How Universal Is the Schmidt Relation? (based on Kumari et al. 2020)

N. Kumari (kumari[at]

Star formation is a complex, multi-scale phenomenon which is central to our understanding of the origin of stars and planetary systems, as well as the structure and evolution of galaxies. Maarten Schmidt attempted to explain this complex process via a simple power-law relation between the densities of the star-formation rate (SFR) and gas (Schmidt 1959, 1963), which is famously called the Schmidt relation and remains one of the most widely investigated relations even after 60 years.

The Schmidt relation is generally expressed as ΣSFR = AΣNgas, where ΣSFR and Σgas are the surface densities of SFR and total gas (atomic and molecular), respectively, N is the power-law index and A is the average efficiency of star formation of the system under study (e.g., star-forming regions, galaxies). Kennicutt (1998) determined the value of N = 1.4 ± 0.1, empirically using a dataset of normal spirals and starbursts and hence established the disk-averaged star-formation relation, called the Schmidt-Kennicutt relation. This relation has been used successfully in various models of galaxy formation and evolution. However, it is not clear whether this disk-averaged relation is fundamental and holds at different scales and environments, which might not be the case because a disk-averaged relation will potentially result in averaging the enormous variations of several properties. Hence, it is essential to investigate this relation at spatially resolved scales.

Spatially resolved Schmidt relation

In the last two decades, several observational analyses have focused on the Schmidt relation at sub-galactic scales. These studies have resulted in a multitude of power-law indices of the Schmidt relation, leading to different implications and interpretations, which cast doubt on whether the relationship is fundamental and universal. Moreover, the spatially resolved studies generally point towards a linear molecular gas Schmidt relation (e.g., Bigiel et al. 2008) in contrast to a super-linear total gas Schmidt relation for entire galaxies. The discrepancy in results may be due to various factors such as the validity of SFR diagnostics at local scales, appropriate molecular gas tracers, and the conversion factor of CO to molecular gas.

This article concerns one such factor, the "diffuse background" which refers to the component of the interstellar medium unrelated to the "current" star formation. It is based on a recent article (Kumari et al. 2020) and is one of the very few studies to explore the effect of diffuse background on spatially resolved Schmidt relation. This work shows that removal of the component from SFR tracers and atomic gas results in a similar global and local Schmidt relation, where N = 1.4 ± 0.1 and agrees with the dynamical models of star formation (Elmegreen et al. 2015), accounting for the flaring effects in the outer regions of galaxies.

Accounting for diffuse background

Using multi-wavelength data from surveys such as Spitzer Infrared Near Galaxies Survey (SINGS), Key Insights on Nearby Galaxies: A Far-Infrared Survey with Herschel, The H Ⅰ Nearby Galaxy Survey, and HERA CO-Line Extragalactic Survey, Kumari et al. (2020) analyze the Schmidt relation at local scales (0.5­–2 kpc) within nine nearby spiral galaxies. We used Nebuliser software on the images of the SFR tracers (Hα, FUV and MIPS 24 µm), as well as atomic gas to separate the diffuse component from these images, by essentially splitting the overall light distribution as a function of spatial scale. Figure 1 shows the images of the SFR tracers of one of the sample galaxies, before and after subtraction of diffuse background and highlights the complex, varying nature of this component (bottom panel). On average, the fraction of diffuse background accounts to ~34% in Hα, ~43% in FUV, ~37% in 24 µm and ~75% in H Ⅰ, and varies from galaxy to galaxy.

galaxies diffuse area removed
Figure 1: Upper panel: Original images of SFR tracers, Hα, FUV and MIPS 24 µm. Middle panel: Images after diffuse background subtraction using Nebuliser, and containing only potential star-forming regions. Bottom panel: Images showing the complex, spatially varying nature of the diffuse background.

We use Hα maps of sample galaxies to select potential star-forming regions, as well as the regions in between, and perform aperture photometry on images of SFR tracers and gas tracers (atomic H Ⅰ and molecular CO). SFR tracers such as Hα and FUV suffer from internal dust attenuation, which we correct by combining them with infrared MIPS 24 µm data. We then estimate SFR from attenuation-corrected luminosities of Hα and FUV by using SFR recipes from Calzetti et al. (2007) and Leroy et al. (2008), respectively. Finally, we study the Schmidt relation for atomic gas, molecular gas, and total gas for all galaxies, using data both before and after subtraction of diffuse background.

Elmegreen model satisfies total gas Schmidt relation

Figure 2 shows the total gas Schmidt relation, i.e., SFR surface density against total gas (atomic + molecular) surface density for all regions (with S/N > 3) within all sample galaxies, where the diffuse background has been subtracted from SFR tracers as well as atomic gas. We find that the best-fit line (black line) to these data agrees very well with a dynamical model (yellow line; Elmegreen 2015) with constant scale height (H = 100 pc), meaning that there is no flaring. Such a model does not agree with the Schmidt relation study where we do not subtract the diffuse background, or where the diffuse background is subtracted only from SFR tracers, or from both SFR tracers and gas tracers. This might indicate that removing the diffuse background component using Nebuliser essentially removes the atomic gas from vertically extended regions in the flared outskirts of galaxies, which do not contribute to the current star formation.

scatter chart
Figure 2: Total gas Schmidt relation where the diffuse background is subtracted from SFR tracers as well as atomic gas. The blue points with green error bars correspond to all identified regions within all sample galaxies.  We fitted ΣSFR and Σgas in logarithmic space, using an unweighted fit justified by the fact that systematic uncertainties as large as 30–50% are present on both axes related to SFR calibration and CO-to-H2 conversion factor [X(CO)]. SFR estimates assume a Kroupa IMF, and molecular gas estimates assumes an X(CO) factor of 2 × 1020 cm–2 (K km s–1)–1. The dynamical model of Elmegreen (2015) explains the best-fit line very well. (Adapted from Kumari et al. 2020.)


Agreement between local and global Schmidt relation

Figure 3 shows the total gas Schmidt relation for all spatially resolved measurements in the current galaxy sample, along with integrated measurements from several studies including spiral galaxies, starbursts, low surface brightness galaxies, and dwarf galaxies. We find that the  power-law index of the local (black line) and global (magenta) Schmidt relation are identical within the uncertainties. Moreover, the best-fit line to the spatially resolved data also passes through the integrated measurements corresponding to irregular and LSB galaxies.

Schmidt relations scatter plot
Figure 3: Comparison of total gas Schmidt relations at global and local scales, showing an agreement between their power-law indices. Blue points with green error bars denote the spatially resolved data from Kumari et al. (2020), where the diffuse background is subtracted from SFR tracers and atomic gas. Global data comprised of starbursts (stars) and spirals (yellow dots) from Kennicutt 1998, dIrrs (squares) from Roychowdhury et al. (2017) and low-surface brightness galaxies from Wyder (2009). For this comparison, SFR are estimated for a Salpeter IMF and molecular gas estimates assume a conversion factor of 2.8 × 1020 cm–2 (K km s–1)–1.

However, an offset is observed in the zero points of the global and local relation, and a closer look at such Schmidt relation plots for individual galaxies suggests significant variations in the power-law index from galaxy to galaxy, which might result due to various systematic effects. Though such systematic effects and their sources need to be explored further, the current study suggests that both atomic and molecular gas in the disk might contribute to star formation at both local and global scales, and diffuse background subtraction has probably revealed the atomic gas component contributing toward star formation. This study is thus a step toward demystifying the universality of the Schmidt relation, should that exist. 


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