Characterizing Earth analogs may require a moderate or high-resolution spectrograph
A primary goal of the Habitable Worlds Observatory (HWO) is to detect and measure the abundance of biosignature molecules, such as water (H2O) and oxygen (O2), in the atmosphere of Earth analogs. This is expected to require deep spectroscopic observations lasting hundreds of hours per planet. In this context, it is essential to optimize the spectral resolution of the spectrograph to both maximize the number of planets that can be studied over the lifetime of the mission, and also to reduce the risks of false detections. The purpose of this work is to provide a framework to explore the spectral resolution design trade-space for HWO. This framework must be valid and comparable across all spectral resolutions from low (R<100) to high resolutions (R>10,000), and account for the spectral correlation of the residual starlight (i.e., speckle noise chromaticity). Leveraging the concept of "template matching", we develop a simulation toolkit based on the Python package EXOSIMS to compute the detection significance of planets and molecules. We then simulate observations of Earth analogs around 164 stars using representative mission parameters to explore the effects of the detector noise and the correlated speckle noise floor. Our findings suggest that a moderate or high resolution spectrograph (R>1,000) will provide higher sensitivity to critical molecules compared to a low resolution spectroscopy mode (e.g., R~140). The correlated speckle noise may also entirely suppress our ability to detect bio-signatures at low spectral resolutions. We conclude that a more comprehensive study combined with detailed models of its stability, and other sources of correlated noise, is necessary to fully explore the trade space of spectral resolution and detectability of key species.