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.”

“…derived from an educated combination of the dustcorrected 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 2021) luminosity functions, appropriately converted in SFR (see Kennicutt & Evans 2012).”

“At those kpc scales ΣSFR exhibits a strong correlation with the surface gas density (Σgas ) in star-forming galaxies (also known as Schmidt-Kennicutt relation, see, rSK, Kennicutt & Evans 2012, and reference therein).”

“…is given by Σ(SFR) = CSFR,HαLHα Apix (15) = CSFR,HαFHα4πd2 cos i Apix , (16) where the Hα luminosity-to-SFR calibration factor CSFR,Hα = 5.3× 10−42 M yr−1 erg s−1 (Hao et al. 2011; Murphy et al. 2011; Kennicutt & Evans 2012), d is the luminosity distance in cm, and Apix is the pixel area in kpc2.”

“However, we have found that at the spatial resolution of our simulations, the resulting molecular hydrogen surface density has a maximum value of 2 M pc−2: half of the observed value for the Milky Way (Wolfire et al. 2003; Kennicutt & Evans 2012).”

“…being mostly sensitive to young stellar populations with ages .10 Myr, while FUV and TIR probe star formation on recent timescales of ∼100 Myr (e.g., Kennicutt & Evans 2012), the ratio of these SFR estimates, SFR(Hα+WISE 22µm)/SFR(FUV+TIR), provides an indication of how much star formation…”

“Galaxies are observed to exhibit a tight correlation between their globally averaged gas surface density, Σg, and star formation rate surface density, ΣSFR (e.g., Kennicutt 1998; Genzel et al. 2010; Kennicutt & Evans 2012).”

“Both the stellar mass of a galaxy and its star formation rate (SFR) can be measured by observations of galaxies using various estimators (Kennicutt & Evans 2012).”

“This number can be converted to the total amount of mass turned into stars assuming a particular IMF (e.g. Kennicutt 1998; Kennicutt & Evans 2012; Madau & Dickinson 2014).”

“We follow the ultraviolet and FIR SFR estimation procedure in Kennicutt & Evans (2012), which is well calibrated from a combination of SFR tracers at different wavelengths.”

“We study the UV properties of this galaxy to probe recent star formation (past a few 100 Myr, Kennicutt & Evans 2012) over scales of ∼ 288 pc.”

“The solid grey line depicts the expected star formation rate from the Kennicutt-Schmidt relation (Kennicutt 1998; Kennicutt & Evans 2012) and the grey shaded region is the factor of three observational error in the observed relation.”

“The chemical composition and kinematics of galaxies are linked to massive star chemical yields, strong stellar winds, and supernova explosions (Ceverino & Klypin 2009; Kennicutt & Evans 2012).”

“SFR on these timescales approximately correspond to Hα and UV based SFR measurements, which represent the formation of young stars with ages 10Myr and star formation in the last ∼100Myr, respectively(e.g., Kennicutt & Evans 2012).”

“11 of Kennicutt & Evans (2012).”

“On an SFR surface density versus gas surface density plot, this model would show a steeper dependence of SFR density on gas surface density than the classical Kennicutt–Schmidt relationship (e.g., Kennicutt & Evans 2012), above a critical gas surface density (for details see Somerville 2015).”

“…Hβλ4382Å lines (from the literature; e.g. Chen et al. 2005; Christensen et al. 2014; Straka et al. 2016; Møller et al. 2018; Rhodin et al. 2018), or (in the case of the DLA towards B1629+120), from the U -band continuum (Rao et al. 2003), using standard SFR calibrations (Kennicutt & Evans 2012).”

“(3) The calibration by Murphy et al. (2011, 2012) was adopted in the extensively cited review by Kennicutt & Evans (2012).”

“2) make it difficult to separate the Outer Arm from the Perseus Arm in Hα; 2) extinction makes distant Hα more difficult to observe (Madsen & Reynolds 2005); 3) the scale height of the warm ionized medium (WIM) is large enough (1 − 1.4 kpc; Haffner et al. 1999; Gaensler et al. 2008; Savage & Wakker 2009; Schnitzeler 2…”

“This recipe results in an SFR 68 per cent of what would be derived using the Kennicutt (1998) formula, largely because of differences in the assumed IMF characteristics (Calzetti et al. 2007; Kennicutt & Evans 2012).”

“…by observations, often through the detection of the CO (J = 1− 0) rotational line as a molecular gas tracer, and some combination of stellar UV, Hα from HII regions, and dust thermal emission in the infrared (IR) due to heating from young stars (e.g Kennicutt & Evans 2012, and references therein).”

“Emission from these warm dust grains is directly correlated with the star formation rate (SFR) since it is heated by emission from young, massive stars (Kennicutt 1998a; Kennicutt & Evans 2012).”

“Star formation rarely takes place in isolation; stars form primarily within multiple systems and often within, or nearby, massive stellar clusters (see, e.g., Kennicutt & Evans 2012).”

“Star formation in a galaxy primarily depends upon its gas reservoir (Schmidt 1959; Kennicutt 1998; Kennicutt & Evans 2012).”

“These studies make use of a variety of tracers for SF and gas, and there are many complications in calibrating each (e.g., Kennicutt & Evans 2012; Calzetti 2013; Tacconi et al. 2020; Saintonge & Catinella 2022; Belfiore et al. 2023), including dust attenuation for SF tracers and systematic effects…”

“The tracks of fixed stellar mass in this figure are derived from our LIR–λpeak relationship, where LIR is converted to a star formation rate (Kennicutt & Evans 2012) then to stellar mass (using the Speagle et al. 2014 relation).”

“…the ALMA data are the total infrared luminosity (LTIR, rest-frame 3–1100 μm), far-infrared luminosity (LFIR, rest-frame 42.5–122.5μm), and the dust mass, from which we can again calculate an independent star formation rate (e.g., Helou et al. 1988; Kennicutt & Evans 2012; Carilli & Walter 2013).”

“In each case we obtain calibration coefficients that are between 0.15 − 0.35 dex higher than adopted by Murphy et al. (2011) (see also Kennicutt & Evans 2012).”

“The focus on how gas is converted into stars has guided the exploration of both nearby and distant galaxies (Kennicutt & Evans 2012; Madau & Dickinson 2014).”

“(5) This range of areal mass accretion rate encompasses the mean star formation rate surface density of the Milky Way disk, 〈ΣSFR,MW〉 = 0.0033 M yr−1 kpc−2 (Kennicutt & Evans 2012).”

“10 Myr, Kennicutt & Evans 2012) which is especially important when investigating rapid quenching mechanisms (such as ram pressure).”

“Many SFR indicators have been proposed and utilized over the years (Kennicutt 1998; Kennicutt & Evans 2012), but two classes of methods stand out as the most practical over a wide range of redshifts: 1) SFRs based on the nebular line emission (Kennicutt 1983) and 2) SFRs based on the stellar…”

“This expression was shown by Elmegreen (2015) to fit the observations in Kennicutt & Evans (2012) for total galaxy disks, and it also fits the set of observations in Krumholz et al. (2012) for the same range of Σgas (i.e., Krumholz et al. 2012 determined a coefficient of 1.9× 10−4 and a power of…”

“Instead, there exists a range of possible methods – such as a luminosity-weighted mean, a percentage intensity change, or a percentage of the cumulative emission – that can result in differences up to an order of magnitude in timescale (Leroy et al. 2012; Kennicutt & Evans 2012).”

“For example, the [O III]λ5007 line emitted by star formation regions by itself can reach a surface brightness of 1 ×10−15 erg s−1 cm−2 arcsec−2 in starburst systems, if we adopt typical [O III] luminosities (Moustakas et al. 2006) and star formation surface densities (Kennicutt & Evans 2012).”

“…(HMXB; donor-star masses >∼ 2.5 M⊙) population is thought to provide a relatively unobscured measure of SFR, a quantity that is difficult to determine well using measurements of the heavily-obscured UV light that is generated by the most massive, short-lived stars (e.g., Kennicutt & Evans 2012).”

“The CSFR is manly provided by the integrated light of galaxies in the rest-frame UV and IR wavebands (Kennicutt 1998; Kennicutt & Evans 2012).”

“…our derived star formation rates show a constant systematic offset across the parameter range (of a factor of 2, where MAGPHYS are lower than those estimates from Ibar et al. 2015 using LIR), which likely arises from differences in SFR definition/calibration (see e.g. Kennicutt & Evans 2012).”

“This figure is originally from (12); the version here is from (26).”

“Assuming a star formation rate calibration following Kennicutt & Evans (2012) these average luminosities correspond to SFR ≈ 90M yr−1 and SFR ≈ 70M yr−1 respectively, consistent with the ISM mass scaling value derived above, although the SFRs could be a factor of three higher if the galaxies are…”

“For example, the recent review of Kennicutt & Evans (2012) define the TIR over 3–1100 µm.”

“…UV luminosity functions of late-type galaxies have been corrected for the SFR dependent dust extinction and converted into SFR functions using the Kennicutt & Evans (2012) calibration log ( L1500 L⊙ ) = log ( SFR M⊙ yr−1 ) + 9.825− 0.4A1500(log SFR), (A4) via the equation d2N(log SFR) d log…”

“…Another relation used to study the properties of the ISM is the empirical power-law relation that connects the star formation surface density (ΣSFR) and the gas surface density (Σgas) available to form stars, i. e., the relation given by ΣSFR ∝Σαgas (Kennicutt & Evans 2012, and references therein).”

“…star formation rate of ∼ 16M⊙ yr −1 (Stanway et al. 2014) would lead to a predicted thermal infrared luminosity LFIR ∼ 10 11 L⊙, while the radio continuum emission detected at 4.5 GHz would suggest a thermal infrared luminosity LFIR ∼ 6 × 10 9 L⊙ (using conversions from Kennicutt & Evans 2012).”

“…of observational facilities has led to high-resolution, high-sensitivity multiwavelength probes of SF and gas across larger samples of galaxies, as well as the first resolved studies within external galaxies (see Kennicutt & Evans 2012 and references therein for a comprehensive overview).”

“M relation for the Hubble Space Telescope Frontier fields galaxies, based on rest-frame UV observations, the Kennicutt & Evans (2012) relation and the Meurer et al. (1999) dust correction law.”

“The value for αKS is higher here compared to the value presented in Section 2.2.4 for GMCs since the latter is for cold molecular clouds and the former is the disk-averaged star formation law (Kennicutt & Evans 2012).”

“These average tdep values approximately correspond to those of the disk and starburst regimes found in Schmidt– Kennicutt diagrams (e.g., Daddi et al. 2010a; Genzel et al. 2010).”

“Star formation in galaxies are characterized by the Kennicutt-Schmidt (KS)-law (Schmidt 1959; Kennicutt 1998; Kennicutt and Evans 2012), which is a galactic-scale empirical correlation between the area-averaged Star Formation Rate (SFR) (ΣSFR [M⊙ yr −1 kpc−2]) and gas surface density (ΣH2+H [M⊙pc…”

“(16) The UV luminosity can be then estimated from the SFR using a relation based on GALEX NUV data (Murphy et al. 2011; Hao et al. 2011; Kennicutt & Evans 2012): log(νLν,UV,SFR) = log(SFR) + 43.17.”

“Although both UV and MIR emission are associated with recent star formation (e.g., Hao et al. 2011; Kennicutt & Evans 2012), they actually probe different timescales in the evolution of star-forming regions.”

“The linear relation between LTIR and Mclump can be expressed as: LTIR L⊙ = 101.80±0.15 Mclump M⊙ (4) Following Kennicutt & Evans (2012), we can convert LTIR to a star formation rate (SFR; Ṁ∗) as: log( Ṁ∗ M⊙ yr−1 ) = log( LTIR ergs s−1 )− 43.41 (5) The use of extragalactic relation between LTIR and SFR may significan…”

“Star formation efficiencies (SFEs) and rates (SFRs) play an vital role in theoretical descriptions of star formation and cloud evolution (e.g., Kennicutt & Evans 2012).”

“Our stellar mass determinations were obtained from SED fitting (see Section 3), and our estimates of SFR were derived using the reddening corrected photometric measurements of the objects’ UV continua and the Kennicutt & Evans (2012) SFR calibration (Section 5).”

“For example, studies of the relationship of molecular gas and recent star formation rate in both nearby or distant galaxies (e.g., review by Kennicutt & Evans 2012) implicitly assume that molecular gas as traced by CO observations is inside molecular clouds and participates in the current star…”

“However, our Hα and NUV estimates of star formation rate for this clump agree well (2.8 M⊙ year−1 and 2.3 M⊙ year−1; Table 10), although Hα and NUV are sensitive to star formation on different timescales (∼10 Myrs and ∼200 Myrs, respectively; Kennicutt & Evans 2012).”

“The total Hα luminosity of the knots in the outer half of the tail of about 2.4×1038 erg s−1 (Fumagalli et al. 2011) corresponds to a SFR of ∼ 1.3×10−3 M⊙ yr−1 over the last∼ 10 Myr (Kennicutt & Evans 2012)7.”

“As such, these tracers are less affected by variations in the star formation history of a region or galaxy or, as in the case of IR SFR tracers, by variations in the dust content (Kennicutt & Evans 2012; Calzetti 2012).”

“As noted by Kennicutt & Evans (2012), lower metallicity systems have enhanced ultraviolet emissivity for a given star formation rate (∼ 0.07 dex for Z = 0.1Z⊙).”

“1 was not directly detected in any band, the inferred SFR(UV, SED) is comparable with the SFR derived with Hα luminosity (36±6 M yr−1) assuming the Hα luminosity–SFR conversion in Kennicutt & Evans (2012).”

“Based on these estimates, the stars in the central region of these ETGs are formed in extreme environments through a starburst (e.g., Bouche et al. 2007; Daddi et al. 2010; Kennicutt & Evans 2012).”

“This result is consistent with the sensitivity of FIR luminosity to dust heated by stars over long timescales that leads to overestimates for systems with large stellar mass fractions from evolved stars and hence low sSFRs (e.g., Kennicutt & Evans 2012).”

“We define ΣSFR in LIER regions as the average rate of star formation in the last 10 Myr, consistent with the star formation timescale probed by Hα (Kennicutt & Evans 2012).”

“…range) to SFR, calculated assuming a Kroupa IMF (Hao et al. 2011; Murphy et al. 2011; 11 http://home.strw.leidenuniv.nl/~jarle/SDSS/ 12 www.bass-survey.com Kennicutt & Evans 2012): = - LSFR 3.89 10 , 144 IR· · ( ) where the SFR is in units of Me yr −1 and LIR is the total IR luminosity in erg s−1.”

“They are raw materials from which new stars form (Kennicutt & Evans 2012), and are spiral arm tracers (Dame et al. 2001; Donovan Meyer et al. 2013).”

“The dark green dashed line represents the σsSFR–Må relation when SFRs are obtained using the FUV luminosity (Kennicutt & Evans 2012) and the IRX–β relation (Meurer et al. 1999; Bouwens et al. 2012; Katsianis et al. 2017b) while the stellar masses are calculated through the SED fitting technique.”

“In star-forming galaxies (which are usually not BCGs), observations suggest that gas depletion time is shorter (star formation efficiency is higher) when the SFR is higher, especially in starburst galaxies (Kennicutt & Evans 2012).”

“…at rates of several to several hundred solar masses per year (e.g. McNamara 2004; O’Dea et al. 2008; McDonald et al. 2011; Donahue et al. 2015; Tremblay et al. 2015; McDonald et al. 2018) place BCGs among starbursts on the Kennicutt-Schmidt relation (Kennicutt 1998; Kennicutt & Evans 2012).”

“(Kennicutt & Evans 2012 and Calzetti 2013 have reviewed this subject.)”

“2 Specifically, 10 Myr corresponds to the Hα star formation indicator (see, e.g., Table 1 in Kennicutt & Evans 2012).”

“…scatter of 0.3− 0.5 dex when compared to other SFR proxies (i.e. UV+IR or far-infrared indicators), the median SFRs determined by SED-fitting are consistent with the medians determined from other indicators for SFR< 50M yr −1 (Wuyts et al. 2011; Kennicutt & Evans 2012; Yang et al. 2017).”

“The high SFR of the two nuclei inferred from radio observations (∼ 200 M yr−1, e.g., Barcos-Muñoz et al. 2015; Varenius et al. 2016) agrees with their FIR luminosity, assuming a standard relationship between the SFR and the FIR luminosity (Kennicutt & Evans 2012).”

“Stars form in condensations of cold H2 gas (Kennicutt & Evans 2012).”

“…reduced depletion times have been observed within dense galaxy centers (Leroy et al. 2013), and trends between tdep and gas density (Kennicutt 1998; Kennicutt & Evans 2012; Genzel et al. 2010), stellar surface density (Boselli et al. 2014), and the dynamical time of the gas (Kennicutt 1998;…”

“Recent work has shown that large-scale star formation in galaxies is strongly linked to the molecular gas reservoir, in particular the dense molecular gas, and less so to the total amount of neutral gas (H2 + H i) (Kennicutt & Evans 2012; Lada et al. 2012).”

“…the majority of cold molecular hydrogen (H2) in typical clouds is invisible in emission due to the fact that the H2 molecule has low mass and therefore requires high temperatures (the lowest level corresponds toE/k ≈ 510 K) to excite its rotational transitions (Kennicutt & Evans 2012).”

“…star formation (∼6.3 ± 0.2 M yr−1) in the central gas disk is L2–10 keV, 0 = (3.7 ± 0.1) × 1040 erg s−1, based on the relation SFR (M yr−1) = 1.7 × 10−40 L2–10 keV, 0 (erg s−1) determined by Ranalli et al. (2003) and adjusted to the Kroupa (2001) initial mass function by Kennicutt & Evans (2012).”

“This is in stark disagreement with observations indicating inefficient star formation and relatively short GMC lifetimes (e.g. Evans 1999; Krumholz & Tan 2007; Shirley et al. 2007; Kennicutt & Evans 2012).”

“In other words, typical calibration constants are appropriate for regions physically large enough for the IMF to be well-sampled and for which the SFH has been continuous long enough for a given SFR indicator to reach equilibrium ( e.g., 5 – 100 Myr; Kennicutt 1998; Kennicutt & Evans 2012 ) .”

“Because of the ability of dust to capture and reprocess UV radiation from young stars and the observed excellent correlation between midIR, Hα, and UV emission in galaxies, the mid-IR has been widely used as a star formation tracer (e.g., see reviews in Kennicutt & Evans 2012 and Calzetti 2013).”

“Future work may benefit from a more direct consideration of the relationships between plasma density and physical processes that operate on scales smaller than optical morphology, such as the relationship between gas density and SFR (i.e., the Kennicutt–Schmidt law, Kennicutt & Evans 2012).”

“Given that typical estimates for tHα are 5–10Myr (e.g., Kennicutt & Evans 2012; Leroy et al. 2012; Haydon et al. 2020), the tgas of our sample at the 150 pc scale, therefore, decreases from ∼5 to 25Myr for the high-M* galaxies, to ∼5–15Myr for the intermediate-M* galaxies, and to a few megayears…”