The last 2 years of T Pyx observations (visual and V band)

Further to my posts earlier this year:

1. Outburst of recurrent nova T Pyx
2. T Pyx on the way back down
3. T Pyx still rising (actually)

the current light curve shows that T Pyx has declined from its peak of around magnitude 6 to around magnitude 11, approximately 5 magnitudes in as many months:

Decline in magnitude of T Pyx

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.

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 periods 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.

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.

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.

My last T Pyx update said that it was on the way back down. Almost as soon as I’d posted that, the nova’s brightness started to rise again. This is how it looked on June 11 2011.

T Pyx (in Visual and Johnson V bands) still on the rise

Is this latest rise related to the short-term variations mentioned in the T Pyx AAVSO Light Curve of the Week summary?

Or, perhaps it has something to do with the waves of material outlined here, quoting Michael M. Shara:

“Ground-based and Hubble telescope observations have allowed Shara to reconstruct a sequence of a T Pyxidis blast. When the nova erupts, it flings waves of gaseous material at progressively slower speeds: the first wave of hot gas flies through space at 4.5 to 6.7 million mph (2,000 to 3,000 kilometers per second), the last at 446,000 to 670,000 mph (200 to 300 kilometers per second). About a few weeks after this eruption, the first waves of speedy debris collide with slow-moving fossil material from the previous outburst, possible forming the gaseous blobs. Shara observed, for example, fast-moving gas from the 1966 eruption plowing into slow-moving material from the 1944 detonation. As the speedy, newly ejected material slams into the older, plodding debris, it heats up, glows brilliantly, and slows almost to a halt. Eventually the bright material fades as it cools down.”

As I said in my initial post, it’s fascinating to watch this unfold.

T Pyx light curve (visual and Johnson V bands) on May 31 2011

This AAVSO page about T Pyx mentions short-term variations in the 1966 outburst’s light curve, also evident in the current light curve.

You can learn more about VStar, and the context in which it got started, at CitizenSky. I have not developed VStar alone. I’ve had help from domain experts, AAVSO staff, and other developers.

If you want to try VStar, just click the green Download button on the SourceForge page. If you have Java 1.6 or higher installed on your Windows, Mac, Linux, or OpenSolaris machine, the latest version of VStar will be downloaded and run (via Java Web Start technology).

VStar is still an active, ongoing project. There’s plenty left to do. One key area of focus right now is the addition of a modelling capability and more period analysis functionality. If you are a developer looking for an interesting Science-related project to contribute to, try it out and have a look at the SourceForge bug & issue tracker to see if anything interests you.

Data analysis (e.g. finding periods in variable star data) is a growth area for amateur astronomers. VStar is growing into a tool that makes that easier to get into.

Now, back to coding…

The faint southern constellation Pyxis is bordered by Vela, Antlia, Hydra, and Puppis.

There are only about 10 recurrent novae known in our galaxy.

These objects belong to a sub-class of cataclysmic variables, a binary star system in which a white dwarf accumulates matter from a companion star. This eventually sustains runaway nuclear fusion leading to a substantial increase in brightness.

The image below is an artist’s rendering of the cataclysmic variable, RS Oph, that last went into outburst in 2006, reaching naked eye visibility (similarly in 1985, 1967, 1958).  Another one, U Sco, went into outburst early last year.

Example of a Cataclysmic Variable (RS Oph) (http://apod.nasa.gov/apod/image/0607/rsoph_pparc_big.jpg)

The 1966 T Pyx outburst reached magnitude 6. It will be interesting to see what its maximum brightness ends up being this time around.

The discoverer of T Pyx was Henrietta Leavitt of Cepheid variable fame. Michael Linnolt, in Hawaii, first reported the current outburst on April 14. Here’s the AAVSO alert notice.

Some of the early confirmation observations were visual estimates by Australian amateurs such as Alan Plummer and Steve Kerr. Photometric estimates appeared soon after, including some from former ASSA member, Peter Nation.

The following plot (using VStar) shows the current and 1966 outbursts along with the many fainter-than observations (in yellow) so commonly recorded in between outbursts. These are where the observer has said: “I can’t see T Pyx, but I can see a faint comparison star, so it’s fainter than that”.

T Pyx data back to 1920 showing visual and fainter-than observations

The 1966 outburst started in early Dec 1966 and T Pyx’s magnitude didn’t reach maximum until early January 1967, then took about 6 months to fall back to pre-outburst levels. From the onset of that outburst, T Pyx took about 2 days to go from mag 13 to around mag 9.5, then around 2 weeks to climb to 7.5, and approximately two more weeks to reach around mag 6. The next light curve plot (visual and Johnson B bands) shows this:

T Pyx 1966 outburst

The current outburst has been in progress for three and a half weeks. After an initial rapid rise of several magnitudes in the first few days from around 14.5 to 7.5, T Pyx has continued an overall upward trend (apart from a couple of brief dips) to a visual magnitude of around 6.8. This is easily visible in 7×50 binoculars.

What follows are three light curve plots showing AAVSO International Database observations from just before the start of the outburst up until May 11.

The first light curve shows only visual estimates.

T Pyx current outburst (visual band)

The second light curve shows visual and Johnson V photometric bands.

T Pyx current outburst (visual and Johnson V bands)

The third light curve shows all bands that T Pyx is being observed in, including infrared.

T Pyx current outburst (visual and various photometric bands)

It’s interesting to notice that the 1966 event was recorded in just a couple of bands, whereas the current one is being recorded in several. That’s a common trend when you look at AAVSO data in recent years, given the equipment now available to amateur astronomers, and the increasing number of telescopes that can be accessed via the Internet (e.g. global rent-a-scope).

Notice that the magnitude range varies with band, particularly relative to visual and Johnson V observations.

The visual estimate of magnitude 6.9 at the cross-hairs on May 2nd is my single contribution so far. Pyxis consists of fairly faint stars, so I spent a few nights just getting used to the binocular and low power telescopic fields before attempting an estimate.

It’s fascinating to watch this event unfold. Of course, given its distance, we are actually seeing an outburst that happened more than 3000 years ago.

Further reading:

• http://www.aavso.org/vsots_tpyx
• T Pyx: The story that just won’t die (written before the outburst)
• http://en.wikipedia.org/wiki/T_Pyxidis

The SKA will provide a sensitivity that is about 50 times greater than any radio telescope before it. The sheer size and complexity of this thing is staggering. It will consist of 3000 dishes spread across a couple of thousand kilometres with a combined collecting area of about 1,000,000 square metres (i.e. 1 square kilometre).

There are plenty of technical challenges to solve in areas like data storage, database technologies, and the need for green energy to handle the SKA’s power requirements. A super-computer will be required on-site to process the signals collected by the SKA in real-time.

Here are some factoids from SKA publicity material:

• The SKA will generate enough raw data to fill 15 million 64GB iPods every day.
• The SKA will use enough optical fibre to wrap around the Earth twice.
• The SKA will be so sensitive it could detect an airport radar on a planet 50 light years away.

Some questions the SKA will be help to answer, or provide more insight into, are:

1. How were the first stars and black holes formed?
2. How do galaxies evolve?
3. What is the nature of Dark Energy?
4. Are there Earth-like planets around other stars?
5. What generates giant magnetic fields in space?

As mentioned at the RiAus talk, part of the excitement lies in what the SKA may be used to discover that we had no clue about in the first place, i.e. serendipity.