Stars/Sun/Neutrinos/Lecture

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This "neutrino image" of the Sun is produced by using the Super-Kamiokande to detect the neutrinos from nuclear fusion coming from the Sun. Credit: R. Svoboda and K. Gordan (LSU), and NASA.

Neutrinos are being produced by processes above the photosphere and probably within 2-4 solar radii as most solar flares give off energy close to and into the chromosphere.

Neutrons[edit]

Data from the Climax, Colorado, surface neutron monitor is an indicator of primary cosmic rays in the GeV range. Credit: John N. Bahcall and William H. Press.

The data on the right "from the Climax, Colorado, surface neutron monitor [...] is an indicator of primary cosmic rays in the GeV range."[1]

"Variation with the solar cycle [dotted curve of sunspot data] is evident."[1]

"The tendency of the cosmic-ray modulation to lag sunspots (at least at times of sunspot decline) is visible, as is the somewhat more sawtooth form of the cosmic rays."[1]

"The surface neutron flux [...] is largest at solar minimum and smallest at solar maximum, and [...] has the same sense as the 37Ar production variations."[1]

"Primary cosmic rays below ~1 GeV are shielded by heliospheric currents which build up during solar maximum; see, e.g., Simpson 1989 and references there in."[1]

Neutrinos[edit]

All of the data from the Homestake solar neutrino experiment are shown versus dates. Credit: John N. Bahcall and William H. Press.

The first piece of information that seems to be needed are the reactions that produce the higher energy neutrinos: νµ and ντ.

For antiproton-proton annihilation at rest, a meson result is, for example,

[2]
[3] and
[4]

"All other sources of ντ are estimated to have contributed an additional 15%."[4]

[4]

for two neutrinos.[4]

[4]

where is a hadron, for two neutrinos.[4]

The "data set [on the right from the Homestake solar neutrino experiment] now spans almost two complete solar cycles."[1]

Electrons[edit]

Beam of electrons are moving in a circle in a magnetic field (cyclotron motion). Lighting is caused by excitation of atoms of gas in a bulb. Credit: Marcin Białek.

Free electrons in vacuum can be influenced by electric and magnetic fields [so] as to form a fine beam. At the spot of collision of the beam with the particles of the solid-state matter, most portion of the kinetic energy of electrons is transferred into heat. The main advantage of this method is the possibility of very fast local heating, which can be precisely electronically (computer) controlled. The high concentration of power in a small volume of matter, which can be reached in this way results in very fast increase of temperature in the spot of impact causing the melting or even evaporation of any material, depending on working conditions. This makes the electron beam an excellent tool in many applications.

Sun[edit]

Main sources: Stars/Sun and Sun (star)

The highest flux of solar neutrinos come directly from the proton-proton interaction, and have a low energy, up to 400 keV. There are also several other significant production mechanisms, with energies up to 18 MeV.[5]

Sunspot cycles[edit]

This figure shows a detected 94 % correlation between scaled sunspot numbers and neutrino detections. Credit: John N. Bahcall.
37Ar production data are shown above inverted sunspot data. Credit: John N. Bahcall and William H. Press.

"Neutrinos can be produced by energetic protons accelerated in solar magnetic fields. Such protons produce pions, and therefore muons, hence also neutrinos as a decay product, in the solar atmosphere."[6]

"Energetic protons in the solar corona could explain Figure 2 [at right] only if (1) they tap a substantial fraction of the entire energy generated in the corona, (2) the energy generated in the corona is at least 3 times what has been deduced from the observations, (3) the vast majority of energetic protons do not escape the Sun, (4) the proton energy spectrum is unusually hard (p0 = 300 MeV c-1, and (5) the sign of the variation is opposite to what one would predict. As the likelihood of all of these conditions being fulfilled seems extremely small, we do not believe that neutrinos produced by energetic protons in the solar atmosphere contribute significantly to the neutrino capture in the 37Cl experiment."[6]

"The 37Ar production rate [at second right] in the Homestake solar neutrino experiment is anticorrelated (significance level of parts in 105) with solar activity (as measured by sunspot number) in the second two-thirds of the data, approximately 1977-1989; no significant correlation is substantiated in the first third of the data, 1970-1977."[1]

The following is a list of solar variation or solar cycles (sometimes called sunspot cycles), tracked since 1755 following the original numbering proposed by Rudolf Wolf in the mid-19th century[7][8] The source data are the revised International Sunspot Numbers (ISN v2.0), as available at SILSO.[9] Sunspot number counts exist since 1610[10] but the cycle numbering is not well defined during the Maunder minimum.[11] It was proposed that one cycle might have been lost in the late 18th century,[12] but this still remains not fully confirmed.

The smoothing was done using the traditional SIDC smoothing formula.[13] Other smoothing formulas exist, and they usually give slightly different values for the amplitude and timings of the solar cycles. An example is the Meeus smoothing formula,[14] with related solar cycles characteristics available in this STCE news item.[15]

In the table below, the number of spotless days is the number between the maximum of the previous solar cycle and the maximum of the new solar cycle. As an example, there were 817 spotless days during the transit from solar cycle 23 to solar cycle 24.

Solar Cycle Start Smoothed minimum ISN Maximum Smoothed maximum ISN Time of Rise (years) Duration (years) Spotless days[16][17][18]
Solar cycle 1 1755 February 14.0 1761 June 144.1 6.3 11.3
Solar cycle 2 1766 June 18.6 1769 September 193.0 3.3 9.0
Solar cycle 3 1775 June 12.0 1778 May 264.3 2.9 9.3
Solar cycle 4 1784 September 15.9 1788 February 235.3 3.4 13.6
Solar cycle 5 1798 April 5.3 1805 February 82.0 6.8 12.3
Solar cycle 6 1810 August 0.0 1816 May 81.2 5.8 12.8
Solar cycle 7 1823 May 0.2 1829 November 119.2 6.5 10.5
Solar cycle 8 1833 November 12.2 1837 March 244.9 3.3 9.7
Solar cycle 9 1843 July 17.6 1848 February 219.9 4.6 12.4
Solar cycle 10 1855 December 6.0 1860 February 186.2 4.2 11.3 655
Solar cycle 11 1867 March 9.9 1870 August 234.0 3.4 11.8 406
Solar cycle 12 1878 December 3.7 1883 December 124.4 5.0 11.3 1028
Solar cycle 13 1890 March 8.3 1894 January 146.5 3.8 11.8 736
Solar cycle 14 1902 January 4.5 1906 February 107.1 4.1 11.5 934
Solar cycle 15 1913 July 2.5 1917 August 175.7 4.1 10.1 1023
Solar cycle 16 1923 August 9.4 1928 April 130.2 4.7 10.1 534
Solar cycle 17 1933 September 5.8 1937 April 198.6 3.6 10.4 568
Solar cycle 18 1944 February 12.9 1947 May 218.7 3.3 10.2 269
Solar cycle 19 1954 April 5.1 1958 March 285.0 3.9 10.5 446
Solar cycle 20 1964 October 14.3 1968 November 156.6 4.1 11.4 227
Solar cycle 21 1976 March 17.8 1979 December 232.9 3.8 10.5 272
Solar cycle 22 1986 September 13.5 1989 November 212.5 3.2 9.9 273
Solar cycle 23 1996 August 11.2 2001 November 180.3 5.3 12.3 309
Solar cycle 24 2008 December 2.2 2014 April 116.4 5.3 In progress 817
Solar cycle 25 First spot[19] 137
Average 9.3 178.7 4.4 11.04

Chromospheres[edit]

Influence of the high energy cutoff of proton energies is simulated and graphed. Credit: G. de Wasseige, P. Evenson, K. Hanson, N. van Eijndhoven, and K.-L. Klein.{{fairuse}}
The effective neutrino cross sections by plasma instability. Credit: Yukio Tomozawa.{{fairuse}}

The parts of the Sun above the photosphere are referred to collectively as the solar atmosphere.[20]

"Solar flares convert magnetic energy into plasma heating and kinetic energy of charged particles such as protons. Protons injected downwards from the coronal acceleration region will interact with the dense plasma in the low solar atmosphere. [The] pion production channel through proton-nucleus interactions in the chromosphere [includes hadronic acceleration and subsequent interactions in the chromosphere with the] decay of charged pions [to] solar flare neutrinos [...]."[21]

"The production of neutrinos by protons with energies below 500 MeV can be neglected."[21]

"The evidence of an upper cutoff in the accelerated proton spectrum has been demonstrated by Dj. Heristchi et al. [11]."[21]

For "different upper cutoff values, i.e. 1, 2, 3 and 5 GeV [the] difference in the solar flare neutrino flux directed to the Earth due to the variation of the upper cutoff of the accelerated proton distribution [...] above or equal to 3 GeV basically yield the same result."[21] This is shown in the image on the right.

"The enhancement of the neutrino cross section in the chromosphere region by plasma instability leads to an energy dependence peaked at the unitarity bound. Therefore, the effective neutrino cross section behaves as a function of energy as described in [the second figure down on the right]. The soar maximum and minimum give a similar result except the latter has a slower rise (or equivalently peaked at a higher energy as shown in [the figure]."[22]

"As a result, higher energy neutrinos have a similar cross section for the solar maximum or minimum, while there is a distinctive difference at lower energies for the two cases (the threshold effects near the peak region in [the figure])."[22]

"This feature explains why Kamiokande which has a threshold neutrino energy of 7.5 MeV did not see a drop in neutrino flux during the solar maximum of ~ 1990-1991. On the other hand, the Homesteak C1 experiment with a threshold of 0.8 MeV observed the anticorrelation. At much lower energy below the peak region (< 0.5 MeV), the enhancement effect is insignificant so that there is no deficiency of low energy neutrinos. This may predict a moderate anticorrelation (of the order of 15 %) for the Gallium experiment which has the threshold energy of 0.2 MeV. The anticorrelation of the Gallium experiment stems from neutrinos with energy greater than 0.5 MeV which is sensitive to the C1 experiment. It is clear that this model does not require an unusually large magnetic moment for neutrinos to explain anticorrelation."[22]

The figure on the right "provides an explanation for the degree of neutrino flux depletion [which] is maximum for the C1 experiment since enhancement of the cross section is the highest (the peak region), while Kamiokande has a less depleted neutrino flux due to smaller enhancement at higher neutrino energies. The Gallium experiment has the lowest depletion since the enhancement of the cross section is small for 0.2 MeV < E < 0.5 MeV."[22]

"A suitable reaction [to detect neutrinos from hydrogen fusion] is 71
Ga
e, e-) 71
Ge
."[23]

"Its low threshold of 233 keV [17] allows the detection of pp neutrinos. The product 71
Ge
has a convenient half-life (11.43 d) [18] and can be isolated by radio-chemical techniques."[23]

The "first neutrino data obtained with GALLEX [was] in 14 runs during the period 14 May 1991-31 March 1992 ("GALLEX I") [solar maximum at November 1989], covering 295 d of exposure."[23]

"The main result of 83 ± 19 (stat.) ± 8 (syst.) SNU (lσ) is to be compared with the outcome of the SAGE experiment: (stat.) ± 32 (syst.) SNU (lσ) [19] and with the standard solar model prediction range ) SNU ("3σ")[3]. For 1σ-comparability we have, in SNU, 83±21 (GALLEX), (SAGE) and 132 ± 7 (SSM [3])."[23]

"Our result implies the first detection ever of the pp neutrinos".[23]

Transition regions[edit]

[Transition Region and Coronal Explorer] (TRACE) produced a 19.5 nm wavelength image of the transition region as a low, bright fog over the surface of the Sun and as a thin bright nimbus around the prominence itself. Credit: TRACE Data Center.

The solar transition region is a region of the Sun's atmosphere, between the chromosphere and corona.[24] It is visible from space using telescopes that can sense ultraviolet. It is important because it is the site of several unrelated but important transitions in the physics of the solar atmosphere:

  • Below, most of the helium is not fully ionized, so that it radiates energy very effectively; above, it is fully ionized.
  • Below, gas pressure and fluid dynamics dominate the motion and shape of structures; above, magnetic forces dominate the motion and shape of structures, giving rise to different simplifications of magnetohydrodynamics.

"The thin region of temperature increase from the chromosphere to the corona is known as the transition region and can range from tens to hundreds of kilometers thick. An analogy of this would be a light bulb heating the air surrounding it hotter than its glass surface. The second law of thermodynamics would be broken.

Coronal clouds[edit]

Def. a cloud, or cloud-like, natural astronomical entity, composed of plasmas at least hot enough to emit X-rays is called a coronal cloud.

As of December 5, 2011, "Voyager 1 is about ... 18 billion kilometers ... from the [S]un [but] the direction of the magnetic field lines has not changed, indicating Voyager is still within the heliosphere ... the outward speed of the solar wind had diminished to zero in April 2010 ... inward pressure from interstellar space is compacting [the magnetic field] ... Voyager has detected a 100-fold increase in the intensity of high-energy electrons from elsewhere in the galaxy diffusing into our solar system from outside ... [while] the [solar] wind even blows back at us."[25]

The source of heat that brings the coronal cloud near the Sun hot enough to emit X-rays may be an electron beam heating effect due to "high-energy electrons from elsewhere in the galaxy diffusing into our solar system from outside".[25]

Solar flares[edit]

"One of [...] the outstanding problems of the outer atmosphere of the Sun is the identification of the physical mechanisms that give rise to the eruption of solar flares."[26]

There is a "hydrodynamic response of the solar atmosphere to the injection of an intense beam of electrons [as described] in a numerical simulation of a solar flare."[26]

"The hydrodynamics is predicted [...] and the geometric form is of a semi-circular loop having its ends in the photosphere. [...] the loop is filled at supersonic speed with plasma at temperatures characteristic of flares. At the same time a compression wave is predicted to propagate down towards the photosphere. After the heating pulse stops, the plasma that has risen into the loop, starts to decay and return to the condition it was in before the pulse started."[26]

The "impulsive phase of a flare [may be] initiated by an electron beam (having a power-law energy spectrum down to some minimum energy) depositing its energy in a model atmosphere representing the pre-flare condition."[26]

There may be "a magnetic field parallel to the electron beam, and sufficiently strong that the electrons and subsequent flare plasma are contained within the beam dimensions, and transport negligible thermal energy in transverse directions."[26]

The "pre-flare atmosphere is [...] for the chromosphere with a suitable extension into the corona."[26]

An "input beam pulse of 1011 erg cm-2 s-1 for 10 s is capable of filling a loop structure with plasma at a peak temperature of over 30 million degrees K, with associated flare velocities of over a thousand kilometers per second. Associated with this upward flaring material, is a compression wave moving towards the photosphere, and attaining particle densities of up to 1014 cm-3."[26]

"[N]eutrino flux increases noted in Homestake results [coincide] with major solar flares [14]."[27]

"The correlation between a great solar flare and Homestake neutrino enhancement was tested in 1991. Six major flares occurred from May 25 to June 15 including the great June 4 flare associated with a coronal mass ejection and production of the strongest interplanetary shock wave ever recorded (later detected from spacecraft at 34, 35, 48, and 53 AU) [15]. It also caused the largest and most persistent (several months) signal ever detected by terrestrial cosmic ray neutron monitors in 30 years of operation [16]. The Homestake exposure (June 1–7) measured a mean 37Ar production rate of 3.2 ± 1.5 atoms/day (≈19 37Ar atoms produced in 6 days) [13]; about 5 times the rate of ≈ 0.65 day −1 for the preceding and following runs, > 6 times the long term mean of ≈ 0.5 day−1 and > 2 1/2 times the highest rates recorded in ∼ 25 operating years."[27]

Coronal loops[edit]

The image shows solar coronal loops observed by the Transition Region And Coronal Explorer (TRACE), 171 Å filter. Credit: TRACE/NASA.
The image shows the cooling post-flare arcade (rotated by -90 degrees so that north is to the right) 6h after the flare (at 00:11 UT on September 8. Credit: TRACE/NASA.

"Almost as soon as Active Region 10808 rotated onto the solar disk, it spawned a major X17 flare. TRACE was pointed at the other edge of the Sun at the time, but was repointed 6 hours after the flare started. The image on the left shows the cooling post-flare arcade (rotated by -90 degrees so that north is to the right) 6h after the flare (at 00:11 UT on September 8); the loop tops still glow so brightly that the diffraction pattern repeats them on diagonals away from the brightest spots. Some 18h after the flare, the arcade is still glowing, as seen in the image on the right (at 11:42 UT on September 8). In such big flares, magnetic loops generally light up successively higher in the corona, as can be seen here too: the second image shows loops that are significantly higher than those seen in the first. Note also that the image on the right also contains a much smaller version of the cooling arcade in a small, very bright loop low over the polarity inversion line of the region."[28]

Nearly all of the TRACE images of coronal loops and the transition region indicate that material in these loops and loop-like structures returns to the chromosphere.

"Normally, solar energetic particle (SEP) events associated with disturbances in the eastern hemisphere are characterized by slow onset and lack of high-energy particles. The SEP event associated with the first major flare (X17) [...] is among very few such events over several decades in that although the source region was on the east limb, the particle flux started to rise only a few hours from the flare onset, while the flux of protons with energies in excess of 100 MeV went up by more than a factor of one hundred. We do not understand how these energetic particles can reach the Earth from that side of the Sun, because there should be no magnetic connectivity."[28]

Surface fusions[edit]

This neutrino spectra is expected in Borexino (accounting for the detector’s energy resolution). Credit: C. Arpesella and the Borexino Collaboration.{{fairuse}}

Based on the 3He-flare flux from the Sun's surface and Surveyor 3 samples (implanted 15N and 14C in lunar material) from the surface of the Moon, the level of nuclear fusion occurring in the solar atmosphere is approximately at least two to three orders of magnitude greater than that estimated from solar flares such as those of August 1972.[29]

Although 7Be is usually assumed to have been produced by the Big Bang nuclear fusion, excesses (100x) of the isotope on the leading edge[30] of the Long Duration Exposure Facility (LDEF) relative to the trailing edge suggest that fusion near the surface of the Sun is the most likely source.[27] The particular reaction 3He(α,γ)7Be and the associated reaction chains 7Be(e-e)7Li(p,α)α and 7Be(p,γ)8B => 2α + e+ + νe generate 14% and 0.1% of the α-particles, respectively, and 10.7% of the present-epoch luminosity of the Sun.[31] Usually, the 7Be produced is assumed to be deep within the core of the Sun; however, such 7Be would not escape to reach the leading edge of the LDEF.

"Solar neutrinos from 8
B
decay have been detected at the Sudbury Neutrino Observatory via the charged current (CC) reaction on deuterium and the elastic scattering (ES) of electrons. The flux of νe's is measured by the CC reaction rate to be ϕCCe) = 1.75 ± 0.07(syst) ± 0.05(theor) 106 cm-1 s-1. Comparison of ϕCCe) to the Super-Kamiokande Collaboration’s precision value of the flux inferred from the ES reaction yields a 3.3σ difference, assuming the systematic uncertainties are normally distributed, providing evidence of an active non-νe component in the solar flux. The total flux of active 8
B
neutrinos is determined to be 5.44 ± 0.99 106 cm-1 s-1."[32]

"The data reported here were recorded between November 2, 1999 and January 15, 2001 and correspond to a live time of 240.95 days."[32]

  + ? MeV

The following fusion reactions produce neutrinos and accompanying gamma-rays of the energy indicated:

A "direct measurement of the 7
Be
solar neutrino signal rate performed with the Borexino low background liquid scintillator detector [...] is the first real-time spectral measurement of sub-MeV solar neutrinos. The result for 0.862 MeV 7
Be
is 47 ± 7stat ± 12sys counts/(day · 100 ton), consistent with predictions of Standard Solar Models and neutrino oscillations with LMA-MSW parameters."[33]

In the image on the right is the neutrino "spectra expected in Borexino (accounting for the detector’s energy resolution). The solid black line represents the neutrino signal rate in Borexino according to the most recent predictions of the Standard Solar Model (11) including neutrino oscillations with the LMA-MSW parameters. The solid red line illustrates the contribution due to 7
Be
neutrinos. pp neutrinos contribute to the spectrum below 0.3 MeV and the edge at 1.2 MeV is due to pep neutrinos."[33]

Earth[edit]

Main source: Draft:Earth
The neutrino fluxes arriving at Earth (solid) compared with those produced in the solar atmosphere (dashed). Credit: C.A. Argüelles, G. de Wasseige, A. Fedynitch, and B.J.P. Jones.{{fairuse}}

Here on the Earth's surface the νe flux is about 1011 νe cm-2 s-1 in the direction of the Sun.[34]

"The total number of neutrinos of all types agrees with the number predicted by the computer model of the Sun. Electron neutrinos constitute about a third of the total number of neutrinos. [...] The missing neutrinos were actually present, but in the form of the more difficult to detect muon and tau neutrinos."[34]

"[L]ow-altitude regions of downward electric current on auroral magnetic field lines are sites of dramatic upward magnetic field-aligned electron acceleration that generates intense magnetic field-aligned electron beams within Earth’s equatorial middle magnetosphere."[35]

"Cosmic rays interacting in the solar atmosphere produce showers that result in a flux of high-energy neutrinos from the Sun."[36]

In the image on the right, "The fluxes arriving at Earth (solid) compared with those produced in the solar atmosphere (dashed). The lines show the result for a specific shower model (H4a, SIBYLL-2.3 interaction model and MRS prompt). The bands show the uncertainty region across all models. The three panels show the flux for each neutrino flavor, in both neutrinos and antineutrinos."[36]

"Indirect detection is an independent and complementary method of searching for dark matter. The technique relies on searching for annihilation products of dark matter particles in astrophysical environments [14, 15], where the local dark matter density is expected to be high enough to facilitate copious [weakly interacting massive particles] WIMP self-annihilation. Potentially detectable annihilation products include neutrinos, gamma rays, positrons, antiprotons and anti-nuclei [1]. A channel that has drawn particular attention is the production of high-energy neutrinos from WIMP self-annihilation in the solar core. The Sun would act as a concentrator of dark matter particles if and only if WIMPs interact sufficiently often with regular matter to effectively transfer their kinetic energy to solar material as they traverse the Sun, causing them to pool near the center. Thus the strength of this signature depends on both the self-annihilation cross section (calculable in WIMP models) and the WIMP-proton cross section."[36]

"Just as cosmic rays impinging on the Earth’s atmosphere produce air showers, leading to hadrons which decay to atmospheric neutrinos [35], cosmic rays interacting in the solar atmosphere also produce a high-energy neutrino flux. This flux was studied in references [25–27]. The main conclusion was that this flux of neutrinos is small, and therefore unlikely to be useful for detailed study of (for example) neutrino oscillations."[36]

"The production of neutrinos in solar showers is different from their production in terrestrial air showers in a few key ways. First, the region of solar atmosphere where the majority of production is localized is significantly less dense and further extended than its terrestrial counterpart. This allows for longer decay lengths of high-energy hadrons before they are absorbed through inelastic interactions, reducing the suppression of the high-energy neutrino flux observed in the Earths atmosphere. On the other hand, the solar core is very large and dense relative to the Earth, so more high-energy neutrinos are lost through interactions when propagating across it. Finally, the path lengths in the solar atmosphere are long enough (thousands of kilometers) that high-energy muons decay and produce a sizeable contribution to the solar atmospheric neutrino flux, whereas in terrestrial air showers these would be stopped abruptly in the Earths crust."[36]

"The most important region for neutrino production in the solar atmosphere lies at densities of 1 × 10−4g cm−3 [which lies in the convection zone, not the core]."[36]

Jupiter[edit]

"Field-aligned equatorial electron beams [have been] observed within Jupiter’s middle magnetosphere. ... the Jupiter equatorial electron beams are spatially and/or temporally structured (down to <20 km at auroral altitudes, or less than several minutes), with regions of intense beams intermixed with regions absent of such beams."[35]

Hypotheses[edit]

Main source: Hypotheses
  1. All or a portion of the photosphere is being heated by electron bombardment; i.e., electron beam heating.

See also[edit]

References[edit]

  1. 1.0 1.1 1.2 1.3 1.4 1.5 1.6 John N. Bahcall and William H. Press (1 April 1991). "Solar-cycle modulation of event rates in the chlorine solar neutrino experiment". The Astrophysical Journal 370 (04): 730-742. doi:10.1086/169856. http://adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1991ApJ...370..730B&link_type=ARTICLE&db_key=AST&high=. Retrieved 2016-11-22. 
  2. Eberhard Klempt, Chris Batty, Jean-Marc Richard (July 2005). "The antinucleon-nucleon interaction at low energy: annihilation dynamics". Physics Reports 413 (4-5): 197-317. doi:10.1016/j.physrep.2005.03.002. http://adsabs.harvard.edu/abs/2005PhR...413..197K. Retrieved 2014-03-09. 
  3. Eli Waxman and John Bahcall (December 14, 1998). "High energy neutrinos from astrophysical sources: An upper bound". Physical Review D 59 (2): e023002. doi:10.1103/PhysRevD.59.023002. http://prd.aps.org/abstract/PRD/v59/i2/e023002. Retrieved 2014-03-09. 
  4. 4.0 4.1 4.2 4.3 4.4 4.5 K. Kodama, N. Ushida1, C. Andreopoulos, N. Saoulidou, G. Tzanakos, P. Yager, B. Baller, D. Boehnlein, W. Freeman, B. Lundberg, J. Morfin, R. Rameika, J.C. Yun, J.S. Song, C.S. Yoon, S.H.Chung, P. Berghaus, M. Kubanstev, N.W. Reay, R. Sidwell, N. Stanton, S. Yoshida, S. Aoki, T. Hara, J.T. Rhee, D. Ciampa, C. Erickson, M. Graham, K. Heller, R. Rusack, R. Schwienhorst, J. Sielaff, J. Trammell, J. Wilcox, K. Hoshino, H. Jiko, M. Miyanishi, M. Komatsu, M. Nakamura, T. Nakano, K. Niwa, N. Nonaka, K. Okada, O. Sato, T. Akdogan, V. Paolone, C. Rosenfeld, A. Kulik, T. Kafka, W. Oliver, T. Patzak, and J. Schneps (April 12, 2001). "Observation of tau neutrino interactions". Physics Letters B 504 (3): 218-24. http://www.sciencedirect.com/science/article/pii/S0370269301003070. Retrieved 2014-03-10. 
  5. A. Bellerive, Review of solar neutrino experiments. Int.J.Mod.Phys. A19 (2004) 1167-1179
  6. 6.0 6.1 J. N. Bahcall and G. B. Field and W. H. Press (September 1, 1987). "Is solar neutrino capture rate correlated with sunspot number?". The Astrophysical Journal 320 (9): L69-73. doi:10.1086/184978. http://articles.adsabs.harvard.edu//full/1987ApJ...320L..69B/L000069.000.html. Retrieved 2013-07-07. 
  7. Kane, R.P. (2002). "Some Implications Using the Group Sunspot Number Reconstruction". Solar Physics 205(2), 383-401.
  8. "Did You Say the Sun Has Spots?". Space Today Online.
  9. Sunspot numbers. Royal Observatory of Belgium. Retrieved 19 May 2017. 
  10. Hathaway,, D. (2015). "The solar cycle". Living Reviews in Solar Physics 12: 4. doi:10.1007/lrsp-2015-4. 
  11. The Maunder minimum. November 2017. 
  12. Usoskin, et al.. "A solar cycle lost in 1793-1800: Early sunspot observations resolve the old mystery". Astrophys. J. Lett. 700: L154. doi:10.1088/0004-637X/700/2/L154. 
  13. SIDC smoothing formula. Royal Observatory of Belgium. Retrieved 19 May 2017. 
  14. Meeus, J. (1958). "Une formule d'adoucissement pour l'activité solaire". Ciel et Terre 74: 445. 
  15. The solar cycle's new clothes. Royal Observatory of Belgium. Retrieved 8 July 2015. 
  16. Spotless Days. Retrieved 29 July 2014. 
  17. What's Wrong with the Sun?. NASA. Retrieved 29 July 2014. 
  18. Spotless Days Page. Royal Observatory of Belgium. Retrieved 3 April 2017. 
  19. The first sunspot of cycle 25 is seen!. Royal Observatory of Belgium. Retrieved 22 December 2016. 
  20. K.D. Abhyankar (1977). "A Survey of the Solar Atmospheric Models". Bull. Astr. Soc. India 5: 40–44. http://prints.iiap.res.in/handle/2248/510. 
  21. 21.0 21.1 21.2 21.3 G. de Wasseige, P. Evenson, K. Hanson, N. van Eijndhoven, and K.-L. Klein (1 December 2015). "Evaluation of expected solar flare neutrino events in the IceCube observatory". Proceedings of Science. https://arxiv.org/pdf/1512.00204. Retrieved 2018-5-28. 
  22. 22.0 22.1 22.2 22.3 Yukio Tomozawa (28 August 1995). N. Iucci and E. Lamanna, ed. Anticorrelation Between Neutrino Flux and Activity in the Sun, In: 24th International Cosmic Ray Conference. 4. Rome, Italy: International Union of Pure and Applied Physics. pp. D1259–62. Bibcode:1995ICRC....4.1259T. Retrieved 2 June 2018. 
  23. 23.0 23.1 23.2 23.3 23.4 P. Anselmann and the GALLEX Collaboration (16 July 1992). "Solar neutrinos observed by GALLEX at Gran Sasso". Physics Letters B 285 (4): 376-389. doi:10.1016/0370-2693(92)91521-A. http://www.academia.edu/download/42335367/Solar_neutrinos_observed_by_GALLEX_at_Gr20160207-21604-vb74ar.pdf. Retrieved 2018-6-07. 
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