Bojan Arbutina

MODIFIED EQUIPARTITION CALCULATION FOR SUPERNOVA REMNANTS

Determination of the magnetic field strength in the interstellar medium is one of the more complex tasks of contemporary astrophysics. We can only estimate the order of magnitude of the magnetic field strength by using a few very limited methods. Besides the Zeeman effect and Faraday rotation, the equipartition or minimum-energy calculation is a widespread method for estimating magnetic field strength and energy contained in the magnetic field and cosmic-ray particles by using only the radio synchrotron emission. Despite its approximate character, it remains a useful tool, especially when there are no other data about the magnetic field in a source. In this paper, we give a modified calculation that we think is more appropriate for estimating magnetic field strengths and energetics in supernova remnants (SNRs). We present calculated estimates of the magnetic field strengths for all Galactic SNRs for which the necessary observational data are available. The Web application for calculation of the magnetic field strengths of SNRs is available at http://poincare.matf.bg.ac.rs/~arbo/eqp/.

THE RADIO SURFACE-BRIGHTNESS-TO-DIAMETER RELATION FOR GALACTIC SUPERNOVA REMNANTS: SAMPLE SELECTION AND ROBUST ANALYSIS WITH VARIOUS FITTING OFFSETS

In this paper, we present new empirical radio surface-brightness-to-diameter (?-D) relations for supernova remnants (SNRs) in our Galaxy. We also present new theoretical derivations of the ?-D relation based on equipartition or on a constant ratio between cosmic rays and magnetic field energy. A new calibration sample of 60 Galactic SNRs with independently determined distances is created. Instead of (standard) vertical regression, used in previous papers, different fitting procedures are applied to the calibration sample in the log ?-log D plane. Non-standard regressions are used to satisfy the requirement that values of parameters obtained from the fitting of ?-D and D-? relations should be invariant within estimated uncertainties. We impose symmetry between ?-D and D-? due to the existence of large scatter in both D and ?. Using four fitting methods that treat ? and D symmetrically, different ?-D slopes ? are obtained for the calibration sample. Monte Carlo simulations verify that the slopes of the empirical ?-D relation should be determined by using orthogonal regression because of its good performance in data sets with severe scatter. The slope derived here (? = 4.8) is significantly steeper than those derived in previous studies. This new slope is closer to the updated theoretically predicted surface-brightness-diameter slope in the radio range of the Sedov phase. We also analyze the empirical ?-D relations for SNRs in a dense environment of molecular clouds and for SNRs evolving in the lower-density interstellar medium. Applying new empirical relations to estimate distances of Galactic SNRs results in a dramatically changed distance scale.

THE ORTHOGONAL FITTING PROCEDURE FOR DETERMINATION OF THE EMPIRICAL Σ-D RELATIONS FOR SUPERNOVA REMNANTS: APPLICATION TO STARBURST GALAXY M82

The radio surface brightness-to-diameter (Σ-D) relation for supernova remnants (SNRs) in the starburst galaxy M82 is analyzed in a statistically more robust manner than in the previous studies that mainly discussed sample quality and related selection effects. The statistics of data fits in the log Σ-log D plane are analyzed by using vertical (standard) and orthogonal regressions. As the parameter values of D-Σ and Σ-D fits are invariant within the estimated uncertainties for orthogonal regressions, slopes of the empirical Σ-D relations should be determined by using the orthogonal regression fitting procedure. Thus obtained Σ-D relations for samples which are not under severe influence of the selection effects could be used for estimating SNR distances. Using the orthogonal regression fitting procedure, the Σ-D slope β 3.9 is obtained for the sample of 31 SNRs in M82. The results of implemented Monte Carlo simulations show that the sensitivity selection effect does not significantly influence the slope of the M82 relation. This relation could be used for estimating distances to SNRs that evolve in a denser interstellar environment, with number density up to 1000 particles per cm3.

On calibration of some distance scales in astrophysics

We present a method for distance calibration without using standard fitting procedures. Instead, we use random resampling to reconstruct the probability density function (PDF) of calibration data points in the fitting plane. The resulting PDF is then used to estimate distance-related properties. The method is applied to samples of radio surface brightness to diameter (� –D) data for the Galactic supernova remnants (SNRs) and planetary nebulae (PNe), and period– luminosity (PL) data for the Large Magellanic Cloud (LMC) fundamental mode classical Cepheids. We argue that resulting density maps can provide more accurate and more reliable calibrations than those obtained by standard linear fitting procedures. For the selected sample of the Galactic SNRs, the presented PDF method of distance calibration results in a smaller average distance fractional error of up to ≈16 percentage points. Similarly, the fractional error is smaller for up to ≈8 and ≈0.5 percentage points, for the samples of Galactic PNe and LMC Cepheids, respectively. In addition, we provide a PDF-based calibration data for each of the samples.

The Σ D relation for planetary nebulae

We present an extended analysis of the relation between radio surface brightness and diameter – the so-called Σ − D relation for planetary nebulae (PNe). We revise our previous derivation of the theoretical Σ − D relation for the evolution of bremsstrahlung surface brightness in order to include the influence of the fast wind from the central star. Different theoretical forms are derived: Σ ∝ D −1 for the first and second phases of evolution and Σ ∝ D −3 for the final stage of evolution. Also, we analyzed several different Galactic PN samples. All samples are influenced by severe selection effects, but the Malmquist bias seems to be less influential here than in the supernova remnant (SNR) samples. We derived empirical Σ − D relations for 27 sample sets using 6 updated PN papers from which an additional 21 new sets were extracted. Twenty four of these have a trivial form of β ≈ 2. However, we obtain one empirical Σ − D relation that may be useful for determining distances to PNe. This relation is obtained by extracting a recent nearby (<1 kpc) Galactic PN sample.

Modified Equipartition Calculation for Supernova Remnants. Cases α = 0.5 and α = 1

The equipartition or minimum energy calculation is a well-known procedure for estimating the magnetic field strength and the total energy in the magnetic field and cosmic ray particles by using only the radio synchrotron emission. In one of our previous papers, we have offered a modified equipartition calculation for supernova remnants (SNRs) with spectral indices 0.5 < α < 1. Here we extend the analysis to SNRs with α = 0.5 and α = 1.

Interstellar medium structure and the slope of the radio Σ–D relation of supernova remnants

We analyze the influence of fractal structure of the interstellar matter (ISM) density on the parameter values for the radio surface brightness to diameter (

Radio Evolution of Supernova Remnants Including Nonlinear Particle Acceleration: Insights from Hydrodynamic Simulations

\Sigma-D

The Minimum Mass Ratio for Contact Close Binary Systems of W Ursae Majoris-type

) relation for supernovae remnants (SNRs). We model a dense ISM as a molecular cloud with fractal density structure. SNRs are modelled as spheres of different radius scattered in the modelled ISM. The surface brightness of the SNRs is calculated from the simple relation

Radial dependence of extinction in parent galaxies of supernovae

\Sigma \propto \rho^{0.5}D^{-3.5}