Anahata: A Real-Time Stellar Oscillation Sonification System Integrating Kepler–TESS Photometry, Gaia Astrometry, and Multi-Paradigm Audio Synthesis

Asteroseismology and TESS Photometry

Solar-like oscillations are stochastically excited by near-surface convection and are characterised by a comb-like pattern of modes separated by the large frequency separation \(\Delta\nu \propto \bar{\rho}^{1/2}\) (Chaplin & Miglio 2013). Space-based photometric missions provide the continuous, high-precision time series necessary to resolve these modes. TESS observes each sector of \(\sim 27\) days at a 2-minute short cadence (SPOC pipeline; Jenkins et al. 2016) or 10-minute (QLP) cadence, making it the primary resource for bright, naked-eye seismic targets. The Kepler mission (Koch et al. 2010) provides 30-minute long-cadence (LC) and 1-minute short-cadence (SC) data over 4-year baselines.

Sonification of Astronomical Data

Worrall (2019) provides a comprehensive framework for data sonification, distinguishing audification (direct conversion of a waveform) from parameter mapping sonification (PMS), in which data dimensions are mapped to independent auditory variables such as pitch, timbre, loudness, and spatial position. Anahata employs PMS: each extracted oscillation mode constitutes one voice; its frequency sets the synthesiser's fundamental pitch; its amplitude modulates voice loudness; and its phase angle determines stereo placement.

Prior astronomical PMS work includes sonification of exoplanet transits (Zanella et al. 2022), neutron-star merger gravitational waves (Abbott et al. 2017), and Milky Way gas dynamics (Galaxy Sonification Project 2021). The specific sonification of asteroseismic mode spectra has been explored by Bellinger (2019), but these systems remain desktop-bound and non-interactive.

Progressive Web Applications and the Web Audio API

The Web Audio API (W3C 2023) exposes a graph-based audio processing model in modern browsers, enabling sample-accurate scheduling of oscillators, filters, convolution reverb, and dynamic compression. The look-ahead scheduler pattern described by Wilson (2013) - a high-resolution timer offset of \(\sim 200\,\text{ms}\) driving sub-25 ms scheduling ticks - is employed in Anahata to achieve glitch-free audio on resource-constrained mobile devices.

Progressive Web Applications combine the reach of the web with native-application capabilities: offline caching via Service Workers, installability via the Web App Manifest, and access to device sensors (GPS, DeviceOrientation).

Star Catalogue Construction from Gaia DR3

The Anahata star catalogue is seeded from the ESA Gaia Data Release 3 (Gaia Collaboration 2023), which provides astrometric solutions, photometry, and spectrophotometric data for \(\sim 1.8 \times 10^9\) sources. A magnitude-limited (\(G < 15\) mag, configurable) full-sky query is executed against the gaiadr3.gaia_source table via the astroquery.gaia interface (Ginsburg et al. 2019):

SELECT source_id, ra, dec, phot_g_mean_mag, bp_rp
FROM gaiadr3.gaia_source
WHERE phot_g_mean_mag < 15
  AND ra IS NOT NULL
  AND dec IS NOT NULL
  AND phot_g_mean_mag IS NOT NULL
  AND bp_rp IS NOT NULL
ORDER BY phot_g_mean_mag ASC

The resulting catalogue contains positions, Gaia \(G\) magnitudes, and \(B_P - R_P\) colour indices for \(\sim 50{,}000\) naked-eye sources. This catalogue is served directly to the web frontend and rendered as an interactive sky overlay via the Aladin HiPS sky atlas library.

Lightcurve Acquisition

For any target identified by its TESS Input Catalogue (TIC) or Kepler Input Catalogue (KIC) identifier, the Anahata backend downloads calibrated photometric light curves through the lightkurve library (Lightkurve Collaboration 2018). The acquisition follows a deterministic priority ladder designed to maximise temporal resolution while rejecting community-processed HLSP files.

Lightcurve acquisition priority ladder for TIC and KIC targets.

HLSP products are rejected by a filename-prefix filter (hlsp_) applied before any data download. For each accepted strategy, the system attempts a bulk download_all().stitch() call to concatenate all available sectors or quarters into a single normalised time series. Typical data volumes range from \(\sim 10{,}000\) points (single Kepler LC quarter) to \(\sim 1.2 \times 10^5\) points (three TESS SPOC sectors stitched). The output is a plain-text CSV with columns time (BJD), flux (normalised), and flux_err.

Outlier Rejection and Pre-conditioning

Prior to frequency analysis, a rolling-window \(4\sigma\) outlier rejection step is applied. For each data point \(i\), a local median \(\tilde{f}_i\) is computed within a half-window of 50 samples, and the global median absolute deviation (MAD) provides a robust scale estimate:

Points satisfying \(|f_i - \tilde{f}_i| > 4\hat{\sigma}\) are replaced with \(\tilde{f}_i\). The factor \(1.4826\) ensures consistency with the standard deviation for Gaussian noise while remaining unaffected by non-Gaussian outliers (Rousseeuw & Croux 1993).

The Lomb–Scargle Periodogram

The core frequency-extraction engine - PyFEM (Period Fitting and Extraction Module) - implements an oversampled Lomb–Scargle (LS) periodogram (Scargle 1982; Zechmeister & Kürster 2009) evaluated over the frequency interval \([\nu_{\min}, \nu_{\rm Nyq}]\). The Nyquist frequency for an unevenly sampled time series is estimated as:

where \(\widetilde{\Delta t}\) is the median of all positive inter-point time intervals. For a 2-minute TESS cadence this yields \(\nu_{\rm Nyq} \approx 360\,\text{d}^{-1}\) (\(\sim 4167\,\mu\text{Hz}\)), well covering the p-mode envelope of solar-type stars.

Iterative Pre-whitening and Peak Extraction

Dominant oscillation modes are extracted via iterative pre-whitening - an iterative sinusoidal fit-and-subtract loop. At each iteration:

1. The LS periodogram is computed on the residual flux series.
2. The frequency \(\hat{\nu}\) of maximum power is identified.
3. The local signal-to-noise ratio (SNR) is estimated within a window of half-width \(\Delta\nu_{\rm snr}\) centred on \(\hat{\nu}\): \[ \mathrm{SNR}(\hat{\nu}) = \frac{A(\hat{\nu})}{\mathrm{median}\bigl(A(\nu) : |\nu - \hat{\nu}| < \Delta\nu_{\rm snr}\bigr)} \]
4. A sinusoidal component at \(\hat{\nu}\) with optimised amplitude \(A\) and phase \(\phi\) is subtracted from the residuals.
5. The process repeats until \(n_{\rm peaks}\) significant modes have been extracted.

The oversampling factor \(\Omega = 6\) ensures robust peak localisation for closely spaced modes. Default extraction parameters: \(n_{\rm peaks} = 10\), \(\Delta\nu_{\rm snr} = 1.0\,\text{d}^{-1}\).

Output Format

Extracted oscillation descriptors are stored as JSON with the following schema (example: TIC 83232658):

{
  "name": "TIC 83232658",
  "ra": 213.841152085095,
  "dec": -25.3725969129698,
  "scale_factor": 1000.0,
  "dist_pc": 715.804,
  "frequencies": {
    "freq":  [60.93, 23970.86, 163.47, ...],   // Hz (scaled)
    "amp":   [95.05,  60.44,  100.00, ...],    // arbitrary units
    "phase": [ 0.21,   0.86,    0.13, ...]     // [0, 1]
  }
}

The scale_factor (default 1000.0) encodes the linear rescaling applied when converting from cycles per day to Hertz for sonification:

Frequencies exceeding 18 kHz after scaling are classified as "ultrasonic" and are repurposed as LFO (low-frequency oscillator) sweep rates rather than fundamental pitches.

Web Audio API Synthesiser Archetypes

The browser synthesis engine defines seven distinct synthesiser archetypes, each implemented as a function returning a Web Audio API node graph. All archetypes accept five parameters: ctx, freq, amp, phase, and startTime.

Anahata Web Audio API synthesiser archetypes.

Polyphony Management and Real-Time Reliability

A maximum polyphony ceiling of \(P_{\max} = 5 + 3v_c\) voices is maintained (where \(v_c\) is the configured voice-count parameter). The eviction strategy uses an age guard based on the _startedAt timestamp attached to each node at creation time: only nodes whose scheduled start time satisfies \(t_{\rm start} \leq t_{\rm now} + 50\,\text{ms}\) are eligible for eviction, preventing premature termination of nodes not yet in their attack phase.

Long-duration ambient playback on Android requires suppressing the screen-off sleep cycle (which throttles JavaScript setTimeout). Anahata requests a Screen Wake Lock at session start, re-acquires it on page visibilitychange events, and uses the Media Session API to register play/pause/stop handlers. The look-ahead sequencer uses a 25 ms tick with a 200 ms lookahead window (Wilson 2013). Each node is stopped via a short exponential gain decay (\(\tau \approx 27\,\text{ms}\)) before termination, reducing audible discontinuities to below the perceptual threshold of \(\sim 1\,\text{ms}\).

FoxDot/SuperCollider Pathway

For compositional exploration and live performance, a parallel synthesis pathway routes the same oscillation JSON descriptor into FoxDot (Kirk 2016), a Python-based live-coding environment backed by a SuperCollider audio server. Seven compositional profiles are provided:

• Stars - balanced, BPM 90; bell, ambient pads, klank wash.
• Universe - ultra-slow, BPM 40; two-octave sub-bass shift, cavernous reverb (room=0.99, mix=0.98).
• Nova - energetic, BPM 140; one-octave up, rapid arpeggios, metallic transients.
• Black Hole - heavy, BPM 55; three-octave down, sine gravitational hum, dense sub-bass.
• Gravity Well - gentle, BPM 70; emphasis on sustained sine pads and soft bell tones.
• Deep Space - grounded, BPM 80; bass and mid-register focus with slow LFO modulation.
• Space Ambient Mix - free-form; generative texture blending all frequency bands.

Backend: Flask REST API

The Python backend is a Flask application providing three primary API endpoints:

POST /api/lightcurve

Downloads and preprocesses the light curve for a given target_id (TIC or KIC), returning the CSV path, total point count, resolved mission, and cadence.

POST /api/frequencies

Runs PyFEM on a given CSV file, returning extracted oscillation parameters and Nyquist frequency.

GET /api/stream/<job_id>

Server-Sent Events (SSE) stream delivering per-step log lines during long-running analysis jobs, enabling real-time progress feedback in the browser UI.

Jobs are managed in an in-memory registry with UUID keys; a LogCapture class redirects stdout from the analysis worker thread to a per-job queue.Queue, which the SSE endpoint drains asynchronously. The cone-search endpoint (POST /api/cone_search) queries both the Gaia DR3 catalogue and MAST for TIC/KIC identifiers within a configurable angular radius (default 4 arcsec).

Stellar Frequency Analyser Application (starproc/app.py)

The Anahata Stellar Frequency Analyser (astral/starproc/app.py) is a self-contained Flask web application that provides a browser-based graphical interface to the full data pipeline: star search, light-curve acquisition, PyFEM frequency extraction, and JSON/SuperCollider export. The application is structured around three workflow tabs - Find Stars, Make Music, and Export to Anahata.

Find Stars Interface

Star selection supports two modes: (1) direct entry of a TIC or KIC identifier; and (2) a Random Sky Coordinate generator, which draws a random (RA, Dec) pair from the Gaia DR3 catalogue, executes a cone search to resolve the nearest TIC identifier, and proceeds to light-curve acquisition.

Figure 2

Figure 2. Anahata Stellar Frequency Analyser - Find Stars tab. (Upper panel) Direct TIC/KIC identifier entry. (Middle panel) Random sky coordinate generator that resolves the nearest TIC via cone search. (Lower panel) Pipeline options controlling search radius, frequency bounds, S/N threshold, peak count, oversampling factor, and output directory.

Naked-Eye Sky Map Widget

The interface embeds a real-time Naked-Eye Sky Map widget rendered on an HTML canvas using the same Gaia DR3 \(G < 15\) mag catalogue as the main Anahata PWA. On successful cone-search resolution, the matched TIC target is highlighted with a pulsing red reticle and its basic catalogue metadata are displayed beneath the map.

Figure 3

Figure 3. Naked-Eye Sky Map widget embedded in the Stellar Frequency Analyser. The canvas displays Gaia DR3 naked-eye sources in a gnomonic projection; a pulsing red target reticle marks the resolved TIC source. Dragging the canvas rotates the field; clicking any star sets it as the pipeline target.

Real-Time Pipeline Log

Once a pipeline run is triggered, a Server-Sent Events (SSE) stream delivers per-step log lines to a log panel in the browser. The log reports the resolved acquisition strategy (mission, author, cadence, sector count), the number of data points stitched, and the full table of extracted oscillation modes with their frequency (c/d), amplitude, phase, SNR, and per-mode noise floor.

Figure 4

Figure 4. Real-time pipeline log streamed via SSE. The log shows the resolved acquisition strategy (mission, cadence, sector count, data points saved), followed by the extracted oscillation modes listed as tuples of (frequency in c/d, amplitude, phase, SNR, noise floor).

Analysis Plots: Light Curve and Sky Atlas

After extraction, the application renders two diagnostic panels: an Aladin Lite sky-atlas widget centred on the target coordinates (PanSTARRS DR1 HiPS layer), and the photometric light curve (normalised flux vs. BJD) showing data quality, baseline length, and any inter-sector normalisation offsets.

Figure 5

Figure 5. Analysis plots panel. Upper: Aladin Lite sky-atlas view (PanSTARRS DR1 HiPS layer) centred on the target coordinates, providing an optical field reference. Lower: Stitched TESS light curve (normalised flux vs. BJD) showing the photometric time series used as input to the PyFEM frequency extraction module.

Lomb–Scargle Periodogram

The final output panel displays the oversampled Lomb–Scargle periodogram computed by PyFEM. Extracted peak positions are overlaid as colour-coded stem markers, identifying the dominant oscillation modes subsequently stored in the JSON descriptor.

Figure 6

Figure 6. Lomb–Scargle periodogram output panel. The blue curve shows the periodogram amplitude as a function of frequency; magenta circles on teal stems mark the peaks extracted by the iterative pre-whitening loop. Extracted peak frequencies are written to the JSON oscillation descriptor and passed to the Web Audio synthesis engine.

Frontend: Progressive Web Application

The frontend is a single-page PWA served as static HTML/CSS/JavaScript, requiring no build toolchain. Key components include:

• Sky Renderer - custom canvas-based renderer driven by the Gaia DR3 catalogue, displaying 50,000 naked-eye stars as interactive symbols aligned to the device GPS heading. An optional live-sky mode overlays the star field on the device camera feed.
• Star Hunt Mode - device camera displayed as a live full-screen background. Compass heading (DeviceOrientationEvent) and GPS position (Geolocation API) are fused to derive the telescope pointing direction. A proximity-modulated low-pass filter (\(f_{\rm LPF}\): 300–8000 Hz) and gain ramp make the star louder as the device approaches alignment.
• Astral Player - a standalone page serving the Web Audio engine in isolation from the sky viewer, for focused listening to any pre-processed star in the catalogue.
• Service Worker - pre-caches the application shell and star catalogue JSON, enabling full offline functionality after initial load.

GPS and Celestial Coordinate Alignment

Rendering the star catalogue correctly over a live camera feed requires transforming catalogue equatorial coordinates \((\alpha, \delta)\) into the topocentric horizontal frame (altitude \(a\), azimuth \(A\)) of the device. The pipeline follows the classical methods of Meeus (1998).

Greenwich Mean Sidereal Time (GMST) is computed from the J2000.0 epoch:

where \(T\) is the current Julian Date and \(T_0 = 2451545.0\). Altitude and azimuth follow from the hour angle \(H = \mathrm{LMST} - \alpha\):

A magnetic declination correction \(\Delta D\) is applied using a simplified World Magnetic Model polynomial (Chulliat et al. 2020): \(\psi_{\rm true} = \psi_{\rm magnetic} + \Delta D\). Stars are projected onto the HTML canvas using a gnomonic (tangent-plane) projection:

Anahata Sky View Interface

The Anahata Sky View is the primary user-facing interface for star discovery and sonification. The canvas re-renders at up to 30 fps, recomputing alt/az positions for all catalogue stars on each frame. Tapping a star symbol selects it, loading its JSON oscillation descriptor and populating the information panel and frequency grid.

Figure 7

Figure 7. Anahata Sky View interface - the primary star-discovery and sonification screen. (A) Interactive canvas star map with Gaia DR3 naked-eye overlay; (B) GPS re-projection and compass heading alignment; (C) live camera toggle compositing the star field over the device feed; (D) artificial satellite mode; (E) star-selection visor; (F) selected-star information panel (name, distance, spectral type, oscillation mode count).

Astral Player Interface

The Astral Player (astral.html) is a focused listening page that separates the synthesis engine from the sky-navigation interface. The frequency grid serves a dual role: a data-inspection view of the raw oscillation descriptor, and a per-mode mute/solo toggle during playback.

Figure 8

Figure 8. Astral Player interface (astral.html), the focused listening mode. (A) Scrollable stellar catalogue list with randomised-star shortcut; (B) active synthesiser voices; (C) maximum active channel scale control; (D) extracted oscillation-mode frequency grid (colour-coded by band: green = audible, amber = near-ultrasonic LFO, red = sub-audible LFO); (E) Aladin Lite sky-atlas panel centred on the target star's RA/Dec; (F) synthesiser visualiser.

Data Flow Summary

Figure 9 summarises the full end-to-end data flow from observation archive to audio output. The primary production path runs: archives → catalogue construction → target selection → light-curve acquisition → pre-conditioning → PyFEM extraction → JSON output → parameter mapping → Progressive Web App → browser audio. The optional FoxDot/SuperCollider pathway (shown dashed) branches at the JSON output stage.

Catalogue Overview

The current Anahata release includes hundreds of pre-processed stellar oscillation descriptors. Targets were selected to span a range of oscillation frequencies, spectral types, and distances, covering all sky positions to provide sonic variety across the synthesiser archetypes. Each target has multiple extracted oscillation modes (up to hundreds of frequencies) stored in JSON format, plus a corresponding SuperCollider .scd synthesis file.

Case Study: TIC 83232658

TIC 83232658 (\(\alpha = 213.84^\circ\), \(\delta = -25.37^\circ\), \(d = 715.8\,\text{pc}\)) illustrates the range of frequencies emerging from the pipeline. The ten extracted modes span:

• Low-frequency group: \(\{60.9, 163.5, 266.1, 320.2, 403.7\}\,\text{Hz}\) (after scaling) - maps to audible Bell, Klank, and Ambient voices.
• Mid-frequency group: \(\{620.7, 1444.8\}\,\text{Hz}\) - Nova and Deepspace voices.
• Near-ultrasonic group: \(\{23{,}689, 23{,}836, 23{,}971\}\,\text{Hz}\) - repurposed as LFO sweep rates (separation \(\approx 145\)–\(147\,\text{Hz}\)).

The dominant mode amplitude (163.5 Hz) is 100 vs. the weakest retained mode at \(\approx 1.0\) - a 40 dB dynamic range, mapping to a gain range of \([0.05, 1.0]\) in the audio domain.

Sonic Character Across Archetypes

For a given star descriptor, the seven archetypes produce qualitatively distinct sonic characters while sharing the same underlying harmonic ratios:

• Bell/Klank: percussive, decaying, metallic - highlights the overtone structure.
• Ambient: sustained, warm, pad-like - emphasises fundamental frequencies.
• Deepspace: slow, resonant, with rhythmic transients at the dominant oscillation period.
• Universe: massive, diffuse, cluster-detuned - evokes stellar interiors.
• Blackhole: sub-bass drone with impulsive noise transients - evokes extreme gravity.
• Nova: fast, bright, energetic - evokes stellar outbursts.

Scientific Validity and Perceptual Fidelity

Anahata preserves three fundamental properties of the asteroseismic mode spectrum in the audio domain: (1) frequency ratios (via the direct mapping of Eq. 4 with uniform octave shift); (2) amplitude hierarchy (via normalised gain mapping); and (3) phase relationships (via stereo panning). Scale quantisation optionally breaks the first invariant for musical palatability. When disabled, the Web Audio engine renders the exact oscillation spectrum as a superposition of sinusoidal tones, constituting a form of direct audification.

The primary scientific limitation is the loss of temporal structure: the light-curve time domain is not preserved. Only the frequency domain is transmitted to the audio engine. Future work could encode mode linewidths as synthesiser amplitude-modulation depths.

Latency and Real-Time Performance

The Web Audio look-ahead scheduler achieves typical output latencies of \(\sim 50\)–\(80\,\text{ms}\) on Android Chrome 122 and \(\sim 20\)–\(40\,\text{ms}\) on desktop. The 15–20 ms synthesiser attack ramps exceed typical Android hardware buffer sizes (\(\sim 4\)–\(6\,\text{ms}\)), preventing zero-crossing click artefacts at note onset.

Accessibility and Public Engagement

A deliberate design goal is zero-friction access: no app store, no software installation, no login. The PWA is installable from the browser address bar and subsequently available offline. The star-hunt mode provides a gamified, embodied engagement pathway - physically rotating the phone to "find" a singing star by sound alone - which has been found in informal testing to increase engagement time significantly relative to passive listening.

Current limitations: The pipeline extracts dominant amplitude peaks without identifying them as \(\ell=0, 1, 2\) modes. Future integration with background model fitting would enable mode labelling. The live-coding pathway requires manual installation of SuperCollider and FoxDot, limiting accessibility for non-technical users.

Future directions: simultaneous sonification of multiple stars as a "stellar orchestra"; replacement of the 2D sky atlas with a WebXR spatial audio scene positioning stars at their true celestial coordinates; and application of the same pipeline to other time-domain datasets (LIGO/Virgo strain, black-hole accretion light curves).