Abstract

This study explores the effects of different assumptions and systematics on the determination of the local, spatially resolved star formation law. Using four star formation rate (SFR) tracers (H alpha with azimuthally averaged extinction correction, mid-infrared 24 mu m, combined H alpha and mid-infrared 24 mu m, and combined far-ultraviolet and midinfrared 24 mu m), several fitting procedures, and different sampling strategies, we probe the relation between SFR and molecular gas at various spatial resolutions (500 pc and larger) and surface densities (Sigma(H2) approximate to 10-245 M-circle dot pc(-2)) within the central similar to 6.5 kpc in the disk of NGC 4254. We explore the effect of diffuse emission using an unsharp masking technique with varying kernel size. The fraction of diffuse emission, f(DE), thus determined is a strong inverse function of the size of the filtering kernel. We find that in the high surface brightness regions of NGC 4254 the form of the molecular gas star formation law is robustly determined and approximately linear (similar to 0.8-1.1) and independent of the assumed fraction of diffuse emission and the SFR tracer employed. When the low surface brightness regions are included, the slope of the star formation law depends primarily on the assumed fraction of diffuse emission. In such a case, results range from linear when the fraction of diffuse emission in the SFR tracer is f(DE) less than or similar to 30% (or when diffuse emission is removed in both the star formation and the molecular gas tracer) to super-linear (similar to 1.4) when f(DE) greater than or similar to 50%. We find that the tightness of the correlation between gas and star formation varies with the choice of star formation tracer. The 24 mu m SFR tracer by itself shows the tightest correlation with the molecular gas surface density, whereas the H alpha corrected for extinction using an azimuthally averaged correction shows the highest dispersion. We find that for R 0.5R(25) the local star formation efficiency is constant and similar to that observed in other large spirals, with a molecular gas depletion time tau(dep) similar to 2 Gyr.