Download Getting an image of Sirius B

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.