find that adiabatic g-modes trapped by the interior carbon-rich layer offer potentially useful signatures of this reaction rate probability distribution function. Probing the carbon-rich region is relevant because it forms during the evolution of low-mass stars under radiative helium-burning conditions, mitigating the impact of convective mixing processes. We make direct quantitative connections between the pulsation periods of the identified trapped g-modes in variable WD models and the current experimental 12 C α , γ 16 O reaction rate probability distribution function. We find an average spread in relative period shifts of Δ P / P ≃ ±2% for the identified trapped g-modes over the ±3 σ uncertainty in the 12 C α , γ 16 O reaction rate probability distribution function—across the effective temperature range of observed DAV and DBV WDs and for different WD masses, helium shell masses, and hydrogen shell masses. The g-mode pulsation periods of observed WDs are typically given to six to seven significant figures of precision. This suggests that an astrophysical constraint on the 12 C α , γ 16 O reaction rate could, in principle, be extractable from the period spectrum of observed variable WDs. 

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3. New Determination of the ¹² C(α, γ) ¹⁶ O Reaction Rate and Its Impact on the Black-hole Mass Gap

   https://doi.org/10.3847/1538-4357/acb7de  

   Shen, Yangping; Guo, Bing; deBoer, Richard J.; Li, Ertao; Li, Zhihong; Li, Yunju; Tang, Xiaodong; Pang, Danyang; Adhikari, Sucheta; Basu, Chinmay; et al (March 2023, The Astrophysical Journal)

   Abstract We present a precise measurement of the asymptotic normalization coefficient (ANC) for the¹⁶O ground state (GS) through the¹²C(¹¹B,⁷Li)¹⁶O transfer reaction using the Quadrupole‐3‐Dipole (Q3D) magnetic spectrograph. The present work sheds light on the existing discrepancy of more than 2 orders of magnitude between the previously reported GS ANC values. This ANC is believed to have a strong effect on the¹²C(α,γ)¹⁶O reaction rate by constraining the external capture to the¹⁶O ground state, which can interfere with the high-energy tail of the 2⁺subthreshold state. Based on the new ANC, we determine the astrophysicalS-factor and the stellar rate of the¹²C(α,γ)¹⁶O reaction. An increase of up to 21% in the total reaction rate is found within the temperature range of astrophysical relevance compared with the previous recommendation of a recent review. Finally, we evaluate the impact of our new rate on the pair-instability mass gap for black holes (BH) by evolving massive helium core stars using the MESA stellar evolution code. The updated¹²C(α,γ)¹⁶O reaction rate decreases the lower and upper edges of the BH gap about 12% and 5%, respectively. 

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4. Seismic Signatures of the ¹² C(α, γ) ¹⁶ O Reaction Rate in White Dwarf Models with Overshooting

   https://doi.org/10.3847/1538-4357/ace620  

   Chidester, Morgan T; Timmes, F X; Farag, Ebraheem (August 2023, The Astrophysical Journal)

   Abstract We consider the combined effects that overshooting and the¹²C(α,γ)¹⁶O reaction rate have on variable white dwarf (WD) stellar models. We find that carbon–oxygen (CO) WD models continue to yield pulsation signatures of the current experimental¹²C(α,γ)¹⁶O reaction rate probability distribution function when overshooting is included in the evolution. These signatures hold because the resonating mantle region, encompassing ≃0.2M_⊙in a typical ≃0.6M_⊙WD model, still undergoes radiative helium burning during the evolution to a WD. Our specific models show two potential low-order adiabatic g-modes,g₂andg₆, that signalize the¹²C(α,γ)¹⁶O reaction rate probability distribution function. Both g-mode signatures induce average relative period shifts of ΔP/P= 0.44% and ΔP/P= 1.33% forg₂andg₆, respectively. We find thatg₆is a trapped mode, and theg₂period signature is inversely proportional to the¹²C(α,γ)¹⁶O reaction rate. Theg₆period signature generally separates the slower and faster reaction rates, and has a maximum relative period shift of ΔP/P= 3.45%. We conclude that low-order g-mode periods from CO WDs may still serve as viable probes for the¹²C(α,γ)¹⁶O reaction rate probability distribution function when overshooting is included in the evolution. 

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5. The $$^{12}$$C$$(\alpha ,\gamma )^{16}$$O reaction, in the laboratory and in the stars

   https://doi.org/10.1140/epja/s10050-025-01537-1  

   de_Boer, R J; Best, A; Brune, C R; Chieffi, A; Hebborn, C; Imbriani, G; Liu, W P; Shen, Y P; Timmes, F X; Wiescher, M (April 2025, The European Physical Journal A)

   Abstract The evolutionary path of massive stars begins at helium burning. Energy production for this phase of stellar evolution is dominated by the reaction path 3$$\alpha \rightarrow ^{12}$$ $\alpha {\to }^{12}$C$$(\alpha ,\gamma )^{16}$$ ${(\alpha ,\gamma )}^{16}$O and also determines the ratio of$$^{12}$$ $_{}^{12}$C/$$^{16}$$ $_{}^{16}$O in the stellar core. This ratio then sets the evolutionary trajectory as the star evolves towards a white dwarf, neutron star or black hole. Although the reaction rate of the 3$$\alpha $$ $\alpha$process is relatively well known, since it proceeds mainly through a single narrow resonance in$$^{12}$$ $_{}^{12}$C, that of the$$^{12}$$ $_{}^{12}$C$$(\alpha ,\gamma )^{16}$$ ${(\alpha ,\gamma )}^{16}$O reaction remains uncertain since it is the result of a more difficult to pin down, slowly-varying, portion of the cross section over a strong interference region between the high-energy tails of subthreshold resonances, the low-energy tails of higher-energy broad resonances and direct capture. Experimental measurements of this cross section require herculean efforts, since even at higher energies the cross section remains small and large background sources are often present that require the use of very sensitive experimental methods. Since the$$^{12}$$ $_{}^{12}$C$$(\alpha ,\gamma )^{16}$$ ${(\alpha ,\gamma )}^{16}$O reaction has such a strong influence on many different stellar objects, it is also interesting to try to back calculate the required rate needed to match astrophysical observations. This has become increasingly tempting, as the accuracy and precision of observational data has been steadily improving. Yet, the pitfall to this approach lies in the intermediary steps of modeling, where other uncertainties needed to model a star’s internal behavior remain highly uncertain. 

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