statistical tools applied to the magellanic bridge statistical tools applied to the h i magellanic...
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![Page 1: Statistical Tools applied to the Magellanic Bridge Statistical tools applied to the H I Magellanic Bridge Erik Muller (UOW, ATNF) Supervisors: Lister Staveley-Smith](https://reader033.vdocuments.mx/reader033/viewer/2022042718/56649ef25503460f94c044dd/html5/thumbnails/1.jpg)
Statistical Tools applied to the Magellanic Bridge
Statistical tools applied to the HI Magellanic Bridge
Erik Muller (UOW, ATNF)
Supervisors: Lister Staveley-Smith (ATNF)
Bill Zealey (UOW)
![Page 2: Statistical Tools applied to the Magellanic Bridge Statistical tools applied to the H I Magellanic Bridge Erik Muller (UOW, ATNF) Supervisors: Lister Staveley-Smith](https://reader033.vdocuments.mx/reader033/viewer/2022042718/56649ef25503460f94c044dd/html5/thumbnails/2.jpg)
Statistical Tools applied to the Magellanic Bridge
Introduction• Statistical tools provide a means to
– compare populations of similar objects between different systems
– Understand and model general trends and behaviours.– Distinguish between sub-populations
• Spectral correlation function (SCF): Measures spectral similarity as a function of radial separation
• Power spectrum analysis (PS): Measures power as a function of scale, and as a function of velocity range.
• Both SCF and PS have been used to infer information about the third spatial dimension.
![Page 3: Statistical Tools applied to the Magellanic Bridge Statistical tools applied to the H I Magellanic Bridge Erik Muller (UOW, ATNF) Supervisors: Lister Staveley-Smith](https://reader033.vdocuments.mx/reader033/viewer/2022042718/56649ef25503460f94c044dd/html5/thumbnails/3.jpg)
Statistical Tools applied to the Magellanic Bridge
Data set (ATCA +Parkes): Peak pixel HI map, Magellanic Bridge
![Page 4: Statistical Tools applied to the Magellanic Bridge Statistical tools applied to the H I Magellanic Bridge Erik Muller (UOW, ATNF) Supervisors: Lister Staveley-Smith](https://reader033.vdocuments.mx/reader033/viewer/2022042718/56649ef25503460f94c044dd/html5/thumbnails/4.jpg)
Statistical Tools applied to the Magellanic Bridge
Spectral Tools 1:• Specral Correlation function:
– Compares two spectra separated by Δr, and makes an estimate of their ‘similarity’
– A 2D map of mean SCF shows rate of change (or degree of corrleation) of SCF with Δr and θ
– Has been used to confirm a characteristic length for the scale height of the LMC, by measuring the radius of decorrelation (Padoan et al. 2001)
– In this case, SCF shows that MB spectra has a longer decorrelation length in the east-west direction. (Tidal stretching)
![Page 5: Statistical Tools applied to the Magellanic Bridge Statistical tools applied to the H I Magellanic Bridge Erik Muller (UOW, ATNF) Supervisors: Lister Staveley-Smith](https://reader033.vdocuments.mx/reader033/viewer/2022042718/56649ef25503460f94c044dd/html5/thumbnails/5.jpg)
Statistical Tools applied to the Magellanic Bridge
• Spatial power spectrum– Used to show the range of spatial scales present
in source– Highlights any process favouring a particular
scale. (Eg. Elmegreen, Kim, Staveley-Smith, 2001)
– Using velocity averaging, is can be used to show the relative contributions of density and velocity dominated fluctuations. (Lazarian & Pogosyan, 2001)
Spectral Tools 2:
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Statistical Tools applied to the Magellanic Bridge
Spectral Correlation functionHow it works:
r
oo S
rSS
,()( r
rr r
ro vrTvT
vrTvTrS
22
2
),(),(
),(),(1),(
rr
rrr
)(
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S N r
W
dvvT
NQ r
2),(1)(
rr
Δr Δr Δr
![Page 7: Statistical Tools applied to the Magellanic Bridge Statistical tools applied to the H I Magellanic Bridge Erik Muller (UOW, ATNF) Supervisors: Lister Staveley-Smith](https://reader033.vdocuments.mx/reader033/viewer/2022042718/56649ef25503460f94c044dd/html5/thumbnails/7.jpg)
Statistical Tools applied to the Magellanic Bridge
SCF output maps:
![Page 8: Statistical Tools applied to the Magellanic Bridge Statistical tools applied to the H I Magellanic Bridge Erik Muller (UOW, ATNF) Supervisors: Lister Staveley-Smith](https://reader033.vdocuments.mx/reader033/viewer/2022042718/56649ef25503460f94c044dd/html5/thumbnails/8.jpg)
Statistical Tools applied to the Magellanic Bridge
T maps
SCF maps
55 pixels
37 pixels
![Page 9: Statistical Tools applied to the Magellanic Bridge Statistical tools applied to the H I Magellanic Bridge Erik Muller (UOW, ATNF) Supervisors: Lister Staveley-Smith](https://reader033.vdocuments.mx/reader033/viewer/2022042718/56649ef25503460f94c044dd/html5/thumbnails/9.jpg)
Statistical Tools applied to the Magellanic Bridge
•+ve and –ve fit departures•+ve departures at ~250-380pc (14’-22’ at 60kpc)•-ve departures for sub images where signal is lower and less well distributed throughout.
Fits in E-W and N-S directions (central 5 rows/columns)
ΣT=7.5x105 K.km/s ΣT=8.4x105 K.km/s ΣT=9.4x105 K.km/s
ΣT=1.0x106 K.km/s
ΣT=1.0x106 K.km/s ΣT=1.1x106 K.km/s ΣT=1.1x106 K.km/s ΣT=1.1x106 K.km/s
![Page 10: Statistical Tools applied to the Magellanic Bridge Statistical tools applied to the H I Magellanic Bridge Erik Muller (UOW, ATNF) Supervisors: Lister Staveley-Smith](https://reader033.vdocuments.mx/reader033/viewer/2022042718/56649ef25503460f94c044dd/html5/thumbnails/10.jpg)
Statistical Tools applied to the Magellanic Bridge
SCF summary:• In general, decorrelation of spectra separated by
Δr occurs at ~200-400pc• Estimated thickness of MB is ~5kpc, based on distance
measurements for two OB associations separated by ~7’ (Demers & Battinelli, 1998)
• Results of SCF are difficult to interpret in the same way for LMC, PS analysis may help.
• SCF behaves strangely for datacubes containing low S/N
• The line of minimum rate of change of SCF is points almost, but not quite, E-W, towards the SMC and LMC.
![Page 11: Statistical Tools applied to the Magellanic Bridge Statistical tools applied to the H I Magellanic Bridge Erik Muller (UOW, ATNF) Supervisors: Lister Staveley-Smith](https://reader033.vdocuments.mx/reader033/viewer/2022042718/56649ef25503460f94c044dd/html5/thumbnails/11.jpg)
Statistical Tools applied to the Magellanic Bridge
Spatial Power spectrum• Measures the rate of change of power with spatial scale
• Works on Fourier inverted image data (edges are rounded by convol with a gaussian)
• Channels with significant signal selected (60 channels)
• Filtered to reduce leakage from low spatial frequencies (image convolved with 3x3 unsharp mask, then divided back into FFT data)
• Un-observed UV data is masked out.
• Power-law fit to dataset (γ) (IDL poly_fit).
• A range of velocity increments are examined to determine the relative contributions of density (thin regime) and velocity (thick regime) fluctuations.
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Statistical Tools applied to the Magellanic Bridge
Spatial Power spectrum cont.
ATCA + Parkes data
(+Gaussian rounding)
FFT (im2+r2)
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Statistical Tools applied to the Magellanic Bridge
Power law fit for
Bri
ghtn
ess2 [
K2 ]
Spatial Power spectrum cont.
γ – velocity binsize
Transition from thin to thick regime(velocity to density dominated regime)
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Statistical Tools applied to the Magellanic Bridge
General result:• All Power spectra, for all velocity bins are featureless and
well fit with by a single power law:• No processes present that lead to a dominant scale (c/w LMC)• More ‘3 dimensional’ than the LMC (Similar to SMC). i.e. no
characteristic thickness.
• Power spectra steepen for increasing velocity bin size (ΔV~<20km/s)
• Transition from ‘thin’ velocity dominated (spectral ΔV ~< integrated ΔV thickness) to thick, density dominated regime.
• γ changes from ~-2.90 - ~-3.35, consistent with Kolmogorov Turbulence. (Lazarian & Pogosyan, 2000)
• Source of turbulence?– Processes that do not show a scale preference:
• Stirring & instabilites from tidal force of LMC and SMC?• Energy deposition into ISM from stellar population?
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Statistical Tools applied to the Magellanic Bridge
PS from other systems:• LMC (Elmegreen, Kim & Staveley-Smith, 2001)
• much steeper; γ ~<2.7 (Entire velocity range, two linear fits)• LMC spectra turns over at r~100pc
– attributed to line-of-sight thickness of LMC.
• SMC (Stanimirovic, Lazarian, 2001)• SMC and MB cover same range of γ:
– γSMC~ 3.4 at ΔV ~100km/s– γMB~ 3.3 at ΔV ~100km/s
• linear (featureless) over entire range of Δv• does not appear to approach a characteristic Δv
• Galaxy (Dickey et al. 2001)• Analysed for smaller range of Δv (0-20 km/s)• Inner Galaxy γ ~ -2.5 - -4, consistent with Kolmogorov
turbulence.
• All systems show steepening of γ with ΔV.
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Statistical Tools applied to the Magellanic Bridge
SMC and Galaxy γ with ΔV
SMC γ with ΔV. (Stanimirovic & Lazarian, 2001)
Galaxy γ with ΔV. (Dickey et al 2001) (N.B. Inverted γ scale, linear ΔV scale)
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Statistical Tools applied to the Magellanic Bridge
Overall
• There is no suggestion of a departure from a power law fit to MB spatial power spectra, despite a decorrelation at ~200-400pc found using SCF. (c/w Padoan et al, 2001)
• SCF shows more persistent correlation in W-E direction (due to its tidal origin)
• PS shows transition from γ =~-2.9 to γ =-3.35, through thin to thick regime, consistent with Kolmogorov turbulence.