Sampling a random variable distributed according to Planck`s Law

Barnett, C.S.; Canfield, E. H.

doi:10.2172/420378

“…Seed photons are launched randomly from each of these patches, according to the selected emission model. This can easily be achieved for the blackbody model using a series expansion method (see e.g., Barnett & Canfield 1970). In the case of the magnetized atmosphere and condensed surface models, we use an acceptance/rejection method (von Neumann 1951;Press et al 1992).…”

Section: Numerical Implementationmentioning

confidence: 99%

Fitting XMM-Newton observations of the AXP 1RXS J170849.0−400910 with four magnetar surface emission models, and predictions for X-ray polarization observations with IXPE

Krawczynski

¹

,

Taverna

²

,

Turolla

³

et al. 2022

A&A

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Context. Phase-resolved spectral and spectropolarimetric X-ray observations of magnetars present us with the opportunity to test models of the origin of the X-ray emission from these objects, and to constrain the properties of the neutron star surface and atmosphere. Aims. Our first aim is to use archival XMM-Newton observations of the magnetar 1RXS J170849.0−400910 to ascertain how well four emission models describe the phase-resolved XMM-Newton energy spectra. Our second aim is to evaluate the scientific potential of future spectropolarimetric observations of 1RXS J170849.0−400910 with the Imaging X-ray Polarimetry Explorer (IXPE) scheduled for launch in late 2021. The most salient questions are whether IXPE is able to distinguish between the different emission models, and whether IXPE can unambiguously detect the signatures of quantum electrodynamics (QED) effects in strong magnetic fields. Methods. We used numerical radiation transport calculations for a large number of different system parameters to predict the X-ray flux and polarization energy spectra of the source 1RXS J170849.0−400910. Based on the numerical results, we developed a new model to fit phase-resolved and phase-averaged X-ray spectral (i.e., XMM-Newton and IXPE) and spectropolarimetric (IXPE) data. In order to test the sensitivity of IXPE to strong-field QED effects, we fit a simulated IXPE observation with two versions of the model, i.e., with and without QED effects accounted for. Results. The fixed-ions condensed surface model gives the best description of the phase-resolved XMM-Newton spectra, followed by the blackbody and free-ions condensed surface models. The magnetized atmosphere model gives a poor description of the data and seems to be largely excluded. Simulations show that the IXPE observations of sources such as 1RXS J170849.0−400910 will allow us to cleanly distinguish between high-polarization (blackbody, magnetized atmosphere) and low-polarization (condensed surface) models. If the blackbody or magnetized atmosphere models apply, IXPE can easily prove QED effects based on ∼200 ksec observations as studied here; longer IXPE observation times will be needed for a clear detection in the case of the condensed surface models. Conclusions. The XMM-Newton data have such a good signal-to-noise ratio that they reveal some limitations of the theoretical models. Notwithstanding this caveat, the fits clearly favor the fixed-ions condensed surface and blackbody models over the free-ions condensed surface and magnetized atmosphere models. The IXPE polarization information will greatly help us to figure out how to improve the models. The first detection of strong-field QED effects in the signal from astrophysical sources seems possible if an adequate amount of time is dedicated to the observations.

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“…This can easily be achieved for the blackbody model using a series expansion method (see A&A proofs: manuscript no. aanda e.g., Barnett & Canfield 1970). In the case of the magnetized atmosphere and condensed surface models, we use an acceptance/rejection method (von Neumann 1951;Press et al 1992).…”

Section: Numerical Implementationmentioning

confidence: 99%

Fitting XMM-Newton Observations of the AXP 1RXS J170849.0-400910 with four magnetar surface emission models, and predictions for X-ray polarization observations with IXPE

Krawczynski,

Taverna,

Turolla

et al. 2021

Preprint

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Context. Phase-resolved spectral and spectropolarimetric X-ray observations of magnetars present us with the opportunity to test models of the origin of the X-ray emission from these objects, and to constrain the properties of the neutron star surface and atmosphere. Aims. Our first aim is to use archival XMM-Newton observations of the magnetar 1RXS J170849.0−400910 to ascertain how well four emission models describe the phase-resolved XMM-Newton energy spectra. Our second aim is to evaluate the scientific potential of future spectropolarimetric observations of 1RXS J170849.0−400910 with the Imaging X-ray Polarimetry Explorer (IXPE) scheduled for launch in late 2021. The most salient questions are whether IXPE is able to distinguish between the different emission models, and whether IXPE can unambiguously detect the signatures of quantum electrodynamics (QED) effects in strong magnetic fields. Methods. We used numerical radiation transport calculations for a large number of different system parameters to predict the X-ray flux and polarization energy spectra of the source 1RXS J170849.0−400910. Based on the numerical results, we developed a new model to fit phase-resolved and phase-averaged X-ray spectral (i.e., XMM-Newton and IXPE) and spectropolarimetric (IXPE) data. In order to test the sensitivity of IXPE to strong-field QED effects, we fit a simulated IXPE observation with two versions of the model, i.e., with and without QED effects accounted for. Results. The fixed-ions condensed surface model gives the best description of the phase-resolved XMM-Newton spectra, followed by the blackbody and free-ions condensed surface models. The magnetized atmosphere model gives a poor description of the data and seems to be largely excluded. Simulations show that the IXPE observations of sources such as 1RXS J170849.0−400910 will allow us to cleanly distinguish between high-polarization (blackbody, magnetized atmosphere) and low-polarization (condensed surface) models. If the blackbody or magnetized atmosphere models apply, IXPE can easily prove QED effects based on ∼200 ksec observations as studied here; longer IXPE observation times will be needed for a clear detection in the case of the condensed surface models. Conclusions. The XMM-Newton data have such a good signal-to-noise ratio that they reveal some limitations of the theoretical models. Notwithstanding this caveat, the fits clearly favor the fixed-ions condensed surface and blackbody models over the free-ions condensed surface and magnetized atmosphere models. The IXPE polarization information will greatly help us to figure out how to improve the models. The first detection of strong-field QED effects in the signal from astrophysical sources seems possible if an adequate amount of time is dedicated to the observations.

show abstract

“…In Section 3, we describe the SIMC method employed with a focus on how the implementation differs for the two formulations of transport. Correct frequency sampling of the source terms in the difference formulation requires an extension of the relatively mature techniques used to sample the Planck spectrum [20]. This is discussed in Appendix A.…”

Section: Introductionmentioning

confidence: 99%

“…In this event, the p.d.f. turns into a Planckian and is sampled using the method of [20]. The other limiting situation is when the temperatures are close.…”

mentioning

confidence: 99%

Symbolic implicit Monte Carlo radiation transport in the difference formulation: a piecewise constant discretization

Brooks

¹

,

McKinley

²

,

Daffin

³

et al. 2005

Journal of Computational Physics

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Sampling a random variable distributed according to Planck`s Law

Abstract: rhis is an informal report intended primarily for internal or limited external Estribution. The opinions and conclusions stated are those of the author and may )r may not be those of the Laboratory.

Cited by 4 publications

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Fitting XMM-Newton observations of the AXP 1RXS J170849.0−400910 with four magnetar surface emission models, and predictions for X-ray polarization observations with IXPE

Fitting XMM-Newton observations of the AXP 1RXS J170849.0−400910 with four magnetar surface emission models, and predictions for X-ray polarization observations with IXPE

Fitting XMM-Newton Observations of the AXP 1RXS J170849.0-400910 with four magnetar surface emission models, and predictions for X-ray polarization observations with IXPE

Symbolic implicit Monte Carlo radiation transport in the difference formulation: a piecewise constant discretization

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