What will it finally take to accurately measure the distance to Betelgeuse?

Question

Comments below What is the maximum distance measurable with parallax? discuss challenges associated with parallax measurements of Betelgeuse and link to Wikipedia’s Betelgeuse; Distance measurements which contains the intriguing paragraph:

In 2008, using the Very Large Array (VLA), produced a radio solution of 5.07±1.10 mas, equaling a distance of 197±45 pc or 643±146 ly.⁸³ As the researcher, Harper, points out: "The revised Hipparcos parallax leads to a larger distance (152±20 pc) than the original; however, the astrometric solution still requires a significant cosmic noise of 2.4 mas. Given these results it is clear that the Hipparcos data still contain systematic errors of unknown origin." Although the radio data also have systematic errors, the Harper solution combines the datasets in the hope of mitigating such errors.⁸³ An updated result from further observations with ALMA and e-Merlin gives a parallax of 4.51±0.8 mas and a distance of 222 (+34/−48) pc.[10] Further observations have resulted in a slightly revised parallax of 4.51±0.80.¹⁰

⁸³Harper et al. (2008) A New VLA-Hoppocaros Distance to Betelgeuse and its Implications

¹⁰Harper et al. (2017)A Updated 2017 Astrometric Solution for Betelgeuse

Looking at section 3.1 of Harper et al. (2008):

As discussed in Section 1, Betelgeuse required a significant additional error source (cosmic noise) to obtained the expected χ2. The actual nature of this cosmic noise is not known but it may be related to photocenter movement which is unlikely to be random in position on short timescales and would likely provide a systematic error in the astrometric solution. The position angle of the star's rotation axis has been measured from spatially resolved ultraviolet Hubble Space Telescope spectra. Uitenbroek et al. (1998) found ~55° (measured East of North) from absorption features in Goddard High Resolution Spectrograph data, and Harper & Brown (2006) found ~65° from emission features in multi-epoch Space Telescope Imaging Spectrograph data. The distribution of photocenters, perhaps driven by convective and Coriolis terms, may have a special relation to the rotation axis. The stellar proper motion vector also has a position angle of 68° and brightness fluctuations that occurred preferentially near the stellar equator might induce scatter in the parallax displacements, although fluctuations due to stellar rotation itself, would be unlikely because of the ~17 yr rotational period (Uitenbroek et al. 1998).

If I understand correctly; the problem with measuring Betelgeuse's position accurately is that it is so large and non-uniform that its "photocenter" (radio, optical, or otherwise) can be significantly different than its center of mass.

And the problem with obtaining accurate parallax determinations is that its non-uniformity changes on timescales comparable to a year. If it were much faster or much slower, it would not be so much of a challenge.

Interferometric optical imaging of Betelgeuse confirm dramatic non-uniformity across its disk.

Question: What will it finally take to accurately measure the distance to Betelgeuse?

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To see how nonuniform Betelgeuse appears optically: (feel free to edit and add better links)

• this answer to What else could the Event Horizon Telescope Observe?
• this answer to How far have individual stars been seen by radio telescopes?
• Why can't the surfaces of stars be observed? links to Wikipedia's List of stars with resolved images
• This answer to Betelgeuse in false colors, is this common?

Answer 1

The problem is that the apparent diameter of Betelgeuse is about 50 mas (milliarcsecond --- 1 mas is about 5 nano-radians) while its parallax is about 5 mas and its shape and surface brightness are both irregular and variable.

Given that, the current measurements are amazingly accurate. So I can identify about three approaches to doing this measurement, and I don't know enough to know which one(s) might really work, or which might be expected to work first.

1. Measure the distance without using parallax. This most likely means getting an accurate estimate of the absolute brightness or all, or part of, the disk of the star and comparing that with the apparent brightness. Spectroscopy might give an accurate idea of the temperature, which should in turn allow the brightness to be calculated and interferometry might allow the measurement to be restricted to a small area near the centre of the disk which was not obviously a star-spot or anything.

2. Simultaneously image the disk and measure its position relative to background stars, allowing the position of the centre of mass to be estimated accurately.

3. Increase the baseline of the parallax measurement. A pair of telescopes on opposite sides of Saturn's orbit, for instance would have 10 times the baseline, and more or less ten times the accuracy.

Update: It seems the Gaia consortium now expects to work around the brightness constraints and get data for all stars. From the Wikipedia page

Although it was originally planned to limit Gaia's observations to stars fainter than magnitude 5.7, tests carried out during the commissioning phase indicated that Gaia could autonomously identify stars as bright as magnitude 3. When Gaia entered regular scientific operations in July 2014, it was configured to routinely process stars in the magnitude range 3 – 20.[57] Beyond that limit, special procedures are used to download raw scanning data for the remaining 230 stars brighter than magnitude 3; methods to reduce and analyse these data are being developed; and it is expected that there will be "complete sky coverage at the bright end" with standard errors of "a few dozen µas".[58]

I don't know how much that will help with Betelgeuse though, due to its large apparent diameter.

Answer 2

So the Hipparchos parallax of Betelgeuse doesn't seem accurate enough?

If only someone would launch an even more advanced astrometric satellite than Hipparchos.

Actually the ESA has launched an even more advanced astrometric satellite, Gaia, expected to operate from 2013 to about 2022. And it is possible that Gaia has already produced more accurate parallax measurements of Betelgeuse.

[Added 06-02-2020. Someone said that Betelgeuse is too bright for Gaia to observe. Since Betelgeuse is the 10th brightest star, excluding the Sun, as seen from Earth, that means that several of the stars that are brightest as seen from Earth can not be studied by Gaia. Possibly future space observatories will have the capability to measure those few very bright stars as well.]

And if that is not enough, possibly someday copies of the Gaia satellite, or even more advanced astrometric observatories, might be launched to the L4 and L5 points of Jupiter, among the Trojan asteroids.

Parallax observations made from Earth, or by satellites orbiting Earth, have a maximum possible baseline of about 2 Astronomical Units (AU) if made six months apart when Earth is on opposite sides of its orbit.

Observatory satellites at Jupiter's L4 and L5 positions would always be about 10.4 AU apart.

Observatory satellites at Saturn's L4 and L5 positions would always be about 19.08 AU apart.

Observatory satellites at Uranus's L4 and L5 positions would always be about 38.44 AU apart.

Observatory satellites at Neptune's L4 and L5 positions would always be about 60.12 AU apart. A baseline 30.06 times greater than using observatories on Earth.

And of course the observatory satellites in Jupiter's L4 and L5 positions would sometimes be on opposite sides of the Sun from those in Neptune's L4 and L5 positions.

And of course if replicas of the Gaia satellite, or even more advanced observatories, are sent out of the solar system in several different equidistant directions, they will eventually exceed the distance to Neptune's orbit and have even larger baselines to make their parallax observations from.

And that might be necessary to get extremely precise measurements of the positions and distances to the nearest stars before unmanned probes or manned expeditions are sent to them.

And of course one mission of unmanned or manned voyages to other star systems would be to make astrometric observations and parallax measurements from distances light years from Earth. For example, with a baseline of light years, the parallaxes of every star in the Andromeda Galaxy could be measured and a three dimensional map of it could made, in addition to mapping the positions of stars in our galaxy much more precisely.

[Added June 2 2020. Observations of the direction to Betelgeuese from Earth's orbit can produce a cylinder of space with the diameter of Betelgeuse and extending hundreds and thousands of light years into space. Betelgueuse is somewhere along that cylinder of space. Observations of the direction to Betelgueuse from another star system light years away would produce a similar cylinder with a different orientation. Where the two cylinders partially or totally intersected would be where Betelgeuse is, and could be a much shorter length of cylinder than produced by observations from only one solar system.]

So possibly the distance to Betelgeuse will be measured precisely sometime before the first unmanned or manned spacecraft are sent to the nearby stars.