Estimating SFR in star‐forming galaxies - astro-wiki/astrowiki GitHub Wiki

By Lulu Zhang, originally posted on 2020 July 1.

The basic goal of measuring SFR is to identify emission that probes newly or recently formed stars, while avoiding as much as possible contributions from evolved stellar populations.

For measuring SFRs in resolved regions, such as regions within the Milky Way, the principle is to count individual objects or events (e.g., supernovae) that trace the recent star formation (Chomiuk & Povich 2011). While for unresolved systems, measurements of SFR is merely measures of luminosity, either monochromatic or integrated over some wavelength range, and the principle is to measure continuum or line emission that are sensitive to the short-lived massive stars, namely, the star forming activities (Calzetti 2013; Kennicutt & Evans 2012).

In general, SFR indicators in the UV/optical/near-IR range ($\sim$⁠0.1–5 μm) probe the direct stellar light emerging from galaxies, while SFR indicators in the mid/far-IR ($\sim$⁠5–1000 μm) probe the stellar light reprocessed by dust. Tracers include hydrogen recombination lines, from the optical, through the near-IR, all the way to radio wavelengths, forbidden metal lines, and, in the millimetre range, the free-free emission. The X-ray emission produced by high-mass X-ray binaries, massive stars, and supernovae can also, in principle, be used to trace SFRs. Finally, the synchrotron emission from galaxies can be calibrated as a SFR indicator (Condon 1992), since cosmic rays are produced and accelerated in supernova remnants, and core-collapse supernovae represent 70% or more of the total supernovae in star-forming galaxies (Boissier & Prantzos 2009).

1. Ultraviolet Continuum

  • The UV emission of galaxies longward of the Lyman-continuum break directly traces the photospheric emission of young stars and, hence, is one of the most direct tracers of the recent SFR. As UV flux primarily originates from the photospheres of O- through later-type B-stars ($M_\ast\ge3M_\odot$), it measures star formation averaged over a $\sim$⁠100 Myr timescale.
  • The primary disadvantage of the UV is its sensitivity to interstellar dust attenuation and necessary correction is usually required (Hao et al. 2011).

2. Optical Emission Lines

  • Young, massive stars produce copious amounts of ionising photons that ionise the surrounding gas. Hydrogen recombination cascades produce line emission, including the well-known Balmer series lines of Hα (0.6563 μm) and Hβ (0.4861 μm), which represent the most traditional SFR indicators (Kennicutt 1998, Kennicutt et al. 2009). For example, Hα nebular emission arises from the recombination of gas ionized by the most massive O- and early-type B-stars ($M_\ast\ge17M_\odot$). It therefore traces star formation over the lifetimes of these stars, which is on the order of a few million years.
  • From the first principle, the relation between the intensity of a hydrogen recombination line and the ionising photon rate is dictated by quantum mechanics, for a nebula that is optically thick to ionising photons (case B, Osterbrock & Ferland 2006).
  • The largest systematic errors affecting Hα-based SFRs are dust attenuation and sensitivity to the population of the upper IMF in regions with low absolute SFRs (e.g., Cerviño et al. 2002; Lee et al. 2009).

3. Infrared Signatures of Star Formation

Interstellar dust absorbs approximately half of the starlight in the Universe and re-emits it in the IR, so measurements in the IR are essential for deriving a complete inventory of star formation.

Circus Galaxy IR SED
Circus Galaxy infrared spectral energy distribution highlighting key spectral tracers of star formation (blue), black hole accretion (red), and warm molecular gas (green). Figure taken from Pope et al. (2019).

3.1. dust spectral features (PAH)

  • The IR emission by PAHs is an IR fluorescence process where absorption of a single FUV photon from newly formed stars leads to electronic excitation. This electronic energy is eventually radiated away through the IR vibrational modes of PAHs. Thus PAH molecules exhibit its potential to be an indirect tracer of the strength of UV radiation field and namely the SFR (Allamandola et al. 1989; Shipley et al. 2016, Xie & Ho 2019).

3.2. atomic fine-structure emission lines

  • Atomic fine-structure emission lines, such as [Ne II] 12.7 μm, [Ne III] 15.5 μm, and [S III] 18.7 μm, 33.5 μm are produced in the H II-regions surrounding young stars and have been shown to correlate extremely well with the star-formation rates derived from the dust continuum and hydrogen recombination lines (e.g., Ho & Keto 2007; Meléndez et al. 2008; Inami et al. 2013; Zhuang et al. 2019).

3.3. dust continuum

  • The shape of the mid-to-far IR dust continuum itself is sensitive to the relative heating by AGN and star formation (e.g., Veilleux et al. 2009; Kirkpatrick et al. 2015). For each galaxy, simple conversion between the far-infrared luminosity and the emitted flux from young stars (e.g., Murphy et al. 2011; Kennicutt 1998) allows for a derivation of the current SFR in each source but they always rely on model fitting and assumptions about the stellar populations and dust distributions in galaxies.

4. Radio Continuum

  • Radio continuum emission from galaxies covering about 0.25–30 cm (1–120 GHz) is powered by a mix of physical emission processes, each providing independent information on the star formation and interstellar medium properties of galaxies. From the well-established FIR-radio correlation (e.g., Helou et al. 1985; Condon 1992), non-thermal synchrotron emission act as a valuable tracer of the total amount of star formation in galaxies, unbiased by dust.
  • However, the mix of radio emission from different physical processes sometime will result in large uncertainty in the SFR calibrated by radio emission. What's more, cosmic ray electrons lose energy through inverse Compton scattering off photons from the cosmic microwave background (CMB). This loss of energy scales as $(1+z)^4$ so that non-thermal radio emission from galaxies should become severally suppressed with increasing redshift.

Model spectrum for an SFG
A model radio-to-infrared spectrum for a star-forming galaxy, showing that observations at frequencies spanning 2–10 GHz provide direct access to free-free emission, whose contribution increases with frequency, and thus with the rest-frame emission from high-$z$ galaxies. Figure taken from Pope et al. (2019).

5. X-ray emission

  • The component of X-ray emission that does not arise from AGN accretion disks is dominated by massive X-ray binaries, supernovae and supernova remnants, and massive stars, all associated with young stellar populations and recent star formation. Furthermore, the observed 2–10 keV fluxes of galaxies are observed to be strongly correlated with their IR and nonthermal radio continuum fluxes (e.g., Bauer et al. 2002; Ranalli et al. 2003; Symeonidis et al. 2011), thereby strengthening the link to the SFR.
  • Because the relation between X-ray luminosity and SFR cannot be calibrated from first principles, this calibration is usually bootstrapped from the IR or radio (Ranalli et al. 2003)

6. References

Most content above is from Calzetti 2013; Kennicutt & Evans 2012; Pope et al. 2019 and more detail therein.

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