Star Formation in the Milky Way and Nearby Galaxies

“Various objections and caveats to this appealing picture have been registered (e.g., Swift & Williams 2008; Reid et al. 2010; Clark et al. 2007; Hatchell & Fuller 2008).”

“More recent determinations over a wider range of masses, including brown dwarfs, indicate a clear flattening at lower masses, either as broken power laws (Kroupa et al. 1993) or a log-normal distribution (Miller & Scalo 1979; Chabrier 2003).”

“This uncertainty range does not include all possible systematic errors, arising for example from changes in X(CO) or the IMF with increasing surface density or SFR. Major systematic changes in either of these could easily change the derived value of N by as much as 0.2–0.3.”

“The High-density Regime The two regimes discussed above were able to reproduce all of the early observations of the large-scale star formation law by Kennicutt (1989, 1998b) and Martin & Kennicutt (2001).”

“The results cited here use the Starburst99 models of Leitherer et al. (1999), which are regularly updated in the on-line version of the package.”

“The High-density Regime The two regimes discussed above were able to reproduce all of the early observations of the large-scale star formation law by Kennicutt (1989, 1998b) and Martin & Kennicutt (2001).”

“This section focusses on the transformational results which have come from the Spitzer Space Telescope (Werner et al. 2004) and the Herschel Space Observatory (Pilbratt et al. 2010).”

“The mass dependence of the SSFR has been explored by numerous investigators (e.g., Brinchmann et al. 2004; Salim et al. 2007; Schiminovich et al. 2007; Lee et al. 2007).”

“For extragalactic studies, this subject has been revolutionised by the launch of the Galaxy Evolution Explorer (GALEX) mission (Martin et al. 2005a).”

“The masses of embedded young clusters (Lada & Lada 2003), OB associations (McKee & Williams 1997), and massive open clusters (Elmegreen & Efremov 1997; Zhang & Fall 1999), follow a similar relation with γcluster ∼ 1.”

“…average the star-formation activity over different time intervals, e.g., the Hα SFR-indicator is sensitive to the star-formation activity over the past 6 Myr, whereas the SFR derived from rest-frame UV continuum averages over a time period of 100 Myr (e.g., Kennicutt & Evans 2012; Calzetti 2013).”

“Equation 7 corresponds to the calibration by Murphy et al. (2011, see also Kennicutt & Evans 2012) and we prefer this approach because it links us cleanly to previous work comparing HCN and CO, which has focused mostly on the integrated IR luminosity as a star formation rate tracer.”

“Therefore, whenever possible, we also measured galaxy IR luminosities (8–1000µm; LIR) to estimate directly the levels of UV power obscured and reprocessed by dust (see, e.g., Kennicutt 1998 and Kennicutt & Evans 2012 for reviews).”

“14A recent review of such ’Star-Formation Laws’ in nearby galaxies is presented by Kennicutt & Evans (2012).”

“Star formation in the MW is discussed in the recent review of Kennicutt & Evans (2012).”

“1 IN T RO D U C T I O N The total infrared (IR) luminosity (LIR) of galaxies has been used to infer the star formation rate (SFR) of galaxies for decades (see Kennicutt 1998a; Kennicutt & Evans 2012 for reviews).”

“…Molecular Clouds (GMCs), the actual seeds of star formation, themselves could profoundly impact their star formation capabilities as evidenced by the large scatter of observed star formation rates (SFRs) in local Galactic GMCs (Mooney & Solomon 1988; Kennicutt & Evans 2012; Heiderman et al. 2010).”

“The observed stellar emission traced either by FUV or Hα has to be corrected for dust attenuation, and this correction is usually made using observational dust tracers such as the TIR or 24 µm luminosities (Kennicutt et al. 2009; Calzetti et al. 2010; Hao et al. 2011; Kennicutt & Evans 2012).”

“We derive the star formation rate for the whole system from the LTIR ≈ 3.5× 1010 L reported by Sanders et al. (2003, this has been adjusted to our adopted distance) and the IR-to-SFR conversion of Kennicutt & Evans (2012).”

“…star formation tracers: Hα, FUV and 24 µm On average, interstellar dust absorbs roughly half the starlight of typical spiral galaxies and re-emits it in the infrared; therefore, observations in the infrared are essential for deriving a complete inventory of star formation (Kennicutt & Evans 2012).”

“In addition to mass, we also estimate an unobscured star formation rate (SFR) for each galaxy based on the estimated rest-frame NUV flux at effective wavelength λeff = 2267 Å and the corresponding calibration coefficient from Kennicutt & Evans (2012).”

“The SFR also requires a conversion that is related not only to the IMF, but also to the fact that the SED modeling used by Saintonge et al. to estimate SFRs is sensitive to activity over ∼100Myr, while the Hα we use is sensitive over a much shorter timescale of ∼10Myr (e.g., Kennicutt & Evans 2012).”

“Despite signi fi cant evolution in galaxy properties over cosmic time, SFR measurements are still based on locally calibrated diagnostics using nearby galaxies ( Kennicutt & Evans 2012 ) .”

“Star Formation Rate Surface Density and Stellar Mass We convert the observed properties into a star formation rate surface density, ΣSFR, assuming the Hβ and FUV star formation rate calibrations from Kennicutt & Evans (2012) and dividing by 2πr250,NUV following Naidu et al. (2020).”

“From the measured Hα flux extracted in a region of 1.6” × 1.6” around the clump, assuming the star formation rate calibration of Kennicutt & Evans (2012), and correcting for dust extinction using the Balmer decrement Hα/Hβ assuming a Calzetti (2000) extinction law, we derive a star formation rate…”

“Rich clusters are an important, perhaps the dominant, mode of star formation in the Galaxy (see reviews by Lada & Lada 2003; Allen et al. 2007; Kennicutt & Evans 2012).”

“Since gas surface density is directly linked to the SSFR via the Schmidt–Kennicutt (Kennicutt & Evans 2012) relation, it can explain the observed increase of cluster formation efficiency.”

“If we adopt the “standard” FIR–SFR conversion factor for local galaxies (Kennicutt & Evans 2012) this upper limit on the FIR luminosity translates into an 2σ upper limit on the IR-derived star formation rate of SFR 12 M yr−1, which is consistent with the SFR inferred for the rest-frame UV…”

“This emission also traces the star-formation activity over 100Myr (Kennicutt & Evans 2012).”

“The emission lines trace the most recent star formation and measure the rate at which stars form (Kennicutt 1998; Kennicutt & Evans 2012).”

“By using the Kennicutt & Evans (2012) relation Log(SFR/M yr−1) = Log(LHα/erg s−1) - 41.27, we derived a total SFR from Hαnar of SFR∼ 50 M yr−1 for LBQS0109 and SFR∼ 90 M yr−1 for HB8903, which is consistent with the wide ranges of SFR observed in star-forming and QSO host galaxies at similar…”

“Kennicutt & Evans (2012), in their Figure 7, show that the star formation rate per unit area Σ̇? falls off more slowly than the surface density of molecular gas Σgas.”

“However, despite the conversionof gas into stars being a cornerstone of astrophysics and cosmol gy, we lack a clear understanding of the physics governing this process (Kennicutt & Evans 2012).”

“…in which galaxies reside are relatively well-constrained (e.g. Springel et al. 2005b; Planck Collaboration et al. 2014), connecting these haloes to the visible galaxy population hinges critically on the unknown physics of star formation and feedback (McKee & Ostriker 2007; Kennicutt & Evans 2012).”

“The molecular phase of the interstellar medium (ISM) is the birthplace of stars, and therefore it plays a central role in the evolution of galaxies (see the reviews in Kennicutt & Evans 2012; Bolatto et al. 2013; Carilli & Walter 2013).”

“The TIR-derived SFR is calculated using Equation 12 in Kennicutt & Evans (2012), log10SFRTIR (M yr −1) = log10LTIR − 43.41 (1) where LTIR is the TIR luminosity calculated using our TIR flux estimates and the distances to the galaxies.”

“Calzetti et al. (2013) and also for example Kennicutt & Evans (2012) provide a more detailed discussion of various SFR tracers and their interrelations.”

“The calibration itself usually leads to a 0.3 dex scatter on a galaxy basis (see also Condon 1992; Murphy et al. 2011; Kennicutt & Evans 2012).”

“We subsequently correct the Balmer-line SFR quantities for the escape of ionizing photons.”

“Several studies have thus derived calibrations of the star formation rate (SFR) based on LT IR (Kennicutt 1998; Pérez-González et al. 2006; Kennicutt et al. 2009; Kennicutt & Evans 2012).”

“The 0.1–1.0 M yr 1-☉ kpc −2 SFRáS ñ values for globular cluster formation inferred here are lower than the most extreme values observed in intense starbursts and luminous infrared galaxies: 10–100 M yr 1-☉ kpc −2 (e.g., Kennicutt & Evans 2012).”

“This emission has also become a widely used tracer of key astrophysical quanitites, including the star formation rate and the interstellar radiation field (see review by Kennicutt & Evans 2012).”

“Often SFRs are inferred using direct flux-to-SFR conversions which are derived via fixed assumptions about the properties of galaxy stellar populations (e.g. Kennicutt & Evans 2012).”

“The cloud mass spectrum, which describes the distribution by number of clouds of different masses, is possibly related to the mass functions of clusters and stars (Kennicutt & Evans 2012, and references therein).”

“Possible criteria of the starburst following are a high SFR with gas-consumption timescales of less than 1 Gyr and SFR surface density averaged over the disk above 0.1 M year−1 kpc−2 (Kennicutt and Evans 2012).”

“To estimate the star formation rates of our targets we used the SED-derived LIR,SF and the relationship from Kennicutt & Evans (2012), correcting to a Chabrier IMF by dividing by 1.7 (Chabrier 2003).”

“The combination of different SFR estimators is also needed to evaluate the potential differences between the current-day SFR given by Hα and that given by tracers sensitive to intermediate-aged stellar population (Kennicutt & Evans 2012; Calzetti 2013).”

“The IR luminosity is arguably the most reliable tracer of starforming activity and is well correlated with other tracers (see Kennicutt, 1998a; Kennicutt & Evans, 2012, for reviews).”

“…to the time-scale traced by recombination lines such as H α, whereas UV and FIR emission traces star formation over roughly the past 100 Myr (e.g. Kennicutt & Evans 2012).2 The instantaneous star formation rate of the gas particles covers a larger range of star formation rates because it is not…”

“Non-parametric models for the star formation history are commonly chosen because of their flexibility to account for a wide range of star formation history shapes, but such parameterizations systematically measure older ages with increased uncertainty 68 .”

“In the standard SFR calibrations from Kennicutt & Evans (2012), equating the UV SFR to the Hα SFR implies log10(ξion/Hz erg −1) = 25.12.”

“…and because molecular gas is the ISM phase that immediately precedes SF, observations of CO play a crucial role in understanding the ecosystems within and of galaxies across cosmic history (see reviews by, e.g., Kennicutt & Evans 2012; Bolatto et al. 2013; Carilli & Walter 2013; Heyer & Dame 2015).”

“Due to different timescales of Hα and UV light (Kennicutt & Evans 2012; Shivaei et al. 2015b), at the onset of a burst, there are more ionizing photons produced at a given UV luminosity and hence a larger ξion, while after the end of the burst, the ratio of ionizing to non-ionizing fluxes decreases.”

“Molecular gas observations of galaxies throughout cosmic time are fundamental to understand the cosmic history of formation and evolution of galaxies (see reviews by Kennicutt & Evans 2012; Carilli & Walter 2013).”

“Star formation follows amodified Kennicutt-Schmidt star formation relation (Kennicutt 1998b; Kennicutt & Evans 2012), and clouds occupy a volume filling factor of fclump = 0.01.”

“We have further selected objects with predicted Hβ flux of > 5× 10−18 erg s−1 cm−2 scaled from SFR in the catalog to Hα flux by using a conversion of Kennicutt & Evans (2012), assuming an intrinsic Hα/Hβ ratio of 2.86, and applying dust extinction by using E(B − V )star from the catalog with the…”

“A121, page 4 of 13 The free-free emission originates from H ii regions that are produced by massive stars (M > 15 M ), and therefore traces the star formation averaged over 3–10 Myr, which is the lifetime of O stars (e.g. Kennicutt & Evans 2012).”

“…1.1× 109M⊙, following MH2 [M⊙] = 5.5LCO(2−1) [K km s −1 pc2], where we assume a typical values for the CO(2-1)-to-CO(1-0) ratio of 0.8 (e.g., Leroy et al. 2009), and a standard Galactic CO(1-0)-to-H2 conversion factor of 2 × 1020 cm−2(Kkms−1)−1 (e.g., Kennicutt & Evans 2012; Feldmann et al. 2012).”

“…a relation between magnetic field strength and gas surface density, it is well-known that the gas surface density also correlates with star formation activity, known as the Kennicutt-Schmidt-relation (Schmidt 1959; Kennicutt 1998; Kennicutt et al. 2008; Walter et al. 2008; Kennicutt & Evans 2012).”

“For each galaxy we can infer the star-formation rate from both the UV (SFRUV) and FIR (SFRFIR) emission by adopting the calibrations presented in Kennicutt & Evans (2012).”

“The corresponding dust-obscured SFR estimated directly from the IR luminosity (Kennicutt & Evans 2012) is also indicated on the right axis.”

“We, therefore, converted the LMLVL SFRs to a Chabrier (2003) IMF using the scaling from Kennicutt & Evans (2012).”

“1 IN T RO D U C T I O N Our understanding of the mass assembly and star formation processes of the Universe has improved greatly over the past few decades (for in-depth reviews, see Kennicutt & Evans 2012 and Madau & Dickinson 2014).”

“…the dust is heated by star formation, we integrate the dust spectral energy distribution between the rest-frame wavelengths of 8 and 1000µm (e.g., Kennicutt & Evans 2012) to obtain the total infrared luminosity LTIR and convert LTIR to a SFR. Adopting a modified black body with the canonical Td…”

“We convert FUV, NUV, 12, and 22 μm intensity, Iν, to an estimate of the recent SFR using S » n- - -[ ] [ ] ( )M K Iyr kpc MJy sr , 3SFR 1 2 1 where K=1.04×10−1, 1.04×10−1, 3.77×10−3, and 2.97× 10−3 for FUV, NUV, 12μm, and 24 μm bands, respectively (Kennicutt & Evans 2012; Jarrett et al. 2013).”

“This star formation occurs at a rate following a volumetric Schmidt (1959) relation, with an imposed efficiency per free fall time of ∗ = 0.02, as motivated by observations (Kennicutt 1998; Kennicutt & Evans 2012; Narayanan et al. 2008, 2012; Hopkins et al. 2013).”

“…an optically thin modified blackbody spectrum with a dust temperature of Tdust = 35 K and a dust emissivity index of βdust = 1.6, and then applying: log ( SFRIR/M yr−1 ) = log (LIR/W) − 36.44, (9) which is the SFRIR calibration from Kennicutt & Evans (2012), converted to a Chabrier (2003) IMF.”

“1 (Evans et al. 2009; Bigiel et al. 2010; Kennicutt & Evans 2012).”

“Precise estimates of star formation rate (SFR) in galaxies also require correction for dust extinction (e.g., Steidel et al. 1999; Takeuchi et al. 2010; Kennicutt & Evans 2012).”

“For this galaxy, we converted Lobs70 to L obs 24 , using scaling relations from Kennicutt & Evans (2012) and Galametz et al. (2013).”

“Using the stellar population synthesis models of Bruzual & Charlot (2003) for constant star formation, we find equilibrium time scales (reaching 90% of the equilibrium value (Kennicutt & Evans 2012)) of 5 and 100 Myr for LHα and LUV , respectively.”

“Using the extinction-corrected luminosity of the narrow Hα emission from Reines et al. (2013) and the relation in Kennicutt & Evans (2012), we compute upper limits on the SFR for each galaxy by assuming that all the narrow Hα emission within the SDSS fiber is due to star formation.”

“Collisions of galaxies resulting in the overpressuring of their ISM and inducing enormous star formation rates are generally referred to as starbursts and are often observed as ultra luminous infrared galaxies (ULIRGs, Kennicutt & Evans (2012)).”

“Both the stellar mass and the star formation rates depend on the choice of the IMF, and SED-fitting method (e.g., Bastian et al. 2010; Kennicutt & Evans 2012; Leja et al. 2020).34 This temporal integral of the star formation rate density lies above the measured stellar mass density ρstars by a…”

“2) to correct the mass and Kennicutt & Evans (2012) to correct the SFR.”

“…desika.narayanan@ufl.edu forming galaxies is dominated by massive stars, direct measurements of UV starlight from galaxies (alongside an assumption of a stellar initial mass function) serves as one of the more straight forward methods for deriving a galaxy’s SFR (e.g. Kennicutt & Evans 2012).”

“We leave for future work the discussion of other SFIs that have more complex, non-linear relationships with the ionizing photon production rate (e.g. [O II] 372.7 nm, [Ne II] 12.8 µm, [Ne III] 15.6 µm – Kennicutt & Evans 2012).”

“This is not surprising, given the strong correlation between LIR and SFR (e.g. Kennicutt 1998; Kennicutt & Evans 2012).”

“Furthermore, how the necessary mass reservoir is assembled and tens of solar masses are accreted (rate Ṁ ∼ 10−4 − 10−2 M yr−1) on a timescale that is widely believed to be about 105 yr is also largely unclear (Kennicutt & Evans 2012; Behrend & Maeder 2001; Krumholz 2015).”

“3–3% for GMCs in the Milky Way and in nearby galaxies (see Figure 3 and e.g. Krumholz and Tan, 2007; Kennicutt and Evans, 2012; Leroy et al., 2017; Utomo et al., 2018; Krumholz et al., 2019), although it increases slightly towards dense subregions within GMCs, reaching 3–6% at n ∼ 5 × 10 cm−3 (Evans et al.”

“It would be valuable to revisit this alternative style of approach in light of more recent work on the relationship between SFR and gas density, as reviewed, for example, by Kennicutt & Evans (2012).”

“Star formation rate: assuming the Case-B condition, we convert the Hβ luminosity to SFR using the formula = ´ ´b- - -( ) ( )M LSFR yr erg s 2.86 101 H 1 41.27 (Kennicutt & Evans 2012).”

“Stars: SFR function from UV and FIR luminosity SFR can be inferred by lines (mainly Lyα and Hα) and by continuum emission (mainly UV, FIR, radio and X-ray) of star forming galaxies (for a review, see Kennicutt & Evans 2012).”

“1 IN T RO D U C T I O N Ultraviolet (UV) continuum emission provides the most direct tracer of star formation activity in a galaxy (e.g. Kennicutt & Evans 2012), albeit it must be corrected for the impact of dust obscuration to derive complete star formation rates (SFR).”

“Moreover, the current Galactic star formation rate of 3.5M⊙ yr−1 assumed in the Wang et al. computations is higher than the modern estimates, close to 2M⊙ yr−1 (Kennicutt & Evans 2012).”

“This point becomes particularly accute given the fact that there is no evidence that most of the regions within molecular clouds are collapsing, and if so that they are collapsing at τ 0ff (see e.g. Kennicutt & Evans 2012).”

“Along its evolution, Althæa SFR-stellar mass relation is compatible with high-z observations (e.g. Jiang et al. 2016), and agrees with the Schmidt-Kennicutt relation (Schmidt 1959; Kennicutt 1998; Kennicutt & Evans 2012; Krumholz et al. 2012).”

“We use the calibration proposed by Murphy et al. (2011; 2012) and then adopted in the widely cited review by Kennicutt & Evans (2012) Lsync ≈ 1.9× 1028 erg s−1 Hz−1 Ṁ⋆ M⊙ yr−1 ( ν GHz )−αsync [ 1 + ( ν 20GHz )0.5 ]−1 F [τsync(ν)] (7) where αsync ≈ 0.75 is the spectral index (e.g., Condon 1992),…”

“In particular, the minimum flux density sampled by us, 60 µJy at 1.3 mm, corresponds to a total IR luminosity L(8−1000 µm) = 6 × 1044 erg s−1, corresponding to a SFR = 40 M yr−1 (Kennicutt & Evans 2012), nearly independent of redshift.”

“…cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsarc. u-strasbg.fr/viz-bin/cat/J/A+A/643/A141 reflected in the Schmidt–Kennicutt relationship (e.g. Kennicutt 1998; Kennicutt et al. 2007; Bigiel et al. 2008; Leroy et al. 2008, 2013; Genzel et al. 2012; Kennicutt & Evans 2012; Kumari et al. 2020).”

“The power-law exponentγ is related to the indexα in the power law fitting the number distribution against mass, which is often used to describe structures in gas, (Kennicutt & Evans 2012) dN/dM = AMα (4) by α = γ − 1.”

“Assuming a Kroupa IMF, SFRUV is calculated using the relation from Kennicutt & Evans (2012): L LlogSFR log 9.7 7UV ( )( ) ( )n= -n SFRUV is then combined with SFRIR to give a total SFR.”

“3.5 SFR versus LIR Both the far-IR (40-500 μm) luminosity, LFIR, and the total (8−1000 μm) IR luminosity, LIR, are commonly used to estimate the SFR using relations such as (Kennicutt & Evans 2012) SFR/M yr−1 = 1.5 × 10−10 LIR/L .”

“These are the key results for efforts to understand Milky Way and extragalactic SF (Kennicutt & Evans 2012).”

“…Kennicutt 1998a; Elmegreen 1999; Kroupa 2001; Massey 2003; Alves et al. 2007; Fardal et al. 2007; McKee & Ostriker 2007; Wilkins et al. 2008; Pflamm-Altenburg & Kroupa 2009; Kennicutt & Evans 2012; Narayanan & Davé 2012; Conroy 2013; Belczynski et al. 2014; Krumholz 2014; Madau & Dickinson 2014).”