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.”

“…following a volumetric Schmidt (1959) relation, with an enforced efficiency per free fall time of ff = 0.02 as motivated by observations (e.g. Kennicutt 1998; Kennicutt & Evans 2012; Krumholz et al. 2012; Narayanan et al. 2012; Vutisalchavakul et al. 2016; Heyer et al. 2016; Leroy et al. 2017).”

“The star formation law in spiral and starburst galaxies is well-characterized by the Kennicutt-Schmidt (KS) relation (Kennicutt 1998; Kennicutt & Evans 2012), which takes the form( ΣSFR M yr−1 kpc−2 ) = 2.5×10−4 ( Σgas M pc−2 )1.4 .”

“Stars form in cold dense clouds composed of molecular gas (see reviews by McKee & Ostriker 2007; Kennicutt & Evans 2012; Tan et al. 2014).”

“Kennicutt & Evans (2012) pointed out that the gas surface density can crudely be divided into three regions: low density (Σgas < 10M⊙pc −2), intermediate density(10M⊙pc −2 < Σgas < 100 − 300M⊙pc −2), and high density (Σgas > 100− 300M⊙pc −2).”

“Observationally, star formation rates scale with the abundance of molecular gas (Gao & Solomon 2004; Bigiel et al. 2008; Kennicutt & Evans 2012) or the fraction of dense molecular gas (Lada et al. 2010, 2013; Evans et al. 2014; Lada et al. 2017), but there has been some disagreement about how that…”

“Observationally, the obscured and unobscured SFRs are obtained from combining total IR and observed UV luminosities with a theoretically motivated calibration (e.g. Kennicutt & Evans 2012).”

“This time interval approximately corresponds to the timescale traced by recombination lines such as Hα (Kennicutt & Evans 2012).”

“Star formation occurs within dense (n(H2) ∼ 102 − 105cm−3), massive (104 − 106 M⊙), and cold (Tgas ∼ 10 − 50 K) giant (10 ∼ 100 pc) molecular clouds (GMC) (Kennicutt & Evans 2012), where atomic gas, mainly atomic Hydrogen (HI), is trans- Send offprint requests to: G. Orellana formed into molecular…”

“…scaling relations such as the size-line width relation,a.k.a. Larson’s law (Larson 1981; Solomon et al. 1987; Rosolowsky et al. 2008; Bolatto et al. 2008), and star formation laws, such as the Schmidt-Kennicutt law (the S-K law hereafter, Schmidt 1959; Kennicutt 1998; Kennicutt & Evans 2012).”

“…example, at 20 μm, emission from PAHs and smaller grains ( 0.01 μm) dominate and are associated with the most intense radiation fields around the youngest SFRs, whereas at 100 μm, emission from a more diffuse component associated with larger grains ( 0.01 μm) is seen (e.g. Kennicutt & Evans 2012).”

“The FUV and NUV SFR calibrations by Kennicutt & Evans (2012) are very similar, which further supports using the FUV and NUV images as independent SFR measurements, assuming a continuous star formation history (SFH).”

“Individual clouds in our Galaxy have a mean density of a few times 102 cm−3 and have global star formation efficiencies ranging from 2% to 8% (Kennicutt & Evans 2012).”

“The total infrared emission (integrated in the wavelength range from, e.g., 8 to 1000µm) is known to be a good tracer of the embedded star formation in galaxies (see Kennicutt & Evans 2012, and references therein).”

“Each of these indicators traces star formation in somewhat different ways, averaging over different timescales (e.g., Kennicutt & Evans 2012).”

“Sun-like stars are born from the gravitational collapse of the dense cores of molecular clouds comprised of dust and gas 1,2 .”

“01 M ⊙ yr − 1 (Kennicutt & Evans 2012).”

“cgkim@astro.princeton.edu ∗ NASA Hubble fellow Galactic star formation rates (SFRs) and the physical state of the interstellar medium (ISM) are observed to be tightly connected (e.g., Kennicutt & Evans 2012; Sun et al. 2020, 2023; Barrera-Ballesteros et al. 2021).”

“We selected the 100 Myr timescale in Figure 4 in order to match the typical timescales in UV observations of star formation ( e.g., Kennicutt & Evans 2012; Leroy et al. 2012 ) .”

“Following Kennicutt & Evans (2012), we first convert the dust-corrected UV absolute magnitude at 1500 ˚A into monochromatic luminosity, i.e.”

“The UV stellar continuum is mostly generated by O and B stars with typical lifetimes of ∼100–200Myr (Kennicutt & Evans 2012).”

“We estimate the star formation rates (SFRs) of Mrk 709 S, Mrk 709 N and the bridge using Hα fluxes deter- mined from our HST images and the following relation from Kennicutt & Evans (2012): log SFR (M yr −1) = log LHα − 41.27, (1) where LHα is the luminosity of Hα in units of erg s −1.”

“5 1 1( ) ( Å) ( ) ( ) This relation assumes the same intrinsic stellar population model as used to derive E(B−V )star from βUV, and it is slightly different from that of Kennicutt & Evans (2012), where the constant term is 43.35.”

“For both low and high−z QSOs, we computed the SFR from the far-IR emission which is dominated by the cold dust component tracing the SF-related IR luminosity following the scaling relation found in the local universe: SFR/M yr −1 = 1.49× 10−10LIR/L (Kennicutt & Evans 2012).”

“In order to check how this impacts our results, we repeat our star formation rate estimates considering the calibration for the NUV (CNUV=43.17; Kennicutt & Evans 2012).”

“UV slope β was used to obtain the the dust-corrected UV magnitude, which is then used to obtain an SFR estimate with the Kennicutt & Evans 2012 factor.”

“…1–13 (2017) equivalent width of EW(Hα) = −59±10 Å, a total line flux of f(Hα) = (2.8 ± 0.4) × 10−18 erg s−1 cm−2, and a luminosity of L(Hα) = (9.7 ± 1.4) × 1038 erg s−1 which, following the calibration of Kennicutt & Evans (2012), leads to a star formation rate (SFR) of (5 ± 0.8) × 10−3 M yr−1.”

“The second SFR indicator is purely based on the rest-frame UV corrected for dust following Kennicutt & Evans (2012): LSFR 1.72 10 1600 10 , 3AUV, 10 0.4 UV, Meurer= ´b - ( Å ) · ( ) where the units of SFR and luminosity are the same as in Equation (1).”

“While star formation rates can be readily probed through deep Hα or FUV imaging (see, e.g., the review by Kennicutt & Evans 2012), these are sensitive only to timescales of 100Myr, the lifetime of the massive UV-producing stars.”

“…100871, China; yanxia.xie@pku.edu.cn, lho.pku@gmail.com 2Department of Astronomy, School of Physics, Peking University, Beijing 100871, China, shang- guan@pku.edu.cn 3Department of Physics and Astronomy, University of Missouri, Columbia, MO 65211, USA lia@missouri.edu 2 (Kennicutt & Evans 2012).”

“The SFRs associated with the LIR obtained from these libraries are provided by standard calibrations (e.g. Kennicutt & Evans 2012), which rely either on observations of nearby galaxies (e.g. Chary & Elbaz 2001; Dale & Helou 2002) or on modelling of the dust emission (e.g. Draine & Li 2007).”

“Studies of the molecular gas content of galaxies find that star-forming galaxies follow a well-defined power-law correlation between star formation rate density and molecular gas surface density, known as the Kennicutt-Schmidt Law (see review in Kennicutt & Evans 2012).”

“The H2 molecule, while abundant, has no dipole moment and its lowest vibrational state is difficult to excite at typical molecular cloud temperatures (10–20 K; Kennicutt & Evans 2012).”

“At very small scales or low luminosities, this non-linearity could be introduced by the incomplete sampling of the stellar IMF (e.g. Kennicutt & Evans 2012) and thus poor measurement of the SFR which depends strongly on the high stellar mass sampling.”

“There are galaxies at all redshifts observable with star formation rates that indicate they will run out of fuel within a few Gyrs without replenishment.”

“The star formation rate was estimated by a combination of the IR and FUV emission, the FUV being emitted by massive young OB stars, and the IR being the thermal emission of dust (Kennicutt & Evans 2012 and references therein).”

“We use typical values for the stellar disk of the Milky Way (Kennicutt & Evans 2012; Rix & Bovy 2013) and observations from Ivison et al. (2010b) for the high-z case.”

“We did not correct for this IMF difference, since the difference in the stellar mass and SFR estimations based on Chabrier and Kroupa IMFs is small compared to the other uncertainties (Chomiuk & Povich 2011; Kennicutt & Evans 2012; Madau & Dickinson 2014).”

“For example, one method of estimating the star formation rate in a galaxy is by assuming the far-infrared emission represents the bolometric luminosity of newly formed stars (Kennicutt 1998; Kennicutt & Evans 2012).”

“This result suggests that star formation is strongly governed by the available gas mass and internal regulation, a result that is at least broadly reminiscent of results obtained in detailed studies of star formation rates in galaxies (Kennicutt & Evans 2012), rather than external factors.”

“A recent review on the properties of star formation was presented by Kennicutt & Evans (2012).”

“…in a GMC is converted into stars and along with the star formation efficiency (SFE) provides a fundamental physical parameter for characterizing the evolution of star-forming regions and galaxies (see, e.g. Kennicutt 1998; Calzetti et al. 2009; Kennicutt & Evans 2012 for reviews of SFR indicators).”

“Various continuum and multi-wavelength products have been used to calculate SFRs (see Kennicutt 1998a; Kennicutt & Evans 2012, for reviews) with many of these tracing their reasoning back to the Kennicutt-Schmidt Law (Schmidt 1959; Kennicutt 1998b).”

“While one should remind that the uncertainties on SFR rate calibrations are still large (Botticella et al. 2012; Kennicutt & Evans 2012), it also true that there is a number of possible biases in the SN rate estimates.”

“…arises because, at UV wavelengths, up to 90% of the emission in the far-UV (FUV) and near-UV (NUV) is from stars that are younger than 100Myr and 300Myr, respectively; conversion to an SFR therefore assumes that the SFR has been uniform over that period of time (e.g., Kennicutt & Evans 2012).”

“Because the rest-frame UV continuum emission traces massive young stars that have a short ( ∼ 100 Myr) lifetime, they are used to estimate star formation rates (SFRs) through the empirical relations (e.g., Kennicutt 1998; Kennicutt & Evans 2012).”

“This is the typical timescale for which UV and IR star formation indicators are sensitive (Kennicutt & Evans 2012).”

“…timescales (where the NUV traces the direct continuum from OB-type stars with lifetimes of ∼ 10 − 100 Myr while the PAH and IR emission can include heating from longer-lived stellar stars with lifetimes of 500 Myr to 1 Gyr (Salim et al. 2009; Salim & Narayanan 2020; Kennicutt & Evans 2012).”

“…it is found that star formation takes place in the clumps and cores within giant molecular clouds (GMCs), so SFR is linearly correlated with the amount of molecular gas (H2, traced by CO) instead of the atomic gas (Baan et al. 2008; Bigiel et al. 2008; Leroy et al. 2008; Kennicutt & Evans 2012).”

“In particular, we have assumed a linear relation between the gas supply and the SFR while empirical results would suggest a non-linear relation (e.g., Kennicutt 1998; Kennicutt & Evans 2012; de los Reyes & Kennicutt 2019; Kennicutt & de los Reyes 2021).”

“Observed scaling relations between the interstellar medium (ISM) and star formation in massive star-forming galaxies imply ISM depletion times of a few Gyr at low z (for a review, see Kennicutt & Evans 2012; see Leitner & Kravtsov 2011) and under 1 Gyr at z> 1 (e.g., Tacconi et al. 2013).”

“Fig.15 demonstrates the relation of the stellar mass of the galaxies derived from Starlight with SFR (measured from the Hα luminosity without extinction correction) (Dopita & Ryder 1994; Kennicutt 1998; Panuzzo et al. 2003; Dopita 2005; Kennicutt & Evans 2012).”

“Both radio and Hα fluxes are SFR diagnostics (e.g., Kennicutt & Evans 2012, for a review), thus they can be used to compare the expected SFR in disk and tail.”

“This lends more support to the use of the composite SFR indicators from Kennicutt & Evans (2012) for the Central Region.”

“Paβ AS A STAR FORMATION RATE INDICATOR Following the Kennicutt & Evans (2012) SFR relation for Hα and Hα/Paβ = 17.6 (assuming Case B recombination, T = 104 K, and ne = 104 cm−3; Osterbrock 1989), SFR is calculated from Paβ as: log(SFRPaβ)[M /yr] = log[L(Paβ)] − 40.02 + 0.4APaβ (3) This equation…”

“…measures the attenuation of the total UV light from young and intermediate-age populations (up to a few ×108 yr) processed by dust in H ii regions for those stars still embedded in their birth clouds and dust in the diffuse ISM for all stars contributing to the UV emission (Kennicutt & Evans 2012).”

“…which corresponds to the lifetime of 9M stars (Georgy et al. 2013). c© xxxx RAS, MNRAS 000, 1–20 Galactic-scale hydrodynamic simulations of 26Al 5 For the Milky Way the star formation rate surface density increases towards the Galactic centre (see Fig.7 of Kennicutt & Evans 2012, for instance).”

“For the serendipitous LUCI source l2 we derived a star formation rate of >5 M /yr based on its Hα luminosity4 (e.g. Kennicutt & Evans 2012).”

“We estimate the star formation rates (SFRs) of our target BCD galaxies using far-UV (FUV; 1528 Å) and mid-infrared (IR; 25 µm) luminosities via log SFR(M yr −1) = log L(FUV)corr − 43.35 log L(FUV)corr = L(FUV)obs + 3.89L(25 µm) (1) (Kennicutt & Evans 2012; Hao et al. 2011; Murphy et al. 2011).”

“As described in the text we assumed the Kennicutt & Evans (2012) relation log(SFR) [M /yr] = log(LUV) [erg/s]− 43.35 for the conversion between SFR and UV luminosity.”

“SFRs were computed from rest-frame UV luminosities at λ ≈ 2800Å that are corrected for extinction by applying a foreground-screen Calzetti reddening law (A2800 ≈ 1.79AV):SFRUV,cor[M⊙yr −1] = 2.59 × 10−10LUV,cor[L⊙] (Kennicutt & Evans 2012).”

“Where a redshift for the source is known, we use the 1.4 GHz flux to star formation rate (SFR) calibration of Kennicutt & Evans (2012) to estimate a 3σ upper limit on the star formation rate (assuming a radio spectral slope of -1).”

“…colours and sSFRs. Star formation rates for SDSS galaxies often rely on Hα and/or [OII] emission line luminosities (see reviews by Kennicutt 1998; Kennicutt & Evans 2012), so the SFRs and sSFRs for AGN-contaminated and low S/N galaxies can be poorly constrained (e.g. Hopkins et al. 2003;…”

“…is the value found in the non-thermal superbubble (Heesen et al. 2015); this is also the global value if we use the hybrid Hα + 24 μm calibration (Kennicutt & Evans 2012) to calculate SFRhyb = 0.052 M yr−1 and convert this to UIRF with a galactocentric radius of rint = 0.7 kpc (Heesen et al.…”

“We corrected the Hα luminosity using both the Balmer decrement and the 8 µm data with the relation provided in Kennicutt et al. (2009) and Kennicutt & Evans (2012).”

“…γHI+H2 between the surface densities of the SFR and total gas remains roughly constant as a function of region size (Figure 17), and is in agreement with the slope observed for whole galaxies (Kennicutt 1998; Kennicutt & Evans 2012) and for the star–forming regions in M 51 (Kennicutt et al. 2007).”

“We finally use the relation by Kennicutt & Evans (2012), LHα [erg s −1] = 1.86× 1041 SFR [M yr−1] , (9) to obtain the average volumetric emissivity for Hα radiation.”

“A similar trend is shown in Kennicutt & Evans (2012) averaged on the whole MW.”

“For a detailed description of the multiple 24µm calibrations (linear and non-linear), see Calzetti et al. (2010), and for a general review, see Kennicutt & Evans (2012).”

“It appears to hold in the disk of our Milky Way and also in distant galaxies (Kennicutt & Evans 2012).”

“…half a century ago Schmidt (1959) conjectured that the rate of SF should vary as a power law of the gas density, and later Kennicutt (1998) suggested the parametrization in terms of mass surface densities SFR = A Ncold gas, valid for starforming galaxies, with N 1.4–1.5 (Kennicutt & Evans 2012).”

“…nuclear ring of NGC 6951, for instance, Mazzuca et al. (2008) derived the current SFR ∼ 1.4 M⊙ yr −1 based on the old Hα–SFR relation of Kennicutt (1998), which is known to yield a larger SFR by a factor of ∼ 1.47 than the newly calibrated relation (e.g., Hao et al. 2011; Kennicutt & Evans 2012).”

“Emission from PAHs has been used to trace the star formation rate (Peeters et al. 2004; Calzetti et al. 2007; Belfiore et al. 2023), interstellar radiation field, and PAH abundance (e.g., Draine et al. 2007; Kennicutt & Evans 2012; Whitcomb et al. 2023a; Baron et al. 2024b; Sutter et al. 2024).”

“The instantaneous SFRs of galaxies in the sample were estimated directly from the dust corrected H α λ 6565 emission line fl uxes ( Kennicutt & Evans 2012 ) listed in Table 6.”

“To calculate the SFR surface density of this region, we can convert the total dust continuum flux arising from this clump into a SFR using the scaling relation of Kennicutt & Evans (2012).”

“Star formation happens in cold molecular gas (e.g., see review of Kennicutt & Evans 2012) and then young massive stars (often found in young massive clusters, or YMCs) drive energetic winds and radiation that may heat up or destroy giant molecular clouds, a process known as stellar feedback (e.g.,…”

“These UV + IR SFR indicators also suffer from systematic uncertainties from the different samples/simulations they are calibrated on, which involve mostly star-forming galaxies (Kennicutt & Evans 2012).”

“…the dust-corrected UV (e.g., Oesch et al. 2018; Bouwens et al. 2021), IR (e.g., Gruppioni et al. 2020; Zavala et al. 2021), and radio (e.g., Novak et al. 2017; Ocran et al. 2020) luminosity functions, appropriately converted into SFR (see Kennicutt & Evans 2012) using our assumed Kroupa (2001) IMF.”

“…China, 20A Datun Road, Chaoyang District, Beijing 100012, China 11University of Utah, Department of Physics and Astronomy, 115 S. 1400 E., Salt Lake City, UT 84112, USA jkbarrerab@astro.unam.mx namical structure of the disk of the galaxy as a whole (Kennicutt & Evans 2012, and references therein).”

“(17) Since then, many observations have further explored this KennicuttSchmidt law (e.g., Kennicutt & Evans 2012), including at smaller scales (e.g., Kennicutt et al. 2007) and higher redshifts (e.g., Bouché et al. 2007a), and exploring relations between ¤Σ∗ and the molecular gas content and/or…”

“…interstellar medium, where thermal pressure support is negligible, only ∼ 1% of the gas mass converts to stars per free-fall timescale (e.g., Krumholz & Tan 2007; Krumholz et al. 2012; Leroy et al. 2017; Utomo et al. 2018), or ∼ 10% per galactic orbit (e.g., Kennicutt 1998; Kennicutt & Evans 2012).”

“As discussed in Section 3.3, we assume a linear relation between the LIR and the SFR (Kennicutt 1998; Kennicutt & Evans 2012), with the constant factor being 3.89 × 10−44 M yr−1 erg−1 s.”