SVD Spectral Decomposition for Stellar/Planetary Signal Separation: Earth and Venus Atmospheric Analogues as Coronagraphic Contrast Benchmarks for HWO - Presentation to PHYSCOS Second Early Career Workshop [September 2025]

Presentation submitted to the NASA Physics of the Cosmos (PhysCOS) 2nd Early Career Workshop, September 23–25, 2025. This work frames the coronagraphic contrast floor for the Habitable Worlds Observatory (HWO) using Venus and Earth as bracketing atmospheric analogues. Venus (CO₂/H₂SO₄, contrast ~10⁻⁹) and Earth (O₂/O₃/H₂O, contrast ~10⁻¹⁰) span the detection regime HWO must operate in, with Earth sitting at the hard floor that defines the pointing-stability and contrast budget requirement. An SVD-based spectral decomposition method is presented using the method of snapshots on a high-dimensional stellar flux basis (wavelengths × stars). The stellar subspace is constructed from the dominant eigenmodes and removed via null-space projection, isolating the planetary biomarker signal in the orthogonal complement. The method is motivated by the Roman GRISM survey geometry as a high-dimensional input basis and validated conceptually against HITRAN-derived absorption features for the Venus/Earth atmospheric pair. The central result is that at the 10⁻¹⁰ contrast floor, the Venus analogue survives stellar-shape subtraction while the Earth analogue does not, surfacing the sub-2×10⁻¹⁰ contrast and sub-milliarcsecond pointing requirement subsequently verified in a separate Basilisk GNC simulation pipeline.