1. From Point of Light to Astrophysical Model
The Research Reach of the Modern Amateur
Illustrated with a study of NSV 1000 (Hyi) by
Tom Richards & Col Bembrick
Southern Eclipsing Binaries Research Group of Variable Stars South
(VSS-SEBRG)
This presentation is online at
MOTIVATION
Encourage CCD/digital camera photometric research on variable stars
PIPELINE
Will illustrate by showing the pipeline for Eclipsing Binary research
That pipeline applies with changes to many other areas of variable star research
RESEARCH VALUES
Vitally important astrophysical laboratory
Common in the sky but mostly poorly studied
Each one can add something significant to our understanding
Excellent for amateur research

2. The Research Pipeline Observatory Setup Imaging
Calibration, Photometry
Light Curve
Time of Minimum
Curve Fitting with astrophysical parameters
Orbital Period
Astrophysical Model
Period Change
Publication

3. Observatory Setup – can you handle these?
Computer
Telescope with CCD camera, or telephoto digital camera
Driven mount to track a target all night
Continuous imaging all night
All-night imaging needs needs camera control software

4. Target for the night
What magnitude can you image with second exposures?
In the Ephemerides app find a target binary which:
Has an eclipse with >2h astronomical darkness either side
Eclipses near meridian
Is in your mag range
URLs for all software in the last slide.
signal/noise ratio > 1000
It may be a target you’ve followed before, or in the VSS-SEBRG list.

5. Colour Imaging? Digital cameras automatically take colour
Astro CCD cameras are greyscale, but can add photometric filters
Now take your night’s images – while sound asleep in bed.
I use Astrodon Johnson B and V, Sloan r’ and i’;
Be consistent in filter choice for multi-night work on a given target.
No photometric filter necessary for minima-timing work, red cuts moonlight.
Must use a photometric filter for astrophysical modelling.

6. Processing your night’s images
You may have many hundreds of images of same star field
Your processing software will do the following
Calibration (bias-removal, dark-subtraction, flat-fielding)
Photometry (raw measurement of star image intensities)
Star matching (across all your frames)
(I use MuniWin, a front-end to Daophot routines)

7. Preparing for light curve analysis
Find in your field a Comparison star (C):
You use C to obtain the difference V-C in raw mags across all your night’s images.
And find one or two checK stars (K)
K is used to test the stability (C-K) of C.
C should be:
About same colour index as your target star V (important)
About the same mag as V (quite important)
Near to V in the field (flat-fielding is never perfect!)
Some people use several C’s (ensemble) but this has problems
The raw mags are too unstable to use by themselves.
K Same criteria as for C, but they’re less important
C-K should stay constant in all your night’s images.
Stdev of C-K gives your mag error for V-C

8. Producing a light curve
Tell software to find V- C mag across all your night’s images (from one filter!)
And to measure C-K mag similarly
V-C mag process will output a light curve plot and mag data
Is the C-K plot flat?
What’s its standard deviation?
V-C vertical range 0.4 mag.
C-K vertical range 0.04 mag, stdev mag
And a table of <HJD, V-C mag, mag error> for all images
standard deviation in C-K as a realistic measure of the V-C error.

9. Finding the Time of Minimum aka Epoch, E
There’s special software that uses statistical or Fourier routines, etc.
Enter your output photometric data for V and ask it to find the time of minimum.
I use PERANSO and Minima25
It outputs HJD of minimum plus error.
The VSS-SEBRG explains what to do with it; we collect & publish these annually in a refereed international journal.

10. Get the orbital period P
Take time-series over several well-spaced nights & find several minima
Go to AAVSO’s VSX portal to find (approximate) period P
That’s a guide to finding your P from your minima
But it may be a bit different!
Catalogued period P (usually near enough to reality for point 3 below)
Catalogued zero epoch T0 (HJD of one minimum, usually near enough)
Also collected in VSS-SEBRG.
P is a publishable result.
A year’s work folded on the period of NSV (PERANSO)
P = / days

11. Obtain from VSX an historic time of minimum or epoch E0.
Calculate the time one of your minima should have occurred
But the minimum you Observed might be different
So plot O-C against cycle number for all your minima (and any others)
Has the period changed? En = E0 + nP (time of min. after n orbital cycles)
O-C and hence P Increasing, decreasing or constant, this is publishable!
O times getting behind C times at increasing rate, so P is steadily decreasing
(Erdem et al 2001A&A E)

12. Astrophysical Modelling (Richards & Bembrick, “A Photometric Study Of The Eclipsing Binary NSV 1000”, JAAVSO 2018)
What sort of binary can cause your (phased) light curve?
You will characterise the 2 stars by 3 sets of parameters (Assumed + Adjustable  Output)
Assumed (look them up)
T1, temp of brighter star
Gravity brightening,
Limb darkening,
Reflection coefficient
Adjustable (by you)
T2, temp of fainter star
Inclination of orbit, i
Fillout, f (“fatness”of light curve)
Mass ratio, q = m2/m1
Output (by modelling software)
Calculated light curve
3-D model of binary system
Shape size separation & luminosity parameters (relative!)
Light curve diagram is of your light curve
Assumed: T1 from colour index, rest from tables given T1. They affect uniformity of surface brightness of the 2 stars.
Adjustable: I is angle between axis of orbit and line of sight. 90deg when orbit edge-on (best eclipses)
F is actually a measure of gravitational potential (Lagrange points, Roche surfaces, etc.)
Output Assumed + adjustable params enable calculation of shape & LC of binary system. Calculated LC is overlaid on your LC, with residuals

13. Adjust the Easier Parameters
In software – we used BinaryMaker 3 (
Starting point: look up similar light curve in CALEB (
Effect of adjustments seen in calculated (“synthetic”) light curve.
Temperature, T2
Adjust temperature to match relative eclipse depths (too hot here)
Fillout, f
Try to to match “fatness” of light curve (too high here)
Inclination, i
Adjust to match eclipse depths (i too high here)
From CALEB get starting parameters
Temperature is of fainter star – it’s only temp diff that matters.
Fillouts same for contact binaries, so need only one.
In 3rd diagram, we had the eclipse depths right then changing the fillout changed the depths.
So the 3 params are not independent. Adjust them jointly.

14. That leaves the mass ratio (q)
Step 4, Mass ratio, q
Work through a range of values to find one that minimized the residuals (q-search)
Mass ratio wrong – overall poor fit
Residuals are sum of squares of point-by-point differences between calculated (synthetic) and observed LCs
Note minima fit too shallow, but had it right at Step 1.
Explain repeat & idea of convergence
Then repeat steps 1,2,3 & even 4
as often as needed (gasp!)

15. Visualising the Results
Red ellipses how orbits of mass centres of stars around the mass centre of the system (+ sign)
Publish!

16. How to make output parameters absolute
Photometric analysis only gives mass ratios and relative sizes & luminosities
2 ways to make absolute:
Doppler spectroscopy to measure orbital velocities (needs vastly bigger telescopes).
(not as reliable) Place the (brighter) star in the H-R diagram and then use mass-luminosity laws
Spectroscopy: Orbital velocities + inclination I + period P fixes absolute size of orbit, hence absolute masses & sizes.
Using H-R: Place on main sequence (reasonable assumption, & luminosity class probably known) then tables based on many star measurements give absolute masses & sizes.
Then tables then give absolute luminosities, & hence distance.

17. Getting going on this research
Review this presentation at
Read the VSS-SEBRG website
Contact Tom Richards to join the group & get data access etc.
Contact Tom for CCD mentoring & advice
Contact Mark Blackford for digital-camera mentoring and advice

18. That’s the end – of the beginning Here’s a list of the equipment and software used for the NSV 1000 project
Tom’s Equipment at Pretty Hill Observatory, Kangaroo Ground, Victoria, AU
RCOS 0.41 m Ritchey-Chretien OTA with automated instrument rotator, cooling, heating, focusing
Astro-Physics 1200GTO German equatorial mount
SBIG STXL-6303e CCD camera with Astrodon B, V, r’, i’ filters
Automated AstroDome
Boltwood Cloud Sensor II
Software on Windows PC
Ephemerides to select target
ACP to automate observatory
Clarity for sky monitoring
MaxIm-DL for camera control
MuniWin to process & measure images
PERANSO to analyse light curves
BinaryMaker 3 to model eclipsing binaries
CALEB to explore eclipsing binary light curves and models
EXCEL calculation and database spreadsheets supplied by VSS-SEBRG
Can’t read? Never mind. Presentation available on VSS website (previous slide)
Equipment listed is rather high-end. Don’t worry, a driveway C8 can do the job.