THE SPATIALLY RESOLVED STAR FORMATION LAW FROM INTEGRAL FIELD SPECTROSCOPY: VIRUS-P OBSERVATIONS OF NGC 5194

We investigate the relation between the star formation rate (SFR) surface density (Sigma(SFR)) and the mass surface density of gas (Sigma(gas)) in NGC 5194 (a.k.a. M51a, Whirlpool Galaxy). Visible Integral field Replicable Unit Spectrograph Prototype (VIRUS-P) integral field spectroscopy of the central 4.1 x 4.1 kpc(2) of the galaxy is used to measure H alpha, H beta, [O III]lambda 5007, [N II]lambda lambda 6548,6584, and [S II]lambda lambda 6717,6731 emission line fluxes for 735 regions similar to 170 pc in diameter. We use the Balmer decrement to calculate nebular dust extinctions, and correct the observed fluxes in order to accurately measure Sigma(SFR) in each region. Archival HI 21 cm and CO maps with spatial resolution similar to that of VIRUS-P are used to measure the atomic and molecular gas surface density for each region. We present a new method for fitting the star formation law (SFL), which includes the intrinsic scatter in the relation as a free parameter, allows the inclusion of non-detections in both Sigma(gas) and Sigma(SFR), and is free of the systematics involved in performing linear regressions over incomplete data in logarithmic space. After rejecting regions whose nebular spectrum is affected by the central active galactic nucleus in NGC 5194, we use the [S II]/H alpha ratio to separate spectroscopically the contribution from the diffuse ionized gas ( DIG) in the galaxy, which has a different temperature and ionization state from those of H II regions in the disk. The DIG only accounts for 11% of the total H alpha luminosity integrated over the whole central region, but on local scales it can account for up to a 100% of the H alpha emission, especially in the inter-arm regions. After removing the DIG contribution from the H alpha fluxes, we measure a slope N = 0.82 +/- 0.05, and an intrinsic scatter epsilon = 0.43 +/- 0.02 dex for the molecular gas SFL. We also measure a typical depletion timescale tau = Sigma(HI+H2)/Sigma(SFR) approximate to 2 Gyr, in good agreement with recent measurements by Bigiel et al. The atomic gas density shows no correlation with the SFR, and the total gas SFL in the sampled density range closely follows the molecular gas SFL. Integral field spectroscopy allows a much cleaner measurement of H alpha emission line fluxes than narrow-band imaging, since it is free of the systematics introduced by continuum subtraction, underlying photospheric absorption, and contamination by the [N II] doublet. We assess the validity of different corrections usually applied in narrow-band measurements to overcome these issues and find that while systematics are introduced by these corrections, they are only dominant in the low surface brightness regime. The disagreement with the previous measurement of a super-linear molecular SFL by Kennicutt et al. is most likely due to differences in the fitting method. Our results support the recent evidence for a low, and close to constant, star formation efficiency (SFE = tau(-1)) in the molecular component of the interstellar medium. The data show an excellent agreement with the recently proposed model of the SFL by Krumholz et al. The large intrinsic scatter observed may imply the existence of other parameters, beyond the availability of gas, which are important in setting the SFR.