Oliver Lomax Matthew Bates & Anthony Whitworth 6th September 2018 The Wonders of Star Formation
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1 Machine learning quantification of cluster structure Oliver Lomax Matthew Bates & Anthony Whitworth 6th September 2018 The Wonders of Star Formation
2 Outline
3 Outline Q parameter, used to measure substructure in star clusters, is unreliable.
4 Outline Q parameter, used to measure substructure in star clusters, is unreliable. We have tools available to do better!
5 Outline Q parameter, used to measure substructure in star clusters, is unreliable. We have tools available to do better! Disclaimer: I am neither an observer or an N-body numericist!
6 Q parameter Q = m s m = N m P i=1 m i (N m + 1) E 1 E R PN s s i s = i=1 N s R Cartwright and Whitworth, 2004, MNRAS, 348, 589
7 Q parameter Q = m s m = N m P i=1 m i (N m + 1) E 1 E R PN s s i s = i=1 N s R Minimum Spanning Tree Cartwright and Whitworth, 2004, MNRAS, 348, 589
8 Q parameter Q = m s m = N m P i=1 m i (N m + 1) E 1 E R PN s s i s = i=1 N s R Minimum Spanning Tree Complete Graph Cartwright and Whitworth, 2004, MNRAS, 348, 589
9 Q parameter Q = m s m = N m P i=1 m i (N m + 1) E 1 E R PN s Radial Profile Box Fractal s = i=1 s i N s R (r) / r P (sub-cube) = 2D 2 E Q & 0.8 Q. 0.8 Cartwright and Whitworth, 2004, MNRAS, 348, 589
10 Q parameter Q = m s Cluster # N N m P Lupus IC m = i=1 m i (N m + 1) E 1 E R ρ Oph IC Cha I PN s Taurus s = i=1 s i N s R Comerón (2008) Lada et al. (2006); Muench et al. (2007) Bontemps et al. (2001) Barrado y Navascués et al. (2001) Luhman (2007) Luhman et al. (2010) Cartwright and Whitworth, 2004, MNRAS, 348, 589
11 m-s plots Cluster # N Lupus IC ρ Oph IC Cha I Taurus Comerón (2008) Lada et al. (2006); Muench et al. (2007) Bontemps et al. (2001) Barrado y Navascués et al. (2001) Luhman (2007) Luhman et al. (2010) Cartwright, 2009, MNRAS, 400, 1427
12 m-s plots Cluster # N Lupus IC IC 348 ρ Oph IC Cha I Taurus Comerón (2008) Lada et al. (2006); Muench et al. (2007) Bontemps et al. (2001) Barrado y Navascués et al. (2001) Luhman (2007) Luhman et al. (2010) Cartwright, 2009, MNRAS, 400, 1427
13 m-s plots Cluster # N Lupus IC IC 348 ρ Oph IC Cha I Taurus Comerón (2008) Lada et al. (2006); Muench et al. (2007) Bontemps et al. (2001) Barrado y Navascués et al. (2001) Luhman (2007) Luhman et al. (2010) Cartwright, 2009, MNRAS, 400, 1427
14 m-s plots Cluster # N Lupus IC IC 348 ρ Oph IC Cha I Taurus Comerón (2008) Lada et al. (2006); Muench et al. (2007) Bontemps et al. (2001) Barrado y Navascués et al. (2001) Luhman (2007) Luhman et al. (2010) Cartwright, 2009, MNRAS, 400, 1427 Taurus
15 m-s plots Cluster # N Lupus IC IC 348 ρ Oph IC Cha I Taurus Comerón (2008) Lada et al. (2006); Muench et al. (2007) Bontemps et al. (2001) Barrado y Navascués et al. (2001) Luhman (2007) Luhman et al. (2010) Cartwright, 2009, MNRAS, 400, 1427 Taurus
16 m-s plots Cluster # N Lupus IC IC 348 ρ Oph IC Cha I Taurus Comerón (2008) Lada et al. (2006); Muench et al. (2007) Bontemps et al. (2001) Barrado y Navascués et al. (2001) Luhman (2007) Luhman et al. (2010) Cartwright, 2009, MNRAS, 400, 1427 Taurus
17 Stop using square models
18 Stop using square models
19 Stop using square models D=2.4 D=1.8 D=1.5 Goodwin and Whitworth, 2004, A&A, 413, 929
20 Stop using square models D=2.4 D=1.8 Taurus D=1.5 Goodwin and Whitworth, 2004, A&A, 413, 929
21 Fractional Brownian Motion A generalisation of classical Brownian motion. Used to interpret properties of molecular clouds (e.g. Stutzki et al., 1998, Elia et al., 2014). Parameterised by the Hurst index H H and a standard deviation σ. Relatively simple to generate in Fourier space: P (k) / k = E + 2H σ
22 Fractional Brownian Motion A generalisation of classical Brownian motion. Used to interpret properties of molecular clouds (e.g. Stutzki et al., 1998, Elia et al., 2014). Parameterised by the Hurst index H H and a standard deviation σ. Relatively simple to generate in Fourier space: P (k) / k = E + 2H σ
23 Q parameter is rubbish
24 Q parameter is rubbish
25 m-s plots
26 Machine learning m Cluster distribution is whitened, i.e. Cov(x)=I H Parameters estimated using minimum spanning tree and complete graph. Neural net method used to map edge length moments of graphs to underlying parameters. s σ M n (x) = 1 N! NX 1/n (x i µ x ) n i=1 GitHub: github.com/odlomax/clusterfrac
27 Parameter Estimation
28
29
30 Cluster # N Lupus IC ρ Oph IC Cha I Taurus Comerón (2008) Lada et al. (2006); Muench et al. (2007) Bontemps et al. (2001) Barrado y Navascués et al. (2001) Luhman (2007) Luhman et al. (2010)
31 Cluster # N Lupus IC ρ Oph IC Cha I Taurus Comerón (2008) Lada et al. (2006); Muench et al. (2007) Bontemps et al. (2001) Barrado y Navascués et al. (2001) Luhman (2007) Luhman et al. (2010)
32 Cluster # N Lupus IC ρ Oph IC Cha I Taurus Comerón (2008) Lada et al. (2006); Muench et al. (2007) Bontemps et al. (2001) Barrado y Navascués et al. (2001) Luhman (2007) Luhman et al. (2010)
33 Cluster # N Lupus IC ρ Oph IC Cha I Taurus Comerón (2008) Lada et al. (2006); Muench et al. (2007) Bontemps et al. (2001) Barrado y Navascués et al. (2001) Luhman (2007) Luhman et al. (2010)
34 HANS!
35 HANS! Conclusions
36 HANS! Conclusions Q analysis of stellar structures has some serious shortcomings, mainly due to models.
37 HANS! Conclusions Q analysis of stellar structures has some serious shortcomings, mainly due to models. Fractional Brownian motion (FBM) provides a convenient model of star cluster morphology, related to molecular clouds.
38 HANS! Conclusions Q analysis of stellar structures has some serious shortcomings, mainly due to models. Fractional Brownian motion (FBM) provides a convenient model of star cluster morphology, related to molecular clouds. Machine learning techniques can be used to modernise Q analysis.
39 HANS! Conclusions Q analysis of stellar structures has some serious shortcomings, mainly due to models. Fractional Brownian motion (FBM) provides a convenient model of star cluster morphology, related to molecular clouds. Machine learning techniques can be used to modernise Q analysis. So far, we can classify clusters, and generate synthetic analogues. Simulations needed to better understand physical meaning of parameters.
40 HANS! Conclusions Q analysis of stellar structures has some serious shortcomings, mainly due to models. Fractional Brownian motion (FBM) provides a convenient model of star cluster morphology, related to molecular clouds. Machine learning techniques can be used to modernise Q analysis. So far, we can classify clusters, and generate synthetic analogues. Simulations needed to better understand physical meaning of parameters. Article: Lomax et al., 2018, MNRAS, 480, 371 arxiv: GitHub: github.com/odlomax/clusterfrac
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