The tidal effect on the Earth is well known. Twice a day, on ocean shores, the sea raises to the "high tide" level. In the following hours, (approximately six hours later) it lowers down to the "low tide" level. And this cycle goes for ever. This effect, known since the oldest ages of mankind, is said to have been attributed to the Moon only recently. One quotes Galileo who refused to link the tides to the Moon... But it seems that the old time sailors, not embarassed by rationality reasons, knew this fact from immemorial times.
Some other effects exist, which give an amplitude modulation of the tides :
As the Earth is under the gravity effect of the Sun and the Moon, the Sun is submitted to the gravity effect of the planets. On the Earth, the situation is simple, as there is a big effect (the Moon), a weak effect (the Sun), and the other effects (the planets) are close to zero. On the Sun, the situation is more complicated. We get two strong effects (Jupiter and Venus), two weaker effects (Earth and Mercury). The other planets give effects close to zero. To give a relative scale, for the M/R^{3} fraction, if the Earth's effect is equal to 1, Mercury has approximately the same value, Jupiter and Venus having approximately a value of 2.
Now let's imagine that we are Sunians (the inhabitants of the Sun). Our sideral day (SD), rotation regarding to the stars, lasts 27 sunians hours (SH). Some people say this number has been chosen because it is the cube of three, being regarded as sacred by our ancestor. Some other say that one SH equals one day for the inhabitants of the third planet (Earth), who visited us long times ago, but this opinion is a subject of controversy as no form of life could exist on these cold planets. Now what are the tidal rythms on the surface of our star ? Jupiter is almost fixed among the stars. So we have a high tide due to Jupiter every 13.6 SH. The Earth rotation in the sky is a little slower, and it gives a high tide every 14.6 SH. Venus is still slower and gives a high tide every 15.3 SH. Mercury is the slowest and gives a high tide every 19.5 SH. According to the theory, the effects of Venus and Jupiter are approximately equivalent, giving tides two times higher than Earth and Mercury.
In fact, it turns that the tides have effects deeply inside our star and that these internal effects are non linear regarding to the amplitude of the tides. This makes the sum of two equal high tides more effective than twice the effects of a single tide. In addition, the time during which the highest tides last at planets syzygies is important to trigger some special events in the core of our star. The consequence is that, as the Earth has a speed close to Jupiter's or Venus' one, Earth-Jupiter syzygies or Earth-Venus syzygies last a long time. So, when in syzygie with Jupiter or Venus; Earth has a stronger effect than the simple M/R^{3} coefficient would imply. On the contrary, Mercury is very slow in our sky. So, the tidal effects of Mercury fall out of a resonnance frequency of the Sun and moreover, the syzygies of Mercury with one of the tree other planets last a short time.
The high tides periods (syzygie or opposition) for the three important couples are :
Ve-Ju (Venus-Jupiter) : 118.5 SH (or 4.4 SD).
Ea-Ju (Earth-Jupiter) : 182.6 SH (or 6.76 SD)
Ve-Ea (Venus-Earth) : 291 9 SH (or 10.8 SD)
The actual situation of these three cycles is not a resonnance situation (or one must take large integer numbers to find resonnances). But a nice effect occurs : it turns that 5 times the high tide period of the Ve-Ea couple is 592.5 SH (21.9 SD)., 3 times the period of the Ea-Ju couple is 547.9 SH (20.3 SD) and 2 times the period of the Ve-Ea couple is 583.9 SH (21.6 SD). This means that if a triple high tide situation occurs, with the three planets aligned with ourselves, a close situation will arrive about 21 SD later. The highest tides on our star occur every 21 of our days ! In fact, the axis of the planets in syzygie having a slow drift, the exact time beetween 2 such events is 22 of our days (594 SH). But, as the resonnance is not perfect, it turns that after a perfect triple high tide (Ve-Ea-Ju syzygie or opposition), the next one 22 SD later will be a little weaker (the planets passing in an angular sector of -say- 4 degrees in the sky. The next one, 22 days later will be weaker, the planets passing in an angular sector of -say- 8 degrees. And so on. After 3 or 4 periods of 22 SD, the sector in which the planets gather is larger than 15 degres and the triple syzygie effect is not so strong. An amazing effect is that, as the ratio taken beetween the double Ve-Ea high tides and the triple Ve-Ea-Ju is two, it turns that during the successive triple high tides situations, every 22 SD, Venus and Earth are always in the same situation, either in cunjunction, either in opposition.
When it happens that the triple VeEaJu high tide disappears, it turns that another triple high tide situation begins to arise, with a changed situation for Earth and Venus : if they were in opposition, they are now in cunjunction, and vice-versa. At the beginning it is a weak triple high tide situation (the planets in a sector of 15 degres), then 22 SD later, it's a little higher (the planets in a sector of 11 degres) and so on. After 3 or 4 triple high tides, we get a maximum high tide with the planets in a sector of 3 degres. And the cycle goes on.
It turns that one counts six or seven successive triple high tides with Venus and Earth in the same situation in a "burst" of VeEaJu syzygies. On the following burst, Venus and Earth having changed their situation, one can also count 6 to 7 syzygies. If we count 6 in the even burst, we will count 7 in the odd one and inversely. The time beetween the even and the odd burst being not exacly one half of the delay beetween two high tides, due to phase shift, it turns that the complete cycle lasts exactly 13 Venus-Earth syzygies cycles.
This number is important, because our star has a magnetic oscillation cycle. It shows altrnately a direct polarity (the north magnetic pole being on it's north geographic pole and the south on the south), and an inverse polarity (the north magnitic pole being on the south geographic pole and the south on the north). It turns that this magnetic oscillation, due to complexes processes which occur deeply inside our star, is synchronized on the VeEaJu complete syzygie cycle, with a 90° phase shift. When the VeEaJu syzygies with VeEa in cunjunction disapear, the polarity is direct and maximum. When the VeEaJu syzygie is maximum, the tree planets aligned, the magnetic field reverses. And so on... The sunspots appear during the magnetic field reversals. And we, Sunians, know that well as we take our holydays at that time to enjoy swimming in the spots...
Our star is a magnetic oscillator, with a self oscillation period close to 13 Ve-Ea syzygies cycles. It is synchronized on this external excitation signal, by a coupling effect beetween the acoustical waves induced deeply in the core and the magneto-hydro-dynamic processes which occur there. In fact, it turns that the regular situation described above for the VeEaJu syzygies is corrected by some side effects. Planets are not all in the same plane, and this plane is not the Sun's equatorial plane. The tidal effects are stronger when the planets align on an axis close to the intersection of the planet orbital plane and the Sun's equatorial plane. The planets are not cycling regularly on circles, but on ellipses, and the axes of these ellipses rotate slowly during time. Being on ellipses, the tidal effects change when the planets approach or get farther from the Sun. All this gives a modulation of the previously described effect. This can explain that a certain periods, magnetic cycles are stronger (and also sunspot cycles).