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Mapping Stellar Surfaces via Simulation-Based Inference

Conaire Deagan

Macquarie University Seminar

21st August 2026

Étienne Léopold Trouvelot, Group of Sun Spots, 1875

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Conaire Deagan, c.deagan@unsw.edu.au, conaired.github.io

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What do I mean by “mapping” stellar surfaces?

vs

Immaculate

maculate

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Why map stellar surfaces?

  • Why not?

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  • Tells us about:
    • The inside of stars
    • The outside of stars

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Why is this a problem?

unresolved

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Star makes signals

From signals make star?

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Can you recover a stellar surface from signals?

Sort of…….

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Can you recover a stellar surface from signals?

Is it a unique surface?

Yes, you can get a solution

No, there are many solutions

How many?

Technically, infinite.

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Are all solutions equally valid?

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Rotating

(modified) figure 1 of Luger et al 2021a

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<-- Possible Surfaces -->

<-- Possible Surfaces -->

Likelihood

Posterior

<-- Probability -->

<-- Probability -->

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Discrete spot model

  • Latitude
  • Longitude
  • Radius
  • Contrast

4 params

x N spots

  • Radius and contrast are degenerate

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  • Ordering degeneracy += Multi-modality

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  • Changing dimensionality

Solvable, but makes sampling hard

Conaire Deagan, c.deagan@unsw.edu.au, conaired.github.io

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Discrete spot model priors

  • Spots are discrete circles, with sharp edges
  • (Usually) single brightness

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  • Distributed to maximise entropy - e.g. Vogt, Penrod, Hatzes 1987

Lanza, Bonomo, Rodono 2007

Can sample and get a posterior, but often get stuck in local minima if not careful

Conaire Deagan, c.deagan@unsw.edu.au, conaired.github.io

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Pixel Grid Model

  • Generally better

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  • Must choose pixel size 🡪 limits localisation

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  • Comes from matrix inversion
    • Regularise with tikonov
    • Overly smooth spots

Matrix inversion, by default, gives a single solution

(not very Bayesian)

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Spherical Harmonics

 

 

 

 

 

 

 

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Spherical Harmonics

 

Cons:

  • Hard to enforce priors
  • Very high dimensional

Pros:

  • Very nice mathematically
  • Good for information theory
  • Rotations are a breeze
  • Can make any shape

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Want we want from a model prior

  • Spot shape flexibility
  • Arbitrary number of spots
  • Compact spots
  • Sparse surfaces
  • Positive flux

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Easy with SH

Easy with SH

No closed form

No closed form

No closed form

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Situation with Spherical Harmonics

  • Hard to sample
  • Analytic models infeasible
  • But useful from an information theory perspective
    • See Deagan & Montet 2026, Taaki et al 2026a/b, Luger et al 2021a, Dholakia & Pope 2026

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  • Just use Simulation-Based Inference (SBI) !

Conaire Deagan, c.deagan@unsw.edu.au, conaired.github.io

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SBI

Black box

Signals go in

Surfaces come out

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SBI vs MCMC (+ variants)

SBI

MCMC

  • Approximates a posterior

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  • Prior can be inferred from data

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  • Requires training a NN

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  • Gives full posterior as a single forwards pass

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  • Gives actual posterior

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  • Needs analytic prior

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  • No training required

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  • Need many many samples to get posterior

Conaire Deagan, c.deagan@unsw.edu.au, conaired.github.io

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My Model

Black box

Signals go in

Surfaces come out

Photometric light curve

and/or X astrometric signal

and/or Y astrometric signal

Full posteriors of:

  • 961-D Spherical harmonics coefficients (L = 30)
  • The observers inclination
  • The noise levels

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My Model

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My Model

Variational Auto-Encoder

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My Model

Variational Auto-Encoder

Embedding Network

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My Model

Variational Auto-Encoder

Embedding Network

The flow

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The Variational Auto-encoder

Encoding network

Latent space

Decoding network

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The Variational Auto-encoder

Encoding network

Latent space

Decoding network

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The Variational Auto-encoder

Encoding network

Latent space

Decoding network

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The Variational Auto-encoder

Encoding network

Latent space

Decoding network

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The Variational Auto-encoder

Encoding network

Latent space

Decoding network

 

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The Variational Auto-encoder

Encoding network

Latent space

Decoding network

 

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The Variational Auto-encoder

Decoding network

Random latent draws

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My Model

Variational Auto-Encoder

Embedding Network

The flow

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My Model

Variational Auto-Encoder

Embedding Network

The flow

96D

~965D

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My Model

Variational Auto-Encoder

Embedding Network

The flow

96D

~965D

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My Model

~216x3 D

Embedding Network

~96D

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My Model

~216x3 D

Embedding Network

~96D

Learned summary statistic

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My Model

~96D

+

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My Model

~96D

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My Model

=

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My Model

Unobservable cap

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My Model

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My Model

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My Model

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My Model

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My Model� (Phot)

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My Model� (Phot + Astrometry)

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Photometry

Photometry + Astrometry

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Photometry

Photometry + Astrometry

SPOT LOCALISATION!

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Photometry + Astrometry

<-- Based on Sigma Gem!

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*noiseless

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Less False Positives

Less False Negatives

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Less False Positives

Less False Negatives

Better

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* noiseless

* noiseless

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* noiseless

* noiseless

With Noise

Black = visible sphere

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Conclusion

Using SBI, 100ppm photometry + TOLIMAN-like noise*, Sigma Gem is recoverable very well!

< --- My website

Conaire Deagan, c.deagan@unsw.edu.au, conaired.github.io

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Power at spot scales

Hope for smaller spatial scales?

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