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By Conaire Deagan

Supervised by Dr Ben Montet

Star-spots, stellar

dynamos, and

habitable exoplanet

astrometry

16,000-km-wide active sunspot region imaged on January 28, 2020. Credit: NSO/AURA/NSF

c.deagan@unsw.edu.au conaired.github.io

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This is a star

This is a planet

Planet pulls on star

Some people want to measure this

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Some people want to measure this

Planet pulls on star

However,

Stellar activity

is a roadblock

Spots

Flares

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How much do

stars wobble*?

* Photometric Centroid

Motion

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HH

What is the magnitude of the stellar noise?

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HH

Ca-II Filter

<---------------

Blue Filter

---------------->

Over 60 000 images
Over an entire solar cycle (~10years)
Used three different wavelengths

Data from the Precise Solar Photometric Telescope (PSPT) instrument at the Mauna Loa Solar Observatory (MLSO)

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Absolute

The wavelengths between the filter differ by 16nm

The jitter is between 1-2 orders of magnitudes bigger for Ca-II

In all wavelengths, the STD in the X (East-West) direction is ~10% higher than the in the Y (North-South) direction.

Can infer that spots are rare at the rotational pole.

So, I got the data, processed it and ended up with this plot – the Absolute activity induced astrometric Jitter. I’ve only plotted the blue filter and the calcium filter for clarity – the red is quite similar to the blue. The Y-axis here is aligned with the rotational pole, and the X axis is normal to this, i.e. essentially latitude and longitude – the units here are milli solar radii.

Now I want to emphasise that these wavelengths are only 16nm apart, but you can see that the magnitude of astrometric noise is between 1-2 magnitudes different.

I’d also like to note that standard deviation in the equatorial X axis is roughly 10% higher than in the Y axis – which can allow us to infer that Sun-spots rarely form near the poles. We already obviously know this for the Sun, but this an indication about what we could possibly learn about the distribution of star spots on other stars using astrometric telescopes and hence learn some more about stellar dynamos in other stars.

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~ 1μas signal

(Expected from an Earth-analog at Alpha Cen )

It’s possible to detect an Earth-analogue planet if the wavelength filter selection is wise

So we can plot the jitter over time – here the Y-axis is the standard deviation of the jitter on a log scale, and we can quite clearly see the presence of the solar-cycle. So it follows that by observing other stars with astrometric telescopes we can also potentially learn more about any stellar cycle.

Anyway – This is roughly the expected signal that an Earth-like planet around alpha-cen would give – about 1 micro arcsecond deflection – which very roughly corresponds to a couple of milli solar radii.

Clearly, we should avoid the Calcium lines – or any other particularly active wavelengths . We can also see that the astrometric noise of a sensible wavelength choice is about 10x smaller than the expected planetary signal.�So that’s awesome – we have shown that astrometric noise due to stellar activity won’t prevent these missions. But while I was doing this work I discovered something even more interesting.

Add some dates in words or in a textbox

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Region that has been cleaned

Region that has not been cleaned

Does this matter? Yes.

This region is where flares have the largest impact

It’s a fairly large section of the solar disc

Has a lever-arm like effect on the centroiding

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Magnitude of photometric centre deflection has been increased by a factor of 500.

This pattern probably contains information about the star

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Magnitude of photometric centre deflection has been increased by a factor of 500.

This pattern probably contains information about the star

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Magnitude of photometric centre deflection has been increased by a factor of 500.

Rendering this is computationally expensive

(2048x2048 ~ 4.2 million pixels per frame)

The path that is traced out can be complex

You can see on the right that depending on the set-up the paths traced can be quite complex – thus can contain a lot of information. However, the gif you are seeing has about 4.2 million pixels, and has on the order of 100 frames – so you are looking at about half a billion pixels which is computationally expensive. While you can scale the resolution down , for a number of reasons, this rapidly destroys the signal. So we need another way to generate these curves.

Geometrically, these curves turn out to be essentially damped roulette curves, somewhat similar to elliptical catenarys. I explored trying to generate these curves geometrically but unfortunately there is no easy analytical functions describing these. However, it did lead me to a much more efficient way of calculating these curves. Instead of rendering the full image,

Cut stuff here

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Instead, render this.

Much quicker
Equally spaced

Easy to scale resolution up and down
In the limit, the paths are the same

(Fibonacci Spiral Covering)

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The Sun

Circa Oct 2014

Simulated image

Expected signal

(Assuming no spots on the back of the Sun)

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Typical Corner Plot of Model Output

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Reasonable range for ‘large’ spots on the Sun

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On the Sun, star spots usually appear within a band of latitudes

�Roettenbacher et al. 2016, Nature, 533, 217

This is not the case on ζ- Andromedae

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Future Work: Investigating Stellar Dynamos

We can probably determine the presence or absence of an Sun-like dynamo

Given a number of large enough spots over a long enough period of time

We can constrain the latitude of star spots to within 10s of degrees.
Using hierarchical Bayesian modelling, we can infer the latitude and spread of spots.

Credit: NASA

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Summary

Depending on wavelength, astrometric recovery of planetary signals is possible

We can infer the inclination of stars to high precision

We may be able to detect the presence/absence of a Sun-Like dynamo

c.deagan@unsw.edu.au conaired.github.io

Photo credit: Mike Garbett, Walsall, UK. Equipment: Lunt 60, Baader Ceramic Wedge, DMK41

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“Observed” Data

Do Random Search of Parameter Space

Using best set of parameters, perform a minimisation

Nelder-Mead

Algorithm

TNC

Algorithm

Save best set of parameters

Repeat N-times adding an extra spot each repeat

Use Bayesian Information Criterion to select best model.

Perform an MCMC to recover parameters with uncertainties.

Model Fitting

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Planet is inside the heliospheric current sheet at all times

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Planet is only periodically within the heliospheric current sheet

==> Different Atmospheric chemistry, different planetary magnetic field, etc

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What about TOLIMAN?

Alpha Cen is a Binary system – can you recover the signal?

Yes! The two components have a significant difference in rotation period so you can use Fourier analysis to decompose the signal.

Isn’t the pointing inaccuracy of TOLIMAN too high for this?

That’s an engineering problem.
But yes, depending on pointing accuracy, for relative astrometry these results do not necessarily hold.
For absolute telescopes this would work

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Damped roulette curves?

In the differential geometry of curves, a roulette is a kind of curve, generalizing cycloids, epicycloids, hypocycloids, trochoids, epitrochoids, hypotrochoids, and involutes.

Roughly speaking, a roulette is the curve described by a point (called the generator or pole) attached to a given curve as that curve rolls without slipping, along a second given curve that is fixed