Re-examination of constraints on the Maxwell-Boltzmann distribution by Helioseismology

HE Jian-Jun; ZHANG Li-Yong; HOU Su-Qing; XU Shi-Wei

doi:10.1088/1674-1137/37/10/104001

Chinese Physics C> 2013, Vol. 37> Issue(10) : 104001 DOI: 10.1088/1674-1137/37/10/104001

Re-examination of constraints on the Maxwell-Boltzmann distribution by Helioseismology

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Nuclear reactions in stars occur between nuclei in the high-energy tail of the energy distribution and are sensitive to possible deviations from the standard equilibrium thermal-energy distribution, the well-known Maxwell-Boltzmann Distribution (MBD). Strong constraints on such deviations were made previously with the detailed helioseismic information of the solar structure. With a small deviation parameterized with a factor exp[-δ (E/kT)²], it was shown δ restricted between -0.005 and +0.002. These constraints have been carefully re-examined in the present work. We find that a normalization factor was missed in the previous modified MBD. In this work, the normalization factor c is calculated as a function of δ. It shows the factor c is almost unity within the range 0< δ ≤0.002, which supports the previous conclusion. However, it demonstrates that δ cannot take a negative value from the normalization point of view. As a result, a stronger constraint on δ is defined as 0≤ δ ≤0.002. The astrophysical implication on the solar neutrino fluxes is simply discussed based on a positive δ value of 0.003. The reduction of the ⁷Be and ⁸B neutrino fluxes expected from the modified MBD can possibly shed alternative light on the solar neutrino problem. In addition, the resonant reaction rates for the ¹⁴N(p, γ)¹⁵O reaction are calculated with a standard MBD and a modified MBD, respectively. It shows that the rates are quite sensitive even to a very small δ. This work demonstrates the importance and necessity of experimental verification or testing of the well-known MBD at high temperatures.

References

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Degl'Innocenti S et al. Phys. Lett. B, 1998, 441: 291-298[2] Landau L D, Lifshitz E M. Statistical Physics. Oxford: Pergamon Press, 1980[3] Huang K. Statistical Mechanics (2nd Edition). New York: John Wiley Sons, Inc., 1987[4] Rolfs C E, Rodney W S. Cauldrons in the Cosmos. Chicago: Chicago University Press, 1988[5] Fowler W A, Caughlan G R, Zimmerman B A. Ann. Rev. Astron. Astrophys., 1967 5: 525-570[6] Clayton D D. Principles of Stellar Evolution and Nucleosynthesis. Chicago: Chicago University Press, 1983[7] Ciacio F, Degl'Innocenti S, Ricci B. Astr. Astrophy. Suppl. Ser., 1997, 123: 449-454[8] Bahcall J N, Pinsonneault M. Rev. Mod. Phys., 1992, 64: 885-926[9] Angulo C et al. Nucl. Phys. A, 1999, 565: 3-183

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HE Jian-Jun, ZHANG Li-Yong, HOU Su-Qing and XU Shi-Wei. Re-examination of constraints on the Maxwell-Boltzmann distribution by Helioseismology[J]. Chinese Physics C, 2013, 37(10): 104001. doi: 10.1088/1674-1137/37/10/104001

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Received: 2013-04-23
Revised: 1900-01-01

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沈阳化工大学材料科学与工程学院沈阳 110142

Re-examination of constraints on the Maxwell-Boltzmann distribution by Helioseismology

Corresponding author: HE Jian-Jun,

Corresponding author: XU Shi-Wei,

Received Date: 2013-04-23
Accepted Date: 1900-01-01
Available Online: 2013-10-05

Abstract: Nuclear reactions in stars occur between nuclei in the high-energy tail of the energy distribution and are sensitive to possible deviations from the standard equilibrium thermal-energy distribution, the well-known Maxwell-Boltzmann Distribution (MBD). Strong constraints on such deviations were made previously with the detailed helioseismic information of the solar structure. With a small deviation parameterized with a factor exp[-δ (E/kT)²], it was shown δ restricted between -0.005 and +0.002. These constraints have been carefully re-examined in the present work. We find that a normalization factor was missed in the previous modified MBD. In this work, the normalization factor c is calculated as a function of δ. It shows the factor c is almost unity within the range 0< δ ≤0.002, which supports the previous conclusion. However, it demonstrates that δ cannot take a negative value from the normalization point of view. As a result, a stronger constraint on δ is defined as 0≤ δ ≤0.002. The astrophysical implication on the solar neutrino fluxes is simply discussed based on a positive δ value of 0.003. The reduction of the ⁷Be and ⁸B neutrino fluxes expected from the modified MBD can possibly shed alternative light on the solar neutrino problem. In addition, the resonant reaction rates for the ¹⁴N(p, γ)¹⁵O reaction are calculated with a standard MBD and a modified MBD, respectively. It shows that the rates are quite sensitive even to a very small δ. This work demonstrates the importance and necessity of experimental verification or testing of the well-known MBD at high temperatures.