1. Colour Photometry in Astrophysics
Stan Walker
Variable Stars South

2. ABSTRACT
Colour photometry as a simple alternative to spectra was introduced with the development of filtered photoelectric photometry in the 1950s. It is cruder in some ways and relies heavily upon empirical relationships . But it is quicker and simpler than spectra and can reach much fainter magnitudes. This presentation initially explains what it is and how it has been used with a variety of practical examples. It then discusses observational possibilities in a range of astrophysical aspects of stars which show evolutionary or other changes in the light and colour curves.

3. WHY IS IT USEFUL?
Much of amateur observational astronomy is time series photometry – TSP – with the goal of detecting changes in the period of pulsation or eclipses. But this tells us little about the physical structure of the star itself.
In doing colour photometry we are moving into the realm of astrophysics – studying temperature changes and such things as gas and dust clouds, or the presence of an unseen companion star.
It also tells us much more about the star we’re looking at. Whether it’s a supergiant or main sequence object, at what stage of evolution, does the temperature change during a cycle and a variety of other things.

4. THE JOHNSON-COUSINS UBVRI STANDARD PHOTOMETRIC SYSTEM
This system is defined by filters the passbands of which are as shown in the illustration.
Also shown are some hydrogen Balmer absorption lines. Alpha in the R filter, beta, gamma etc. in B and U. There are many lines at the end of the series in the U filter.
But to match individual telescope/detector systems to the standard system it is necessary to work with pairs of filters.

5. Filters and Colour Systems
We have five filters to choose from in the UBVRI system. The system is set so that with an A0 type spectrum all values are identical. Quite sensibly the main filter to which everything relates is V – a reasonably close match to the average human eye. But how do we arrange the rest? We begin by defining filter pairs to give ‘colours’ – U-B, B-V, V-R, R-I and V-I.
Returning to the black body curve the temperature of a star is a fundamental property. By observation B-V has been determined over a wide range of stars so that a B-V colour or value can be changed into a temperature – see the next slide for an example. V-R can also be used but the scale is smaller and the hydrogen alpha line creates problems. So with the responses of CCD detectors the longer scale of V-I is often used but it has its limitations.
Other relationships are interesting. With stars enveloped in gas clouds the U-B/B-V colour will be distorted by excess U radiation. In cooler objects warm dust clouds often distort the V-R/R-I relationship. So the colours in many cases indicate that the target star is complex with a shell of ejected material.

6. ANOTHER VIEW OF COLOUR & TEMPERATURE
Two stars K at left K at right.
Hotter stars Vega 9600K Deneb 8500K Sirius 9900K
Cooler stars beta Ceti 4800K Aldebaran 3900K Mira K

7. AN EMPIRICAL B-V TEMPERATURE RELATIONSHIP
Relationships
Spectral-Colour
Vmag – filter colours
Temperature at surface
Luminosity correction for adding to M(V)
Each luminosity class is different I - VII
So what do we do with all of this?

8. THE ECLIPSING BINARY V777 SAGITTARII
This star is very unusual. It comprises a K5Ib supergiant and an A type companion. Eclipses occur every days with a 2 day ingress or egress and totality of 51 days. Similar to zeta Aurigae.
The table of supergiant colours gives 1.60 for B-V and 1.80 for U-B indicating some reddening due to interstellar material but this is not unexpected, given that it lies within 3o of the direction of the galactic centre. This suggests that the original mid-B class of the hot star is probably correct , with unreddened B-V of and U-B of
State V B U B-V U-B
Uneclipsed
Eclipsed
Change
Hot A Star

9. KZ PAVONIS – ANOTHER BINARY STAR
This is a fairly typical Algol EB showing a primary and secondary eclipse with a slight reflection effect which causes the star to be brightest near the secondary eclipse.
The primary eclipse appears partial, but may be marginally total, and is slightly late if the light elements of the General Catalogue of Variable Stars are used. So either the original period or epoch is wrong, or the period is changing slightly. But the secondary eclipse appears total. The average B-V of the system is 0.38, indicating a combined temperature of ~6700K. At primary eclipse the colour is 0.63, so that the temperature of the cool star is
~5800K, and at secondary eclipse when we see only the hot star, 0.30 or ~7200K..

10. DWARF NOVA STRUCTURE & OUTBURSTS
Cool star in contact with Roche lobe boundary
White dwarf star with disc
Outbursts associated with overful disc collapse, accretion heating of white dwarf
Now little for amateurs but monitoring frequency of outbursts

11. COLOUR LOOPS IN DWARF NOVAE
VW Hydri is an SU UMa star with long and short outbursts. It has a short orbital period of 107 minutes.
The colour loop is similar to other CVs but the initial rise is dominated by an apparent cooling of B-V from 0.10 to There is also a pause at this level.
From then on the rise is similar to around B-V and U-B But the colours continue to move blueward in the initial stages of the decline. In quiescence it appears considerably hotter than SS Cygni at B-V 0.10, say 9000K.
The initial cooling may be associated with the partial collapse of the disc obscuring the white dwarf for a time but after that we see accretion heating.
VW Hydri
Graphs from Jeremy Bailey - measures from Auckland Observatory

12. COLOUR LOOPS IN DWARF NOVAE
A cooler star than VW Hydri. The quiescent state has B-V at 0.40 but U- B at An object at ~7000K with a luminous gas component.
Rise sees apparent temperature increase – B-V 0.2, U-B 0.1, normal
At maximum B-V -0.15, U-B -0.80, colours of a normal early B star.
Decline sees B-V change by 0.55 to original state, U-B by 0.10.
What have we seen? During the rise the white dwarf component become much hotter and dominates the energy output. At maximum the radiation resembles a black body.
At minimum the system is much cooler with strong emission from excited gas
SS Cygni
Graph from Jeremy Bailey.

13. COLOURS AS EVOLUTIONARY MARKERS IN PULSATING STARS
BH Crucis was discovered by Ron Welch of the Auckland Observatory in This graph shows the light curve and colours for the eight years after discovery.
It is a dual maxima Mira with a period then of 421 days. Note the large colour/temperature changes during a pulsation cycle.
There is also a marked strengthening of the U-B colour during the second maximum. Why???

14. COLOUR & TEMPERATURE CHANGES
A few Mira and other cool LPV stars have shown period changes. R Hydrae, R Aquilae and R Centauri – the latter two are still in progress. These take one to two centuries to complete and are usually attributed to a helium flash event.
But three stars have shown period changes of ~25% over two decades – BH Crucis and LX Cygni. This may well be a change in the pulsation mode overtone. T Ursae Minor is another.
Larger than normal colour change during cycle
Distinct change in colour after period change
Much cooler star
Indications of large expansion of radius
We’re measuring this star again in

15. BH CRUCIS
The Periodogram above shows the change from the 421 days of the first five cycles to the current 525 days.
At the top left are individual measures of some cycles with them averaged in the lower graph.
Since the star has brightened and cooled then the relationship L = T4 * R2 indicates a considerable expansion.
Work with intensities

16. THE CEPHEID l CARINAE
Everyone looks at this star. The graph shows the actual filter curves rather than B-V and U-B. Whilst pulsating variable stars have the greatest amplitudes at shorter wavelengths this star is extreme in that the U amplitude is almost three times that in V. Maxima also occur earlier at shorter wavelengths.
There has been one major period change about 50 years ago and there may be cyclic variations on a time scale of about a decade.
The small amplitude in V and the larger change in the U filter suggest that there may be a substantial contribution from a rather red star in the measures.
U Carinae dV = 1.2 dU = 2.7

17. L2 PUPPIS - A BRIGHT SEMI-REGULAR
L2 Puppis was a bright semi-regular variable star for most of the 20th century. Over the last few decades it has faded so that at maximum it now reaches only 6.0 visually.
The inverted U-B colour curve we thought indicated that there may well be a fainter blue companion which affects the colours. Some DSLR measures of this star would be valuable
Like most Miras and SR stars it switches between two periods, in this case and 135 days, shown in the lower graph where the vertical scale shows days early – or late +.

18. L2 PUPPIS – MORE RECENT IDEAS
The dust cloud ejection model ~2000, later Kervella et al, detected the actual gas and dust cloud as visible nebulosity
This explained colour changes measured by the Auckland group
Emission from gas cloud affects B and U
B-V and U-B get redder as the star fades – but emission from nebula remains constant or may brighten
Terry Bohlsen in 2016 has U-B even brighter although the star is two magnitudes fainter than the curves shown in the previous slide.
What we’re now seeing is that whilst the star’s B-V and U-B are fainter the ultra- violet emission from the gas in the cloud remains the same. Thus the measured B-V and U-B star plus U-B gas are identical.

19. WHAT COLOUR PHOTOMETRY CAN AMATEURS USEFULLY DO?
Cepheids
Miras
Semi-regular stars
Eclipsing binaries
LPVs, RV Tauri, Type 2 Cepheids or W Virginis stars
S Doradus stars, Z Andromedae stars, all with erratic brightenings
Look at Variable Stars South website or the posters about what we do

20. CEPHEID COLOUR PHOTOMETRY
One aspect of our Cepheid project is TSP – the monitoring of period changes
We’ve seen two examples of evolutionary changes in other types of stars – BH Crucis and L2 Puppis
DSLR measures in BVR are aimed at detecting colour and light curve shape changes. Cepheids are very regular – but not perfect – in their pulsations.
ST Puppis is a very erratic pulsator and is certainly low-mass highly-evolved
RS Puppis is surrounded by a dust shell – why?
If we don’t look we’ll never know

21. MIRA COLOUR PHOTOMETRY
Study of Miras by RASNZ VSS, BAA, AAVSO TSP study of period changes
Success rate ~1-5% perhaps, per century – not all that exciting
Some Miras show humps and bumps on LC or Dual Maxima
These seem to be better candidates for period changes
Measure B and V with DSLR cameras to study temperatures
CCD cameras can do BVRI
These stars are bright in J and H but the amplitudes are low
Leave the standard TSP period change monitoring to the visual observers

22. HIGHLY EVOLVED LOW MASS STARS
Look at the mid-range brightness/ temperature area MV 0.0 to -5.0
Different types of stars in apparent behaviour
Probably closely related
Red SR stars RV Tauri W Virginis
All low mass, highly evolved, luminous
Faster evolution due to luminosity/mass ratio
L2 Puppis a good example. Is it an R CrB star in the making?

23. CONCLUSION
There are many areas where amateurs can make very useful contributions to
astronomical research beyond visual measures of stars.
The simplest area is BVR photometry of brighter stars using DSLR cameras with inbuilt filters
More expensive but able to reach fainter magnitudes is CCD photometry or classical photometry using single star detectors.
BVRI photometry is suited to cooler objects, JH photometry extends this into the infra red. UBV photometry is suited to hot and often massive stars. Emission objects often require full UBVRI filters.
Variable Stars South has many projects with realistic short time scales for results. Members exchange advice or mentor newcomers and cooperate on specific targets. See our posters around this room.

24. There are other applications.
Albert Jones rang AO February 1987 – I think I’ve found a nova or SN! We made the first UBV measures. And repeated the following night.
In the early stages the expanding shell is black body like so B-V gives a good temperature. So we knew the temperature and brightness on nights 0 and 1.
By using L = T4 * R2 the drop in temperature shown by B-V must be compensated by an increase in R. A simple calculation gave a number which transformed into ~10,000 km/sec. Hence it was a supernova.
Cepheids are fairly regular pulsators. This involves a movement of the measured surface towards and away from the observer. Applying the same relationship the relative radius at any one measure can be determined. So dR/dT provides a velocity in km/sec. Subtracting the known velocity relative to the Sun we can construct a radial velocity, RV, curve.