Dale Kershaw all-sky camera
Dale Kershaw AllSky Camera 8bit Video Photometry
Six variable stars measured frame by frame in 2023 with the Dale Kershaw all-sky camera at the Canterbury Astronomical Society's R F Joyce Observatory in West Melton, Christchurch (Minor Planet Center observatory code R65).
- Four Cepheids
- β Doradusl Carinaeη Aquilaeκ Pavonis
- Two eclipsing binaries
- ζ PhoenicisV Puppis
Most periods agree with the published values within about two standard errors.
Section 1
Do the frames trace the star’s cycle?
Pick a star, then fold its frames on a trial period. If the period is right the scattered points line up into one curve.
- Kept frame
- Sigma-clipped
- In a thin bin
- Bin mean with standard error
- Model refitted at the chosen period
Six fitted periods, each within 0.58 % of the published value.
Section 2
Which period does the data prefer?
Instead of trying periods by hand, the periodogram scores every trial period at once; the tallest peak is the best fold.
- Literature period
- Fitted period
- Half the fitted period, eclipsing binary only
- Period the light curve is folded on
- Numbers above peaks are their periods in days
For five of the six stars the tallest peak is at the fitted period; for ζ Phoenicis it is at half that period.
Section 3
What would the star look like?
With the curves in hand, each star is rebuilt in 3D from published sizes and orbits, and its brightness follows our fitted curve.
Models are illustrative. Sizes and orbits are published values, not fits to this camera; only the brightness comes from the West Melton curve.
Size comes from angular diameters measured by long-baseline interferometry (Kervella et al. 2004, with the VLT Interferometer, for β Doradus, ℓ Carinae and η Aquilae; Breitfelder et al. 2015 for κ Pavonis), and brightness from the West Melton light curve above. Temperature is not measured, so it is solved from the other two using luminosity = radius² × temperature⁴. The slider exaggerates the size and colour swings; brightness is shown as it is.
η Aquilae sits near the edge of the camera frame, so its brightness curve is less certain than the others. The radius curve is a one-harmonic fit through 11 limb-darkened diameters.
κ Pavonis is a type II Cepheid, much smaller and older than the classical Cepheids here, and its period changes abruptly and randomly. Its diameters are uniform-disk values, and our brightness template is a classical-Cepheid shape, so both are only approximate for this star. The radius curve is a one-harmonic fit through 12 diameters.
The orbit, sizes and eclipse geometry are the solution Southworth (2021) fitted to TESS photometry and published radial velocities. The solid curve is our fit: a PHOEBE model of that system in the V band, with its depth and timing fitted to our frames. The dashed curve is the PHOEBE model itself, before fitting. Use the view buttons to look from Earth or from above, and drag to turn the system.
The masses, radii, temperatures and separation are the Andersen et al. (1983) values as summarised on James Kaler’s Stars page, not a fit to our data. The orbit is drawn circular and the 79° inclination is our reading of the Kaler page, so the geometry is approximate. Both stars are Roche surfaces: the secondary fills its lobe, which gives it a teardrop shape pointing at the primary, and gravity darkening makes each surface dimmer where gravity is weaker. The solid curve is our fit of a PHOEBE model in the V band, and the dashed curve is the PHOEBE model before fitting. Our eclipse is deeper than the model; the cause is unknown. Use the view buttons to look from Earth or from above, and drag to turn the system.
The ring marks the mean radius. The Sun is drawn at its true size, and the orbit rings show Mercury and Earth.
The sky as West Melton sees it. Drag to turn the system.
Looking down the orbital axis, with Earth toward the bottom. Drag to turn the system.
- West Melton fitted curve
- Bin means with standard error
- Derived curve
- Interferometric diameters
- West Melton fitted curve
- Bin means with standard error
- PHOEBE V-band model, before fitting
Model parameters and their sources
| Quantity | Value | Unit | Basis | Source and notes |
|---|
How the model is built
A Cepheid is a sphere shaded with a linear limb-darkening law. Its colour is the blackbody colour of the temperature at the current phase, with a little extra saturation so the hue shows on screen, and the surface mottling is decoration only. Glow and disc brightness follow the V-band flux from the West Melton fitted curve.
For the eclipsing binaries the orbit is solved with Kepler’s equation and the stars are placed about their common centre of mass. ζ Phoenicis is drawn as two spheres. V Puppis is drawn as two Roche surfaces: for each direction from a star’s centre the surface is found by bisection on the Kopal potential (a circular orbit with both stars rotating in step with it), at the potential that gives the primary its published radius and at the critical potential for the secondary, which therefore fills its lobe. Gravity darkening scales the local temperature as gravity to the power 0.25. Each star’s colour is the blackbody colour of its temperature and does not change across the surface. There is no reflection and no mass-transfer stream. The light curves are PHOEBE models in the V band, not computed in the page. Earth view looks along the line of sight with a very narrow field of view. Above view looks down the orbital axis.
The sky is always dark in this view, whichever theme the page uses.
Brightness is measured; size and orbit are borrowed from papers, and the table says which is which.
Section 4
The six stars side by side
The same measurements, one row per star.
| Star | Type | Frames fitted | Nights | Period (days)MeasuredLiterature | Amplitude or eclipse depth (mag)MeasuredLiterature |
|---|
- For eclipsing binaries the depth of the primary eclipse is shown; for Cepheids the peak-to-peak amplitude is shown.
Appendix A
How the frames were cleaned and fitted
The camera
- Camera and lens. The Dale Kershaw all-sky camera: a fixed ZWO ASI120MC colour camera with a 2.1 mm fisheye lens covering 150°.
- R F Joyce Observatory, West Melton, Christchurch: latitude −43.498°, longitude 172.350° east, height 100 m, as used in the analysis. Minor Planet Center code R65.
- Sensor. An unfiltered Bayer colour sensor. The page works from the video, which is 8-bit, 1280 × 960 pixels and H.264 compressed.
- Stars. About 2 pixels across. The Bayer pattern and the compression add scatter to each frame’s measurement.
- Lens fit. Fitted from the stars themselves in the Moon analysis, as an equidistant fisheye with two small distortion terms: focal length 594.6 px, image centre (698.2, 539.8) px. The 1280 × 960 frame covers 122° across the middle row and 92° up the middle column.
- Brightness. Corrected for position in the frame, which absorbs vignetting.
- Time. Each frame’s time is the stamp minus 15 s, taken as the middle of the exposure.
The measurements
- Each point is one frame of the camera’s video, measured by PSF fitting.
- Each is referred to a set of comparison stars of similar brightness.
- Magnitudes are on an approximate scale tied to catalogue values, not a standard filter.
- Frames the analysis flagged as unusable (low altitude, cloud, clipped stamps) are not in the data.
Cleaning
- Sigma clipping. A template is fitted to the frames. Frames more than — robust standard deviations from it are marked clipped, and this repeats until the set stops changing.
- Thin bins. Phase bins holding fewer than — frames are dropped by default.
- Refitting. The model is refitted to the kept frames whenever the fold period changes, so the curve, the bin means and the residuals all follow the period you choose.
The standard shapes
- What is fitted. Each star is fitted with a standard shape, leaving only the phase, the mean magnitude and an amplitude scale free.
- Cepheids. The V-band shapes of Yoachim et al. (2009), evaluated at the star’s published period. κ Pavonis is a type II Cepheid, so the classical shape is only an approximation for it.
- ζ Phoenicis. A PHOEBE model from the Southworth (2021) solution, with its published third light.
- V Puppis. A PHOEBE model from the masses, radii, temperatures and separation of Andersen and colleagues (1983) as quoted on the Kaler Stars page, with the orbital inclination set so the model matches the published V amplitude.
- Amplitude scale. It absorbs the difference between our camera and the V band. A scale far from one means the camera sees a larger or smaller swing than the model.
Timing and phase
- The camera clock drifts, by up to about 3 minutes, so eclipse timing is good to a few minutes.
- The photometry of each binary includes its faint companions.
- Phase is zero at maximum light for the Cepheids and at primary eclipse for the binaries.
- Times are days since the start of 2023, in UTC, except for ζ Phoenicis, whose times are barycentric.
Appendix B
References
- Leavitt, H. S., Pickering, E. C. 1912, Periods of 25 variable stars in the Small Magellanic Cloud, Harvard College Observatory Circular 173, 1–3.
- NASA, Hubble views the star that changed the universe, science.nasa.gov/missions/hubble/hubble-views-the-star-that-changed-the-universe.
- Kervella, P., Nardetto, N., Bersier, D., Mourard, D., Coudé du Foresto, V. 2004, Cepheid distances from infrared long-baseline interferometry. I. VINCI/VLTI observations of seven Galactic Cepheids, Astronomy & Astrophysics 416, 941–953, doi:10.1051/0004-6361:20031743.
- Breitfelder, J., Kervella, P., Mérand, A., Gallenne, A., Szabados, L., Anderson, R. I., Willson, M., Le Bouquin, J.-B. 2015, Observational calibration of the projection factor of Cepheids. I. The type II Cepheid κ Pavonis, Astronomy & Astrophysics 576, A64, doi:10.1051/0004-6361/201425171.
- Gieren, W. P., Fouqué, P., Gómez, M. 1998, Cepheid period–radius and period–luminosity relations and the distance to the Large Magellanic Cloud, The Astrophysical Journal 496, 17–30, doi:10.1086/305374.
- Yoachim, P., McCommas, L. P., Dalcanton, J. J., Williams, B. F. 2009, A panoply of Cepheid light curve templates, The Astronomical Journal 137, 4697, doi:10.1088/0004-6256/137/6/4697.
- Southworth, J. 2021, Rediscussion of eclipsing binaries. Paper I. The totally-eclipsing B-type system ζ Phoenicis, The Observatory, arXiv:2012.05559.
- Andersen, J., Clausen, J. V., Giménez, A., Nordström, B. 1983, Absolute dimensions of eclipsing binaries. II. The early-type semidetached system V Puppis, Astronomy & Astrophysics 128, 17–28.
- Kaler, J., V Puppis, Stars, University of Illinois, stars.astro.illinois.edu/sow/vpup.html.