Eclipsing Binaries
Converting your observations into a light
curve
If you have observed the whole eclipse in one
night its easy to create a light curve
However, we often have to combine
observations made on different nights, either
because the eclipse takes too long, or because
the weather interrupts our observations
Beta Lyrae has an orbital period of just under 13 days
Here are my observations of beta Lyrae
from 2009 …
Beta Lyrae mags
Date
28/05/2009
29/05/2009
30/05/2009
30/05/2009
31/05/2009
03/06/2009
11/06/2009
15/06/2009
23/06/2009
29/06/2009
03/07/2009
09/07/2009
16/07/2009
24/07/2009
27/07/2009
Time(UT) Mag
23:01
22:37
00:48
22:29
22:49
22:40
22:43
22:43
23:58
23:45
22:49
23:50
00:37
23:33
22:05
3.56
3.81
3.89
3.99
3.81
3.66
4.19
3.71
3.66
3.56
3.71
3.71
3.71
3.51
3.99
Date
31/07/2009
02/08/2009
13/08/2009
17/08/2009
20/08/2009
21/08/2009
27/08/2009
09/09/2009
12/09/2009
15/09/2009
18/09/2009
12/10/2009
12/12/2009
19/12/2009
20/12/2009
Time(UT) Mag
00:24
00:41
22:05
21:16
21:24
20:51
23:27
20:35
19:55
19:54
19:32
18:34
18:05
06:34
06:26
3.79
3.71
3.81
3.76
3.66
3.81
3.66
3.43
3.56
3.53
3.61
3.89
3.53
3.66
3.61
If you simply plot this data as a light curve , the
result is disappointing…
Beta Lyrae in 2009
3.2
Magnitude
3.4
3.6
3.8
4
4.2
4.4
27/04/2009 16/06/2009 05/08/2009 24/09/2009 13/11/2009 02/01/2010
What you would prefer is the next light curve
showing the primary eclipse near phase 0
and a secondary eclipse near phase 0.5
Beta Lyrae in 2009
3.2
Magnitude
3.4
3.6
3.8
4
4.2
4.4
0
0.1
0.2
0.3
0.4
0.5
Phase
0.6
0.7
0.8
0.9
1
Phases
• The difference between the previous two light curves is
that, whereas the first showed the calendar date, the
second shows the phase (the fraction of the orbital period
completed)
• In order to calculate the (predicted) phase at the time of
each observation, we need to know the “orbital elements”
of the system
• The place to look for these is in the General Catalogue of
Variable Stars (GCVS)
GCVS elements
http://www.sai.msu.su/gcvs/cgi-bin/search.htm
For beta Lyrae this gives
Epoch = 2408247.950
Period = 12.913834 days
(the Epoch is the Julian Date of a previous eclipse)
Why Eclipsing Binaries are interesting
- If the orbital periods were fixed, there would be
little reason to observe EBs regularly
- However, for many eclipsing binaries, the
orbital period slowly changes over the years
- by comparing the observed times of eclipses
with the predicted times, amateurs can help
monitor how the orbital period is changing
So, how do we use these elements to convert our
dates and times into (predicted) phases ?
Back in the 1980s …
For each observation you had to ….
•
•
•
•
Look up the Julian Day number
Look up the Decimal fraction of the day
Use a pocket calculator to calculate the phase …
Plot using graph paper
This was very time consuming and prone to errors
The 1990s
• The 1990s brought us PCs and spreadsheets and
made the process so much easier
• First of all, key your observations into a
spreadsheet, with the dates, times and
magnitudes in separate columns …
Excel stores the date as a day number.
To convert it to the Julian Day Number :
type =B2+15019 in cell E2
(you will also need to use the Format drop down menu to set the Cell to General)
Then highlight cell E2, click on the bottom right hand
corner of the cell and drag the mouse down through
column E to repeat the calculation for the other dates
E2 = B2 + 15019
Next we convert the time in column C to a
decimal fraction of a day
The “- 0.5” adjustment is needed
because the Julian Day changes at
midday rather than midnight
F2 = (HOUR(C2)*60+MINUTE(C2))/1440 0.5
We then add together the column E and column F
values to give the JD in column G
Then, in column H, we calculate the number of
orbits that have taken place between the Epoch
Julian Date and the Julian Date of the observation
H2 = (G2 – 8247.95) / 12.913834
We only want to know how far we are through the
latest orbit
so we chop off the part before the decimal point
…. and we are left with the (predicted) phase
I2=MOD(H2 , 1)
Having completed all rows, we copy across the
magnitudes from column D to column J
Then highlight column I (phase) and
column J (magnitude)
and click on the Chart Wizard icon
Chart Wizard then asks which type of graph you
want to plot.
Select the XY Scatter graph …
…click on Next,
add a title,
click on Finish
… and Excel will plot your light curve …
Unfortunately, Excel doesn’t understand Eclipsing
Binaries or Magnitudes or Phases
So we have some work to do to “tidy up”
the light curve …
Tidying up the light curve
First right click on the vertical axis and select
Format Axis from the drop down menu
Then adjust the settings
( Minimum , Maximum , Major Step ,
Values in Reverse Order , at Max value ,
as appropriate )
Adjust the scale on the horizontal axis,
and with a few more adjustments,
the resulting light curve will be more like :-
Beta Lyrae in 2009 (GCVS)
3.2
Magnitude
3.4
3.6
3.8
4
4.2
4.4
0.0
0.1
0.2
0.3
0.4
0.5
Phase
0.6
0.7
0.8
0.9
1.0
Comparing observations with predictions
• In the preceding light curve, primary eclipse was around phase
0.90-0.95 and secondary eclipse was near phase 0.40-0.45.
• Based on the light curve alone, primary eclipse might be
slightly early or might be very late
• Observations over many decades tell us that the observed
eclipses of beta Lyrae are now very out of step with the period
in the GCVS – observed eclipses are later than predicted by
more than 30 orbital periods !