For the work presented here, we have used the MWA’s analytical beam model to calibrate and beamform the data. The analytical beam model is indeed a reasonably good approximation to the MWA’s tile beam, if we consider total intensity alone. For polarisation, the analytical beam model is acceptable (in terms of performance and stability) for observations at zenith angles . 45◦ and
Figure 4.12: An example of the deviation in normalised Stokes Q gain value be- tween the analytical and FEE beam models, as a function of observing frequency, for the directions of the five pointings towards PSR J1752–2806. The legend refers to the pointing positions as presented in Figure 4.1, where ‘p3’ represents the pointing towards zenith.
at frequencies . 270 MHz. Further developments have been made to the MWA tile beam model, including the recent fully-embedded element (FEE) primary beam model (Sokolowski et al., 2017). This is a significant improvement to the analytical model, and provides a more accurate prediction of the polarimetric response at large zenith angles. Therefore, using the FEE model in the calibration and beamforming will likely impart less instrumental polarimetric leakage to the data. This is illustrated in Figure 4.12, which shows the difference between the analytical and FEE beam models for the Stokes Q parameter, for example. The increasing deviation above 270 MHz indicates that the analytical beam model should be used with caution in this range.
In future, we plan to extend this work through improved polarimetric calibra- tion by integrating the FEE beam model into our calibration and beamforming pipeline. This is an important exercise, however, beyond the scope of the present
work, given the much larger computational requirements of the FEE beam model. We also plan to compare the MWA beamformed data with the imaging products (e.g. Lenc et al., 2017), to provide further insights into the calibration and con- sistency between the observing modes, and to investigate any further corrections that could be applied to improve the polarimetric response.
Building on the work in this chapter, we further explore the behaviour of the degree of linear polarisation with frequency and pulse phase for more pulsars towards the Gum Nebula region in Chapter 5.
Probing the ISM towards the
Gum Nebula using Pulsar
Measurements
5.1
The Gum Nebula and its neighbourhood
The Gum Nebula, discovered by Gum (1952), is a very large region of ionised gas. It is an extensive, conspicuous structure in the Hα map in the southern sky, roughly centred at Galactic coordinates (l, b) = (258◦, −6.6◦) with an angular radius of around 22.7◦ (Purcell et al., 2015). Figure 5.1 shows the Hα image of the Gum Nebula from Finkbeiner (2003), constructed using the data from Virginia Tech Spectral line Survey (VTSS; Dennison et al., 1998), Wisconsin H- Alpha Mapper (WHAM; Reynolds et al., 1998), and the Southern H-Alpha Sky Survey Atlas (SHASSA; Gaustad et al., 2001). The Gum Nebula lies relatively close to the Sun, ∼ 450 pc (Purcell et al., 2015; Yao et al., 2017), and is an im- portant structure in the local ISM environment. The ISM along the line-of-sight to the Gum Nebula is known to be complex, consisting of multiple overlapping structures, including several HIIregions, supernova remnants (SNRs), molecular clouds, and an OB star association.
Figure 5.1: An Hα image of the Gum Nebula (Finkbeiner, 2003) in Galactic coordinates. In this image, which spans ∼ 65◦× 50◦, the Gum Nebula is seen as a prominent feature with an angular diameter of ∼ 18◦ (i.e. ∼ 140 pc, assuming a distance of 450 pc; Yao et al., 2017). Positions of the six pulsars used in this study are shown by yellow crosses with the pulsars’ J-names.
Because of its large angular size and significant DM contribution to pulsars within/behind it, the Gum Nebula has been modeled as an independent com- ponent in Galactic electron density distribution models such as TC93 (Taylor & Cordes, 1993), NE2001 (Cordes & Lazio, 2002), and the YMW16 (Yao et al.,
2017). Estimating the 3-D position of the expansion centre of the Gum Nebula, and its size, is essential for building the Galactic electron density distribution models, as well as understanding the origin and evolution of the Gum Nebula. However, this is not a easy task and the various current methods/estimates suf- fer from large uncertainties. According to the Hα emission, the main body of the Gum Nebula appears to be a nearly circular region with a radius of ∼ 18◦ approximately centered on Galactic coordinates (l, b) = (258◦, −2◦) (Reynolds,
1976; Chanot & Sivan, 1983). Woermann et al. (2001) conducted a kinematics study of the Gum Nebula using OH masers at 1667 MHz and molecular line data from the literature. They modeled the Gum Nebula with the kinematic centre (l, b) = (261◦, −2.5◦), and a mean angular radius of 14◦. Adopting a non-uniformly expanding shell model, the best-fitting distance of the expansion centre is 400 pc from the Sun with a plausible uncertainty ranging from 200 to 500 pc. Purcell et al. (2015) modeled the Gum Nebula with a spherical shell centred at (l, b) = (258◦, −6.6◦) with a radius of 22.7◦. The Gum Nebula is also modeled in both NE2001 (Cordes & Lazio, 2002) and the YMW16 electron density model (Yao et al., 2017). NE2001 modeled the Gum Nebula with a centre at (l, b) = (260◦, −1◦), a distance of 500 pc, and a radius of 140 pc (corresponding to an angular radius of 16.3◦). In the YMW16 model, the centre is at (l, b) = (264◦, −4◦), with a distance of 450 pc, and a radius of 125.8 pc (corresponding to an angular radius of 16.2◦).
Weaver et al.(1977) suggested that the ionisation state of the Gum Nebula is maintained by the UV photons emitted from two bright, early-type stars: ζ Pup- pis (an O4 star); and γ2 Velorum (a Wolf-Rayet star with an O7.5 companion). According to optical interferometer data and parallax measurements from Hip-
parcos and Gaia, the distance of ζ Pup is 332+11−11pc (van Leeuwen,2007;Howarth & van Leeuwen,2019), and 336+8−7 pc for γ2 Vel (van Leeuwen,2007;North et al.,
2007). γ2 Vel is believed to be a member of the Vela OB2 association, together with another 81 B-type stars whose average distance is 415±10 pc, as measured by Hipparcos (de Zeeuw et al.,1999). Cantat-Gaudin et al.(2019) confirmed this average distance using recent Gaia DR2 data, and suggest the closest member of the Vela OB2 association lies at a distance of ∼ 330 pc, while the farthest is ∼ 500 pc. One apparent consequence of this stellar association is the creation of a wind-blown bubble within the Gum Nebula, the IRAS Vela shell, which is a ring-like structure in the IRAS (Infrared Astronomical Satellite; Neugebauer et al.,1984) 100 µm far-infrared image with an angular radius of ∼ 7.5◦ (Sahu & Sahu, 1993).
Another interesting structure related to the Gum Nebula is the Vela supernova remnant (Vela SNR). The Vela pulsar (PSR J0835–4510), which is the result of a Type II supernova explosion that occurred ∼ 104 years ago (Taylor et al., 1993) resides in this remnant. The distance of the Vela pulsar was initially thought to be ∼ 500 pc, however, substantially revised by parallax measurements made at the beginning of the 21st century. Using parallax measurements from the Hubble Space Telescope, (Caraveo et al., 2001) estimated the distance of the Vela pulsar to be 294+76−50pc, whereas (Dodson et al.,2003) estimated it to be 287+19−17 pc using VLBI measurements. The X-ray image of the Vela SNR from ROSAT suggests it is roughly a shell with an angular radius of ∼ 4◦, or ∼ 20 pc in size at the Vela pulsar’s distance (Bocchino et al.,1994). Sushch et al. (2011) proposed a model describing the interaction between the Vela SNR and the IRAS Vela shell. They suggest that the observed asymmetry of the Vela SNR is due to the envelope of the Vela SNR physically meeting with the IRAS Vela shell (see Figure 5.2). The resulting complex ISM environment makes the observed propagation effects for the Vela pulsar’s signal exhibit some interesting and unique behaviours. For example, Hamilton et al. (1985) found that there is a significant variation in the
measured DM (from 69.1 to 68.2 pc cm−3) and RM (from 33.6 to 46.2 rad m−2) over fifteen years of observations using a 14-m dish at the University of Tasmania observatory. In this Chapter, using the MWA data and other information from the literature, the DM and RM measured as a function of observing epoch has been extended to cover nearly fifty years. These, along with additional results, are discussed in Section 5.6.
In Chapter 4, we showed that there is a rapid depolarisation exhibited by PSR J0742–2822 at frequencies below ∼300 MHz, much in contrast with the generally expected trend for pulsar emission. We propose that, as the observed scattering is a result of varying paths that the light from the pulsar takes to reach the observer, the depolarisation is therefore due to the variation of RM between these different paths. We can then characterise the spatial structure of the RM across the pulsar scattering disk by examining the extent of this depolarisation. This turbulent ISM plasma also causes scattering, as exhibited by PSR J0742–2822, which displays significant pulse broadening. The intervening scattering material is generally attributed to the Gum Nebula (e.g. Johnston et al., 1998). Motivated by this intriguing result, we further investigated the depolarisation at low-frequencies, and the intervening scattering material, using MWA observations of multiple pulsars in the general direction of the Gum Nebula. The observations, pulsar selection, and data processing are described in Section 5.2. The Faraday spectra and RMs for the target pulsars are presented in Section 5.3. The polarimetric profiles for these pulsars are presented in Section 5.4. The depolarisation at low frequencies is presented and analysed in Section 5.5. In Section 5.6, we present the long-term variation in the ISM propagation properties towards these pulsars, and specifically for the Vela pulsar in more detail. The implications for the size of the Gum Nebula is discussed in Section 5.7.
Galactic Longitude (deg.)
Galactic Latitude (deg.)
-20
-15
-10
-5
0
5
10
15
240
250
260
270
Gum nebula
Vela SNRIRAS Vela Shell
m 20 h RA 7 m 20 h RA 8 m 20 h RA 9 o Dec -55 o Dec -40 o Dec -2 5
Figure 5.2: The modelled shape and sky position of the Gum nebula (the ap- proximate center is shown as the blue square), the Vela SNR (the Vela pulsar is shown by the orange cross), γ2 Vel (the green circle), and the IRAS Vela shell proposed by Sushch et al. (2011).