By Adam Rains
[email protected]
Optical interferometry is tricky. Unlike radio interferometers, which can have telescope separations measured in kilometres (or even across the entire planet in the case of the Event Horizon Telescope!), combining light in the optical is a tad more difficult, requiring that light be brought to some central location and combined in real-time, rather than digitally later on.
Optical interferometers are thus rarer beasts, but since spatial resolution improves with both increasing telescope separation and shorter wavelength, their resolutions can reach the sub-milliarcsecond level with telescope separations of a hundred to a few hundred metres. For reference, one milliarcsecond is about the size of an Australian $1 coin in Wellington, New Zealand when viewed from the northern tip of Queensland in Australia…so pretty small!
The Very Large Telescope Interferometer (VLTI) is unique globally and will continue to be the optical telescope with the highest angular resolution in the southern hemisphere, even as we move into the ELT era. It’s a very powerful facility, able to either combine light from its four 1.8 m Auxiliary Telescopes, or the four 8.2 m Unit Telescopes, with separations of up to 130 m or so. It has a diverse set of instruments covering a wide range of wavelengths, spectral resolutions, and science cases — from resolving the surfaces of giant stars all the way to studying the environments around black holes in the centres of galaxies including our own Milky Way.
For our science, however, spatial resolution was key — our goal was to measure the angular diameters of bright nearby stars to the 1% level (or better!). You might ask though: why use such an advanced facility as a simple measuring tape? There are many reasons! By combining an angular diameter with a bolometric flux through the black body relation (with fluxes obtained through some combination of precision photometry and spectroscopy, or photometry alone), you can obtain the effective temperature of your star to an accuracy and precision not accessible to other techniques. Add a parallax into the mix from the Gaia satellite, and you can work out a stellar radius. With these two measurements you can investigate the environments of planets around your stars, add complementary information to asteroseismic targets, as well as use the stars as temperature standards for spectroscopic surveys. Such information also lets you constrain theoretical models, plus test or build upon empirical relations, letting us understand more distant stars through our knowledge of those closer and more well studied. Moving to larger scales yet again, surface brightness relations which relate angular size to stellar colour are built from such precision measurements and underpin our extragalactic distance scales based on certain standard candles. To these ends, observing a diverse array of stars in temperature, gravity, and metallicity space is critical to ensuring our understanding of stars isn’t a narrow one.
We used the four 1.8 m Auxiliary Telescopes plus PIONIER, the shortest-wavelength (and thus highest spatial resolution) beam combiner on the VLTI to measure the angular diameters of 16 southern stars: 6 dwarfs, 5 sub-giants, and 5 giants (Figure 1 below, see Rains et al. 2020). Ten of these stars had no previous interferometric measurements, and the other six serve as a useful check on cross interferometer/beam-combiner consistency (this latter point is important for such a fundamental technique!). Our smallest star, HR7221, was only a tad larger in angular diameter than our coin from before and was close to the resolution limit of the facility. On the other hand our largest star, λ Sgr, was a factor of four larger and big enough for us to resolve the effects of limb darkening at different wavelengths.
This project involved many firsts for me: the first paper of my PhD, first hands-on stellar astronomy project, first time writing observing proposals as PI, and first time planning observations. Critically though, I needed to become familiar with propagating and accounting for uncertainty, as calibrating optical interferometric data for such extreme precision is a non-trivial endeavour. In order to account for sky, telescope, and instrumental responses, each science target observation must be bracketed by calibrator stars — each as close on sky, as close in magnitude, and as small in angular size as possible (a tricky combination given our stars are already among the brightest in the night-time sky!). For us, this meant two CAL1-SCI-CAL2-SCI-CAL3 observing sequences for each science target, with five unique calibrators in total (one shared between sequences)…so a lot of calibrators! Process this through the standard PIONIER data reduction pipeline, grab some bolometric fluxes from bolometric corrections to Hipparcos-Tycho photometry, add in some bootstrapping and Monte Carlo to account for correlated uncertainties, and you obtain angular diameters, temperatures, and physical radii to mean precisions of 0.82%, 0.9%, and 1.0% respectively. Voila!
The VLTI is the only telescope capable of this science in the southern hemisphere, and given the southerly declination of most of our stars, the only telescope capable of resolving them at all. The Australia ESO Strategic Partnership is critical in giving Australian researchers access to such a powerful facility, enabling Australian astronomers to do interferometry across all wavelengths.