Statistical Tools applied to the Magellanic Bridge Statistical tools applied to the H I Magellanic...

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)

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.

Statistical Tools applied to the Magellanic Bridge

Data set (ATCA +Parkes): Peak pixel HI map, Magellanic Bridge

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)

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:

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

)(

11)(,0 rQ

S N r

W

dvvT

NQ r

2),(1)(

rr

Δr Δr Δr

Statistical Tools applied to the Magellanic Bridge

SCF output maps:

Statistical Tools applied to the Magellanic Bridge

T maps

SCF maps

55 pixels

37 pixels

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

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.

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.

Statistical Tools applied to the Magellanic Bridge

Spatial Power spectrum cont.

ATCA + Parkes data

(+Gaussian rounding)

FFT (im2+r2)

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)

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?

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.

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)

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.