A statistical approachto radio emissionin Supernova Remnants Rino Bandiera - Arcetri Obs., Firenze, ItalyCollab: Oleh PetrukOutline:Regularities in radio emission of SNRsParametric modeling of radio synch. emissionInferences on the evolution of the radio synchrotron emission, and on the acceleration processes in shocks

Particle acceleration in SNRsSNR paradigm for Cosmic-Rays originParticle acceleration is a complex problem (injection especially for electrons)SNRs: a laboratory to test this physicsWhat are the most important particles?Ions: dynamics, link to Cosmic-RaysElectrons: directly observed (from radio to X-rays - synchrotron emission)

Recent investigationsDetailed studies of selected SNRs (SN 1006, Cas A, Tycho, RXJ1713.7-3946, )Are they representative of the average SNR ?High-resolution X-ray images + spectrathe highest energy electrons (synchrotron cutoff)direct measure of synchrotron time (rim thickness) TeV rangeif it is inverse Compton, degeneracy between magnetic field and electron energy could be resolved (but the TeV emission could be hadronic - pion decay)

Is SNR radio astronomy old-fashioned? Radio observations started more than 50 yrs ago Many SNRs are bright radio sources 80 Galactic SNRs already known in the late 60s

The infamous -D relation Sample of shell-type SNRs at known distances Empirical relation, between the average radio surface brightness () and diameter (D) Known since the 70s. Slope estimates:

Used to get distance estimates (from , ) but rather inaccurate

What to get from the -D relation ?Usually considered only as a tool for estimating distances

Take it instead as a diagnostic tool to constrain electron acceleration and / or SNR evolutionespecially if combined with correlations between other quantities

Requirement: samples of SNRs at known distances

Which expansion phase ?Most radio SNRs with sizes ~ 10 50 pcNot too young(Mswept-up>>Mejecta)Not too old(ESNR~ESN)

Sedov phase

Basics of synchrotron emissionIn terms of the energy densities (and p =1/2)

(degeneracy)

The many flavours of the predictionsGiven

Bubble of magnetic fields and electrons: (Shklovsky 1960) + similar (van der Laan 1962; Lequeux 1962; Poveda & Woltjer 1962; Kesteven 1968)If continuous injection of electrons & fresh field THEN emission decreases more slowly. Magnetic fieldcompression:

turbulent amplification:

Particle efficiency

in energy:

in number:

(Bell 1978) Fitting the behaviour of B:(Duric & Seaquist 1986) constant number efficiency for particlesSedov expansion for the SNRFromthen

The Standard Model(from Berezhko & Vlk 2004 The theory of synchrotron emission from SNRs)

Efficient magnetic field amplificationEfficient acceleration of electrons Sedov phaseResulting emission

NO DEPENDENCE ON o !

Changing perspectiveSo far, -D relation taken as the evolutionary track of an average supernova remnantEvidence that is could, instead, be a combined result of SNRs evolving under very different ambient conditionsCorrelation between the SNR size and the ambient density (from thermal X-rays)

The trend of lower densities observed for larger SNR is unmistakable(McKee & Ostriker 1977)

-D as a secondary relationIt may be concluded that variations in the apparent ambient density may indeed be responsible for the slope of the observed -D diagram (Berkhuijsen 1986)

Basic assumptions & considerationsABOUT THE SOURCES:

We observe a combined effect of evolutionary tracks under different ambient conditionsThe slopes of individual tracks may even be different from the best fit -D slopeA SNR in decelerated expansion spends most of its time near its maximum D (as a radio source)The lifetime of a SNR as an efficient radio source may be shorter than its dynamical life

ABOUT THE DATA:

-D-no are a reasonable set of parameters for describing this sampleThe information contained in the data is more than just a slopeThe density of points in the parameter space (selection effects allowing) also depends on the residence time of individual SNRs

Zeroth order approximationNeglecting the SNR evolution:

For Sedov expansion:D-n relation:n relation:DERIVED D relation:Probability of finding a SNR in a region with given density:Cumulative distribution with size: No dependence on the expansion law !!

Endpoint of the radio emitting phase

Nice match with the endpoint of the Sedov phase

Safe to use Sedov expansion in modellingConsistent with !!!What (if any) physical relation ?

Individual SNR evolutionary tracksResiduals of the D(no) fitFixed no, i.e. single SNR evolutionDispersion in the distribution (LOW)Dispersion due to measurement uncertainties?If so, even lower intrinsic dispersion.

A physical meaning for the endpoint ?Decelerated expansion most time spent when D near D2

Why should the efficiency in emitting radio synchrotron (= in injecting electrons?) turn down at the end of the Sedov phase?

Physical arguments:Increase of the compression ratio (even better?)Radiative lower temperature (against?)Alternative reasons?

A parametric statistical modelPhysics is introduced implicitlySelf-similarity is assumed ( ! )Basic assumptions:SNR dynamical evolutionSNR radio emission

or, more simply,

p is the true slope of an individual evolutionary track

Analysis of ideal dataResults of linear regressions:p and q from fitting to the data (2-D regression)m from fitting to the dataw from the cumulative distribution

The expansion law could be only extracted from the distribution across the D(no) correlation

Some results from data analysisSNR samples with information on -D-no (using also extragalactic SNRs)Berkhuijsen (34 radio + X-ray obj)

LMC (28 radio + X-ray obj)

M33 (22 radio + X-ray obj)

2-D analysis of the confidence levels

Near degeneracy in the p-q plane (p = -17/4,q = 0) (Berezhko & Vlk 2004)(p = -2,q = 0)

with a more physical flavour

Assuming Sedov expansion Best fit:

Best- fit solution: Against field amplification

In contradiction with efficient acceleration found in some young SNRs? Not necessarily: middle-age SNRs are those statistically more common.

How robust is this method?BerkhuijsenEven though with different selection effectsM33

Cumulative distributionsObserved cumulative functions N(D) of SNRs in several galaxies show nearly linear behavioursUsual argument: ifthenLinear expansion up to 50 pc ? Mswept~2000 no Msun

Independent of the expansion law

The case of M82Linear N(D), then linear expansion (NOT TRUE) then Vsh>5000 km/s and Ages

Any bias from sample incompleteness? (or also form source misclassifications)Distance determination:exclude our GalaxyHomogenous threshold:exclude our GalaxyDetection limits: flux & surface brightness

-D Relation as a possible artifact (the primary observable being the luminosity)(Green 2004)

An L-D relation does exist !(Arbutina et al 2004)

Do-it-yourselfSimulated dataOn the basis of the above equationsMeasurement uncertainties not includedUseful to study effects related to:Sample incompletenessDetection thresholdsSmall sample statisticsDimensionless quantitiesFactors should be included (shifts in Log) to compare with physical data

Simulation: standard caseNo intrinsic dispersion in the -D plane !+ Linear cumulative

Simulation: parametrized caseDispersion in the -D planeHighly skewedLonger tail to the left sideevol. tracks shallower than -Dsharp endpoint+ Linear cumulative

Residuals in the real cases

Interpreting the dispersionslg(lg D) residualsFurther parameter (energy of SN ?)Details of individual SNR evolution?

Brightening may be reasonable at the end of Sedov epoch (squeezing effect)

Whats next ?Extending the sample toSNRs in nearby galaxiesWell known distancesRather homogeneous samplesInvestigate better effects of:Sample incompletenessDetection thresholds (Maximum likelihood techniques, survival analysis)Barely resolved objectsFalse identificationsAlso using simulated data

Summary of the results-D (+no) relation may contain relevant information on:the physics of electron injection the SNR evolution phasethe distribution of ambient conditionsMost radio SNRs close to the end of their radio lifeElectron acceleration processes close to switch-off limit? Death of radio SNRs close to the end of Sedov phase.Measurement errors do not seem to play a major role.The standard model for synchrotron emission in SNRs does not fit the dataPurely magnetic compression seems to be favoured (at least for middle-age SNRs)

Need for larger, reliable extragalactic samples

Thank you !