# Create Phase Diagram

◦ Phase all the data into a single light curve, based on a start date and a phase period specified by the user With this tool, the user will specify an epoch and a period and a phase plot will be created using this specification. The phase plot can be limited to one cycle with 0 to 1 (or better yet 0 to 2) on the X-axis.

Notes (by Matthew Templeton):

The simplest way to create the phase plot is to offer the user a text box into which they can enter a test period. Once the program checks that the user has entered a valid numerical value > 0, then do the following:

• (very simple) determine an arbitrary phase zero point by setting t(0)=(t(max)+t(min))/2, and subtracting this value from all of the jds in the data set. Divide the resulting jds by the period.
• Loop over all data points and add/subtract the integer part of the number such that the resulting times all fall between zero and 1. (Note, if phase = -0.3, the resulting value would be +0.7, not +0.3).
• Plot the resulting phase points.

In addition to this, I would recommend plotting the data twice, once with phases zero to 1, and again from 1 to 2 -- just replot the array, adding 1 to all of the phase values. Plotting two cycles of the star would allow the user to see at least one full cycle of the star regardless of the phase offset used.

An improved plot would phase the data using as t(0) either the brightest point or faintest point in the light curve. You use the brightest point for pulsating stars, and the faintest for binary stars. This would require (a) that you search the data for the value of t at the brightest or faintest spot, and (b) that the data doesn't have any bad points that are artificially bright or faint.

One way around this is to allow the user to enter in a JD for the phase zero point. This may be ideal for those familiar with time series and light curves, but might be confusing for a layperson.

Notes (by John Greaves):

Setting Max and Min thro' phase 0

The Julian Date and magnitude are mapped to x and y coordinates on a graphical interface upon the screen. If this mapping information is not lost then x and y can be related back to JD and magnitude. Alternatively the graphical screen x position is mapped to a phase value on the phase plot and the adjustment needed to make that value zero made throughout, then all the subzero points adjusted afterwards to lie between 0 and 2, or the > 2 points wrapped around, depending on what direction the adjustement takes. If phase < 0 then add 2 for phase 0 to 2 plots for instance [check this].

Thus a lay person does not necessarily have to understand epoch to get a phase plot through phase zero. Click with the cursor over a datapoint and either the JD from that point is then used as t(0) from a context menu or similar, or the phase from that point is similarly logged and everything shifted accordingly so that phase becomes zero of preferred.

The latter is more illustrative as the point of deepest eclipse or highest maximum is more apparent in a phase plot and the sense of it all stays in sight.

This is sufficient for densely distributed datasets. That is, lots of data. For sparser datasets there is the problem that even for a phase plot the point of minimum can be seen by the eye to lie between two datapoints significantly distant for it to be clear that neither datapoint is adequate for the point of minimum or maximum.

In that case, and as the screen scale of the x axis is likely mapped "to scale" with respect to the values on the x axis, then the x value on the screen should be directly mappable to a Julian date or phase value.

Precision of the chosen point can be a natural function of the zoom level.

Something like that anyway.

This is not as good as deriving an actual epoch of minimum or maximum via software/algorithms and inputting that by hand or automatically as a JD value. However, it is interactive and soon becomes intuitive. People will be able to do this in order to have a nice neat professional looking plot going through phase zero without worrying about epoch, but it will not stop people who wish to look deeper from looking into what epoch is. In fact it might encourage some to take that extra step.

Matthew is correct, plotting the data twice is a must. Some use phase -0.5 to 1 or 0 to 1.5 or -0.5 to 1.5. 0 to 2 is clean and simple and not confusing.

It is also useful in scientific analysis. Some short period pulsating variables have periods very similar to half the period of some short period eclipsing variables. RRc and EW stars are a prime example. By definition EW stars have _two_ minima per period. There are subtle differences in the phaseplot shapes. When a star is not an RRc but an EW with twice the period it is easier to see that fact as "two phases" of the RRc solution will fits "one phase" of the EW solution. Then the plot can be tried again with twice the period first used. And vice versa.

Pulsating stars are usually asymmetric or very sinusoidal in phaseplot. The sinusoidal ones can usually be distinguised from EW class eclipsing binaries (where both minima per period have similar lowest magnitudes) because the latter always have something of a "longitudinally squashed" lightcurve, which when plotted to two phased (thus showing four minima) look "off" with respect to a sinusoid such as can be created by a rotational and some pulsating variables. More, even though the two minima from an EW star are very similar they are not always exactly the same and the subtle difference appears clearly when two phases are plotted.

Compare http://i41.tinypic.com/4jl3j6.gif which contains some EW stars with http://images.astronet.ru/pubd/2009/06/03/0001234975/302_44926_137.gif which is an RRc. Phase is plotted from 0 to 2 throughout.

These are not presented as ideal examples, they are just ones I am familiar with and thus readily able to find. Noticing the minima "widths" are tigther than the maxima "widths" in EW. I tend to describe it as a "concertina" effect for want of anything better.

John Greaves