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April 2014 Carlos Ortega Getting an image of Sirius B A recipe to see Sirius B in your pictures INTRODUCTION Observing this star is not an easy task. Resolving it in a picture was not easy either, until recent years. Sirius B is these days about 10 arc seconds apart from Sirius A [1,2]. Both stars have apparent magnitudes of 8.3 and -1.47 respectively [3]. During visual observations, Sirius B gets confused within the glare of Sirius A. Typically, when you attempt to see it by taking pictures, it either gets located well within the white saturated area of Sirius A or, if you reduce the exposure time to lower Sirius A's glare, it gets too dim to be seen in the image at all. While orbiting around their center of mass, they have been getting farther away now for about a decade. This will keep happening during the next years. The larger their angular separation, the easier to see or photograph Sirius B. I think if people had followed the procedure described below, Sirius B would have started becoming consistently visible in pictures a few years ago. Aside from pictures taken by scientists with professional equipment, it seems there are some lucky pictures of this star taken by some amateur astronomers. However, I have not seen a methodical approach to get this done. The purpose of the procedure below is to provide such an approach to increase your chances to see Sirius B in your pictures. Stars of apparent magnitude of 8 or 9 are normally not difficult to photograph, so Sirius B's brightness is not the problem in itself. The issue is that it is too close to the brightest star in the night sky. The method described here basically requires that your sky allows stars of apparent magnitude of around 9 to be photographed, and therefore should be able to be carried out successfully from backyards in light polluted areas. 1 http://commons.wikimedia.org/wiki/File:Orbit_Sirius_B_arcsec.png. See Figure 3. 2 Calculations based on data presented in http://en.wikipedia.org/wiki/Sirius, are consistent with Figure 3. See Table 1. 3 http://en.wikipedia.org/wiki/Sirius Figure 1: Area of the sky with a vertical angular size of about 4.3 degrees centered on Sirius. The rectangle in the middle shows the frame of Figure 2. Figure 2: Image with a vertical angular size of about 17.9 arcminutes centered on Sirius. The image is intentionally overexposed to clearly show more stars, including the reference star. Sirius B cannot be seen here because it is inside the glare of Sirius A. PROCEDURE Now let's see the detailed steps to get an image of Sirius B together with the reasoning behind them: • As mentioned before, Sirius B has an apparent magnitude of 8.3. • The reference star in Figure 1 and Figure 2 has an apparent magnitude of 8.59 [4], very similar to that of Sirius B. • Because the reference star is slightly dimmer than Sirius B, the method to photograph Sirius B is the following: o Setup your equipment to get a field of view similar to that shown on Figure 2. As we will see later, it will be better to select a little more magnification. It is convenient to keep the reference star visible in the same frame as Sirius A. o Start by taking a picture of Sirius A where the reference star is clearly visible. o Then take several pictures changing your ISO and exposure time to make the reference star gradually dimmer. o When the reference star is almost invisible, take several pictures with that ISO and exposure time. o Due to atmosphere's rapid changing conditions, you will start to see a little dot located slightly North of East of Sirius A in one of every three to ten pictures. It is Sirius B. o If you want, you can stack those pictures to make Sirius B more visible. I prefer to not select the best pictures for the stack, because I do not want to influence the result, and instead let the true average of all pictures show Sirius B if it is really there. 4 Starry Night Pro 6 ERROR ESTIMATION Table 1 shows a calculation of the maximum angular separation between Sirius A and B made from their linear separation and the distance between them and us [3] , as if we were looking at them from a place in space perpendicular to the major axis of the ellipse. The table also compares this result with data extracted from Figure 3 (left ellipse). In addition to that, the table includes a comparison between the current separation of both stars in Figure 3 as seen from Earth (ellipse on the right), and Figures 4, 5 and 6. In both comparisons, data in Figure 3 is assumed to be less reliable, i.e., the other source is supposed to be true. This assumption does not affect the results of the analysis made in this document. The first comparison, in blue in Table 1, serves as a reference to test how accurate the data in these Wikipedia sources is. An absolute error of less than 0.5% shows internal consistency at least between these pieces of data. Figure 3: Sirius B positions relative to Sirius A. The ellipse on the right is the one seen from Earth. [1] Image downloaded from Wikimedia Commons . Figure 5 shows a higher error compared to Figures 4 and 6. As we will see later, the choices we made to get this picture were not the best (exposure time, magnification and number of pictures for the average image). An average error of around 6%, considering that just one pixel in Figures 4, 5 or 6 represents between 3% and 4% of the separation between Sirius A and B, seems to be acceptable. In other words, the error in measuring the separation between both stars might be up to 2 pixels; (image size for Figure 4 is 3888 x 2420 pixels, and Figures 5 and 6 size is 3888 x 2592 pixels). Unless there is a visual deviation caused by the glare of Sirius A, or unless the angles measured using Starry Night have an error consistently shifting the true value in one direction, it is interesting to notice that the pictures have the tendency to show a larger separation between both stars than that predicted by Figure 3. Table 1: Error estimations. Note: Blue and red numbers on this table are not related to blue and red lines in Figure 3. ADDITIONAL REMARKS • When analyzing Figures 4, 5 and 6, we notice that Figure 4 is the one that best shows Sirius B. This might be due to a couple of things: first, as we can see in image captions, this one was taken at a higher magnification than Figure 5 and Figure 6. This allows having about 27% more pixels between Sirius B and Sirius A. Second, this is the average of 73 pictures, which is a number large enough to start removing noise from different sources and distortion caused by atmospheric turbulence. Figure 4: Image taken on 2014-03-18. Afocal photography with Canon EOS Rebel XS with 55 mm. lens, behind a Celestron CPC 1100 telescope with 40 mm eyepiece. Average of 73 pictures with 1/3 second exposure at ISO 1600. This image has a vertical size of 13.3 arcminutes. • Figure 5 is the one where it is most difficult to see Sirius B. This image is the result of the average of only 20 pictures. In addition to that, this image was taken with the shortest exposure, so Sirius B on the best original pictures was hardly visible. Figure 5: Image taken on 2014-04-07. Prime focus photography with Canon EOS Rebel XS directly coupled to a Celestron CPC 1100 telescope. Average of 20 pictures with 1/8 second exposure at ISO 1600. The vertical size of this image is the same as in Figure 2. • Figure 6 has a little more exposure than Figure 5, but it seems still too short. In addition to this, being its magnification the same as in Figure 5, Sirius B is still too close to Sirius A. The higher number of pictures, however, results in a better image than Figure 5. • Based on the previous discussion, it seems that there is a higher chance to succeed in getting a good image of Sirius B if you: o Select a magnification high enough. o Get an average of enough number of pictures. o Take each picture with the right exposure. Within the range that will show Sirius B: too little and it becomes almost invisible; too much and it gets absorbed by Sirius A's white pixels. Figure 6: Same as Figure 5, but average of 129 pictures with 1/6 second exposure at ISO 1600 • You may get a nice view of Sirius B in a few of the many pictures you will be taking for your average images. However, you will also notice some pictures with more than one dot, even in the wrong position, that resemble Sirius B. These effects are caused by rapid changing atmospheric distortion, so you should not unconditionally trust a possible set of best pictures, because you may have some false Sirius B on them. • You have already probably noticed that the image taken on 2014-03-18 (Figure 4), has a different rotation than both images taken on 2014-04-07 (Figures 5 and 6). Even Figures 5 and 6 have a difference of 1.9 degrees between them. The point is that this makes Sirius B to appear at different angles relative to Sirius A in those images. However, further confirmation that the stack of pictures is revealing true information is that in all three images, Sirius B appears almost directly opposite to the reference star in relation to Sirius A. In other words, the line that connects Sirius B and the reference star passes very close to the center of Sirius A, as seen in Figure 7. Figure 7: The line that goes from Sirius B to the reference star. At this image size Sirius B is not visible, but it can be seen in Figures 4, 5 and 6. • Finally, it is worth making the comment that by following this procedure, we were able to see Sirius B in three out of three attempts, working under different conditions of magnification, exposure time and number of pictures taken.