Investigating Super/Granulation with Structure Functions

Jay Fitzpatrick (He/They)

Including: Ancy Anna John, Niamh O’Sullivan, Suzanne Aigrain, Michaël Cretignier

Supervisors: Tim Naylor and Raphie Haywood

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GPRV Workshop, All Souls College, September 2026

Email: ef517@exeter.ac.uk

Can we characterise Supergranulation in stars other than the Sun?

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Talk sections

1. Basics of structure functions (SFs) and why they’re useful
2. Method development: finding granulation in HD 166620
3. Using archival asteroseismology data to investigate supergranulation in ⍺ Cen A

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Talk sections

1. Basics of structure functions (SFs) and why they’re useful
2. Method development: finding granulation in HD 166620
3. Using archival asteroseismology data to investigate supergranulation in ⍺ Cen A

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What is a structure function?

• SFs are a statistical tool and tell you about (RMS) variability/correlation as a function of time-scale

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Lakeland+ 2024, Simonetti+ 1985

Come and chat for resources!

Bin containing pairs of points with similar separations in time

SF Crash Course - Calculation

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RV plot with lines showing time scales calculating SF, maybe animation

F(t)

t

time-scale bounds

( =Δt )

Number of pairs of data points in the bin that is summed over

What is a structure function?

• SFs are a statistical tool and tell you about (RMS) variability/correlation as a function of time-scale

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Lakeland+ 2024, Simonetti+ 1985

Come and chat for resources!

…

Bin containing pairs of points with similar separations in time

What is a structure function?

• SFs are a statistical tool and tell you about (RMS) variability/correlation as a function of time-scale
• In flat regions, uncorrelated noise dominates that time-scale

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Lakeland+ 2024, Simonetti+ 1985

Come and chat for resources!

What is a structure function?

• SFs are a statistical tool and tell you about (RMS) variability/correlation as a function of time-scale
• In flat regions, uncorrelated noise dominates that time-scale
• Slopes indicate correlation

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Lakeland+ 2024, Simonetti+ 1985

Come and chat for resources!

What is a structure function?

• SFs are a statistical tool and tell you about (RMS) variability/correlation as a function of time-scale
• In flat regions, uncorrelated noise dominates that time-scale
• Slopes indicate correlation
• Short time-scale noise can dominate a SF

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Lakeland+ 2024, Simonetti+ 1985

Come and chat for resources!

SFs have a cumulative nature

Orange and green time-series look very similar!

Why SFs for super/granulation?

• We learn about astrophysical and instrumental noise in a model free way

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Why SFs for super/granulation?

• We learn about astrophysical and instrumental noise in a model free way
• They expose both periodic and aperiodic signals

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Why SFs for super/granulation?

• We learn about astrophysical and instrumental noise in a model free way
• They expose both periodic and aperiodic signals
• Using new ways of manipulating SFs, we can learn about our data by binning the time-series

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Things to remember

Structure functions can track RMS as a function of time-scale!

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Things to remember

Structure functions can track RMS as a function of time-scale!

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Things to remember

Structure functions can track RMS as a function of time-scale!

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Bin in time-scale

Things to remember

Structure functions can track RMS as a function of time-scale!

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Bin in time-scale

Bin in time

Things to remember

Structure functions can track RMS as a function of time-scale!

Supergranulation in the Sun

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Anna John+ 2025 (inc. Fitzpatrick), based on work in Lakeland+ 2024

Orange shaded region gives scatter of Solar SFs

• Strong gradient in solar SFs from Supergranulation (Lakeland+ 2024)

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• Time-scale ~1d

Talk sections

1. Basics of structure functions (SFs) and why they’re useful
2. Method development: finding granulation in HD 166620
3. Using archival asteroseismology data to investigate supergranulation in ⍺ Cen A

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Granulation on the quiet K-dwarf - HD 166620

• 2 Nights of HARPS-N RV data
• Remarkably little magnetic activity (Maunder minimum analogue)
• We expect granulation to be the dominant source of astrophysical noise here

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Dalal+ 2023

Anna John+ 2025 (inc. Fitzpatrick)

The quiet K-dwarf - HD 166620

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Anna John+ 2025 (inc. Fitzpatrick)

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SF of HD 166620 (purple stars) is

• Remarkably flat - (uncorrelated noise)

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• But highly featured (some signal at 23 mins?)

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Orange shaded region gives scatter of Solar SFs

The quiet K-dwarf - HD 166620

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Anna John+ 2025 (inc. Fitzpatrick)

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SF of HD 166620 (purple stars) is

• Remarkably flat - (uncorrelated noise)

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• But highly featured (some signal at 23 mins?)

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How can we investigate if this hump feature indicates a signal?

Binning�time-�series

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Binning�time-�series

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• Assume a time series contains

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• Assume only the uncorrelated noise RMS is reduced when we bin

We can calculate the RMS contribution of each

The quiet K-dwarf - HD 166620

Bin the time-series in groups of 3

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Anna John+ 2025 (inc. Fitzpatrick)

Original SF

The quiet K-dwarf - HD 166620

Bin the time-series in groups of 3

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Anna John+ 2025 (inc. Fitzpatrick)

Original SF

WN

fall

The quiet K-dwarf - HD 166620

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Anna John+ 2025 (inc. Fitzpatrick), see also for equations

Original SF

Binned in threes SF

WN

fall

Data

fall

Bin the time-series in groups of 3

Correlated noise RMS:

19 ± 5 cm/s

Were we actually probing granulation?

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Signal has characteristics of granulation!

GP sims of granulation (by Niamh)

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White noise

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Anna John+ 2025 (inc. Fitzpatrick), GP sim credit: Niamh O’Sullivan

Signal has characteristics of granulation!

GP sims of granulation (by Niamh)

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White noise

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Anna John+ 2025 (inc. Fitzpatrick), GP sim credit: Niamh O’Sullivan

We agree with data driven models for the system.

Error bars are scatter not uncertainties!

In the future we want to check our methods against physics-based simulations.

What can we do with a longer baseline?

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Talk sections

1. Basics of structure functions (SFs) and why they’re useful
2. Method development: finding granulation in HD 166620
3. Using archival asteroseismology data to investigate supergranulation in ⍺ Cen A

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5 nights of ⍺ Cen A

• Dominated by the P-modes
• Need to decide on a binning of the time series to use to look at the SFs

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⍺ Cen A

HD 166620

Sun

⍺ Cen A YARARA V2 RVs from Michael Cretignier. Quiet sun RVs from Niamh O’Sullivan

Fitzpatrick+ in prep.

Periodicity hump???

Slope going into 1 day???

5 nights of ⍺ Cen A

• Dominated by the P-modes
• Need to decide on a time series binning to use to look at the SFs

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Fitzpatrick+ in prep.

Figure with solar, HD 166620 and alf Cen A

⍺ Cen A

HD 166620

Sun

⍺ Cen A RVs from Michäel Cretignier. Quiet sun RVs from Ben Lakeland

Can we find a cadence binning to reduce the p-mode contribution enough?

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A time-series (one of Niamh’s GP sims)

Fitzpatrick+ in prep.

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A time-series (one of Niamh’s GP sims)

Binned up by different amounts

Fitzpatrick+ in prep.

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We calculate structure functions of the time-series

Then take slices down in 𝜏 and compare the behaviour with how we expect uncorrelated noise to behave

Fitzpatrick+ in prep.

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Fitzpatrick+ in prep.

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Signal

Uncorrelated

Fitzpatrick+ in prep.

⍺ Cen A

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Bazot+ 2007 mention extra noise due to guiding errors in nights 4+5

⍺ Cen A

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Maybe still a turning point at ~6 mins?

Correlation from p-modes

P-modes bin out more like uncorrelated noise

A (new) signal appears?

Bazot+ 2007 mention extra noise due to guiding errors in nights 4+5

Next steps

• Look at structure functions at interesting points on the previous plots
• Obtain a signal RMS amplitude (that could be attributed to Supergranulation?)
• Comparisons with physics-based models

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Fitzpatrick+ in prep.

Takeaways

• A structure function is a statistical tool allowing us to probe variability as a function of timescale
• Binning up time-series and looking at how the SF changes can reveal hidden signals
• Signals can be characterised with few model assumptions
• Granulation signal independently detected in HD 166620 and agrees with other methods
• Could ⍺ Cen A show signs of Supergranulation?

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Any questions?

Extra slides

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An important distinction

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Binning the RV time-series (points next to each other in time are averaged together)

Time-scale!

Time!

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Bin contains pairs of data points with the same separation in time

One SF bin

One RV bin

One RV bin

One RV bin

Assumption about signal RMS not changing with binning

RMS of simulated granulation (GP) doesn’t reduce in RMS until after the cadence for binning in threes

Original Cadence

Bin in threes cadence

The quiet K-dwarf - HD 166620

Binned in threes

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• Correlated noise RMS:

19 ± 5 cm/s

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Anna John+ 2025

σ₁

σ₃