Amateurs help solve SS Cyg mystery

Amateur observations of the dwarf nova SS Cygni have tipped off professionals to point their radio telescopes to this cataclysmic variable star during outbursts. This has led to a parallax-based refinement of the distance to SS Cyg of around 372 light years instead of 450, and the realisation that it is not as intrinsically bright as was previously thought.

The earlier less accurate HST-based parallax measurement suggested that, in theory, its intrinsic brightness was too high for periodic outbursts to occur and that rather, it ought to be in a stuck-in-outburst state. The revised smaller distance value means that the brightness observed agrees with the outburst behaviour theoretical models for this type of variable star predict.

Here’s the AAVSO summary article regarding the discovery and a light curve of SS Cygni from the AAVSO International Database showing such outbursts (Visual and photometric V band observations):

Obtaining and analysing Kepler data with VStar

In this post I will step through an example of using Kepler data with VStar‘s Kepler observation source plug-in.

After installing the plug-in as per the instructions on the plug-in library page, go to the Kepler data search page and type V0838 Cyg into the Target Name box:

Clicking Search takes you to this dataset result page:

Arbitrarily choose the last dataset entry to give this page:

Notice that the vertical axis is in units of flux instead of magnitude.

Near the top is text thats says: “Light curve file is online (“.fits”). If you click the “online” link you’ll get a page with the data in FITS format. What you really want to do is to save the link/file/page as a file locally, usually via a right-click context menu (in Windows; in Macintosh it’s ctrl-click).

The raw plot obtained from loading this file via VStar’s Kepler observation source plug-in looks like this, via:

and the phase plot (from a DCDFT standard scan; see VStar Analysis menu) at ~0.48 days is:

This looks like an RRAB given the amplitude, period, shape. I came to that conclusion before asking VSX.  A beautiful light curve. You have to zoom in quite a way to see any error bars, such is the nature of Kepler data.

By the way, you can get directly to the Kepler data page via the “External Links: Location” section of the V0838 Cyg VSX search result page!

One of the things I want to add to the Kepler and some other observation source plug-ins is the ability to specify the URL obtained from copying the link address (again from the context menu from the “online” link), in this case:

http://archive.stsci.edu/pub/kepler/lightcurves/0107/010789273/kplr010789273-2012277125453_llc.fits

The Kepler plug-in would then read the http stream directly rather than you having to download a file.

The Kepler plug-in converts flux values to a magnitude value. The amplitude should be what you’d expect but not necessarily the numerical value itself. For this star, VSX says “13.040 – 14.138″. In this case, adding 10 to each observation would bring it within the right range. It’s possible that the plug-in will be tweaked in future to produce a different magnitude range.

Other observation source plug-ins are available for VStar such as for:

• Catalina Sky Survey
• SuperWASP
• AAVSO upload format (as used by WebObs)

An ASAS plug-in is planned.

Polynomial fit to estimate a Mira maximum

Grant Foster’s book “Analyzing Light Curves: A Practical Guide” (section 5.5) gives an example of using polynomials to determine critical points of a light curve, in particular: a Mira maximum.

The book addresses the question of how to determine minima/maxima, especially in the presence of scatter in the data. The following figure shows a 7 degree polynomial fit for a Visual JD range around maximum for Mira.

To obtain this plot, load the data from the AAVSO International Database for the JD range shown (2451460.0764 to 2451559.539), select Polynomial Fit from the Analysis menu or toolbar, select the Visual series, then the number of degrees for the polynomial, in his case: 7.

Experiment with the degree value to see the effect upon the least squares polynomial fit. A 5 days-per-bin mean series (again, based upon the Visual series) makes a useful comparison. This can be changed via the View menu’s Plot Control dialog.

Switching to the Model and Means tabs in turn and clicking the Magnitude column to re-order it, allows the maximum value in the series to be easily found. Selecting such a row causes the cross hair in the plot to move also.

Grant’s discussion goes beyond simple polynomial fits, including a discussion of information criteria or “goodness measures” and a consideration of alternatives such as the Lowess smooth, both of which are on the roadmap for VStar. He also spoke about this in more detail at one of the Astro April Citizen Sky talks about uncertainty in determining time of minimum/maximum.

Given that it is currently near maximum, while writing this entry I also created polynomial fits for filtered ranges of R Car, another long period variable. I’ll leave that for another post though.

On a related note, I’ve been asked by a few people recently about when VStar will include a Time of Minimum/Maximum (ToM) capability such as Kwee-van Woerden for use with eclipsing binary light curves. This is working its way higher up the list.

CLEANest example from Grant Foster’s 1995 paper using VStar

Grant Foster’s 1995 CLEANest Fourier Spectrum paper (Foster, G., 1995, “The CLEANest Fourier Spectrum”, The Astronomical Journal, vol 109, no 4, 1889–1902­) gives a number of examples of applying the CLEANest algorithm to datasets, artificial and real. Two of these use AAVSO visual magnitude estimates: S Ori and AA Cas.

This post shows VStar’s CLEANest implementation applied to AA Cas. Foster 1995 uses an AA Cas dataset in the JD range 2447500 to 2449500. The following shows that dataset loaded from the AAVSO International Database (AID) via VStar’s file menu.

aa Cas Visual JD 2447500 to 2449500

A DCDFT with frequency range can be initiated from VStar’s Analysis menu, selecting the Visual band and specifying minimum and maximum frequencies, the range over which to scan, and frequency resolution over the range.

This results in the following power spectrum (in the Power vs Frequency pane) with the orange squares showing peaks or “top hits”.

aa Cas Visual JD 2447500 to 2449500 power spectrum

These top hits are shown in the next diagram in tabular form.

aa Cas Visual JD 2447500 to 2449500 selection for input to CLEANest(7)

In this example, seven top hits have been selected using combinations of shift-click and control-click  (Windows) or command-click (Mac). The initial input values to CLEANest are not stated in Foster 1995 (section 5, page 1900), but the rows selected above fairly closely correspond to what I think they should be.

Clicking the CLEANest button opens this dialog from the Top Hits pane.

aaCas CLEANest(7) input dialog

Clicking OK here adds seven new top hits with the same power value, shown multiply-selected in the top hits list and annotated on the power spectrum.

Now click Create Model in the Top Hits pane and the following dialog will open.

aaCas CLEANest(7) model creation dialog

Click OK and the main plot will have an additional “model” series added. Dismiss the main DCDFT dialog to return to the main VStar window.

aa Cas Visual JD 2447500 to 2449500 model from CLEANest(7)

Something on my TODO list is to make the model series continuous rather than discrete as it currently appears. The residuals for this model can be viewed by opening the Plot Control dialog from the View menu and setting it as shown, including changing the Days per Mean Series Bin (and clicking Apply).

Dismissing the dialog changes the plot to look like this.

aa Cas Residuals and binned means from Visual JD 2447500 to 2449500 CLEANest(7)

Performing a DCDFT on the residuals with the same frequency parameters as for the visual series, but by selecting the residuals gives the following power spectrum.

aa Cas power spectrum from Residuals

Looking at the Power axis suggests that there is very little discrimination between any of the frequencies.

In addition, the ANOVA value in the Info dialog (File menu) also suggests that there is unlikely to be any signal remaining to be found in the residuals, i.e. the null hypothesis that there is no significant signal present should be accepted.

aa Cas ANOVA from Residuals

NACAA 2012: a personal summary

The National Australian Convention of Amateur Astronomers (NACAA) is held every two years over the Easter long weekend. This year, the 25th NACAA was held in Brisbane at the University of Queensland’s St Lucia campus. The two main convention days are on Saturday and Sunday with Friday and Monday reserved for workshops, colloquia, symposia or other activities.

On Friday April 6th I attended the 2nd Variable Stars South (VSS) colloquium. In the first session, I gave a VStar development update. At the 2008 NACAA I’d met AAVSO Director Arne Henden where we discussed VStar as a possible volunteer project. At NACAA in 2010 I held a one day hands-on workshop covering the initial development since May 2009. VStar has matured somewhat in the last two years and the focus was on new features. I noticed a shift in emphasis from 2010. At that time, workshop attendees were interested in using VStar and looked forward to watching it evolve. This time, I spoke to people who had been making use of it for their research and our conversations over the weekend focussed upon additional features that would help them do what they needed to do.

Subsequent VSS colloquium sessions included:

1. A number of presentations and discussions about the SPADES exoplanet project.
2. Presentations about techniques in DSLR photometry and photometric data reduction.
3. Summary of a paper concerning the eruption of the recurrent nova T Pyxidis in 2011.
4. “Observing the observers” of Eta Carina through its light curve.

Simon O’Toole from the Anglo-Australian Observatory was at the colloquium, primarily for the SPADES sessions. I had some interesting conversations with him about possible VStar futures and data analysis in the morning tea break.

In parallel with the VSS colloquium on Friday was an Astronomy 101 workshop, attended by a mixture of beginners and experts.

There were two streams on each day of the weekend, although both days had a keynote or invited speaker.

Saturday began with a keynote by Dr Tamara Davis and Professor Michael Drinkwater and although wide-ranging, the topic was focussed upon the bulk of the Universe we apparently know little about: Dark Energy and Dark Matter, confirmation of Lambda Cold Dark Matter model, and some trivia about the recent Nobel Prize for Physics, such as the quality of the “paparazzi” (professional astronomers).

Sunday’s John Perdrix address was given by Martin George and was a fascinating glimpse into the life of Grote Reber, the radio astronomy pioneer who moved from Illinois to live in radio-quiet Tasmania. Martin’s historical research and personal anecdotes always make for an entertaining talk. Having lived in Launceston for a decade, I always enjoy catching up with Martin at NACAA.

Here’s a sampling of talks over the two main days:

• Building and using spectroscopes for amateur variable star spectroscopy.
• Making and submitting double star measurements to help improve catalogues, which have a surprising number of errors.
• Analysing an eclipsing binary variable star from observation through to creation of a physical model.
• Supernova discovery methods.
• A talk about Comet Lovejoy, by Terry Lovejoy.
• Talks about this year’s transit of Venus and Total Solar Eclipse.
• Variable star photometry and data analysis talks.
• Meteor observing systems.

Presentations about asteroidal occultation observation and analysis.

There was also a talk about “teaching the teachers” and an interesting presentation about the likely prevalence of life elsewhere in the Universe from a presenter with qualifications in microbiology and chemistry.

For the final Sunday session, I opted for the Brisbane planetarium visit.

I flew back to Adelaide on Monday morning, but that day had two parallel streams: the Sixth Trans-Tasman Symposium on Occultations and an Eclipse Imaging Workshop.

After each day’s sessions we were kept busy with some social event or other: a welcome function on Friday, a dinner on Saturday, and a BBQ on Sunday. At the Saturday dinner, Anthony Wesley was presented with the Berenice and Arthur Page medal for his amazing planetary imaging work.

I stayed at Toowong and took the CityCat ferry to and from the University most days. This and the train made it fairly cheap to get around Brisbane during the weekend.

Overall, it was a great event. It’s my sixth NACAA and I would recommend it to anyone with an interest in communicating with other amateurs around Australia (and a few from New Zealand), finding out what’s going on beyond our borders. The next NACAA will be held in 2014 in Melbourne, hosted by the Astronomical Society of Victoria. I hope to see you there.

Pinwheel Galaxy (M101) supernova light curve

At the February 2012 ASSA General meeting, Kevin Davey spoke about Type Ia supernovae as standard candles. The recent Type Ia supernova in the Pinwheel Galaxy was mentioned during Q&A.

The figure below shows a light curve of the supernova (whose designation is now PTF11kly):

Light curve of SN in M101 (PTF11kly)

The plot shows observations from the AAVSO International Database in multiple wavelengths (visual, various photometric and infrared bands) from August 24 2011 through to Feburary 2 2012.

This shows the characteristic light curve of a Type Ia supernova.

WWZ contour plots

In my last post about WWZ I said this:

What VStar does not currently do is create a 2D plot that represents the WWZ statistic as different colours. It’s an open question as to whether this is necessary, but such plots do have a striking appearance and some may prefer them over 3D plots.

I’ve implemented contour plots for WWZ in VStar now. Here is the plot for the T UMi example in that last post.

T UMi WWZ contour plot

I may tweak the appearance of these plots yet, but this is essentially what they will look like in the forthcoming release.

This is similar to the example plot in Grant’s book on page 235 (Fig 11.14) except that period is on the Y axis rather than frequency. It’s interesting to compare this against where the peaks occur the 3D plot.

I have also added the ability to:

1. Request WWZ and DC DFT in terms of period range rather than frequency range;
2. specify the number of time divisions across the dataset range for WWZ. The improvement in time resolution is most noticeable in the contour plot. In the plot above, I used a value of 80 instead of the default of 50.

An internal VStar team testing release is getting close, hopefully by the end of this week.

Weighted Wavelet Z-Transform (WWZ) in VStar

It’s hard to believe 6 months have elapsed since the last release of VStar. Although there  is no firm date for the next release yet, there has been a lot of progress towards it. I hope it will happen this month, at first internally to the Citizen Sky VStar team.

My last two posts covered a couple of forthcoming features: model creation from period analysis and the CLEANest algorithm. I used examples from Grant Foster’s book Analyzing Light Curves: A Practical Guide to illustrate the new features. I’m still collaborating with Grant and Doug Welch on improvements to CLEANest such as taking into account the harmonics of specified frequencies. Grant has already incorporated into his R version of CLEANest. This aspect of VStar development has been on the back-burner for the last few weeks so in the meantime I decided to implement Weighted Wavelet Z-Transform (WWZ), also covered in Grant’s book (and created by him). I know that Aaron Price has been looking forward to seeing WWZ in VStar.

Again, I have (with permission from AAVSO) had the benefit of a reference implementation in the form of Fortran code available in the AAVSO Software Directory, just as I did with Date Compensated Discrete Fourier Transform (DCDFT) in the form of the Fortran code of TS (also available via the same software directory web page).

Whereas period analysis algorithms like DCDFT, Phase Dispersion Minimisation, Analysis of Variance (AoV) and others (DCDFT is implemented in VStar) provide information about candidate periods in a time series dataset, and CLEANest refines candidate periods, WWZ analyses how a star’s period changes over time: time-frequency analysis. Grant uses the stars T Umi and R Dor as examples.

The T Umi dataset, taken from the AAVSO International Database (AID) in Grant’s example spans the JD range 2,420,000 to 2,455,000.

Creating a phase plot with periods resulting from DCDFT in VStar doesn’t result in an obviously “clean” fit over the time range. WWZ helps to explain why. Applying WWZ to the dataset requires selecting the series to be analysed, then the following parameters:

• Minimum frequency
• Maximum frequency
• Frequency step or resolution
• Decay: the wavelet window; smaller values yield better resolution of variation

This post won’t go into detail about these parameters or the WWZ algorithm. Apart from Grant’s book, the HTML docs accompanying the WWZ Fortran code available in the AAVSO Software Directory are worth reading.

For T Umi, choosing values for the above parameters (entered into a dialog box) of : 0.00001, 0.02, 0.00001, 0.001 give the following plot of period vs time:

This is VStar’s equivalent of Figure 11.16 in Grant’s book.

The WWZ result dialog also gives other plots and data tables derived from the result of analysing each frequency in the specified range and interval over a range of times. One of the tables shows only those time-frequency pairs for which the WWZ statistic is at maximum (distance from 1 denotes degree of variation for a particular time) for each time under test.

The following 3D plot shows period and time on two axes as above, but adds the WWZ statistic on the 3rd dimension:

The ridge of the plot denotes the degree of variation at a particular time-frequency (or time-period in our case) pair. In the VStar dialog tab in which this appears, the mouse can be used to rotate this plot and view it from various angles.

What VStar does not currently do is create a 2D plot that represents the WWZ statistic as different colours. It’s an open question as to whether this is necessary, but such plots do have a striking appearance and some may prefer them over 3D plots. WinWWZ, developed by Geir Klingenberg and Lisa Henkel creates such “contour plots”. Grant also talks about the pros and cons of each kind of plot in his book.

What is currently committed in SourceForge is not the last word before the looming release, and I would appreciate feedback on the current interface. I may yet use a different 3D plot library. VStar currently uses JMathPlot for 3D plots and JFreeChart for all other (2D) plots here and elsewhere in the tool.

Grant’s second example is of R Dor in the JD range 2,426,000 to 2,556,000.

With the visual series selected for analysis and the parameters 0.001, 0.009, 0.0001, 0.005, the period vs time plot appears strange:

until you look at the 3D plot (equivalent to Figure 11.16 in the book):

which, as Grant says, shows that R Dor (at least in the JD range under test) exhibits mode switching, i.e. it switches from one pulsation mode to another (between periods of around 332 and 175 days).

I hope you enjoyed this brief look at another of the new features that will appear in the next release of VStar.

BZ UMa model and CLEANest

Over the last few days I finished coding and unit testing the multi-period analysis CLEANest algorithm implementation in VStar (again, translated from TS). The main missing parts were allowing the user to specify “variable” and “locked” periods in addition to selecting them from a DC DFT period analysis result. I’m at the point where I need feedback.

Apart from the unit tests that show equivalence with the TS program, I’ve been “playing” with a few different datasets and pre-whitening, modelling, CLEANest.

In my last post, I created  a model based upon two periods found through successive refinement (pre-whitening). Tonight I used CLEANest to obtain those periods for a model with fewer steps.

Starting from the DC DFT frequency scan (low frequency: 0, high frequency: 50, resolution: 0.01) of the BZ UMa V band data, we end up (as last time) with a top hits table like this:

Selecting two periods for CLEANest from BZ UMa DC DFT top hits

Also shown is that I have selected the two values used in the two-period model last time before clicking the CLEANest button giving us:

Two periods with same power added by CLEANest to BZ UMa DC DFT top hits

The CLEANest algorithm inserts two new rows at the top with the same highest power. I have selected these above. Switching to the “Power vs Frequency” (power spectrum) tab we see:

Two periods from CLEANest superimposed as "spikes" on BZ UMa DC DFT periodogram

Notice the spikes showing the refined frequencies from the CLEANest algorithm. Switching back to the Top Hits tabbed pane, clicking “Create Model”, we get:

Two period BZ UMa model from CLEANest

I am still quite new to period analysis, including CLEANest (it’s one thing to code it, another to apply it…), so I’m interested in feedback from others regarding the appropriateness of CLEANest in a context like this, and also first impressions regarding usability.

Modelling with VStar

Ever since reading Grant Foster’s description of modelling in Analyzing Light Curves: A Practical Approach, I’ve been keen to incorporate this functionality into VStar. In recent SourceForge commits I’ve implemented a first cut of this.

If you are happy to “live on the bleeding edge”, you are welcome to try it now by checking out from the SourceForge Subversion repository or downloading a tarball. Otherwise, it will be available in the next VStar release.

I want to give an example from chapter 10 in Grant’s book: A day in the life of BZ UMa. BZ UMa is a cataclysmic variable that has undergone numerous outbursts; see this Slacker Astronomy video page re: a BZ UMa poster by Aaron Price.

Grant works through an analysis of just one day of BZ UMa data that shows short-term periodic changes. In talking with Grant, it turns out that the JD range used for the example is 2,454,205.3 to 2,454,205.9 not 2,445,205.3 to 2,445,205.9 as shown in the book.

Obtaining data in the range 2,454,205.3 to 2,454,205.9 from the AAVSO International Database with VStar, and looking at just the V band data gives this light curve:

BZ UMa V band for the JD range 2,454,205.3 to 2,454,205.9

Applying a Date Compensated Discrete Fourier Transform (DC DFT) gives this periodogram:

BZ UMa V band DC DFT

Switching to the Top Hits tab shows that the tallest peak corresponds to a frequency of around 14.18 cycles per day (depending upon exactly what frequency scan parameters you provide; I changed the High Frequency to 100 and the Resolution to 0.01 in the period analysis parameters dialog). In chapter 10, Grant suggests creating a model based upon this main frequency. In VStar, clicking the “Create Model” button in the Top Hits pane will create this and plot it against the V band data as follows:

BZ UMa V Model with main frequency of 14.18 cycles per day.

Apart from the model series, VStar also generates a series called “Residuals” which results from subtraction of the model data from the model source series (V band in this case) data that looks like this:

BZ UMa residuals for model of 14.18 cycles per day

This so-called pre-whitened data has the main frequency removed from the raw V band data. Section 8.6 of Grant’s book is about pre-whitening.

The question then is whether period analysis of the residuals would reveal further signal. A DC DFT of the BZ UMa residuals above gives this periodogram:

BZ UMa DC DFT of residuals from 14.18 cycles per day model

This power spectrum shows a Top Hit of around 28.36. In the light of this additional frequency, Grant suggests creating a model based upon two frequencies, in this case: 14.18 and 28.36. You can of course create a model based upon just this new frequency:

BZ UMa Residuals Model

Now, one of the current limitations of VStar’s implementation of modelling is that you cannot incrementally add to an existing model or combine two or more. I definitely intend to permit both however, in addition (a little later) to the construction of arbitrary models. For now, the best we can do in VStar is to return to the initial V band DC DFT and select two frequencies that are close to these (in this case: 14.18 and about 28.58) giving this model plotted against the V band data:

BZ UMa V band two-frequency model

VStar’s Analysis menu now has a Models item that opens a dialog when selected containing a list of created models. They can be selected for re-plotting or deletion. Only one model-residuals series pair can be viewed at a time. Note also that new tabs in the main VStar window contain tables of the model and residual data. Polynomial fits and their residuals are now also included in the models dialog box.

Of course, model and residual data can also be included in a phase plot. In order for a model to make sense for some stars (e.g. del Cep), a phase plot is pretty much mandatory; not so for the current BZ UMa example.

Grant goes on to use the residuals from this model to identify additional harmonics beyond the fundamental frequency and first harmonic mentioned above to further refine the model. His analysis also adjusts for two groups of observer bias to compensate for consistently different estimates by two observers. VStar’s filter feature can be used to illustrate one such bias group:

BZ UMa Observer aBias

As mentioned already, VStar’s current modelling capability does not yet permit such refinements as observer bias to be included in the model. In any case, I hope this example has provided some insight into where VStar’s modelling functionality is heading.