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A study of Kepler supernova remnant: angular power spectrum estimation from radio frequency data

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 Added by Preetha Saha
 Publication date 2019
  fields Physics
and research's language is English




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Supernova remnants (SNRs) have a variety of overall morphology as well as rich structures over a wide range of scales. Quantitative study of these structures can potentially reveal fluctuations of density and magnetic field originating from the interaction with ambient medium and turbulence in the expanding ejecta. We have used $1.5$GHz (L band) and $5$GHz (C band) VLA data to estimate the angular power spectrum $C_{ell}$ of the synchrotron emission fluctuations of the Kepler SNR. This is done using the novel, visibility based, Tapered Gridded Estimator of $C_{ell}$. We have found that, for $ell = (1.9 - 6.9) times 10^{4}$, the power spectrum is a broken power law with a break at $ell = 3.3 times 10^{4}$, and power law index of $-2.84pm 0.07$ and $-4.39pm 0.04$ before and after the break respectively. The slope $-2.84$ is consistent with 2D Kolmogorov turbulence and earlier measurements for the Tycho SNR. We interpret the break to be related to the shell thickness of the SNR ($0.35 $ pc) which approximately matches $ell = 3.3 times 10^{4}$ (i.e., $0.48$ pc). However, for $ell > 6.9 times 10^{4}$, the estimated $C_{ell}$ of L band is likely to have dominant contribution from the foregrounds while for C band the power law slope $-3.07pm 0.02$ is roughly consistent with $3$D Kolmogorov turbulence like that observed at large $ell$ for Cas A and Crab SNRs.



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The shell type supernova remnant (SNR) Cas A exhibits structures at nearly all angular scales. Previous studies show the angular power spectrum $(C_{ell})$ of the radio emission to be a broken power law, consistent with MHD turbulence. The break has been identified with the transition from 2D to 3D turbulence at the angular scale corresponding to the shell thickness. Alternatively, this can also be explained as 2D inverse cascade driven by energy injection from knot-shock interactions. Here we present $C_{ell}$ measured from archival VLA $5$GHz (C band) data, and Chandra X-ray data in the energy ranges ${rm A}=0.6-1.0 , , {rm keV}$ and ${rm B} =4.2-6.0 , , {rm keV}$, both of which are continuum dominated. The different emissions all trace fluctuations in the underlying plasma and possibly also the magnetic field, and we expect them to be correlated. We quantify this using the cross $C_{ell}$ between the different emissions. We find that X-ray B is strongly correlated with both radio and X-ray A, however X-ray A is only very weakly correlated with radio. This supports a picture where X-ray A is predominantly thermal bremsstrahlung whereas X-ray B is a composite of thermal bremsstrahlung and non-thermal synchrotron emission. The various $C_{ell}$ measured here, all show a broken power law behaviour. However, the slopes are typically shallower than those in radio and the position of the break also corresponds to smaller angular scales. These findings provide observational inputs regarding the nature of turbulence and the emission mechanisms in Cas A.
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We present two estimators to quantify the angular power spectrum of the sky signal directly from the visibilities measured in radio interferometric observations. This is relevant for both the foregrounds and the cosmological 21-cm signal buried therein. The discussion here is restricted to the Galactic synchrotron radiation, the most dominant foreground component after point source removal. Our theoretical analysis is validated using simulations at 150 MHz, mainly for GMRT and also briefly for LOFAR. The Bare Estimator uses pairwise correlations of the measured visibilities, while the Tapered Gridded Estimator uses the visibilities after gridding in the uv plane. The former is very precise, but computationally expensive for large data. The latter has a lower precision, but takes less computation time which is proportional to the data volume. The latter also allows tapering of the sky response leading to sidelobe suppression, an useful ingredient for foreground removal. Both estimators avoid the positive bias that arises due to the system noise. We consider amplitude and phase errors of the gain, and the w-term as possible sources of errors . We find that the estimated angular power spectrum is exponentially sensitive to the variance of the phase errors but insensitive to amplitude errors. The statistical uncertainties of the estimators are affected by both amplitude and phase errors. The w-term does not have a significant effect at the angular scales of our interest. We propose the Tapered Gridded Estimator as an effective tool to observationally quantify both foregrounds and the cosmological 21-cm signal.
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