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Numerical Simulations

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Numerical Simulations of the ISM:What Good are They?Alyssa A. GoodmanHarvard-Smithsonian Center for AstrophysicsPrincipal CollaboratorsHéctor Arce, CfAJavier Ballesteros-Paredes, AMNHSungeun Kim, CfAPaolo Padoan, CfAErik Rosolowsky, UC BerkeleyEnrique Vazquez-Semadeni, UNAMJonathan Williams, U. FloridaDavid Wilner, CfASpectroscopy➜VelocityInformation1.51.00.50.0-0.5Intensity400350300250200150100"Velocity"Observed SpectrumTelescope +SpectrometerRadio Spectral-line Observations of Interstellar CloudsSpectral Line ObservationsThe Superstore:Learning More from “Too Much Data”200020001990199019801980197019701960196019501950Year100101102103104Nchannels, S/N in 1 hour, Npixels102103104105106107108(S/N)*Npixels*NchannelsNpixelsS/NProductNchannelsA Free SampleData: Hartmann & Burton 1999; Figure: Ballesteros-Paredes, Vazquez-Semadeni & Goodman 2001The “Good” Old Days– Low ObservationalResolution– ⇒Models ofspherical, Smooth,Long-lasting“Cloud”Structures And more “structure” came from fragmentationThe New AgeHigh(er) ObservationalResolution (at manyλ’s)⇒Highly irregularstructures, many ofwhich are “transient”on long time scalesSo, are numerical simulationsphysically illuminating in thisNew Age?If so, in what way(s)?How might simulations beimproved (i.e. to better matchobservations)?Numerical MHD:The State ofthe Art 25Years Ago• Two-dimensional “CEL”code• 10’s of hours of CPU time• Only possible to run 1 case• Grid size ~96 x 188 (~1282)• No magnetic fields• No gravity• Heating & cooling treated• R-T and K-H Instabilitiestraced wellStar-formation “triggered” by a spiral-density wave shock. (Woodward 1976)Woodward’sConclusions(1976)Y2K MHDStone, Gammie & Ostriker 1999•Driven Turbulence; M→ K; no gravity•Colors: log density•Computational volume: 2563•Dark blue lines: B-field•Red : isosurface of passive contaminantafter saturationβ=0.01β=1β=T/10 K[]nH2/100 cm-3[]B/1.4 µG[]2But, recall what we actually observeIntensity(position, position,velocity)Falgarone et al. 1994Velocity is the Observer’s "Fourth" DimensionSpectral Line ObservationsMountain RangeNo loss ofinformationLoss of1 dimension• Can no longer examine “large” spectral-line mapsor simulations “by-eye”• Need powerful, discriminatory tools to quantifyand intercompare data sets• Previous attempts are numerous: ACF, StructureFunctions, Structure Trees, Clumpfinding,Wavelets, PCA, ∆-variance, Line parameterhistogramsStatistical ToolsMost previous attempts discard orcompress either position orvelocity informationOriginal (1997) Goals of the“Spectral Correlation Function”Project✔ Develop “sharp tool” for statistical analysis of ISM, using asmuch data of a data cube as possible! Compare information from this tool with other statistical toolsapplied to same cubes❒ Incorporate continuum information! Use best suite of tools to compare “real” & “simulated” ISM! Adjust simulations to match, understanding physical inputs! Develop a (better) prescription for finding star-forming gasThe Spectral Correlation Function• v.1.0 Simply measures similarity ofneighboring spectra (Rosolowsky, Goodman, Wilner &Williams 1999)– S/N equalized, observational/theoretical comparisons showdiscriminatory power• After explaining v.1.0, I’ll show:– v.2.0 Measures spectral similarity as a function ofspatial scale– ApplicationsHow SCF v.1.0 Works• Measuressimilarity ofneighboringspectra within aspecified “beam”size– lag & scalingadjustable– signal-to-noiseaccounted forSee: Rosolowsky, Goodman, Wilner & Williams 1999;Ballesteros-Paredes, Vazquez-Semadeni & Goodman 2001Applicationof the“Raw” SCFgreyscale: TA=0.04 to 0. 3 KAntenna Temperature Map“Raw” SCF MapData shown: C18O map of Rosette,courtesy M. Heyer et al.Results: Padoan, Rosolowsky& Goodman 2001greyscale: while=low correlation; black=highApplicationof the SCFgreyscale: TA=0.04 to 0. 3 KAntenna Temperature Map“Normalized” SCF MapData shown: C18O map of Rosette,courtesy M. Heyer et al.Results: Padoan, Rosolowsky &Goodman 2001.greyscale: while=low correlation; black=highOriginal DataRandomized PositionsSCF Distributions Normalized C18O Data forRosette Molecular CloudNo gravity, No B field No gravity, Yes B field Yes gravity, Yes B fieldSimulationsInsights fromSCF v.1.0Rosolowsky,Goodman, Williams& Wilner 1999Self-Gravitating, Star-Forming RegionUnbound High-Latitude CloudObservationsLag & scalingadjustableOnly lagadjustableOnly scalingadjustableNo adjustmentsWhich of these is not like the others?1.00.80.60.40.20.01.21.00.80.60.40.20.0Mean SCF ValueChange in Mean SCF with RandomizationIncreasing Similarity of Spectra to NeighborsG,O,SFalgarone et al.MacLow et al.L134A 12CO(2-1).L1512 12CO(2-1)Pol. 13CO(1-0)L134A 13CO(1-0)HCl2 C 18O PeaksHCl2 C 18ORosette C 18ORosette C 18O PeaksSNRH I SurveyRosette 13CORosette 13CO PeaksHLCIncreasing Similarity of ALL Spectra in MapThe Spectral Correlation Function• v.1.0 Simply measures similarity of neighboringspectra (Rosolowsky, Goodman, Wilner & Williams 1999)– S/N equalized, observational/theoretical comparisons showdiscriminatory power• v.2.0 Measures spectral similarity as a functionof spatial scale (Padoan, Rosolowsky & Goodman 2001)– Noise normalization technique found– SCF(lag) even more powerful discriminant• Applications– Finding the scale-height of face-on galaxies! (Padoan, Kim,Goodman & Stavely-Smith 2001)– Understanding behavior of atomic ISM (e.g. Ballesteros-Paredes,Vazquez-Semadeni & Goodman 2001)v.2.0: Scale-Dependence of the SCFExample for “Simulated Data” Padoan, Rosolowsky & Goodman 2001“A Robust Statistic”Padoan, Rosolowsky & Goodman 2001High-resolution dataLow-resolution data, area of high-res mapLow-resolution data, full mapThe Spectral Correlation Function• v.1.0 Simply measures similarity of neighboring spectra(Rosolowsky, Goodman, Wilner & Williams 1999)– S/N equalized, observational/theoretical comparisons show discriminatorypower• v.2.0 Measures spectral similarity as a function ofspatial scale (Padoan, Rosolowsky & Goodman 2001)– Noise normalization technique found– SCF(lag) even more powerful discriminant• Applications– Finding the “scale-height” of nearly face-on galaxies! (Padoan,Kim, Goodman & Stavely-Smith 2001)– Understanding behavior of atomic ISM (e.g. Ballesteros-Paredes,Vazquez-Semadeni & Goodman 2001)Galactic Scale Heights from the SCF


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