4 Star Formation Relations

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1 The Wonders of Star Formation - Edinburgh Star Formation Relations (+ Strengthened Cluster Survival) With One Single Model Geneviève Parmentier Astronomisches-Rechen Institut Zentrum für Astronomie Heidelberg Germany

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4 The Wonders of Star Formation - Edinburgh Star Formation Relations (+ Strengthened Cluster Survival) With One Single Model Geneviève Parmentier Astronomisches-Rechen Institut Zentrum für Astronomie Heidelberg Germany

5 Outline Star cluster formation in centrally-concentrated molecular clumps A. Gas-embedded systems What star formation relations characterize such systems? Geneviève Parmentier - Zentrum für Astronomie Heidelberg 5

6 Outline Star cluster formation in centrally-concentrated molecular clumps B. Gas-free systems When the residual star-forming gas is gone, how do such systems evolve? A. Gas-embedded systems What star formation relations characterize such systems? Geneviève Parmentier - Zentrum für Astronomie Heidelberg 6

7 First Star Formation Relation (Volume/Theory) Fig 9 - Wu+2010 HCN3-2 Clump outskirts Slope: 1.5 Clump inner regions o Molecular clumps have volume density gradients o If stars form with a constant star formation efficiency per free-fall time, ε ff, the volumetric star formation relation is a power-law of slope 3/2 o Shell-by-shell representation o Local star formation relation! "#$ = & ''! ()* + '' -./ I.! "#$! ()* Geneviève Parmentier - Zentrum für Astronomie Heidelberg 7

8 Second Star Formation Relation (Surface/Observ.) SFR Stellar mass!"#$% : 2. II. Σ '() Σ. +,- Outskirts: slow star formation o Steeper than its volumetric counterpart o Contour-by-contour representation o Local star formation relation Parmentier & Pfalzner (2013) Centre: fast star formation Geneviève Parmentier - Zentrum für Astronomie Heidelberg 8

9 Sol. N. Molecular Clouds Show Quadratic SF Relations Fig. 1, Gutermuth+ (2011) MonR2 cloud of Solar Neighbourhood Σ YSO Fig. 9, Gutermuth+ (2011) Σ YSO S YSO µ S 2 gas Σ gas Geneviève Parmentier - Zentrum für Astronomie Heidelberg 9

10 Local perspective: Contour-by-contour basis One clump is enough From a Local SF Relation Clump distance: e.g. 500 pc Outskirts: slow star formation Centre: fast star formation Geneviève Parmentier - Zentrum für Astronomie Heidelberg 10

11 to a Global (= Third) SF Relation Local perspective: Contour-by-contour basis One clump is enough Clump at a distance where it cannot be resolved glob ( S gas, S glob SFR ) Clump distance: e.g. 500 pc Outskirts: slow star formation Centre: fast star formation Global perspective: o A population of clumps is needed o e.g. HCN(1-0) molecular clumps o To first order: common free-fall time Slope: 1 Third / linear SF relation III. Σ "#$ Σ &'( Geneviève Parmentier - Zentrum für Astronomie Heidelberg 11

12 Composite SF Relation: II + III * Local:! "#$ ) &'( Global:! "#$! &'( Geneviève Parmentier - Zentrum für Astronomie Heidelberg 12

13 Break-Point in Composite SF Relation * Local:! "#$ ) &'( Global:! "#$! &'( Geneviève Parmentier - Zentrum für Astronomie Heidelberg 13

14 Break-Point in Composite SF Relation * Local:! "#$ ) &'( Global:! "#$! &'( Mind the step! Geneviève Parmentier - Zentrum für Astronomie Heidelberg 14

15 Break-Point in Composite SF Relation Fig. 10, Heiderman+ (2010) Geneviève Parmentier - Zentrum für Astronomie Heidelberg 15

16 Break-Point in Composite SF Relation HCN Clumps Global relation: 1 data-point = 1 HCN clump Fig. 10, Heiderman+ (2010) Geneviève Parmentier - Zentrum für Astronomie Heidelberg 16

17 Break-Point in Composite SF Relation Local relation: 1 data-point = 1 contour HCN Clumps Global relation: 1 data-point = 1 HCN clump Perseus molecular cloud Figs 2 & 10, Heiderman+ (2010) Geneviève Parmentier - Zentrum für Astronomie Heidelberg 17

18 Interpretation of Break-Point Local relation: 1 data-point = 1 contour HCN Clumps Global relation: 1 data-point = 1 HCN clump Perseus molecular cloud Figs 2 & 10, Heiderman+ (2010) Σ th : rather than a density threshold for star formation, the break-point of a composite SF relation (Parmentier 2016, ApJ) Geneviève Parmentier - Zentrum für Astronomie Heidelberg 18

19 Composite SF Relation: II + III * Local:! "#$ ) &'( Global:! "#$! &'( Geneviève Parmentier - Zentrum für Astronomie Heidelberg 19

20 Fourth SF Relation (the very dense gas) 56 IV. Σ /01 = 3 44 Σ ;.< 71 89: Local:! "#$ ) &'( Parmentier 2017, ApJ Global:! "#$! &'( +.- * Global:! "#$ ) &'( Geneviève Parmentier - Zentrum für Astronomie Heidelberg 20

21 4 Star Formation Relations for Molecular Clumps +.- I.. "#$. &'( (local) Parmentier 2017, ApJ +.- IV.! "#$! &'( (global) Parmentier 2016, ApJ III.! "#$! &'( (global) * II.! "#$ ) &'( (local) See also Elmegreen 2018, ApJ Geneviève Parmentier - Zentrum für Astronomie Heidelberg 21

22 Star Formation Relations and Co. Shell - by - shell : Contour - by - contour : r gas r r e ff µ e ff µ t ff gas -1/ 2 gas ( r ) r 3/ 2 gas S 2 SFR» S gas Clump-by-clump (constant! "#$ ): Σ &'( Σ "#$ * Clump-by-clump (increasing! "#$ ): Σ &'( Σ "#$ +/- Geneviève Parmentier - Zentrum für Astronomie Heidelberg 22

23 Star Formation Relations and Co. Shell - by - shell : Contour - by - contour : r gas r r e ff µ e ff µ t ff gas -1/ 2 gas ( r ) r 3/ 2 gas S 2 SFR» S gas Clump-by-clump (constant! "#$ ): Σ &'( Σ "#$ * Clump-by-clump (increasing! "#$ ): Σ &'( Σ "#$ +/- Constant ε ff : the slope is not necessarily 1.5 Slope 1.5 does not necessarily discard a scenario in which star formation proceeds with a constant ε ff Geneviève Parmentier - Zentrum für Astronomie Heidelberg 23

24 Star Cluster Evolution after Gas Expulsion Fig 1, Shukirgaliyev, Parmentier, Just & Berczik (2018) Geneviève Parmentier - Zentrum für Astronomie Heidelberg 24

25 SFE Radial Variations Clump inner regions Σ YSO SFE local e ff = 0.1 Clump outskirts Global SFE 13 % Global SFE 13 % Σ gas Clump inner regions r [pc] Clump outskirts Local Star Formation Relation: Superlinear / Quadratic Local star formation efficiency : SFE local (inner) > SFE local (outer) Figs 3 and 10, Parmentier & Pfalzner (2013) Geneviève Parmentier - Zentrum für Astronomie Heidelberg 25

26 Instantaneous gas expulsion Violent Relaxation Radiallyvarying SFE Radiallyconstant SFE Based on Fig8 in Shukirgaliyev, Parmentier, Berczik & Just (2017) o Clusters reaching a global SFE higher than 13% do survive o Strongly reduced infant mortality o Despite solar-neighbourhood tidal field inclusion! o One model cluster with a global SFE of 25% and a birth mass of 15E3M sun has a dissolution time of 2.9Gyr! Geneviève Parmentier - Zentrum für Astronomie Heidelberg 26

27 Take-Away Messages The slopes of star formation relations measured for molecular clumps depend on: what is measured, how it is measured, on top of SF physics When interpreting star formation relations, first thought should be pitfalls ahead Cluster infant mortality Cluster teenage mortality Geneviève Parmentier - Zentrum für Astronomie Heidelberg 27