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

Abstract
HTML
Reference
Related

PDF

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.

References

[1]

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

[1]	Zuting Luo , Meirong Tang , Zhaoyi Xu . Testing Einstein Maxwell Power-Yang-Mills Hair via Black Hole Photon Rings. Chinese Physics C, 2026, 50(1): 1-18.
[2]	Zhe Wang , Quan Liu , Jian-You Guo . Examination of proton radioactivity in exotic nuclei with a deformed Gamow-like model. Chinese Physics C, 2026, 50(2): 1-10. doi: 10.1088/1674-1137/ae042f
[3]	Muhammad Farhan Taseer , Subhash Singha . Impact of particle production mechanisms on pseudorapidity distribution and directed flow in Au+Au and Cu+Cu collisions at ${ \sqrt{{\boldsymbol s}_{\boldsymbol{ NN}}}}$ = 19.6 GeV using AMPT model. Chinese Physics C, 2025, 49(10): 104101. doi: 10.1088/1674-1137/ade660
[4]	Lola Meliyeva , Obid Xoldorov , Olmos Tursunboyev , Shavkat Karshiboev , Sardor Murodov , Isomiddin Nishonov , Bekzod Rahmatov . Theoretical study of Strong gravitational lensing around Dyonic ModMax black hole: constraints from EHT observations. Chinese Physics C, 2025, 49(12): 125102. doi: 10.1088/1674-1137/adf4a0
[5]	LIANG Jun , LIU Yan-Chun , ZHU Qiao . Thermodynamics of noncommutative geometry inspired black holes based on Maxwell-Boltzmann smeared mass distribution. Chinese Physics C, 2014, 38(2): 025101. doi: 10.1088/1674-1137/38/2/025101
[6]	Yu Hong , Shen Qixing , Zhang Lin . Angular Distribution of Process e⁺e^－→τ⁺τ^－,τ^－→a₁υτ,a₁→ρπ and Characteristics of a₁ Meson. Chinese Physics C, 1994, 18(7): 583-590.
[7]	WU Zhong-Li . ANALYSIS OF THE MOMENTUM DISTRIBUTION WIDTH OF THE PREOJECTILE-LIKE-FRAGMENT FROM HEAVY ION COLLISIONS. Chinese Physics C, 1989, 13(8): 752-754.

Access

Get Citation

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

RIS(for EndNote,Reference Manager,ProCite)

BibTex

Txt

Milestone

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

Article Metric

Article Views(3183)
PDF Downloads(229)
Cited by(0)

Policy on re-use

To reuse of subscription content published by CPC, the users need to request permission from CPC, unless the content was published under an Open Access license which automatically permits that type of reuse.

通讯作者: 陈斌, bchen63@163.com

1.
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.