Studying the Inner Depths of Pulsar Wind Nebulae Using IXPE X-Ray Polarization Data

Mar 24, 2023

Josephine Wong. (Photo courtesy J. Wong.)

by Josephine Wong

Neutron stars are rapidly rotating dense balls of nuclear material formed from the gravitational collapse of the cores of giant stars. Generally, we cannot see them because they are very small and don’t emit much thermal (heat) radiation. But one special class of neutron stars, called pulsars, have jets of radiation, generated by non-thermal processes, that pass by Earth once per cycle as the neutron stars rotate, creating a lighthouse effect whereby they appear to us as pulsating stars (hence the name "pulsar"). In the nearly sixty years since Jocelyn Graham Bell detected the periodic signals from the first pulsar, astronomers have discovered more than 1500 pulsars, radiating in wavelengths from radio to gamma-rays, with rotation periods from milliseconds to tens of seconds.

Many models have been proposed to explain the nature of pulsar emissions. The most basic one is called the “rotation-powered” model, where particles accelerated along the pulsar's magnetic field lines are dragged and rotated around by the spin, powering the observed synchrotron radiation and exerting a torque on the pulsar that causes it to slow down over time (known as magnetic braking). While this model allows us to approximate some pulsar parameters, such as the strength of the surface magnetic field, details of the emission process are unaccounted for. Other plausible models have been proposed, which we'll be able to better constrain using data from the Imaging X-Ray Polarimetry Explorer (IXPE), a small-mission NASA satellite launched in December 2021. (IXPE has already been making headlines; see this November 2022 highlight.)

Figure 1. Animation of the sweep of the pulsar beam, creating a lighthouse effect. The observed intensity of radiation vs. phase (the pulsar's light curve) is plotted in the bottom panel. (Credit: Michael Kramer.)

IXPE’s Debut as NASA’s First X-Ray Polarimeter

Polarimetry—the measurement of the polarization, or the oscillation direction, of the electric field—is an important tool to unravel the mystery of pulsar emission. Electric and magnetic fields oscillate perpendicular to each other in electromagnetic waves. By mapping the polarization of pulsar’s electric fields, IXPE can help us determine the geometry of their magnetic fields. This can help us test and constrain pulsar emission models, since different models make different predictions for how the degree and angle of polarization change as a function of time (or “phase”, if we break time into units of the rotation period). Since X-ray photons tend to originate near particle acceleration sites, and are less affected by absorption than lower energy light, X-ray polarization images will give us a different view of the pulsar magnetosphere (the region around the pulsar that is magnetically controlled).

IXPE has already observed several pulsars, including the young and energetic Crab pulsar shown below. The Crab pulsar hosts a turbulent environment populated by a stream of magnetized, charged particles from the pulsar (called a pulsar wind) that have escaped the magnetosphere through open magnetic field lines. This nebula has its own intrinsic polarization. Due to IXPE's modest resolution, the pulsar’s light is blurred within the surrounding bright nebula.

Figure 2. Radio (left) and X-ray (right) observation of the Crab Pulsar and surrounding Nebula (collectively characterized as a pulsar wind nebula). The more energetic X-ray synchrotron radiation is located in the jet and toroidal shock fronts around the pulsar, while the further extents of the nebula are dominated by radio emission, particularly along the filaments. Notice that the scale of the radio image is six times that of the X-ray image—X-ray observations probe emissions closer to the central pulsar. (One arcmin = 60 arcsec.) (Credit: Modified from Gaensler and Slane, 2006.)

Extracting the Pulsar Polarization

Therefore, any analysis of the pulsar in a source like the Crab requires first separating out its polarization from that of the nebula. In the traditional “on-off fitting” method, the average flux in the off-phase (when the pulsar is at minimum intensity) is treated as pure nebula flux and subtracted from the rest of the light curve. This is a reasonable approximation as the pulsar is very dim in the off-phase, but it can lead to systematic biases in our polarization measurements—especially if the pulsar happens to be highly polarized in the off-phase.

I have been working with KIPAC Professor Roger Romani on developing an improved method of extracting the pulsar polarization called “simultaneous fitting,” using measurements available from several sources. Chandra X-ray observations have provided good measurements of pulsar intensity (light) curves and nebula intensity maps at finer spatial resolution than we could achieve with IXPE. We also use the point spread function of IXPE’s mirrors to determine how irregularities in the mirrors affect the way IXPE “sees” its targets. By using this information, we can simultaneously determine the respective contributions of the pulsar and the nebula to the spatially and temporally varying polarization data and extract their respective polarization properties.

The method of simultaneous fitting has shown promising results with simulated IXPE Crab observations. Compared to the on-off method, it showed an ~60% improvement in recovering the pulsar polarization (see Fig. 3 for details). Also, simultaneous fitting enables us to acquire nebula polarization maps that more clearly resemble the model polarization with smaller uncertainties (shown in Fig. 4).

Comparison of on-off (red) and simultaneous (blue) reconstructed pulsar polarization. Note that IXPE detects linear polarization; thus polarization is reported in units of Stokes Q/I and U/I, which are orthogonal directions of polarization. Simultaneous fitting leads to a better fit to the true (input or “model”) polarization, particularly in the bridge region between phases 0.3 and 0.5, where it mitigates the systematic errors seen in on-off. In total, it gives us a 60% improvement in polarization reconstruction. (Credit: Wong, et al., to be submitted.) — Figure 3. Comparison of on-off (red) and simultaneous (blue) reconstructed pulsar polarization. Note that IXPE detects linear polarization, reported in units of Stokes Q/I and U/I, which are orthogonal directions of polarization. Simultaneous fitting leads to a better fit to the true (input or “model”) polarization, particularly in the bridge region between phases 0.3 and 0.5, where it mitigates the systematic errors seen in on-off. In total, it gives us a 60% improvement in polarization reconstruction. (Credit: Wong, et al., to be submitted.)

Figure 4. Comparison of on-off (middle column) and simultaneous (right column) reconstructed nebula polarization map with the true polarization (left column). Simultaneous maps are less noisy, their average error is smaller by ~50%, and they reproduce the structures in the model more clearly. (Credit: Wong, et al., to be submitted.)

For the future, we plan to apply simultaneous fitting to extract the polarization of IXPE observations such as the Crab and MSH 15-5(2) / PSR B1509-58, a pulsar known colloquially as the “Hand of God” for its striking appearance (see the image in the upper right). With the improvements in certainty and accuracy seen with simultaneous fitting, it will be a useful tool to help us constrain different models of pulsar emission.

The pulsar wind nebula known as the "Hand of God." X-ray light seen by Chandra with energy ranges of 0.5 to 2 kiloelectron volts (keV) and 2 to 4 keV is shown in red and green, respectively, while X-ray light detected by NuSTAR in the higher-energy range of 7 to 25 keV is blue. (Credit: NASA/JPL-Caltech/McGill.)

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