Outline: Regularities in radio emission of SNRs Parametric modeling of radio synch. emission

1. A statistical approachto radio emissionin Supernova RemnantsRino Bandiera - Arcetri Obs., Firenze, ItalyCollab: Oleh Petruk Outline: • Regularities in radio emission of SNRs • Parametric modeling of radio synch. emission • Inferences on the evolution of the radio synchrotron emission, and on the acceleration processes in shocks

2. Particle acceleration in SNRs • SNR “paradigm” for Cosmic-Rays origin • Particle acceleration is a complex problem(injection – especially for electrons) • SNRs: a laboratory to test this physics • What are the “most important” particles? • Ions: dynamics, link to Cosmic-Rays • Electrons: “directly” observed(from radio to X-rays - synchrotron emission)

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

4. (Kesteven 1968) 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

5. (Case & Bhattacharya 1998) The “infamous” Σ-D relation • Sample of shell-type SNRs at known distances • Empirical relation, between the average radio surface brightness (Σ) and diameter (D) • Known since the ’70s. Slope estimates: • Used to get distance estimates (from Σ, θ)but rather inaccurate

6. What to get from the Σ-D relation ? Usually considered only as a “tool” for estimating distances Take it instead as a “diagnostic tool” to constrainelectron acceleration and / or SNR evolution especially if combinedwith correlations between other quantities Requirement: samples of SNRs at known distances

7. Which expansion phase ? Most radio SNRs with sizes ~ 10 – 50 pc • Not too young (Mswept-up>>Mejecta) • Not too old (ESNR~ESN) • Sedov phase

8. Basics of synchrotron emission • In terms of the energy densities (and p =1/2) (degeneracy)

9. The many “flavours” of the predictions • Given • 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 field • compression: • turbulent amplification:

10. Particle efficiency in energy: in number: (Bell 1978) • Fitting the behaviour of B: (Duric & Seaquist 1986) • constant number efficiency for particles • Sedov expansion for the SNR • From then

11. The “Standard Model” (from Berezhko & Völk 2004 “The theory of synchrotron emission from SNRs”) • Efficient magnetic fieldamplification • Efficient acceleration ofelectrons • Sedov phase • Resulting emission NO DEPENDENCE ON ρo !

12. Changing perspective • So far, Σ-D relation taken as the evolutionary track of an “average” supernova remnant • Evidence that is could, instead, be a combined result of SNRs evolving under very different ambient conditions • Correlation betweenthe SNR size andthe ambient density(from thermal X-rays) “The trend of lower densities observed for larger SNR is unmistakable” (McKee & Ostriker 1977)

13. Σ-D as a secondary relation “It may be concluded that variations in the apparent ambient density may indeed be responsible for the slope of the observed Σ-D diagram” (Berkhuijsen 1986)

14. Basic assumptions & considerations ABOUT THE SOURCES: • We observe a combined effect of evolutionary tracks under different ambient conditions • The slopes of individual tracks may even be different from the best fit Σ-D slope • A 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

15. ABOUT THE DATA: • Σ-D-no are a reasonable set of parameters for describing this sample • The information contained in the data is more than “just a slope” • The density of points in the parameter space (selection effects allowing) also depends on the residence time of individual SNRs

16. Zeroth order approximation Neglecting the SNR evolution: For Sedov expansion: • D-n relation: • Σ–n relation: • DERIVED Σ–D relation: • Probability of finding a SNRin a region with given density: • Cumulative distribution with size: No dependence on the expansion law !!

17. (data from Berkhuijsen 1986) (Truelove & McKee 1999) Endpoint of the radio emitting phase Nice matchwith theendpoint ofthe Sedovphase • Safe to use Sedov expansion in modelling • Consistent with!!! • What (if any) physical relation ? <lg D>

18. Data from Berkhuijsen 1986 (37 points) σ=0.18 lgD(no) residuals Individual SNR evolutionary tracks • Residuals of the D(no) fit • Fixed no, i.e. single SNR evolution • Dispersion in the distribution (LOW) Dispersion due to measurement uncertainties? If so, even lower intrinsic dispersion.

19. 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?

20. A parametric statistical model • Physics is introduced implicitly • Self-similarity is assumed ( ! ) Basic assumptions: • SNR dynamical evolution • SNR radio emission or, more simply, pis the true slope of an individual evolutionary track

21. Analysis of “ideal” data Results of linear regressions: • p and q from fittingto the data (2-D regression) • m from fitting to the data • w from the cumulative distribution The expansion law could be only extracted from the distribution across the D(no) correlation

22. Some results from data analysis SNR samples with information on Σ-D-no (using also extragalactic SNRs) • Berkhuijsen (34 radio + X-ray obj) • LMC (28 radio + X-ray obj) • M33 (22 radio + X-ray obj)

23. 2-D analysis of the confidence levels (p = -17/4,q = 0)(Berezhko & Vőlk 2004) (p = -2,q = 0) • Near degeneracy in the p-q plane

24. (g=1.75,h=3.5) (g=1,h=2) …with a more “physical” flavour • Assuming Sedov expansion • Best fit:

25. 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.

26. How robust is this method? M33 Berkhuijsen Even though with different selection effects

27. (Mathewson et al 1983) Cumulative distributions • Observed cumulative functions N(D) of SNRs in several galaxies show nearly linear behaviours • Usual argument: if then • Linear expansion up to 50 pc ? Mswept~2000 no Msun Independent of the expansion law

28. (Muxlow et al 1994) (Muxlow et al 1994) The case of M82 • Linear N(D), then linear expansion (NOT TRUE)then Vsh>5000 km/s and Ages<400 yr (for D=4 pc) • Upper limit to the variability (< 0.1% per yr) THEN cluster wind-driven bubbles, NOT SNRs (Seaquist and Stankovic 2007) Erroneous conclusion

29. (Urosevic et al 2005) Any bias from sample incompleteness? (or also form source misclassifications) • Distance determination: exclude our Galaxy • Homogenous threshold: exclude our Galaxy • Detection limits: flux &surface brightness

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

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

32. Do-it-yourself • Simulated data • On the basis of the above equations • Measurement uncertainties not included • Useful to study effects related to: • Sample incompleteness • Detection thresholds • Small sample statistics • Dimensionless quantities • Factors should be included (shifts in Log) to compare with “physical” data

33. lgR-lgΣ (+no) R-N(R) (100 points) Hist. of lgR(no) residuals Simulation: “standard” case No intrinsic dispersionin the Σ-D plane ! + Linear cumulative

34. lgR-lgΣ (+no) Hist. of lgΣ(lgR) residuals (100 points) Hist. of lgR(no) residuals Simulation: parametrized case Dispersion in the Σ-D plane • Highly skewed • Longer tail to the left side • evol. tracks shallower than Σ-D • sharp endpoint + Linear cumulative

35. lgΣ(lg D) resid.: SIMUL LMC M33 lgD(lg no) resid.: SIMUL LMC M33 Residuals in the real cases

36. lgΣ(lg D) individual SNR lgΣ(lg D) residuals Interpreting the dispersions lgΣ(lg D) residuals • Further parameter (energy of SN ?) • Details of individual SNR evolution? Brightening may be reasonable at the end of Sedov epoch (“squeezing effect”)

37. What’s next ? • Extending the sample to • SNRs in nearby galaxies • Well known distances • Rather homogeneous samples • Investigate better effects of: • Sample incompleteness • Detection thresholds (Maximum likelihood techniques, survival analysis) • Barely resolved objects • False identifications • Also using simulated data

38. Summary of the results • Σ-D (+no) relation may contain relevant information on: • the physics of electron injection • the SNR evolution phase • the distribution of ambient conditions • Most radio SNRs close to the end of their “radio” life • Electron 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 data • Purely magnetic compression seems to be favoured (at least for middle-age SNRs) Need for larger, reliable extragalactic samples

39. Thank you !