H-alpha observation program
Calculation of solar parameters: P, B0, L0, Carrington Rotation number,...
Coronado's Personal Solar Telescope
Observing the Sun (Dutch)
If you ever the doubted solar observing could be dangerous... (Thanks to Patrick Stoker from the Cloudy Nights website).
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Attached files provide for 2007 and 2008 the following parameters: Day (0h UT), Julian day, P, B0 and L0, the Carrington rotation number, the distance earth-sun in astronomical units (1 AU = 149597870 km), the declination of the sun (in degrees), the apparent solar diameter in arc seconds (for a solar diameter of 696000 km), and the time T in seconds that the sun requires to transit over its own diameter.
Solar parameters 2007
Solar parameters 2008
The following table contains the formulae necessary to calculate basic parameters for determining the location of phenomena on the solar surface. These data and formulae can be copy-pasted into an excel-file for further exploitation. The first column contains the header (what is calculated), the second contains some comments (what is the physical meaning of the header), and the last column (column "C") contains the formulae. When correctly applied and after some formatting, the 01 Jan 05-values should read respectively 2,00; -3,04; 13,87; 2024. The accuracy is 0,01°, largely sufficient to calculate precisely the latitude and longitude of a sunspot. If problems or if you want to have the original file immediately, do not hesitate to contact me.
The original calculations were done by Jean Meeus. The article was published by Dirk Laurent in "Werkgroepeninfo" in 1988. The formula for the Carrington Rotation Number originates from "Observing the Sun" by P.O. Taylor.
|dT||Delta T; This value changes slowly in the course of time; it is taken here as 64 seconds.||64|
|t||Number of years since 1850||=(C6-2396758)/365,25|
|T||Number of centuries since 0,5 Jan 1900 ET||=(C6-2415020)/36525|
|k||Conversion factor for degrees to radians||=PI()/180|
|th||Supporting angle related to the true solar rotation||=(C6-2398220)*360/25,38|
|kks||Length of the ascending node of the solar equator on the ecliptic (the sun earth plane)||=73,666667+0,01395833*C7|
|i||Inclination of the solar equator to the ecliptic||7,25|
|kkm||Length of the ascending node of the moon orbit||=259,183275-1934,142008*C8+0,002078*C8^2|
|G||Long term corrections on the solar length||=0,0000739*SIN(C9*(31,8+119*C8))+0,0017778*SIN(C9*(231,19+20,2*C8))+0,00052*SIN(C9*(57,24+150,27*C8))|
|L||Average length of the sun||=279,696678+36000,768925*C8+0,0003025*C8^2+C14|
|M||Average anomaly of the sun||=358,475833+35999,04975*C8-0,00015*C8^2+C14|
|C||Equation of the center||=(1,9194603-0,0047889*C8-0,0000144*C8^2)*SIN(C9*C16)+(0,0200939-0,0001003*C8)*SIN(C9*2*C16)+0,0002925*SIN(C9*3*C16)+0,000005*SIN(C9*4*C16)|
|lambda||Apparent length of the sun (without nutation)||=C15+C17-0,0056933*(1+0,01671*COS(C9*C18))|
|nutL||Nutation in Length||=-0,00479*SIN(C9*C13)-0,00035*SIN(C9*2*C15)|
|nutI||Nutation in Inclination||=0,00256*COS(C9*C13)+0,00015*COS(C9*2*C15)|
|lambdaS||Apparent Length of the sun with Nutation||=C19+C20|
|eclip||Inclination of the ecliptic||=23,452294-0,0130125*C8-0,0000016*C8^2+C21|
|x||Supporting angle; needs to be in the interval [-90°,+90°]||=(ATAN(-COS(C9*C22)*TAN(C9*C23)))/C9|
|y||Supporting angle; needs to be in the interval [-90°,+90°]||=(ATAN(-COS(C9*(C19-C11))*TAN(C9*C12)))/C9|
|eta||Another supporting angle; The correction factor results from the fact that eta needs to be in the same quadrant than lambda-kks+/-180°||=(ATAN(TAN(C9*(C19-C11))*COS(C9*C12)))/C9+C29|
|th||Reduction of theta to the interval [0°, 360°]||=C33+C34|
|CorrL0||Correction to have positive values for L0||=IF(C38<0;IF(C38<-360;"720";"360");"0")|
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H-alpha is the name of a hydrogen line in the red part of the solar spectrum. At 6562,8 Å (656,28 nm), it only lets pass the light of the solar chromosphere. This is the atmospheric layer between the photosphere (the “solar surface” in which one views sunspot groups,…), and the corona (the outer atmosphere visible during total solar eclipses). The chromosphere is especially known for its prominences: accumulations of relatively cool solar plasma entangled between two magnetic fields of opposite polarity. Filaments are actually prominences, but seen against the background of the hotter solar surface, they look like dark curved lines and belts. The chromosphere provides also a much better view on solar eruptions than the photosphere does, thus providing an important link with phenomena in the corona.
Manufacturing the appropriate filter is not an easy thing to do, and up till the late nineties H-alpha filters were very expensive. This is because the price depends on the full width at half maximum (FWHM, bandpass): the smaller this value, the lesser light of neighbouring wavelengths will be able to intrude into the narrow H-alpha line, hence the more detailed the chromospheric image will be. Basically, a bandpass of 1 Å or more mostly shows the prominences, whereas a bandpass of 0,5 Å or less shows especially the surface detail. Bandpasses evolving from 1 to 0,5 Å will progressively show less prominences and more surface detail, but are also more difficult to make. As the filters were temperature sensitive, they needed heating by an electrical powersource in order to keep them at the correct wavelength (e.g. Daystar). The smaller the bandpass, the more sensitive the filter, the harder the manufacturing process and thus the more expensive (price range of $3000 and higher), affordable only to a happy few of amateur astronomers.
In 1999, all that changed. Coronado started to produce filters showing excellent surface details at a very reasonable price ($1500 or more). Moreover, the filters were thermally stable, thus avoiding the need for an external electrical power source, and making them at once a whole lot more user friendly. During the next few years, Coronado improved its product range considerably, especially by developing pure H-alpha telescopes. Finally in 2004, they marketed the Personal Solar Telescope (PST), a 40-mm-viewer costing only $500, but with a bandpass of < 1 Å.
So it took me quite some time to take a decision. On the one hand, there was that cheap PST, presenting without a doubt a good view of the prominences, but probably only little surface detail - at least, that was what I thought -. On the other hand, there was the more expensive ($1500 or more, pending the Blocking Filter needed) SolarMax40-filter (SM40), but showing much better surface detail as well as a decent view on the prominences (bandpass < 0,7 Å). I already had observed through an SM40-filter on MIRA Public Observatory (Belgium) and during some meetings of the Belgian Solar Section. I must say I was quite satisfied with its performance. There was however one more factor in play: I wanted to take my H-alpha viewer everywhere with me at no matter what time. The heavy C8-mounting I use is not particularly inviting for easy transportation, so I was facing the buy of a SM40-telescope package or even a SM60-telescope package, a considerable more expensive solution (resp. $1699 en $3685, without the transportation, customs and importer costs). When Hugo Ruland of Lichtenknecker Optics (LO, Hasselt, Belgium) told me he had some PST's in stock, I immediately decided to take a look. Not even a half hour later, I was driving back home with a PST (and tripod) in the back of my car. Just a few looks through LO’s demo-PST had convinced me to make 13 June 2005 the day on which I bought my Personal Solar Telescope (PST).
What makes the PST so special? It already starts during take-out and set-up. In less than 3 minutes (timed!), the camera tripod is set up, the 3 pound PST is taken out of its box, mounted on the tripod, directed toward the sun, tuned and focused. It probably can even faster, but the foam in which the PST is resting, is very tight making it very difficult to remove the telescope out of the box. Moreover, due to this tight fitting, the tuning ring also turns. As a consequence and prior to each observing session, the PST always needs to be tuned into the right wavelength. Hence, there exists no more advantage of a properly Coronado tuned filter, as advertised in their user’s brochure. The problems can easily be solved by making some cuts and removing some of the foam at the telescope’s tube, tuning ring and eyepiece holder. Moreover, by putting some of the foam on the bottom, one can avoid the telescope sinking to deep into the box. Both actions ease the PST’s removal.
The set-up is largely facilitated by the very handy Sol Ranger. Through a pinhole in front of the "black box", a bright light point is projected on the top of the PST in a glass. The telescope is well aligned with the sun if the bright point is in or near the center of this glass. Finding the sun can’t be simpler and safer than this, as long as you don’t hold your hand in front of the pinhole of course! Adding the SM40-filter ("double-stacking" to get a bandpass of < 0,6 Å) will cover the pinhole partially or completely, making the Sol Ranger no longer operational. During the observation, the presence of the bright point is somewhat disturbing, pending the position of the observer behind the ocular. However, there exists a simple solution to this problem (see further).
The PST is not designed for solar photography. Yet quite a few people have managed to make successful pictures through the PST, especially when using a webcam. It is good to remember though that many images in H-alpha are computer enhanced and provide a solar image that looks much better than the real image. This is really something worthwhile to keep in mind prior to the first look through any H-alpha filter or telescope.
The tuning filter is a ring at the end of the aluminized tube just in front of the "black box" that can be moved over only 130° (handle with care!). Turning this ring allows for an optimization of the H-alpha image. The view varies from an orange patch to a somewhat darker view of the chromosphere, with somewhere in between the most contrast rich balance between surface detail and prominences. Just emphasizing again that, just like all other Coronado-filters, also the PST-filter is thermally stable, meaning there is no need for an (electrical) heating element like for example in most Daystar-designs. This really boosts the user friendliness.
Focusing is done with a knob at the back of the “black box”. My PST features a “hard point” during the focusing process, but focus was always achieved. The PST comes with a standard 12 mm (or 12,5 mm) Kellner ocular. This gives a field of view (FOV) of about 1°, in which the sun, with its apparent diameter of a half degree, easily fits. To me, the Kellner ocular seems to be a very good choice, because it provides the perfect balance between magnification (33x), brightness and detail of the solar image. Focusing was also achieved with all my other oculars (ranging from 7,5 tot 30 mm), but not in combination with the 2x Barlow. The best images (after the Kellner 12) were obtained with a Plössl 7,5 (53x, FOV +/- 0,6°) and Ultima 19 (21x, FOV +/- 2°). If one could compare the solar view through a Kellner 12 with a tangerine, then that through a Plössl 7,5 would be a red orange, and through the Ultima 19 a new, shiny piece of 5 cent. Through none of the oculars, ghost images (false, light poor solar images) were seen. Vignetting (ocular showing smaller FOV than “normal”) was noted only with the Ultima 19, but it was of no hindrance when observing.
As indicated in the brochure, the image contains a “sweet spot” in which details and prominences are best visible. In my PST and when using the Kellner-ocular, this spot is about 0,6° in diameter (solar image fits in perfectly!), and is located somewhat off-center (towards the top, or “south”). Once outside this spot, the H-alpha capability quickly decreases, and especially the prominences darken fastly. Because the sweet spot is quite big, it is not much of a problem, especially when using higher magnifications.
The use of a yellow or orange filter did not improve noticeably the contrast. On the other hand, the use of a big towel over the head (avoiding of stray light) significantly improved contrast and detail. By putting this tissue also a bit over the “black box”, the bright point of the Sol Ranger is covered and no longer disturbing! The sky background in the FOV is reasonably black, which adds in contrast. Pending the amount and the type of clouds, this background can redden noticeably.
The view through the PST is absolutely fabulous. A pleasing bright image is linked to a high contrast and an incredibly amount of surface detail. Personally, I think the image is a bit brighter than and almost as full of detail as through an SM40-filter, despite the difference in bandpass! My feeling is that the central obstruction of the SM40 plays a role in this (though Coronado says it does not), as well as the fact that all parts of the PST are tuned to each other in one instrument. This is certainly not the case with the SM40-filter, which has to be used with a blocking filter on any type of telescope. Some observers consider the view through the SM40 definitely better, but then again, the cost is also (at least) three times higher.
So it is no surprise the PST was chosen by Sky & Telescope as the Hot Product 2005. The “Perfect Solar Telescope” brings quality H-alpha views of prominences and chromosphere within the budgetary reach of most solar observers. The future is orange!
Addendum - We had an observation session yesterday at MIRA Public Observatory (Dutch only), with mainly first-time observers who could compare the PST-image with that through an SM40-filter (mounted on a Skywatcher, Magn. 40x). About half of them gave a light advantage to the PST, the other half gave the edge to the SM40. It must be noted though that most of the SM40-votes came after I changed from the Kellner 12 to the Ultima 19 ocular. I think with the Ultima, the solar image was too small to make some impression on the public. Also because the PST was mounted on a non-motorized drive, I continually had to center the image. Most of the more experienced observers gave the (small) advantage to the PST, especially because of the astonishing surface detail in the sweet spot. Again, if one didn't know better, the PST's bandpass seems rather < 0,7 Å than < 1 Å! They were also very pleased by the incredibly quick and safe set-up (Sol Ranger!).
Other PST reviews
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