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)


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.


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


• 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:


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


SCF output maps:


T maps

SCF maps

55 pixels

37 pixels


•+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


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.


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.


Spatial Power spectrum cont.

ATCA + Parkes data

(+Gaussian rounding)

FFT (im2+r2)


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)


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?


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.


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)


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.

statistical tools applied to the magellanic bridge statistical tools applied to the h i magellanic...

Documents