KIC 8462852 / Tabby's / Boyajian's / WTF Star.

Introduction:

In the 21st century, the quest to discover exoplanets (any planet beyond our solar system - link) has accelerated, with the transit method emerging as a central technique. This method, which detects planets as they cross in front of their stars and create subtle dimming in starlight, has facilitated the discovery of thousands of exoplanets. NASA's Kepler mission revolutionised this process by observing over 100,000 stars over several years, revealing many fascinating celestial phenomena. Among the observed stars, one stands out as particularly enigmatic: KIC 8462852, more famously known as Tabby’s Star, named after astronomer Tabetha Boyajian. Nicknamed the "WTF" (Where’s the Flux?) star, Tabby’s Star exhibits a pattern of brightness variations that remain largely unexplained and set it apart from any other known star.

Tabby’s Star has captured scientific attention due to several unique traits:

• Remarkable drops in brightness of up to 22%, a stark contrast to the typical <1% dips caused by planetary transits.
• A slow, decades-long dimming with occasional brightening, an unprecedented behaviour.
• Brightness fluctuations during dimming events, unlike the smooth patterns expected from planets.
• An absence of infrared radiation, which commonly accompanies such significant dimming.

These characteristics have generated numerous hypotheses and ignited debate on whether Tabby’s Star might point to something extraordinary, including massive dust clouds or hypothetical megastructures.

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The Kardashev Scale:

The Kardashev Scale is a theoretical framework proposed by the Soviet astrophysicist Nikolai Kardashev in 1964 to classify civilisations based on their ability to harness energy. The scale originally had three types:

• Type I civilisation (Planetary civilisation):
  A civilisation that can harness and store all the available energy on its home planet. This includes energy from resources like fossil fuels, solar energy, wind, geothermal, etc. Humanity is not yet a Type I civilisation—we are currently estimated to be at around 0.7 on the Kardashev scale.
• Type II civilisation (Stellar civilisation):
  A civilisation that is capable of harnessing the total energy output of its star. This is where the Dyson Sphere comes into play, which I'll explain in more detail below. A Type II civilisation would not be limited to planetary resources but could exploit the entire power of its solar system, specifically its star.
• Type III civilisation (Galactic civilisation):
  A civilisation advanced enough to harness the energy of an entire galaxy. This level would involve tapping into the energy of billions of stars, possibly using advanced megastructures and forms of energy manipulation we can't yet imagine.

Later theoretical expansions of the Kardashev scale include:

• Type IV (Universal civilisation).
• Type V (Multiversal civilisation).

Where civilisations would exploit energy at scales far beyond single galaxies, potentially manipulating entire universes or multiverses.

The Dyson Sphere:

The concept of a Dyson Sphere was introduced by British-American physicist Freeman Dyson in 1960. Dyson hypothesised that an advanced civilisation (like a Type II civilisation on the Kardashev scale) would require enormous amounts of energy, far more than what could be harvested from a planet alone.

Dyson Sphere Illustration:

Dyson Swarm Illustration:

To meet this energy demand, such a civilisation might build a megastructure around its star to capture most or all of the star's energy output. There are different theoretical designs for a Dyson Sphere, including:

• Dyson Swarm: A vast collection of solar-collecting satellites orbiting the star. This is considered a more practical idea because it doesn’t require a single, continuous shell, which would have engineering difficulties.
• Dyson Bubble: Similar to a swarm but composed of light-weight structures held in place by the star’s radiation pressure, forming a kind of shell without being rigid.
• Dyson Shell: A more traditional idea of a solid or semi-solid shell that completely encases a star. This would capture nearly all of the star’s energy, but constructing such a shell would require almost unimaginable amounts of material.

Intersection of the Kardashev Scale and Dyson Spheres:

The Dyson Sphere represents the kind of megastructure that would be constructed by a Type II civilisation on the Kardashev scale. The intersection between the two concepts lies in the civilisation's energy demands and how they might be met.

Here’s how they intersect:

• Type I to Type II Transition: To transition from Type I to Type II, a civilisation would need to harness energy beyond what its planet offers. The energy output of a star is vastly greater than that of any planetary resources, so building a Dyson Sphere or Dyson Swarm could be a logical next step. By capturing a significant portion of the star’s output, this civilisation could fulfil the Kardashev Scale's criteria for a Type II civilisation.
• Energy Mastery: A Dyson Sphere would allow a civilisation to access nearly the total energy output of its star, an estimated 4×10²⁶ watts for a star like the Sun. This energy could power everything from advanced computational systems to interstellar travel, and even more exotic possibilities like manipulating spacetime or building complex artificial intelligence systems.
• Technological and Material Challenges: Constructing a Dyson Sphere would require technology far beyond what humanity currently possesses. For example, the sheer amount of material needed to build such a structure could exceed the mass of all planets in the solar system. Advanced material science, autonomous manufacturing, and the ability to mine entire asteroids or planets for resources would be necessary.
• Energy Efficiency and civilisation Growth: With a Dyson Sphere, a Type II civilisation would achieve an unprecedented level of energy efficiency, allowing it to power massive interstellar colonies, supercomputers, or even projects like terraforming other planets or generating artificial stars.

Why the Dyson Sphere is Crucial for a Type II civilisation:

The Dyson Sphere (or a variant like a Dyson Swarm) would be the key technology that allows a civilisation to reach and maintain Type II status. Without such a megastructure, there would be no practical way to harness enough energy to power the activities of a civilisation operating on a solar-system-wide scale:

• Stellar Energy Requirements: To put things into perspective, the amount of energy Earth currently consumes annually is roughly 1.5×10¹³ watts (15 terawatts). A Dyson Sphere would grant a civilisation access to 4×10²⁶ watts, a mind-boggling increase of 10 trillion times more energy than what we currently consume.
• Beyond Type II: After reaching Type II, further progression up the Kardashev scale would likely involve interstellar travel and the creation of similar structures around multiple stars, pushing the civilisation into Type III, where entire galaxies are being tapped for energy.

Potential Consequences and Speculation:

• Civilisation Behaviour: A civilisation with Dyson Sphere technology could potentially become self-sufficient within its solar system, or it might seek to explore other star systems to build more Dyson Spheres, advancing to Type III. Such a civilisation might manipulate stellar energies for purposes we can barely imagine, from creating artificial black holes to accelerating interstellar spacecraft to near-light speeds.
• Fermi Paradox: Dyson Spheres are often mentioned in discussions of the Fermi Paradox (the question of why we haven't yet observed evidence of extraterrestrial civilisations). If there were Type II civilisations building Dyson Spheres, we might detect them by observing the dimming or altering of starlight as seen from Earth, or by noticing unusual infrared signatures.

In Summary:

The Kardashev Scale and Dyson Spheres intersect as the scale reaches Type II. A Dyson Sphere (or similar structure) would likely be the technology that allows a civilisation to harness the full energy output of its star, fulfilling the requirements to ascend to a Type II civilisation. This development would represent a major leap in technological sophistication, with far-reaching implications for energy use, exploration, and potentially the future of life in the galaxy.

The classic concept of a Dyson Sphere, would be unlikely due to the immense engineering challenges and the fact that it would need to withstand colossal gravitational forces and heat. Instead, a Dyson Swarm or rotating frame, comprising many smaller structures orbiting the star, seems more plausible for a highly advanced civilisation to capture a significant portion of a star's energy.

This type of structure would be more realistic because it can be built incrementally, starting with satellites or solar collectors in different orbits, without the need to enclose the star fully. A rotating frame around a star, which could take the form of a ring or series of rotating orbital constructs, would be more stable and feasible for energy capture, materials construction, and heat dissipation.

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How to Detect a Dyson Swarm or Rotating Frame:

The detection of such a superstructure would focus on the anomalies it creates with the star's light and energy output, and other observational techniques. Below are a few methods that could be used to detect a Dyson Swarm or rotating structure:

• Infrared Signature:
  • A rotating frame around a star would absorb much of the visible light energy, converting it to heat. The waste heat would be re-radiated in the infrared spectrum, creating a strong infrared signature. If we observed a star where much of the visible light is missing, but the star emits excess infrared radiation (above what’s expected for its type and age), this could indicate the presence of a Dyson Swarm or another energy-capturing structure.
• We look for infrared-excess objects, where the output doesn't match the normal star energy profile. The search for Dyson Swarms is already being conducted through programs like the Glimpse Survey and Wide-field Infrared Survey Explorer (WISE), targeting stars with unusual infrared emissions.
• Transit Dimming (Light Curve Irregularities):
• If parts of the rotating frame occasionally transit in front of the star, they would block portions of its light, creating irregular dips in the star's brightness, much like we detect exoplanets using the transit method. However, unlike a planet, which would cause periodic and regular dips, a Dyson structure's transit would likely cause irregular, non-periodic dips due to its complex shape and movement.
• The star KIC 8462852 (also known as Tabby's Star) has exhibited strange and irregular dips in brightness, sparking speculation that it might be due to large structures (though natural explanations like dust clouds are also likely). [link](https://en.wikipedia.org/wiki/Tabby%27s_Star#:~:text=Tabby's%20Star%20(designated%20as%20KIC,(450%20parsecs)%20from%20Earth.)
• Spectral Shifts:
• The movement of massive structures around a star might also cause small, detectable shifts in the star’s light. As the Dyson Swarm or rotating frame moves toward or away from us, it could induce slight Doppler shifts in the star's spectral lines due to its gravitational influence or light-absorbing properties. However, this method is more subtle and would require precise measurements.
• Dyson Swarm Shadows:
• Depending on the configuration and density of the Dyson Swarm or rotating frame, it might cast partial shadows or create localised starspot-like features. These would be detected by measuring changes in the star’s brightness at different points on its surface as the swarm’s components move in and out of view.
• Pulsar Timing Irregularities:
• Some pulsar timing methods might be used to detect Dyson Swarms if such structures disturb the gravitational balance of nearby systems. Since pulsars are highly regular, any deviation in their timing due to gravitational perturbations caused by a massive superstructure could be detected over long observational periods.
• Radio or Other Electromagnetic Signals:
• It's possible that an advanced civilisation operating a Dyson Swarm could emit artificial signals or unintentionally leak radio or other types of electromagnetic radiation as part of their activities. Searching for these signals in conjunction with infrared-excess stars might provide additional evidence of a superstructure.

Summary:

A rotating Dyson structure (like a swarm or ring) is much more likely than a solid shell. To detect such a structure, astronomers would focus on its infrared signature, irregular light curves, and anomalous spectral or gravitational effects. Such observations could provide strong clues to the existence of extraterrestrial megastructures without the need for a fully enclosed star.

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Data Visualisation:

A Markdown document with the R code for all the visualisations below, using 'TabbysStarFlux.csv' and 'KIC8462852_light_curve.csv': link

The below four plots represent an analysis of the flux (brightness) data for Tabby's Star, a star known for its unusual dips in flux, potentially due to some intervening object or structure.

Tabby's Star Flux Over Time (Top Left)

• Description: This plot shows the flux (brightness) of Tabby’s Star as a function of time. The x-axis represents the time (in BJD - 2454833 format, which is a standard way of expressing time in astronomical datasets). The y-axis shows the flux, a measure of the star's brightness.
• Features:
  • Line Plot: The blue line tracks how the flux changes over time, providing a clear picture of brightness variations.
  • Error Bars: Black error bars indicate the uncertainties in the flux measurements, showing the margin of error for each data point.
  • Trend: The plot shows that the star's flux varies over time, with several noticeable drops in brightness, which might be interpreted as dips. These dips are part of what makes Tabby's Star unusual.
• Interpretation: This plot is crucial for understanding the flux behaviour and detecting when dips in brightness occur, as these dips could provide clues about the star's environment or potential orbiting material.

Smoothed Flux of Tabby's Star Over Time (Top Right)

• Description: This plot uses LOESS (locally estimated scatterplot smoothing) to smooth the flux data over time, providing a clearer view of the overall trend.
• Features:
  • Raw Data Line (Blue): The same flux data from the first plot is represented here, showing the fluctuation in brightness over time.
  • Smoothed Line (Red): The red line is the result of a smoothing technique, which helps highlight long-term trends by averaging out short-term variations.
  • Trend: The smoothed line reveals an overall decrease in the star's brightness over time, especially after around 1200 on the x-axis.
• Interpretation: By smoothing the data, we can see a clearer, long-term decrease in the brightness of Tabby’s Star. This could imply a gradual dimming process, adding to the mystery of its behaviour.

Histogram of Tabby's Star Flux (Bottom Left)

• Description: This histogram shows the distribution of the star's flux values. The x-axis represents the flux, and the y-axis represents the frequency, or how often certain flux values were recorded.
• Features:
  • Bar Heights: Each bar represents a range of flux values, with the height of the bar indicating how frequently the star exhibited that level of brightness.
  • Spread of Flux: The flux values are spread around 0.98 to 1.01, with some peaks at certain values (e.g., around 1.00 and 1.01).
• Interpretation: This plot provides insight into the typical brightness of Tabby’s Star. The most frequent flux value is close to 1.01, but the distribution shows a fair amount of variance, indicating that the star's brightness does not remain constant.

Uncertainty vs. Flux (Bottom Right)

• Description: This scatter plot shows how the uncertainty in the flux measurements varies with the flux values themselves. The x-axis represents the flux, and the y-axis shows the uncertainty (in standard deviation).
• Features:
  • Scatter Points: Each point represents an individual measurement of flux and its associated uncertainty.
  • Linear Smoothing Line (Red): A linear regression line (in red) is added to show the general trend in the data.
  • Uncertainty Trend: There is a slight downward slope in the red line, indicating that as flux increases, uncertainty tends to decrease somewhat, though there is considerable spread in the points.
• Interpretation: This plot helps evaluate the relationship between the brightness of Tabby’s Star and the measurement uncertainties. It suggests that the uncertainties are relatively small and don't vary dramatically with the flux, which is important for ensuring the reliability of the flux measurements.

Interpretation of the Plots:

• The first two plots (top row) provide complementary views of the star’s brightness over time, showing both the raw data and a smoothed trend. They reveal that Tabby’s Star undergoes significant flux variability, with noticeable dips in brightness.
• The histogram (bottom left) summarises the overall distribution of the flux values, indicating that most measurements cluster around a flux of ~1.00, but with notable variability.
• The uncertainty vs. flux plot (bottom right) shows that the uncertainties are not strongly dependent on the brightness of the star, suggesting that the measurements are reliable across the flux range.

The above plots together provide a comprehensive view of how Tabby’s Star’s brightness changes over time, the distribution of its brightness levels, and the relationship between brightness and uncertainty. This information is key to understanding the star’s strange behaviour and could potentially hint at what might be causing the dips in brightness (e.g., orbiting material or other astrophysical phenomena).

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The below two plots represent Lomb-Scargle periodograms, which are used to analyse periodic signals in unevenly spaced data. In the case of astronomical data, like the brightness (flux) of Tabby’s Star, Lomb-Scargle periodograms help detect potential periodicities (repeating patterns) that might not be immediately obvious due to irregular time sampling.

Lomb-Scargle Periodogram ( Frequency (Left Plot))

• Description: This plot analyses the flux data of Tabby’s Star in the frequency domain. The x-axis represents the frequency of potential periodic signals in the data (i.e., how often a pattern repeats per unit time). The y-axis shows the power, which indicates how strong the signal is at each frequency.
• Features:
  • Peak at Low Frequency: The highest power is observed at very low frequencies, with a peak around 0.0007, suggesting that there might be a long-term periodic signal (or even a trend) in the flux data.
  • No Clear Signal at Higher Frequencies: Beyond this peak, the power drops significantly and fluctuates at low levels, indicating that no strong periodic signal exists at higher frequencies (i.e., shorter timescales).
• Interpretation: The strongest signal is at a low frequency, which could indicate a long-term periodicity in Tabby’s Star’s brightness. This might be related to a potential large-scale phenomenon, such as a long-period orbiting object or a long-term trend in the star’s activity.

Lomb-Scargle Periodogram ( Period (Right Plot))

• Description: This plot displays the same analysis but in the period domain. The x-axis represents the period (in units of time), which is the inverse of frequency (i.e., the time duration of one complete cycle of a repeating signal). The y-axis is again the power, which measures the strength of the periodic signal at each period.
• Features:
  • High Power for Long Periods: The highest power is observed for long periods, particularly around 1445 days, which matches the period corresponding to the low-frequency peak in the left plot.
  • Lower Power for Shorter Periods: There is little power for shorter periods, meaning no significant periodic signals exist over short timescales.
• Interpretation: The high power at periods of approximately 1445 days suggests a potential long-term periodic signal in the data, possibly indicating a recurring event with this period. This could be due to an orbiting companion or some other process that affects the brightness of the star on this timescale.

Summary Printouts (Underneath the Plots):

• Frequency Analysis (Left).
  • The strongest signal is at a frequency of 0.00069216, corresponding to a period of approximately 1444.8 days.
  • The peak power is 0.3665, with a p-value of 0.0015571, suggesting that the detected periodicity is statistically significant.
• Period Analysis (Right).
• The period with the highest power is around 1444.8 days, which is the same as the one identified in the frequency domain.
• The power and p-value are the same as in the frequency domain, confirming the consistency of the analysis.

Interpretation of Plots and Summaries:

• Both the above plots suggest that there is a long-period signal (around 1445 days) in the flux data of Tabby’s Star. This could point to some periodic process, such as an orbiting companion or a large-scale structure passing in front of the star, causing its brightness to dip at regular intervals.
• However, no strong short-term periodic signals are detected, which align with the irregular and unusual brightness variations observed in the star.
• The statistical significance (low p-value) supports the reality of this long-term periodicity.

Tabby's Star Light Curves

The plot below shows the light curves (magnitude over time) of Tabby's Star (KIC8462852) and two comparison stars (TYC 3162-1001-1 and TYC 3162-879-1). A light curve, in astronomy, is a graph showing the brightness of a star over time, helping astronomers investigate any changes in the star’s luminosity.

Plot Interpretation:

• Left Plot: This light curve focuses solely on Tabby’s Star (KIC8462852), showing how its brightness varies over the years. With the y-axis reversed, lower values on the axis correspond to brighter magnitudes, highlighting changes in luminosity over time.
• Right Plot: This plot displays the light curves of all three stars, allowing for a comparative analysis over the same period. By observing Tabby’s Star in relation to the two comparison stars, astronomers can determine if its brightness variations are unique or if they might be influenced by external factors affecting all stars in the field.

Observations:

• Tabby’s Star (blue line) exhibits significant brightness fluctuations over time, which is part of what makes it such a compelling object of study in astronomy.
• Comparison Stars (red and green lines) show relatively stable light curves, indicating that the observed brightness variations in Tabby’s Star are likely intrinsic to the star itself rather than caused by external, systematic effects.

These plots visually emphasise the unusual dimming behaviour of Tabby’s Star, which continues to be a subject of investigation in astrophysical research.

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"KIC 8462852 Faded Throughout the Kepler Mission"

The above titled study is summarised below and is available in pdf format, along with the csv file used in this project. link

The document titled "KIC 8462852 Faded Throughout the Kepler Mission" focuses on the unusual photometric behaviour of the star KIC 8462852 (also known as "Tabby's Star"), observed by the Kepler mission. Researchers Benjamin T. Montet and Joshua D. Simon conducted an analysis of Kepler’s full-frame images (FFI) and identified an unusual, long-term fading of KIC 8462852's brightness, lasting over four years. Here’s a summary of the findings and analyses presented in the document:

• Long-Term Dimming: KIC 8462852 dimmed at a nearly constant rate for about three years before showing a rapid decrease in brightness over approximately 200 days. The initial dimming rate was about 0.341% per year, totaling a 0.9% brightness loss. After this, the star’s brightness dropped by over 2% more in just 200 days, followed by a levelling off.
• Comparison with Other Stars: When comparing KIC 8462852’s behaviour to 193 nearby stars and a sample of 355 stars with similar properties, none showed comparable dimming patterns. This suggests the dimming is unique to KIC 8462852, not attributable to general or instrumental effects in the Kepler data.
• Hypotheses Considered:
• Circumstellar Material: The researchers considered a model involving a cloud of material orbiting the star, which could explain the dimming. However, the timescales and light curve shapes did not fit well with this hypothesis.
• Exocomets: Another possibility, based on prior suggestions, was a large family of exocomets passing in front of the star. This model struggles to explain the long-term dimming.
• Instrumental Artefacts: The researchers ruled out instrumental artefacts, such as pixel sensitivity dropouts, as the observed dimming appears consistent across different telescope orientations.
• Background Contamination: The presence of nearby stars in the photometric aperture was also investigated and dismissed as the source of the dimming.
• Comparison to Historical Data: A study using photographic plates from the DASCH archive had previously suggested that KIC 8462852 dimmed by about 0.165 magnitudes per century, though this result was debated. The Kepler findings do not conclusively confirm this long-term trend but suggest that the star has indeed dimmed unusually over recent years, potentially making the historical dimming more plausible.
• Conclusion and Mystery: The document concludes that no known astrophysical mechanisms, like stellar evolution or known variable star behaviour, adequately explain the dimming. The authors propose that KIC 8462852 is undergoing a unique and yet-unexplained phenomenon, encouraging further study to understand the underlying cause of its fading.

This study added to the intrigue surrounding KIC 8462852, fuelling theories about unusual stellar behaviour or, more speculatively, artificial megastructures. However, the authors focus on scientific explanations and encourage more observation to explore this star’s mysterious variability.

"The KIC 8462852 Light Curve From 2015.75 to 2018.18 Shows a Variable Secular Decline"

The above titled study is summarised below and is available as a pdf. link

This document examines the unusual light patterns of the star KIC 8462852, also known as Boyajian’s Star. This star exhibits irregular, significant brightness dips over both short and long timescales, which is atypical for its type. The study spans data from 2015 to early 2018, tracking the star's ongoing dimming trend and recording brightness variations. Researchers used numerous telescopes to gather extensive photometric data in multiple colour bands (B, V, R, and I), showing that dips in brightness follow a chromatic pattern consistent with dust passing in front of the star. Key findings include:

• Secular Decline and Dips: The light curves show a steady dimming, with superimposed dips of varying duration. Dips range from short episodes of less than a day to extended periods lasting months or years, forming a continuum without gaps in the duration spectrum.
• Chromatic Dust Extinction: The different wavelengths (colour bands) indicate that the dips and dimming are caused by small particles, likely dust, with sizes around 0.1 microns. This dust is thought to be pushed away quickly by radiation pressure, suggesting recent formation near the star.
• Observational Limits: Infrared measurements provide no strong indication of warm dust around the star, limiting the amount and distribution of dust and challenging theories involving dust clouds.
• Continuity and Common Mechanism: The study supports the idea that both short-term dips and long-term dimming are driven by the same physical mechanism, likely a dust-based model. This unified model implies that a single set of processes is creating the diverse light variations observed.

This research contributes to ongoing attempts to understand KIC 8462852’s unique behaviour, with chromatic dimming likely caused by circumstellar dust as the leading explanation.

Recent Studies:

The mystery of Tabby’s Star (KIC 8462852), known for its strange, unpredictable light-dimming events, has intrigued astronomers for years. Initial theories included alien megastructures and comet storms, but recent studies confirm the culprit is dust. NASA’s Kepler mission revealed Tabby’s Star dimming by up to 22%, far more than typical exoplanet transits, which only block about 1% of starlight. Unlike other stars with flux dips, Tabby’s Star shows no infrared radiation, ruling out protoplanetary dust clouds and young star formations as explanations.

The detailed analysis showed that the dimming occurs because dust, particularly fine particles around 100 nanometers, preferentially blocks blue light over red. This “chromatic extinction” indicates that dust is consistently present around the star and likely replenished regularly, possibly from a circumstellar dust ring or debris resulting from the “devouring” of a nearby gas giant. Although speculative ideas like alien megastructures have been debunked, ongoing studies aim to uncover the dust’s origin. While the mystery isn’t entirely solved, researchers are confident that Tabby’s Star’s dimming is entirely dust-driven, pointing to complex processes at play around this mature star. link

Conclusion:

In our pursuit of cosmic understanding, anomalies like Tabby’s Star remind us of the vastness of what remains unexplored. The Kardashev Scale and the theoretical Dyson Sphere are tools that allow us to speculate on the possibilities for advanced civilisations, particularly how they might manipulate energy on an astronomical scale. While explanations for Tabby’s Star currently lean toward natural phenomena, its bizarre behaviour continues to inspire curiosity. Future research, enhanced observational techniques, and explorations into megastructures and advanced civilisations may eventually reveal whether Tabby’s Star harbours mysteries beyond the natural or if it simply showcases the strange diversity of our universe.

Patrick Ford ⭐