# Star Catalog Systematic Bias Correction Tables

Spatially resolved position and proper motion corrections for 17 historical star catalogs,
derived by cross-matching against **Gaia DR3** on a HEALPix sky grid.
Intended for reprocessing natural satellite astrometric observations.

---

## Contents

| Path | Description |
|------|-------------|
| [`tables_nside64.zip`](tables_nside64.zip) | 17 sub-tables, baseline (N_side = 64, ~49 152 pixels) |
| [`tables_nside256.zip`](tables_nside256.zip) | 17 sub-tables, BFS-smoothed (N_side = 256, full sky) |
| [`master_nside64.csv`](master_nside64.csv) | All catalogs merged, N_side = 64 |
| [`master_nside256.csv`](master_nside256.csv) | All catalogs merged, N_side = 256 |
| [`figures.zip`](figures.zip) | Sky maps and statistical distributions for all 17 catalogs |
| [`query_bias.py`](query_bias.py) | Minimal bias query tool |
| [`requirements.txt`](requirements.txt) | Python dependencies |

Catalogs covered: `ac` · `acrs` · `act` · `agk1` · `agk3` · `fk4catalogue` ·
`gaiadr1` · `gaiadr2` · `gsc1_2` · `hipparcos` · `ppm` · `sao` · `tycho2` ·
`ucac2` · `ucac4` · `usno_a2` · `yale`

---

## Data Format

Each sub-table in `tables/nside64/` and `tables/nside256/` is a CSV with one row per
HEALPix pixel (NESTED ordering). In this upload package, these directories are provided
inside [`tables_nside64.zip`](tables_nside64.zip) and [`tables_nside256.zip`](tables_nside256.zip);
please unzip both archives before using [`query_bias.py`](query_bias.py).

| Column | Unit | Description |
|--------|------|-------------|
| `ipix` | — | HEALPix pixel index (NESTED) |
| `dRA(mas)` | mas | Position correction Δα·cosδ at J2000.0 |
| `dDEC(mas)` | mas | Position correction Δδ at J2000.0 |
| `pmRA[mas/yr]` | mas yr⁻¹ | Proper motion correction in RA |
| `pmDEC[mas/yr]` | mas yr⁻¹ | Proper motion correction in Dec |

All corrections are in the sense **(catalog − Gaia DR3)**, referred to epoch **J2000.0**.

`nside64` tables are sparse (only pixels with sufficient cross-match data are present).
`nside256` tables cover the full sky via BFS interpolation; pixels far from the original
catalog footprint are extrapolated — use with care for catalogs with limited sky coverage
(AGK1: ~3 %, AC: ~30 %).

---

## Correction Formula

To correct an observation made with catalog *X* at epoch *t* (Julian year):

```
dRA(t)  = dRA₀  + (t − 2000.0) × pmRA
dDEC(t) = dDEC₀ + (t − 2000.0) × pmDEC
```

Subtract `dRA(t)` and `dDEC(t)` from the observed position (both in mas).

---

## Quick Start

```bash
unzip tables_nside64.zip
unzip tables_nside256.zip
pip install -r requirements.txt
python query_bias.py --ra 100.0 --dec 45.0 --catalog ucac4 --time 1995.5
```

Returns a JSON with the bias values from both `nside64` and `nside256` tables,
already propagated to the requested epoch.

---

## Results

All-sky systematic bias maps for three representative catalogs:

**USNO-A2.0** — no proper motions; large-scale positional gradients exceed 200 mas over much of the sky.

![USNO-A2.0 sky map](usno_a2_systematics_map.png)

**AGK3** — photographic plate catalog; plate-boundary discontinuities are clearly visible.

![AGK3 sky map](agk3_systematics_map.png)

**UCAC4** — modern ground-based catalog; corrections are at the few-mas level.

![UCAC4 sky map](ucac4_systematics_map.png)

Sky maps and statistical distributions for all 17 catalogs are in [`figures.zip`](figures.zip).

---

## License

Released under the [Creative Commons Attribution 4.0 International License (CC BY 4.0)](LICENSE).