How to: Photometry

Recently I've gotten very interested in photometry (the measurement of light from stars).  Compared to the deep sky astrophotography I've done in the past the image gathering is actually very straightforward. However the actual analysis is a bit more complicated so I've decided to write a short blog post on this.

Photometry Light Curves

The goal of photometry is to produce a graph that shows the changing light emitted by a star.  One example is the graph below. Its the light curve for the Eclipsing Variable Star U Cephei.

The Star's magnitude is plotted along the y-axis. Since higher magnitudes correspond to dimmer stars its graphed in reverse order.  Time (in Julian Date) is on the x-axis.  Julian Date (JD) is often used because it provides a simple way to record time as rational numbers with having to worry about fractions of hours or daylight savings time or other interesting quirks of a 24 hours clock.  

Hardware

In principle doing differential photometry is very easy.  All you need is a tripod and a DSLR camera that can take long exposure photographs.  If you uses a camera tripod that isn't capable of polar tracking the exposure times will be limited to about 30 seconds (depending of the lens you use) before the stars will begin to trail.  I attached my DSLR camera to my 85 mm refractor and used my tracking mount; in this configuration the exposure time is limited by the saturation limit of the camera.  Depending on the target that can be anywhere from a few tens of seconds to a few minutes. 

Choosing a Target

There are thousands of variable stars within reach of surprisingly modest equipment.  A simple tracking mount and a DSLR camera can record variations in stars as faint as 11th or 12th magnitude.  An 11" telescope can reach as far as 14th or 15th magnitude.  

 

Probably the best place to find lists of Variable Stars would be the American Association of Variable Star Observers. You'll also find a huge amount of reference and resource information on the how-to of pretty much every aspect.

Aside from the magnitude of the variable star you chose there are a few other things you should consider.  How big will the variation be and will your equipment be sufficiently precise to measure it accurately?  How often will minimums occur and will they occur when viewing is favourable?  How high in the sky will the target star be?  For people who have done astrophotography most of this is routine but if you're just getting started its important to keep them in mind.

Software
There are several different software packages that are capable of taking raw camera data and producing useable photometric data.  The three that I recommed are:

1. IRIS
2. AIP4WIN
3. MaximDL

I've used IRIS quite extensively mostly because its free to download. Depending on how precise you want your data it is capable of doing dark, flat and offset subtraction as well as alignment and stacking.  However the interface is not the most straightforward.  Despite this I still use it because its free and there are excellent tutorials available online.

AIP4WIN is another great alternative.  It costs about $100 but comes with an excellent book (or the book comes with AIP4WIN, depending how you look at it) on variable star observing.  Aside from a quick cursory look at it I haven't used it but I heard excellent things about it.

If you want a sleek, well thought out, multiuse software package (and don't mind spending $600) then check out MaximDL.  It will do pretty much everything an astronomer or astrophotographer could ask for, including Photometry.  Beware: The basic and DSLR versions DO NOT come with photometry tools!

Results
Below is the (partial) light curve for W Ursae Majoris.  This is a contact binary system with a period of just over 8 hours. 

   

The x-axis is typically in Julian Date since you don't have to worry about the 24 h clock and things like daylight savings time.  To convert from our normal 24 hour clock/date to Julian Date I've used the USNO Julian Date Converter. The results you get from DSLR or CCD cameras are ADU (analog-digit units); basically a measure of how many photo electrons are recorded in the sensors.  These are basically telling you what the intensity of the star is.  However to create a light curve like the one above you need to change intensity to magnitude.  You can do that using the equation below:

m₁ - m₂ = -2.5 log(I₂/I₁)

This equation will basically tell you the difference in magnitudes between two stars.  So that means you actually have to do a measurement on TWO stars.  One that has a constant magnitude and your variable star.  Then you plug the intensity values into this equation and you get the difference in magnitude.  In fact, spreadsheet programs like Excel can actually automate most of the calculations.  The result will be a nice light curve! And just think about what this curve shows! You're looking at subtle changes in stars light years away! 

Good luck!

Photometry

After a little over 2 years of deep sky photography my interests have turned to Variable Stars and Extra-Solar Planets.  Since November I've been working on creating a light curve for an Eclipsing Binary Star with my DSLR.  My original plan was Algol since its nice and bright and could probably be captured with a simple tripod mounted DSLR. In addition Sky and Telescope has a nice calculator for the minimum (http://www.skyandtelescope.com/observing/objects/variablestars/Minima_of_Algol.html). As I soon found out the nearly 3 day period made it difficult for me to arrange to photograph. Because of work I could only do imaging on the weekends so I was looking for a minimum on the weekend, obviously in the evening and with good weather.  As it turned out, this winter has been terrible in terms of cloud cover.  And the weekends that were clear also tended to be devoid on Algol minimums. 

My alternative was to focus on faster period stars so I settled on the moderately faint W Ursae Majoris.  Not only did this star meet the faster period requirements I wanted (8 hours) but during the winter it was also high in the sky and would be up all night. 

 

 

 

It took about a month to finally get some clear skies but after I found some decent skies the actual data gathering was quite quick. After two consecutive Saturday evenings I was able to gather enough data to produce this light curve:



This was made before I thought to put the orbital phase on the x-axis so the two different nights are represented in different colours.  Its a pretty straightforward light curve that easily shows the minimum of W UMa. The magnitude of W UMa is nearly 8 and varies by just over half a magnitude.  Considering the tools I'm using (an uncooled Canon DSLR) I'm fairly happy with the results.  Over the past few weeks I've gotten much more interested in extra-solar planets and I'm going to see if I can apply the same methods to detecting exoplanet transits; I can across and interesting group that is doing almost that very thing: http://www.planethunters.org/.

However before I get to into this next project I need to see if my camera is up to the task.  For W UMa binary stars the change in brightness is around 0.50 - 0.75 magnitudes.  For extra-solar planets the most I can expect is around 0.0030 magnitudes.  I'm not convinced that change in brightness will actually be above the noise level of the camera's sensor.  So next up will be the test of the noise levels of the Canon T3i.

Stay tuned!

Suburban Astronomy

The winter in Edmonton has not really been kind.  Its not even the cold weather I mind, but the cloudy, snowy weather.  And that's mostly what we've had for the past 3 months.  I've waited patiently and it looks like the next little while will be a bit better. To illustrate that fact, on Monday night the sky was incredibly clear so I set my telescope up in my drive way to test a couple things like polar alignment, light pollution and my new Kendrick's Dew Heaters.  On all scores it was a great night.

The Dew Heaters work great and serve a dual purpose because in the winter its not actually Dew I'm fighting against, its frost.  Although it uses up more power, my 125 hA battery is more than up to the task. 

I've gotten pretty proficient using EQMOD and Stellarium together and on Monday night I added EqAlign to my list of software tools. 

EQ Align works with pretty much any webcam.  Using the program you pick a star on (or close to) the meridian.  Connect your webcam to EQ Align and select a star.  The star has to be fairly bright; I have a Lumunera 135m and I can usually only use magnitude 1 or 2 stars.  Once you select a star you can star the alignment procedure.  The program analyzes the star's drift (I find about 30 s is enough to get an accurate result) and tells exactly how far you need to move your scope in RA.  Once you're satisfied with the RA alignment you move to the east or west and repeat for DEC. 

For anyone who's ever done drift alignment this should sound pretty familiar; and that's because it is.  Its really just a computer assisted drift alignment.  There is nothing overly special about this aside from the fact that it speeds it up.  Using the webcam the computer can pick up drift pretty accurately after only a few seconds.  When I did drift alignment manually I usually had to wait 3 or 4 or more minutes before I could conclusively determine the correct drift. 

Anyway, after about 30 minutes of tinkering with the alignment I couldn't resist testing the fruits of my labour. Since I'm in a suburban area with fairly significant light pollution I chose M42 as a nice bright target.  It was also the first time I imaged it with my 11".  I took nearly a hour's worth of pictures and this is what I got.

I've really pleased with this result.  I can pick out the trapezium stars and there are hints of the much larger nebula cloud that surrounds it.  I can't wait to try this from a dark sky site.

Photometry

This is a brief summary of my early attempts at measuring the light curves for short period binary stars.  My initial attempt has been sort of a proof of concept using Algol as a target.

Objective:
Produce a light curve of the minimum of the transit of Algol

Equipment:

• Canon xTi
• Standard photography tripod
• Canon remote timer

Method:

During the late fall and winter Algol is in an excellent location in the sky for photography. To complete the light curve analysis I'm looking for its not actually necessary to photograph the entire period of the binaries rotation; photographing the length of the minimum is the primary goal.  Fortunately for me Algol has been well studied and the time of the minimum on any given day is available on the Sky and Telescope website:

Sky & Telescope Algol Minimum Calculator

The Algol binary system has a period of 2.8 days and the transit of Algol b takes 10 hours from start to finish.  Ideally this entire transit is what should be photographed.  However this requires 10 hours of clear dark skies during which the minimum occurs.  This is rare and so far I haven't been able to photograph more than a few hours at a time.

Results:

This past weekend I attended the Alberta Science Teachers Conference in Banff and Thursday November 15th at 11:56 pm was a predicted minimum of Algol.  So after the conference ended I set up my camera and recorded about an hour of photos immediately up to the minimum.  After gathering twenty seven 20 second pictures at three minute intervals I converted the .raw files to .tiff files using photoshop.  I was able to analyze these images using SalsaJ and came up with some encouraging data.

Below is a quick time lapse of the images I took.  Some of the pictures were effectively ruined by transient clouds but enough suitable images were obtained to provide a rudimentary proof of concept. 

Using the best 7 data points I was able to using the photometry features of SalsaJ to gather the data below:

 

Image #	Start Time	Target Intensity	Comparison Intensity	Magnitude Ratio
1	21:53:00.00	3519840	4879236	0.72139
2	22:55:00.00	3402002	4836478	0.70340
3	22:57:00.00	3819125	5215910	0.73221
4	22:59:00.00	3773813	5597030	0.67425
5	23:01:00.00	3691644	5714231	0.64604
6	23:03:00.00	3980940	6143964	0.64794
7
8
9
10
11
12
13
14
15	23:27:00	2907813	4760742	0.61079
16
17	23:33:00	3614116	6708249	0.53876

For the photometric analysis the comparison star was Mirfak. Using the ratio of Mirfak to Algol during the image run I created the light curve:

Analysis:

These results are encouraging. Even though the weather resulted in a large gap in the data and there are relatively few points, they consistently show a decrease as the expected minimum approaches.   I'm further encouraged because of the specific results of the photometry.  Mirfak is not a variable star and has an apparent magnitude of 1.8. At its minimum Algol has a magnitude of 3.4.  The ratio of magnitudes of Mirfak/Algol at the minimum of Algol is 0.529 which is very close to 0.538. The deviation could easily be explained by the time difference between my last observation (11:33 pm) and the time of the expected minimum (11:54) or the effects of clouds on the observations.

Conclusion:

While this isn't conclusive I'm quite encouraged by my results.  I've been convinced this method will eventually yield successful results when the weather and transit times allow me to make further observations. If you have any suggestions or comments I'd be happy to hear them.

Fall Observing

I've been busy the past 6 weeks. And thankfully much of it has been observing.  Anyway, I'm going to keep this short and simply post a few of the pics I've taken.  More to come on them later.

 

Telescope: Celestron Edge 11"

Mount: Skywatcher EQ6

Camera: Hutech modified Canon T3i

Exposure: 14 x 5 min at 1600 ISO

 

Telescope: Televue 85 mm

Mount: Skywatcher EQ6

Camera: Hutech modified Canon T3i

Exposure: 11 x 5 min at 1600 ISO

 

Telescope: Televue 85 mm

Mount: Skywatcher EQ6

Camera: Hutech modified Canon T3i

Exposure: 13 x 5 min at 1600 ISO

 

Camera: Canon xTi

Mount: Canon camera tripod

Exposures: 65 x 1 min exposures combine using startrails