Adding a colour correction term to my photometric estimates of the magnitude of Z Ursae Majoris

In a previous post I attempted to obtain an estimate for the magnitude of Z UMa by using a single 30s exposure taken on my Nikon D90 digital camera mounted at the prime focus of my Celestron NexStar 102mm telescope. This was the frame I took with Z and some other stars marked:-

Using the comparison stars 84, X and Y I was able to determine a magnitude estimate of Z of 7.37, 7.34 and 7.44 respectively. I now wondered if it was possible to use colour information about these comparison stars to try and figure out how to transform these magnitude estimates to a more standardised Johnson V system. I know it isn't much data but I thought it was worth having a go.

If you look at the DSLR observing manual of the AAVSO (it is a bit of a mighty tome, but bear with me) then on page 74 it shows how the response of the DSLR's blue, green and red channels differ from Johnson's B, V and Cousins R. Johnson V is supposed to mimic closely the visual response of the human eye. As you can see, a DSLR green channel has a peak which is similar in wavelength to V but it is narrower in response. Each different make of camera will have a slightly different response as a function of wavelength and this is why it would be an advantage to transform the camera's magnitudes to a more standard V system, if possible.

So how do you do this? If we ignore any extinction considerations for the moment (extinction is how a star's brightness is altered by passing through varying thicknesses of the earth's atmosphere) then we can to first order write that

V(Z) = m(Z) + T * D(B-V)

which is essentially equation 6.12 on page 74 of that manual. Here m(Z) is the magnitude of Z UMa determined using the relative brightnesses of Z and the comparison star measured in the camera. T is a transformation coefficient and D(B-V) is the B-V for Z UMa minus the B-V for the comparison star. B-V is the colour index of a star and simply the Johnson B magnitude minus the Johnson V magnitude.

We have already determined m(Z) above to be 7.368, 7.338 and 7.443 for stars 84, X and Y above, respectively. What we need is an idea of what T is and we need to know the colour indices for Z and the comparisons.

To obtain T we need to plot (V - v) against (B-V) (see equation 6.17 on page 76 of the AAVSO manual) for the comparison stars. V is again the Johnson V magnitude for the comparison star, B-V its colour index and v is an 'instrumental magnitude' given as

v = -2.5 log (brightness of comparsion star measured by the camera)

Hopefully, this should look like a straight line with gradient T. I had to glean the data that I needed from various parts of the internet. For star 84 we have V=8.438 and B-V=0.657. This comes from a plot of Z UMa from the AAVSO. Star X is HIP57820 on the Hipparcos catalogue and V=7.858 (see server3.sky-map.org). B-V=0.97 (see universeguide.com). Star Y is HIP58302 with V=8.375 (see server3.sky-map.org) and B-V=0.42 (see universeguide.com). Using this data and the brightness values for 84, X and Y previously obtained as 25.30, 42.01 and 28.73 respectively I was able to plot V-v against B-V:-

Even though I only have three data points (84, X and Y are indicated) I think that there is a reasonable indication that there is a correlation. The straight line drawn by hand through the data has a gradient of -0.19. Using regression analysis using a calculator gives T = -0.186 which is very close!

Now we can use this to apply a correction to our magnitude estimates for the variable Z. One big problem is that Z is very red in colour and so B-V is large. In fact the B-V for this star may also vary over time and any estimate may not be that accurate. The universeguide.com gives this as B-V = 1.33 for this star.

We find that for stars 84, X and Y the D(B-V) values are 0.673, 0.360 and 0.910 respectively. This gives T*D(B-V) of -0.125, -0.067 and -0.169  using T = -0.186. This makes our V estimates 7.243, 7.271 and 7.274 for Z from these stars. The mean of these values is now V = 7.262 +/- 0.017 whereas previously for uncorrected values it was 7.383 +/- 0.054. 

Note that the error has now come down and this is understandable. Some of the variation in the uncorrected estimates must come from the different colours of the comparison stars and this is taken out to a large extent by the transformation.

Looking at the BAAVSS and AAVSO databases for the night of the 2nd/3rd of April there were 11 visual observations of this variable giving 7.118 +/- 0.240. So my V estimate is 0.144 magnitudes fainter but well within the errors. It is expected that even Johnson V and visual estimates will differ for such red stars due to variations in the response of the eye compared to V.

All text and images © Duncan Hale-Sutton 2023

Messier 106 (07/05/2023)

Earlier on the night of the 7th May I took some images of the intermediate spiral galaxy M106 in Canes Venatici (the hunting dogs):-

The above picture (binned x2) was taken with a Celestron NexStar 102 SLT with a Nikon D90 at prime focus. The galaxy is in a wide (2.07x1.38 degree) field and sits just off centre to the left. North is towards the bottom right-hand corner. Unfortunately, even though this image consists of 25x30s at ISO3200 only the central portion of the galaxy is visible. There are low surface brightness spiral arms that extend out much further and the object covers something like a third of a degree (you can click on this image to get an enlarged view). The first frame was taken at 21:54 UT and the last at 22:16 UT and so just before the end of astronomical twilight. The images were processed in DeepSkyStacker and Photoshop.

Other galaxies can also be seen on this image, in particular NG4217 which sits close to a group of foreground stars at the lower left of the picture. There is also NGC4248, NGC4232 and NGC4231 which lie closer to M106. A crop of the original unbinned image is shown below:-

I have processed this to show some hint of the low surface brightness spiral arms that extend to the upper left and lower right. The galaxy NGC4248 can be seen at lower left. A more visible spiral arm of M106 can be seen emerging from the central regions at the 5 o'clock position.

All text and images © Duncan Hale-Sutton 2023

Visual estimate of the magnitude of Z Ursae Majoris (7/5/2023)

Sunday evening we had a decent patch of clear weather for me to do some observing. After carrying out some imaging, I thought I would get an estimate (with my 7x50 binoculars) for the current brightness of the variable star Z UMa which is currently near its maximum. The moon was 2 days past full and not due to rise until 22:27 UT. Twilight is now lasting much longer and Astronomical Twilight ended about 22:20 UT. Soon it will last all night.

Using BAA chart 217.02 to locate the variable, I could see (at 22:44 UT) the little triangle of stars that included H (=8.7 mag.) and Z was shining brightly nearby. I could also see (at 22:48 UT) that it was much brighter than nearby star D (=7.9 mag.). Comparing it with stars A (=6.3 mag.), B (=7.3 mag.) and C (=7.5 mag.) I couldn't really distinguish Z from B in brightness at 22:54 UT. My estimate was therefore magnitude 7.3. By that time the sky was brightening due to the rising of the moon.

All text and images © Duncan Hale-Sutton 2023

Globular cluster M13 (19/4/2023)

Carrying on from my previous post, the other easy target I had a look at on the 19th April was the globular cluster M13 in the constellation of Hercules.

This was the result of 7x30s at ISO1600 taken at the prime focus of my Celestron NexStar 102 SLT using a Nikon D90 camera (the first frame was taken at 22:34 and the last at 22:39 UT). I processed these images in DeepSkyStacker (4.2.6) just using the light frames and some flat frames. The resulting image has been binned x2 and processed in Photoshop. The picture below is a crop of this image:-

 

M13 is certainly a pretty spectacular object. The cluster is about 20 arc minutes in diameter and contains several hundreds of thousands of stars. I have included another object in this picture and that is the spiral galaxy NGC6207 which is top left. For comparison I took the following image in 2016 using the same instrument and camera (but 6 mins of exposure rather than 3 and a half):-

The images are pretty similar but the focusing on the earlier image has caused some pink edges to the stars. The way I have processed my latest image means that you can see stars of the cluster further out from its centre.

All text and images © Duncan Hale-Sutton 2023

The Ring Nebula M57 in a wide field (19/4/2023)

A week ago on the 19th April we had a clear night and so I set up my Celestron NexStar 102 SLT on a HEQ-5 mount. The main purpose was for me to try do some photometry of Melotte 111 (also known as the Coma Star Cluster) but towards the end of the evening I pointed the scope at a couple of other easy targets and one of these was the Ring Nebula in Lyra (which was rising in the north east). This telescope is not ideal for taking images of this planetary nebula because it is relatively small in the 2.07x1.38 degree field but nevertheless I thought I would have a go. The moon on this night was one day before new and astronomical twilight ended at 21:20 UT (22:20 BST).

 

 

M57 is the tiny blueish ellipse near the center of the field (you can click on this image to see it full size). M57 sits between two prominent stars in Lyra - beta and gamma. Beta Lyrae or Sheliak is the brightest star on this image and is to the upper right. North is up, East is to the left. The two stars of similar brightness at the bottom right are nu 1 and 2. I used Astrometry.net to plate solve this image.

This image consists of 10x30s frames at ISO 3200 taken on a Nikon D90 at prime focus (the first frame was taken at 22:42 UT and the last at 22:49). I processed these images in DeepSkyStacker (4.2.6) just using the light frames and some flat frames. The resulting image has been binned x2 and processed in Photoshop. The picture below is a crop of the original unbinned image:-

 

This shows the nebula more clearly and I liked the nice blue colour with a hint of red around the edges. The shell of gas is emitted by a dying star which isn't detected here but can be seen on deeper images. I have imaged this nebula before in 2018 using my 5.5" Orion OMC-140 Maksutov Cassegrain and I reproduced this image here below:-

Here you can see the central star as this is a deeper image (8 minutes on a 5.5 inch as opposed to 5 minutes on a 4 inch) however I think the colour on my lastest image is more accurate.

All text and images © Duncan Hale-Sutton 2023

Venus, Mercury and the Pleiades (12th April 2023)

This month has seen our two inferior planets well placed in the evening sky. Mercury reached greatest elongation east on April 11th and Venus is still climbing away from the sun to reach the same point on June 4th. Elongation is a measure of the angular distance of a planet from the sun. Evening apparitions of Mercury and Venus are always better in spring because the ecliptic is at a steeper angle to the horizon than at other times of the year.

I took this picture eleven days ago on the 12th April (20:05 UT) when we had a brief spell of clear weather at the end of the day. Venus can be seen in the upper left of the image with the distinctive 'Seven Sisters' stars of the Pleiades next to it. Venus at this time was shining at magnitude -4.1 and had a 74% gibbous phase. The planet is so bright that it is causing a bit of flaring in my camera lens. Mercury is low down and just above the horizon at the bottom right of the picture. It was magnitude -0.2 and so was quite a bit fainter.

I also took a more detailed picture (at 20:03 UT) of Venus and the Pleiades together:-

More details about the equipment and the exposures can be found by 'clicking' on either image.

All text and images © Duncan Hale-Sutton 2023

An attempt to obtain a photometric magnitude of Z Ursae Majoris

On the 2nd April I took an extra frame of Z Ursae Majoris with the intention of attempting some photometry with it. This was the frame:-

 

 

This is a single 30s exposure at ISO 800 (taken at 20:44 UT). It looks a bit odd because I have deliberately prevented the brighter stars on it (including Z - marked) from saturating. The stars are also defocused (perhaps by slightly too much) as this will help the photometric measurements. This is actually a binned (x4) jpeg image shown here, but for my measurements I used an uncompressed 16 bit tif.

So how can we go about measuring the magnitude of Z UMa? On the image I have marked three other comparison stars; 84, X and Y. 84 is the star that is referred to on the AAVSO chart X28625AEL (see my previous post). Stars X and Y (my designation) will be referred to below. The method will be to measure the brightness of each of these comparison stars and compare it to the brightness of Z in the green G channel. The green channel is used as this better matches the visual response of our eyes.

Beginning with Z I used Photoshop to open the tif file and place a circular selection around the star of diameter 70 pixels. This was big enough to encompass all the light from the star but not so big as to start adding more light from the background. Using the histogram tool I used the green channel and found that the mean count per pixel was 92.02 over 3852 pixels which gives a total count of 92.02 x 3852 = 354461.04.

I then placed a larger circular selection of 120 pixels diameter centred on the star and measured the green colour count in that. The mean count per pixel in this case was 47.33 over 11304 pixels giving a total count of 47.33 x 11304 = 535018.32. I made sure (by temporarily stretching the image) that this measurement wasn't affected by any hot pixels or background stars. This total count includes light from Z and from the sky background. So the sky background surrounding the star is 535018.32 - 354461.04 = 180557.28. This is spread over an area of pi x (120/2)^2 - pi x (70/2)^2 = pi x 2375 = 7461 pixels. Therefore the mean count per pixel for the sky surrounding Z is 180557.28 / 7461 = 24.20. If we want to obtain the count per pixel that is just due to the star we have to subtract this from what we recorded, namely 92.02 - 24.20 = 67.82 per pixel. 

This is the first main measurement. We now repeat this process for the comparison stars. I used exactly the same circular selections of 70 and 120 pixels for each measurement.

Beginning with star 84. This star has another designation HIP58303. This is a Hipparcos catalogue number. According to the AAVSO they assign this star as having a V magnitude of 8.438. I measured the sky background around this star to be 22.45 counts per pixel and the sky subtracted brightness for the star to be 23.27. Unfortunately, the brightness of the star at the position of 84 on the frame will not be quite the same as the brightness of the star at the position of Z due to vignetting (and for other reasons, such as atmospheric extinction). You can see this to a certain extent by the fact that the sky at the position of 84 is fainter than at the position of Z (22.45 vs 24.20, respectively).

We need to make a correction for this. Below is an image which shows the vignetting of this telescope/camera combination:-

You can see that the image is darker at the edges of the frame. To find how to correct the brightnesses, I put a square selection of 100x100 pixels centred at the position of Z and at the position of star 84. The counts per pixel were, respectively, 61.80 and 56.84. This means that the corrected count per pixel for star 84 should be (61.80/56.84) x 23.27 = 25.30.

Now we estimate the magnitude of Z. The difference in magnitudes between Z and star 84 is given by

m (84) -  m (Z) = 2.5 log10 (brightness of star Z / brightness of star 84)

which implies 

8.438 - m (Z) = 2.5 log10 (67.82/25.30)

and m (Z) = 7.37 (to 2 d.p.).

Now we can make similar calculations for the other comparison stars X and Y.

Star X is HIP57820 (also known as Aniara) and this has a V magnitude of 7.858. The sky brightness at the position of this star is 20.46 per pixel and the sky subtracted count for this star is 36.78. Correcting for vignetting this is 42.01. From this I obtain a magnitude of 7.34 for Z.

Star Y is HIP58302 and has a V magnitude of 8.375. The sky brightness at the position of this star is 19.51 per pixel and the sky subtracted count for this star is 24.99. Correcting for vignetting this is 28.73. From this I obtain a magnitude of 7.44 for Z.

So in all we have three estimates for Z of 7.37, 7.34 and 7.44 which gives a mean of 7.38 +/- 0.05. I think these values are pretty consistent considering I am not using software to produce the results. The problem is that I know that Z had a visual magnitude of about 7 on this date (2nd April 2023) and so my value is too faint.

The problem that needs to be addressed, I think, is that the green G channel of my camera (a Nikon D90) is going to respond differently to the eye (and to Johnson V) and this needs to be corrected for. I need to do this calibration and I need to adopt some photometric software to carry out the processing.

All text and images © Duncan Hale-Sutton 2023