FASHI Data Cubes

• FASHI Data Cubes are multidimensional digital data structures combining radio survey data with hierarchical, algebraic modeling.
• They leverage OLAP operations and rigorous calibration pipelines to process terabyte-scale data for efficient spatial, spectral, and temporal analysis.
• Applications include blind H I censuses, extragalactic source detection, and multi-wavelength cross-survey integration driving cosmic structure studies.

FASHI Data Cubes are multidimensional digital data structures produced and analyzed within the context of the FAST All Sky H I survey (FASHI), leveraging the Five-hundred-meter Aperture Spherical radio Telescope (FAST) and contemporary OLAP, data warehousing, and algebraic cube frameworks. These data cubes combine high-resolution radio astronomical observations with advanced hierarchical, algebraic, and semantic modeling to support scientific discovery and operational analytics across large-scale spatial, spectral, and temporal domains.

1. Survey Architecture and Data Cube Construction

FASHI data cubes are created from systematic drift-scan observations with FAST’s 19-beam receiver, covering the sky observable by FAST (∼22,000 square degrees) in the frequency range 1050–1450 MHz (Zhang et al., 2023). Each data cube comprises two spatial dimensions (RA, Dec) and a spectral (velocity/frequency) dimension, producing a three-dimensional array of measured H I brightness per voxel. The cubes are processed with the HiFAST pipeline, which applies antenna and flux calibration, baseline correction, RFI elimination, standing wave mitigation, and gridding to a 1′ spatial scale, generally with a spectral resolution of ~6.4 km/s per channel and a beam size of ≈2.9′ at 1.4 GHz (Zhang et al., 27 Jan 2024).

The cube structure enables direct slicing, dicing, roll-up, and drill-down operations over the entire survey area. Typical cube instances are massive, with hundreds of thousands of spatial pixels per channel and tens of thousands of velocity channels, yielding terabyte-scale raw datasets.

2. Hierarchical and Algebraic Modeling

Contemporary cube algebra frameworks formalize the multidimensional nature of FASHI cubes. Dimensions can be strictly hierarchical (e.g., spatial: Country→Region→City; time: Year→Month→Day; spectral: redshift, velocity bins), and each hierarchy defines a lattice of aggregation levels (Nevot et al., 7 Jan 2025, Vassiliadis, 2022). Each value at an aggregated level can be expanded to its descendant proxy at the most detailed level (e.g., $v^0 = desc^0_{L^h}(v)$).

The cube algebra supports a formal cube query:

$$q = \langle \mathbf{DS}^{0},\, \phi,\, [L_1, \dots, L_n,\, M_1, \dots, M_m],\, [agg_1(M_1^0), \dots, agg_m(M_m^0)] \rangle$$

where $\phi$ encodes selection predicates, $L_i$ are the levels (hierarchy), and $M_j$ are measures (e.g., integrated H I flux). Operators include Selection (atomic filtering), Roll-Up/Drill-Down (replace levels in dimensions), and comparative operations (containment, overlap, query distance) (Vassiliadis, 2022).

Closed hierarchical cube representations (ℂ operator) substantially reduce computational and storage overhead by eliminating redundant aggregations among strongly correlated data (Nevot et al., 7 Jan 2025).

3. Scientific Applications and Survey Outcomes

FASHI cubes underpin several major scientific programs:

• Blind extragalactic H I census: The cubes facilitate the cataloging of H I sources down to median detection limits of 0.76 mJy/beam (Zhang et al., 2023), covering a redshift range up to $z < 0.09$.
• OH megamaser and H I absorption line searches: Cube-based cross-matching with external catalogs (PSCz, SDSS) yields detection rates comparable to or exceeding those of ALFALFA, with OHM hyperfine ratios quantified as $R_{1667:1665}=1.32–15.22$ (mean 4.74) and well-constrained $L_{OH}$–$L_{FIR}$ relations (Zhang et al., 27 Jan 2024).
• Low-mass galaxy studies: Manual extraction from cubes enables the measurement of H I profiles and masses for Local Volume dwarfs down to $\log M_{HI} \approx 6.83$, with corresponding stellar mass and sSFR (Nazarova et al., 16 Sep 2025).
• H I Mass Function (HIMF): Combined with HIPASS and ALFALFA, FASHI cubes provide robust HIMF measurements, fit by single or double Schechter functions (e.g., $\alpha = -1.30$, $\log M_s = 9.86$), yielding local cosmic $\Omega_{HI} = 0.000454$ (Ma et al., 15 Nov 2024).

Data cubes also permit statistical analyses such as calculation of flux completeness functions, $1/V_{max}$ corrections, and cosmic variance suppression over large volumes.

4. Analytical Operations and Computational Frameworks

A diverse suite of analytical methodologies is available for cube interrogation:

• OLAP Operations: Slice, dice, roll-up, drill-down, and drill-across are supported via both algebraic and semantic web paradigms (e.g., QB4OLAP vocabulary, SPARQL queries) (Etcheverry et al., 2015). This modeling enables users to pivot among dimensions, filter by arbitrary predicates, and aggregate at any hierarchical level.
• Comparative Cube Algebra: Operators for foundational containment (subset relations in cell signatures), same-level containment, intersection, and query distance (via weighted Jaccard metrics for selection atoms and normalized level-height differences) formalize query similarity and result reuse (Vassiliadis, 2022).
• Combination Formulas: The number of possible report configurations is given by $n\times C(n-1, r-1)$, systematically enumerating combinations of dimensions in the hypercube (Warnars, 2010).
• Approximate Cubing Engines: TRACE enables interactive, low-latency querying by maintaining only the top-n most informative slices via sketching and pruning, reducing materialization cost from $O(N\times2^d)$ to $O(n)$ (Sivakumar et al., 12 Jan 2024).

Distributed, GPU-based rendering frameworks allow in-core visualization and manipulation of terabyte-scale cubes at frame rates up to 30 fps over cluster architectures (Hassan et al., 2012).

5. Data Characteristics, Calibration, and Cross-survey Integration

FASHI cubes exhibit the following key properties:

• Spectral resolution: Typically 6.4 km/s/channel.
• Spatial resolution: $2.9'$ per beam at 1.4 GHz, gridded at $1′$ pixel scale.
• Sensitivity calibration: SNR is quantified by $S_{bf}\sqrt{w_{smo}}/\sigma_{rms}$.
• Physical parameter derivation: H I mass via $M_{HI} = 2.356\times10^5/(1+z)\,D^2\,S_{bf}$, optical depth by $\tau_{HI} \approx -\ln(1+S_{HI}/(c_f S_{1.4GHz}))$, and H I column density via $$N_{HI} = 1.823 \times 10^{18} T_s \int \tau_{HI} dV$$ (Zhang et al., 22 Jul 2024, Zhang et al., 2023, Ma et al., 15 Nov 2024).

Cube calibration encompasses completeness corrections, pixel-wise weighting ($f_{rms}$), and cross-survey harmonization. This enables robust HIMF and cosmic abundance estimates and optimizes source extraction pipelines against systematic survey variations.

The cubes are suitable for cross-matching with optical/IR catalogs to validate counterparts and for extending legacy datasets (e.g., ALFALFA) with improved sensitivity and spatial coverage.

6. Future Directions and Scientific Impact

The continued expansion and refinement of FASHI cubes is expected to drive several advances:

• Broadening redshift coverage: Planned extension of the spectral window and deeper integrations will allow detection of higher-$z$ H I and OH sources.
• Hierarchical data cube formalism: Adoption of closed hierarchical representations is anticipated to further reduce storage, query times, and redundancy in highly correlated survey domains (Nevot et al., 7 Jan 2025).
• Enhanced multi-wavelength legacy: As next-generation surveys arrive, FASHI cubes will facilitate synergistic studies encompassing H I, OH, molecular gas, and stellar populations over vast cosmic volumes.
• Increased automation and real-time analysis: Integration of engines such as TRACE and pyCube (Vang et al., 2023) with existing OLAP and semantic models will enable responsive, multi-user, programmatic exploration of large parameter spaces.

FASHI cubes thus provide foundational infrastructure for the ongoing quantification of large-scale structure, galaxy evolution, and intergalactic matter in the local Universe, anchoring multi-disciplinary research that intersects observational radio astronomy, computational analytics, and data science.