Advances in the Direct Study of Carbon Burning in Massive Stars

The ${}^{12}\mathrm{C}+{}^{12}\mathrm{C}$ fusion reaction plays a critical role in the evolution of massive stars and also strongly impacts various explosive astrophysical scenarios. The presence of resonances in this reaction at energies around and below the Coulomb barrier makes it impossible to carry out a simple extrapolation down to the Gamow window—the energy regime relevant to carbon burning in massive stars. The ${}^{12}\mathrm{C}+{}^{12}\mathrm{C}$ system forms a unique laboratory for challenging the contemporary picture of deep sub-barrier fusion (possible sub-barrier hindrance) and its interplay with nuclear structure (sub-barrier resonances). Here, we show that direct measurements of the ${}^{12}\mathrm{C}+{}^{12}\mathrm{C}$ fusion cross section may be made into the Gamow window using an advanced particle-gamma coincidence technique. The sensitivity of this technique effectively removes ambiguities in existing measurements made with gamma ray or charged-particle detection alone. The present cross-section data span over 8 orders of magnitude and support the fusion-hindrance model at deep sub-barrier energies.

Figure 1

3D-rendered CAD drawing of the STELLA apparatus: The volume of the scattering chamber is shown semitransparent in order to allow its interior to be viewed, comprising three annular silicon detectors, and a target holding or rotating mechanism. The large circular carbon target foils are shown with blue frames on their perimeter. The direction of the ${}^{12}\mathrm{C}$ beam (from right to left in the diagram) is shown with the yellow arrow. Only half of the ${\mathrm{LaBr}}_3(\mathrm{Ce})$ gamma-ray array is depicted for clarity of presentation.

Figure 2

Gamma-ray spectra obtained for $E_{\text{beam}}=3.83\mathrm{MeV}$, without coincidence (red dashed showing the internal activity) and in coincidence (black solid) with the alpha particle channel, ${\alpha }_1$.

Figure 3

Charged particle spectra from the ${}^{12}\mathrm{C}+{}^{12}\mathrm{C}$ fusion reaction as a function of lab angle for $E_{\text{rel}}=3.77\mathrm{MeV}$. The bottom spectrum is the singles data without gamma-ray coincidence. The top spectrum is that for alpha-particle events in coincidence with a 1634 keV gamma ray. The locii are shown for different particle groups including protons from the contaminating $d({}^{12}\mathrm{C},p){}^{13}\mathrm{C}$ reaction.

Figure 4

Charged particle spectra from the ${}^{12}\mathrm{C}+{}^{12}\mathrm{C}$ fusion reaction as a function of lab angle for $E_{\text{rel}}=2.16\mathrm{MeV}$. The bottom spectrum is the singles data without gamma-ray coincidence dominated by protons from the contaminating $d({}^{12}\mathrm{C},p){}^{13}\mathrm{C}$ reaction (locus labeled in blue). The top spectrum is that for proton events in coincidence with a 440 keV gamma ray. The locus is shown for the $p_1$ events with the dashed lines indicating three-sigma windows on the proton energy resolution.

Figure 5

$S$-factor measurements for the ${}^{12}\mathrm{C}+{}^{12}\mathrm{C}$ fusion reaction as a function of $E_{\text{rel}}$ for the final system ${}^{20}\mathrm{Ne}+\alpha$. The present data, at the effective beam energy (see text for details), are presented as red circles and compared to earlier measurements (gray symbols) [18, 19, 21, 23]. The blue dash-dotted line is a standard extrapolation of the data [38], while the red dashed line corresponds to a sub-barrier hindrance model [36]. The Gamow windows for $8/10M_{\odot }$ and $25M_{\odot }$ correspond to stellar temperatures of 0.5 and 0.9 GK, respectively.

Figure 6

$S$-factor measurements in similar context as Fig. 5, but for the final system ${}^{23}\mathrm{Na}+p$.