The Schmidt Law at Sixty. Robert Kennicutt University of Arizona Texas A&M University

Transcription

1 The Schmidt Law at Sixty Robert Kennicutt University of Arizona Texas A&M University

2 Log (SFR surface density) Maarten Schmidt conjecture (1959, 1963): - volume/surface densities of star formation scale as power law functions of gas density Why Should We Care About a Simple Power Law? Slope = 1.4 As a remarkable scaling law of nature that begs to be understood As a key sub-grid input ( recipe ) for models and simulations of galaxy formation and evolution As setting vital boundary conditions and clues to the physics of star formation generally Spiral galaxies Starburst s Circumnuclear disks Kennicutt 1998 Log (Gas surface

3 Kennicutt & Evans 2012

4 The Challenge: Identify the key physical drivers and regulators of star formation, and their defining physical (and algorithmic) relationships. accretion of gas from the IGM may ultimately regulate the global SFR formation of a neutral ISM (cooling, thermal instabilities) easy for disks, difficult for massive spheroids dictated by gas density and ambient UV radiation field formation of bound interstellar clouds (Jeans/gravitational instabilities) dictated by gas density and galactic shear, tidal field, shocks formation of a cool neutral phase (thermal/pressure instabilities) dictated by ISM pressure and temperature formation of molecular gas (phase instability) dictated by cloud opacity (to photodissociating UV) and ambient UV field formation of bound molecular cloud clumps, cores dictated by Jeans, fragmentation, turbulence, competitive accretion formation of protoplanetary disks, stars, planets complicated(!), but appears to be deterministic(?) once cores are formed re-injection of energy to ISM from feedback processes All above are necessary conditions, but which are critical drivers is subject to debate. The critical path may change in different interstellar environments, galactic environments, cosmic epochs, etc.

5 The first 30 years 1959: Maarten Schmidt introduces concept of power law scaling between volume densities of cold gas and stars: Schmidt law: r SFR = a r gas n 1963: Schmidt introduces scaling relation in terms of surface densities of gas and stars: S SFR = A S gas N Kennicutt 1997, in The Interstellar Medium in Galaxies (Springer)

6 1980s 1990 s Key enablers surveys of resolved HI in nearby galaxies (mostly WSRT) surveys of resolved CO emission in nearby galaxies (mostly FCRAO) quantitative diagnostics, surveys of SFRs Go beyond correlations of integrated masses/ luminosities to analyze surface densities avoid meaningless cloud counting linear relations low spatial resolution of CO data limited study to global and radially-averaged SF vs gas density correlations Tacconi & Young 1987

7 (Kennicutt 1998) Log (SFR surface density) Slope = 1.4 Starbursts Circumnuclear disks Spiral galaxies Kennicutt 1989, Martin & Kennicutt 2001 Log (Gas surface density)

8 It is tempting to associate both the SF thresholds and the observed slope of the Schmidt law with gravitationallydominated processes S crit = kc /pg Above S crit one expects: S SFR = e SF S gas / t ff = e SF S gas S gas -0.5 = e SF S gas 1.5 NGC 6946: Kennicutt 1989

9 SF disks are gravitationally meta-stable Toomre Q = kc /pgs gas = S crit /S gas z=0 Kennicutt 1989 z~2 SINS/PHIBBS Genzel+ 2014

10 : Spatially-resolved measurements

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14 In short, one can interpret the observed properties of the star formation law on scales of ~250 pc and larger in terms of two completely different pictures: Top down: in which cloud and star formation are primarily driven by gravitational processes (free-fall time, disk instabilities), largely independent of ISM phase or temperature. In this picture the slope of the Schmidt law is driven by dynamics. Causation is driven by gravity and apparent correlations with molecular properties are merely secondary consequences. Bottom up: in which cloud and star formation are primarily driven by the formation of molecular gas and a (near-constant) star formation efficiency per unit molecular gas. In this picture the slope of the Schmidt law is the consequence of a combination of a linear molecular SF law with a (molecular-driven) threshold at low densities. Causation is driven by ISM phase and apparent correlations with bound vs diffuse gas are secondary consequences.

15 But the entire story is not so simple Saintonge Genzel+ 2014, 2015

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17 Silk-Elmegreen Law S SFR ~ S gas / t d Kennicutt 1998 Krumholz+ 2012

18 The Path Forward Updating the Global Star Formation Law Mia de los Reyes Caltech Rob Kennicutt U. Arizona The Laws of Star Formation 2 July 2018

19 (Kennicutt 1998) Log (SFR surface density) Slope = 1.4 Problems with K98 Small sample N = 61 spiral galaxies N = 36 circumnuclear starbursts Starbursts Circumnuclear disks Large uncertainties Measurement uncertainties factor of 2-3 Can t tell if scatter is intrinsic Spiral galaxies Log (Gas surface density)

20 Now: improved multi-wavelength observations SFR densities FUV (GALEX) Dust: ~24μm IR (Spitzer, WISE) UV Gas densities Atomic (HI): 21-cm line Molecular (H 2 ): CO(J = 1 0) IR Final sample N = 154 spiral galaxies N = 90 dwarf galaxies N = 126 circumnuclear starbursts Hα Approach similar to Liu (radio continuum) (Surface densities defined by Hα diameter)

21 Log SFR [M y 1 kpc 2 ] S S Redo K98 analysis for spiral galaxies depl = 10 8 y depl = 10 8 y 10 9 y 10 9 y 4 Bolatto et al. (2013) X (CO ) N = 153 R = y y K98 original data U nw eighted: y = (1.22±0.06)x 3.69 B ivariate: y = (1.65±0.10)x 4.19 Linm ix: y = (1.27±0.06)x 3.75 Spirals Slope: 1.4 ± 0.15 for spirals and starbursts Log HI+ H 2 [M pc 2 ] S Log SFR [M y 1 kpc 2 ] depl = 10 8 y 10 9 y y New data U nw eighted: y = (1.28±0.08)x 3.76 B ivariate: y = (1.73±0.10)x 4.29 Linm ix: y = (1.33±0.07)x 3.83 Bolatto et al. (2013) X (CO ) N = 153 R = S Log HI+ H 2 [M pc 2 ]

22 1. Redo K98 analysis for spiral galaxies S S 0 Spirals Atomic gas 0 Spirals Molecular gas Log SFR [M y 1 kpc 2 ] Molecular vs atomic stuff Log SFR [M y 1 kpc 2 ] N = 153 R = Bolatto et al. (2013) X (CO ) N = 153 R = S Log HI [M pc 2 ] S Log H 2 [M pc 2 ]

23 S 2. Dwarf galaxies: compare to spirals Log SFR [M y 1 kpc 2 ] depl = 10 8 y 10 9 y y Linm ix: y = (1.27±0.08)x 3.78 LSB s (W yder+ 09) dirrs (R oychow dhury+ 17) Spirals Dwarfs Bolatto et al. (2013) X (CO ) N = 165 R = Log S HI+ H 2 [M pc 2 ] Dwarfs with CO detections seem to fall below spirals Also low surface brightness galaxies (LSBs) and dirrs Threshold in star formation law? (e.g., Bigiel 2008)

24 Silk-Elmegreen law 0 1 Log SFR [M y 1 kpc 2 ] S Linm ix: y = (0.77±0.05)x 2.91 Fixed slope unity Spirals Dwarfs Bolatto et al. (2013) X (CO ) N = 135 R = S Log HI+ H 2 [M pc 2 ] / t dyn

25 3. Second-order correlations Metallicity Stellar mass Mass density H 2 /HI ratio Opacity Gas/stars ratio Concentration Diameter of star-forming region Specific star formation rate How to find correlations? Plot against residuals Correlation matrices PCA

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27 Correlation coefficient Correlation matrices Use correlation matrices to see what affects, most

28 S Log SFR [M y 1 kpc 2 ] Dwarf galaxies: alternative scaling laws Fixed slope unity Spirals Dwarfs Bolatto et al. (2013) X (CO ) N = 144 R = Log S HI+ H 2 S 0.5 [(M pc 2 ) 1.5 ] * An alternative version: extended Schmidt law (Dopita 1985, Shi+2011) No threshold! Tighter than Kennicutt-Schmidt (rms smaller by ~0.1 dex) Feedback regulation? (e.g., Kim & Ostriker 2015) Stellar density

29 4. Starburst Galaxies Sample a mix of LIRGs/ULIRGs and circumnuclear disks of nearby (mostly barred) galaxies (N=126 vs 36 in K98) Gas masses from CO(1-0) or CO(2-1) observations SFRs from total IR luminosities SF region sizes from CO maps, IR maps, and/or Paα images

30 Log Log SFR SFR [M [M y y 1 kpc 1 kpc 2 ] 2 ] S S K98 B ivariate: y = (5.10±1.15)x 6.04 Linm Spirals ix: y = (0.95±0.18)x Bolatto et al. (2013) N = X 153 (CO ) R N = = R = Log Log HI [M pc H 2 [M pc 2 2 ] S ] Log SFR [M y 1 kpc 2 ] 0 1 Log SFR [M y 1 kpc 2 ] 2 3 New Data B ivariate: y = (5.10±1.15)x 6.04 Linm ix: y = (0.95±0.18)x 2.96 Linm ix: y = (1.27±0.08)x 3.78 depl = 10 8 y 10 9 y 4 4 Bolatto et al. (2013) N = 153 X (CO ) R = N 0.40 = 165 R = y LSB s (W yder+ 09) dirrs (R oychow dhury+ 17) Spirals Dwarfs Log HI [M pc 2 ] Log S gas [M pc 2 ]

31 S S At first glance, data are well fitted by a common power law with N = 1.50 Log SFR [M y 1 kpc 2 ] Log SFR [M y 1 kpc 2 ] B ivariate: y = (5.10±1.15)x 6.04 Linm Linm ix: ix: y = (0.95±0.18)x y = (1.27±0.08)x LSB s (W yder+ 09) depl = 10 8 y 10 9 y 4 4 Bolatto et al. (2013) N = 153 X (CO ) X CO = R = const N 0.40 = 165 R = y dirrs (R oychow dhury+ 17) Spirals Dwarfs Log HI [M pc 2 ] Log gas [M pc 2 ] S Log Log SFR [M y 1 kpc 2 ] SFR [M y 1 kpc 2 ] B ivariate: y = (5.10±1.15)x 6.04 Linm ix: y = (0.95±0.18)x 2.96 B ivariate: y = (1.08±0.09)x 3.15 Linm ix: y = (0.78±0.05)x 2.91 Fixed slope unity Spirals Dwarfs 4 4 Bolatto et al. (2013) N = X (CO 153) N R = R = Log HI [M pc 2 ] Log S gas / t dyn [M pc 2 G yr 1 ]

32 S Interpretation somewhat different if you fit normal and starburst galaxies separately 0 1 Log SFR [M y 1 kpc 2 ] Log SFR [M y 1 kpc 2 ] B ivariate: y = (5.10±1.15)x 6.04 Linm Linm ix: y ix: = (0.95±0.18)x y = (1.27±0.08)x LSB s (W yder+ 09) N Spirals = 1.05 depl = 10 8 y 10 9 y N = Bolatto et al. (2013) N = 153 X (CO ) R = N 0.40 = 165 R = y dirrs (R oychow dhury+ 17) Dwarfs Log HI [M pc 2 ] Log S gas [M pc 2 ]

33 S Considering the molecular gas SF law alone does not change matters 0 Spirals B ivariate: y = (5.10±1.15)x 6.04 Linm ix: y = (0.95±0.18)x Spirals Log SFR [M y 1 kpc 2 ] Bolatto et al. (2013) X (CO ) a CO = N MW = 153 R = Log SFR [M y 1 kpc 2 ] starbursts a CO = 1.0 Bolatto et al. (2013) X (CO ) N = 153 R = S Log HI H 2 [M pc 2 ] S Log H 2 [M pc 2 ]

34 S Adopting a density-dependent α CO conversion factor reduces bimodality, but also produces a very steep Schmidt law 0 Log SFR [M y 1 kpc 2 ] Log SFR [M y 1 kpc 2 ] B ivariate: Linm ix: y = (5.10±1.15)x y = (1.27±0.08)x Linm ix: LSBy s = (W(0.95±0.18)x yder+ 09) 2.96 N = 1.95 depl = 10 8 y 10 9 y y dirrs (R oychow dhury+ 17) Spirals Dwarfs Log Log HI [M pc 2 ] gas [M pc 2 ] S Bolatto et al. (2013) X (CO ) N = N 153 = 165 R = 0.40 R = 0.78 Bolatto cf. Naryayanan+ 2012

35 Log SFR [M y 1 kpc 2 ] S Log SFR [M y 1 kpc 2 ] B ivariate: y = (5.10±1.15)x 6.04 Linm ix: y = (0.95±0.18)x Linm ix: y = (1.27±0.08)x depl = 10 8 y 10 9 y 4 N = R = 0.40 Bolatto et al. (2013) X (CO ) N = 165 R = y LSB s (W yder+ 09) dirrs (R oychow dhury+ 17) Spirals Dwarfs Log HI [M pc 2 ] S Log gas [M pc 2 ] A concern with very low CO conversion factors is that gas depletion times fall to <<100 Myr Far lower than the dynamical assembly times for the mergers/disks and implying very brief starbursts (or strong selection effects in current LIRG/ULIRG samples)

36 S H (M o /pc 2 ) Is any description based purely on self-gravity or gas phase physically realistic? Are all SF laws based on a simple gas density prescription doomed to fail? Log P/k cf. Elmegreen (1993)

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38 Taurus molecular cloud: Herschel PACS+SPIRE Palmeririm+ 2013

39 Within GMCs star formation is localized to the dense clumps Gray is extinction, red dots are YSOs, contours of volume density (blue is 1.0 M sun pc 3 ; yellow is 25 M sun pc 3 ) Heiderman et al. 2010

40 SF efficiency in molecular clouds varies by factor of 50, but within dense clumps (above S gas ~ 200 M o /pc 2 ) is nearly constant Lada et al 2011

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46 Kennicutt & Evans 2012

47 Renzini & Peng 2015 Wuyts+ 2011

48 Bouchet+ 2008

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54 Kim, Ostriker, Kim 2013

55 Kim+ 2013

56 Kim+ 2013

57 Key Takeaway Points: Observations A monotonic Schmidt power law with N ~ 1.5 remains as a useful recipe for modelling and simulating large-scale star formation over a wide range of physical conditions Complexity lurks beneath the surface of the global Schmidt law. The relations can be scale-dependent, and there is strong evidence for phase transitions, including a threshold at low densities, near the transitions between the atomic/molecular, diffuse/bound, and warm/cool ISM phases. These thresholds are virtually coincident in the solar neighborhood but become distinct from each other in regions of much higher or lower surface density, metallicity, and/or P ISM another apparent transition near the surface density for the formation of bound molecular clumps within clouds. This may be associated with the onset of a high-efficiency SF mode in starburst regions. Whether this transition is discreet or continuous remains to be established

58 Key Takeaway Points: Interpretation Understanding the physics underlying the observed scaling laws and the key regulators and triggers of star formation requires a multi-scale approach (over 1 100,000 pc!), both observationally and theoretically much of the key physics lies at the interfaces between these scales: between galaxies and the CGM/IGM; between clouds and the multi-phase ISM, HI and H2, warm and cool gas; between bound and unbound structures within clouds, and (if you care about the IMF) between molecular clumps and cores. No theoretical picture can be complete without understanding the physical interplay at all of these interfaces observations and theory increasingly point to the importance of feedback and selfregulation as key drivers of the SFR. We are dealing with complex ecosystems, in which physical processes on all scales are relevant and interact with each other. Star formation scaling laws can be seen as (at most) as global thermodynamic characterizations of these spatially and temporally-averaged processes.

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60 the ubiquitous problem of dark H 2

61 2. Dwarf galaxies: systematic effects Log SFR [M y 1 kpc 2 ] Metallicity-dependent X CO (Bolatto+13) SpiralSF law Linm ix: y = (0.56±1.14)x 3.37 Dwarfs Bolatto et al. (2013) X (CO ) N = 12 R = Log HI+ H 2 [M pc 2 ] Lots of CO non-detections and upper limits Relation depends strongly on conversion from CO to H 2 (X CO ) Expected to be higher for metalpoor dwarfs

62 3. Second-order correlations Metallicity H 2 /HI gas ratio

63 3. Second-order correlations Metallicity Correlations between SF law residuals and second-order parameters: Spirals: little/no correlation Dwarfs: moderate correlation Are different star formation processes dominant in dwarf galaxies? (Still working on this!)

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65 Outline Looking back: review of measurements of the Schmidt law 1960s 1980s: early measurements 1980s 1990s: global and radial measurements : spatially resolved measurements consistency and conflicts New results: revisiting the global star formation law Looking ahead: observational and theoretical approaches to understanding the multi-scale star formation scaling laws

66 1 O5V/3_Myr M gas /t Hubble M gas /t dyn dust Edd limit(?) R max =20 kpc S gas /t Hubble S crit threshold

67 Key Takeaway Points A monotonic Schmidt power law with N ~ 1.5 remains as a useful recipe for modelling and simulating large-scale star formation over a wide range of physical conditions. Complexity lurks beneath the surface of the global Schmidt law. The scaling relations can be scale-dependent, and there is strong evidence for phase transitions, one associated with the formation of bound cold gas clouds on the 100 pc scale, and one with the formation of bound star-forming substructures within molecular clouds. Understanding the physics underlying the observed scaling laws and the key regulators and triggers of star formation requires a multi-scale approach (over 1 100,000 pc!), both observationally and theoretically. Much of the key physics appears to lie at the interfaces between these scales: between galaxies and the CGM/IGM, between clouds and the multi-phase ISM, between bound and unbound structures within clouds, and (if you care about the IMF) between molecular clumps and cores. Increasing evidence points to the critical roles of feedback and self-regulation as key drivers of the SFR. We are dealing with complex ecosystems, in which physical processes on all scales are relevant and interact with each other.