We investigate the relation between star formation rate (SFR) and gas surface densities in Galactic star forming regions using a sample of young stellar objects (YSOs) and massive dense clumps. Our YSO sample consists of objects located in 20 large molecular clouds from the Spitzer cores to disks (c2d) and Gould's Belt (GB) surveys. These data allow us to probe the regime of low-mass star formation essentially invisible to tracers of high-mass star formation used to establish extragalactic SFR-gas relations. We estimate the gas surface density (Σ gas ) from extinction (A V ) maps and YSO SFR surface densities (Σ SFR ) from the number of YSOs, assuming a mean mass and lifetime. We also divide the clouds into evenly spaced contour levels of A V , counting only Class I and Flat SED YSOs, which have not yet migrated from their birthplace. For a sample of massive star forming clumps, we derive SFRs from the total infrared luminosity and use HCN gas maps to estimate gas surface densities. We find that c2d and GB clouds lie above the extragalactic SFR-gas relations (e.g., Kennicutt-Schmidt Law) by factors up to 17. Cloud regions with high Σ gas lie above extragalactic relations up to a factor of 54 and overlap with high-mass star forming regions. We use 12 CO and 13 CO gas maps of the Perseus and Ophiuchus clouds from the COMPLETE survey to estimate gas surface densities and compare to measurements from A V maps. We find that 13 CO, with the standard conversions to total gas, underestimates the A Vbased mass by factors of ∼4-5. 12 CO may underestimate the total gas mass at Σ gas 200 M ⊙ pc −2 by 30%; however, this small difference in mass estimates does not explain the large discrepancy between Galactic and extragalactic relations. We find evidence for a threshold of star formation (Σ th ) at 129±14 M ⊙ pc −2 . At Σ gas > Σ th , the Galactic SFR-gas relation is linear. A possible reason for the difference between Galactic and extragalactic relations is that much of Σ gas is below Σ th in extragalactic studies, which detect all the CO-emitting gas. If the Kennicutt-Schmidt relation (Σ SFR ∝ Σ 1.4 gas ) and a linear relation between dense gas and star formation is assumed, the fraction of dense star forming gas (f dense ) increases as ∼ Σ 0.4 gas . When Σ gas reaches ∼300Σ th , the fraction of dense gas is ∼1, creating a maximal starburst.

We present the full catalog of Young Stellar Objects (YSOs) identified in the 18 molecular clouds surveyed by the Spitzer Space Telescope "cores to disks" (c2d) and "Gould Belt" (GB) Legacy surveys. Using standard techniques developed by the c2d project, we identify 3239 candidate YSOs in the 18 clouds, 2966 of which survive visual inspection and form our final catalog of YSOs in the Gould Belt. We compile extinction corrected SEDs for all 2966 YSOs and calculate and tabulate the infrared spectral index, bolometric luminosity, and bolometric temperature for each object. We find that 326 (11%), 210 (7%), 1248 (42%), and 1182 (40%) are classified as Class 0+I, Flat-spectrum, Class II, and Class III, respectively, and show that the Class III sample suffers from an overall contamination rate by background AGB stars between 25% and 90%. Adopting standard assumptions, we derive durations of 0.40 − 0.78 Myr for Class 0+I YSOs and 0.26 − 0.50 Myr for Flat-spectrum YSOs, where the ranges encompass uncertainties in the adopted assumptions. Including information from (sub)millimeter wavelengths, one-third of the Class 0+I sample is classified as Class 0, leading to durations of 0.13−0.26 Myr (Class 0) and 0.27 − 0.52 Myr (Class I). We revisit infrared color-color diagrams used in the literature to classify YSOs and propose minor revisions to classification boundaries in these diagrams. Finally, we show that the bolometric temperature is a poor discriminator between Class II and Class III YSOs.20 Class 0 protostars are the youngest class of YSOs; see §3.1 for the formal definition of this class of objects. 21 The quantity α is defined as the slope of the infrared SED in log(λS λ ) vs. log(λ) and is used to classify YSOs, as discussed in detail in §3.1 and §3.2. While α calculated from extinction corrected photometry is used in later sections, here we use the values calculated from the observed photometry for consistency with the previous studies to which we compare.

We investigate the relation between the star formation rate surface density (Σ SF R ) and the mass surface density of gas (Σ gas ) in NGC 5194 (a.k.a. M51a, Whirlpool Galaxy). VIRUS-P integral field spectroscopy of the central 4.1 × 4.1 kpc 2 of the galaxy is used to measure Hα, Hβ, [NII]λλ6548,6584, and [SII]λλ6717,6731 emission line fluxes for 735 regions ∼170 pc in diameter. We use the Balmer decrement to calculate nebular dust extinctions, and correct the observed fluxes in order to measure accurately Σ SF R in each region. Archival HI 21cm and CO maps with similar spatial resolution 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 Σ gas and Σ SF R , and is free of the systematics involved in performing linear correlations over incomplete data in logarithmic space. After rejecting regions whose nebular spectrum is affected by the central AGN in NGC 5194, we use the [SII]/Hα 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 Hα luminosity integrated over the whole central region, but on local scales it can account for up to a 100% of the Hα emission, especially in the inter-arm regions. After removing the DIG contribution from the Hα fluxes, we measure a slope N = 0.82±0.05, and an intrinsic scatter ǫ = 0.43 ± 0.02 dex for the molecular gas SFL. We also measure a typical depletion timescale τ = Σ HI+H2 /Σ SF R ≈ 2 Gyr, in good agreement with recent measurements by Bigiel et al. (2008). 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 Hα 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 [NII] 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. (2007) 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=τ −1 ) in the molecular component of the ISM. The data shows an excellent agreement with the recently proposed model of the SFL by Krumholz et al. (2009b). The large intrinsic scatter observed may imply the existence of other parameters, beyond the availability of gas, which are important at settin...

We test some ideas for star formation relations against data on local molecular clouds. On a cloud by cloud basis, the relation between the surface density of star formation rate and surface density of gas divided by a free-fall time, calculated from the mean cloud density, shows no significant correlation. If a crossing time is substituted for the free-fall time, there is even less correlation. Within a cloud, the star formation rate volume and surface densities increase rapidly with the corresponding gas densities, faster than predicted by models using the free-fall time defined from the local density. A model in which the star formation rate depends linearly on the mass of gas above a visual extinction of 8 mag describes the data on these clouds, with very low dispersion. The data on regions of very massive star formation, with improved star formation rates based on free-free emission from ionized gas, also agree with this linear relation.