Low frequency spectral energy distributions of radio pulsars detected with the Murchison Widefield Array

TL;DR

This study measures low-frequency radio spectra of 60 known pulsars using the Murchison Widefield Array, providing new flux density data between 72 and 231 MHz and comparing it with existing measurements.

Contribution

First comprehensive low-frequency spectral energy distributions of pulsars observed with the MWA, expanding understanding of pulsar radio emission at these frequencies.

Findings

Good agreement between MWA flux densities and previous measurements

Flux densities measured across 20 frequency bands between 72 and 231 MHz

Enhanced spectral data for 60 pulsars at low radio frequencies

Abstract

We present low-frequency spectral energy distributions of 60 known radio pulsars observed with the Murchison Widefield Array (MWA) telescope. We searched the GaLactic and Extragalactic All-sky MWA (GLEAM) survey images for 200-MHz continuum radio emission at the position of all pulsars in the ATNF pulsar catalogue. For the 60 confirmed detections we have measured flux densities in 20 x 8 MHz bands between 72 and 231 MHz. We compare our results to existing measurements and show that the MWA flux densities are in good agreement.

Tables

Table 1. Table 1: Flux density measurements and spectral indices for the non-recycled pulsars in our sample . The flux density at 200 MHz (S 200 ) is measured from mosaics that are averaged across the full 72–231 MHz bandwidth. Sources identified as variable by Bell et al. ( 2016 ) are marked with (v). See Table  3.2 for sources with broken power law fits (listed as ‘2pl’ in this table). N p subscript 𝑁 p N_{\rm p} is the number of measurements included in the fit. Full SEDs are given in Table 4. Note that Stovall et al. ( 2015 ) and Frail et al. ( 2016 ) measurements were not included in our fits, as discussed in the text.

J name	B name	S200	Fit range	$N_p$	${\alpha }_{\mathrm{fit}}$	SED references
		(mJy)	(MHz)
J0034$-$0721 (v)	B0031$-$07	$292\pm 14$	20–1400	26	2pl	Be16,C98,F16,M00,T93,Z13
J0206$-$4028	B0203$-$40	$32\pm 6$	107–1400	8	$-1.7\pm 0.1$	M78,T93
J0452$-$1759	B0450$-$18	$96\pm 7$	130–1408	16	2pl	D02,F16,L95,T93
J0630$-$2834 (v)	B0628$-$28	$463\pm 5$	74–3100	11	2pl	Be16,C07,C98,D96,F16,J16,L95,T93
J0738$-$4042	B0736$-$40	$165\pm 13$	107–8400	20	2pl	F16,J05,J15,M07,M78
J0809$-$4753	B0808$-$47	$229\pm 14$	200–3100	5	$-2.2\pm 0.1$	F16,J16,T93
J0820$-$4114	B0818$-$41	$116\pm 16$	76–3100	23	2pl	F16,J16,M07,T93
J0820$-$1350	B0818$-$13	$160\pm 7$	76–3100	27	$-1.6\pm 0.1$	C98,F16,J16,L95
J0826$+$2637	B0823$+$26	$243\pm 21$	20–14800	23	2pl	B16,B78,C98,F16,M00,T93,Z13
J0828$-$3417 (v)	B0826$-$34	$400\pm 8$	–	–	–	H04,I16,T93
J0835$-$4510	B0833$-$45	$7075\pm 207$	80–3100	9	2pl	Be16,F16,H14,J16,S95,T93
J0837$+$0610	B0834$+$06	$286\pm 13$	20–1400	10	2pl	C98,F16,J16,L14,M00,T93,Z13
J0837$-$4135	B0835$-$41	$95\pm 16$	115–3100	21	2pl	F16,J16,M07,T93
J0840$-$5332	B0839$-$53	$56\pm 13$	115–1400	16	$-1.6\pm 0.1$	J16,T93
J0855$-$3331	B0853$-$33	$47\pm 8$	130–1408	14	$-1.9\pm 0.1$	F16,J16,L95,T93
J0856$-$6137	B0855$-$61	$85\pm 9$	200–1382	4	$-1.6\pm 0.1$	J16,T93
J0905$-$5127	$-$	$73\pm 15$	92–1400	18	$-2.0\pm 0.1$	H04,I16,T93
J0907$-$5157	B0905$-$51	$106\pm 11$	84–3100	26	2pl	Bh16,F16,J16,M07,T93
J0922$+$0638	B0919$+$06	$100\pm 13$	20–3100	27	2pl	C98,F16,J16,T93,Z13
J0924$-$5302	B0922$-$52	$96\pm 9$	99–3100	24	$-2.0\pm 0.1$	Bh16,J16,M07,T93
J0942$-$5552	B0940$-$55	$73\pm 14$	151–3100	15	2pl	J16,M07,T93
J0942$-$5657	B0941$-$56	$112\pm 11$	400–3100	6	$-1.5\pm 1.9$	J16,M07,M78,T93
J0953$+$0755 (v)	B0950$+$08	$1072\pm 17$	20–3100	36	2pl	Be16,C07,C98,D96,F16
						J16,L95,M00,S95,T93,Z13
J0959$-$4809	B0957$-$47	$50\pm 7$	151–3100	9	2pl	F16,J16,T93
J1001$-$5507	B0959$-$54	$142\pm 12$	400–3100	6	$-1.7\pm 0.1$	J16,M07,T93
J1012$-$2337	B1010$-$23	$47\pm 40$	200–600	4	$-3.2\pm 0.2$	L95,T93
J1047$-$3032	$-$	$24\pm 5$	111–1400	5	$-5.9\pm 0.1$	G98,L98
J1057$-$5226	B1055$-$52	$202\pm 12$	150–843	4	$-1.5\pm 0.1$	Be16,I16,M07,T93
J1116$-$4122	B1114$-$41	$52\pm 7$	92–3100	19	2pl	F16,J16,T93
J1121$-$5444	B1119$-$54	$101\pm 15$	122–1400	15	$-2.1\pm 0.1$	H04,J16,T93
J1136$+$1551	B1133$+$16	$684\pm 61$	20–1408	33	2pl	B16,C07,C98,D96,F16
						J16,L95,M00,T93,Z13
J1327$-$6222	B1323$-$62	$284\pm 48$	143–3100	17	2pl	J16,M07,T93
J1359$-$6038	B1356$-$60	$402\pm 94$	115–1400	21	2pl	Be16,M07,M78,N08,T93
J1430$-$6623	B1426$-$66	$190\pm 28$	130–3100	18	2pl	H04,J15,M07,T93
J1453$-$6413	B1449$-$64	$684\pm 23$	76–1400	24	2pl	Be16,M07,N08,T93
J1456$-$6843	B1451$-$68	$738\pm 21$	76–1400	24	2pl	Be16,M07,T93

Equations

$$S_{\nu }=S_{{\nu }_0}{\left(\frac{\nu }{{\nu }_0}\right)}^{\alpha }$$

$$S_{\nu }=\{\begin{array}{ll}{S}_{{\nu }_0}{\left(\frac{\nu }{{\nu }_0}\right)}^{{\alpha }_{\mathrm{lo}}}& \text{if}\nu <{\nu }_{\mathrm{br}}\\ S_{{\nu }_0}{\left(\frac{{\nu }_{\mathrm{br}}}{{\nu }_0}\right)}^{{\alpha }_{\mathrm{lo}}}{\left(\frac{\nu }{{\nu }_{\mathrm{br}}}\right)}^{{\alpha }_{\mathrm{hi}}}& \text{if}\nu >{\nu }_{\mathrm{br}}\end{array}$$

Full text

1 INTRODUCTION

Pulsars are generally observed at high time resolution in order to detect and resolve their pulses. However, many can also be detected in continuum interferometric images via their phase-averaged emission (e.g., Kaplan et al., 1998) which offers additional useful information. For example, in contrast to difficulties in absolute flux calibration of single dish observations (e.g., Lorimer & Kramer, 2012), interferometers allow accurate flux density measurements that can be used to help constrain pulsar emission mechanisms (Malofeev & Malov, 1980; Lorimer et al., 1995; Karastergiou et al., 2015) and derive the pulsar luminosity function, and hence Galactic pulsar birth rate (Lorimer et al., 1993). Separately, interferometry can be used to determine accurate positions (and eventually proper motions and parallaxes) for pulsars (e.g., Chatterjee et al., 2009; Deller et al., 2009, 2011, 2016) to aid or augment pulsar timing (e.g., Gaensler et al., 1999; Lorimer & Kramer, 2012).

Pulsars have been observed across the entire electromagnetic spectrum, from frequencies as low as 10 MHz (Hassall et al., 2012) up to 1.5 TeV (Ansoldi et al., 2016). At radio frequencies the spectral behaviour of the majority of pulsars can be described by a power law of the form $S_{\nu}\propto\nu^{\alpha}$ where $\alpha$ is the spectral index and $S_{\nu}$ is the flux density at frequency $\nu$ (Lorimer et al., 1995). Pulsars typically have steep spectra with the mean spectral index of non-recycled pulsars around $\alpha=-1.6$ (e.g. Sieber, 1973; Lorimer et al., 1995) and millisecond pulsars (MSPs) around $\alpha=-1.8$ (e.g. Kramer et al., 1999; Maron et al., 2000). Simulations by Bates et al. (2013) that take into account selection biases present in the distributions of known pulsars show the underlying spectral index is likely to be $\alpha\approx-1.4$.

Typical single-dish pulsar observations can have poor flux calibration (as bad as $\sim 50$%) due to an absence of reliable calibration sources, unknown positions in primary beams (at least initially), and the difficulties in calibrating single-dish telescopes (see O’Neil 2002; Lorimer & Kramer 2012). Even observations with arrays that have been coherently beamformed can have poor flux calibration, since calibration relies on modelling and characterising the performance across the fields-of-view and over time, often without the ability to verify and track the performance during the science observation. These issues are discussed by, for example, Bilous et al. (2016). In contrast, imaging observations can be less sensitive (limited both by confusion, and also by the duty cycle of the pulsations) but can be calibrated very robustly through simultaneous observations of hundreds or thousands of sources.

Only a small fraction of radio detected pulsars have had their continuum flux densities measured across a range of frequencies; for example in the ATNF Pulsar Catalogue 1919 out of 2573 sources have zero or one radio continuum flux density measurements listed. Low frequency observations of pulsars are important for investigating their spectral indices, and in particular in determining the frequency of their spectral turnovers. Spectral turnovers have been observed in a small number of sources at frequencies below 400 MHz (e.g. Sieber, 1973; Ellingson et al., 2013) and in roughly $10\%$ of pulsars in total (Maron et al., 2000). The cause of spectral turnovers is not known, but it is thought to be either synchrotron self-absorption in the emission region, or thermal absorption by a gas cloud in the line of sight to a pulsar (Sieber, 1973). One of the aims of a low frequency study of pulsars is to collect a larger sample of sources that exhibit spectral turnovers and hence help address this question by relating the presence of turnovers to other intrinsic or extrinsic parameters.

With good spectral coverage, continuum observations of pulsars can be used for modelling pulsar emission mechanisms, and studying the statistical properties of pulsar populations in a way that is independent of their time-varying properties such as period and dispersion measure (Lorimer et al., 1995). Continuum observations have the advantage that they are less susceptible to interstellar propagation effects (dispersion and scattering) that smear out the emission over the pulse phase. The reliability of flux density measurements can be adversely affected by interstellar scintillation, which is very strong at low frequencies (Rickett, 1977; Bhat et al., 2014). However, for most pulsars the scintillation bandwidth will be much smaller than our observation bandwidth so that the scintillation will saturate: only for the nearest pulsars will a finite number of scintles cause significant variability (Bell et al., 2016).

Low frequency continuum studies of pulsars have been conducted by a number of groups. Kouwenhoven (2000) measured Westerbork Northern Sky Survey (WENSS) 325 MHz flux densities for 39 pulsars and Kuniyoshi et al. (2015) provide 74 MHz VLA Low Frequency Sky Survey, redux (VLSSr; Lane et al., 2014) and 325 MHz WENSS flux densities for 10 millisecond pulsars detected in the VLSSr. Kaplan et al. (2000) reported 365 MHz flux densities for 6 pulsars in the Texas survey catalogues (Douglas et al., 1996). Two recent LOw-Frequency ARray (LOFAR; van Haarlem et al., 2013) projects have measured low frequency fluxes for 158 non-recycled (or normal) pulsars (Bilous et al., 2016) and 48 millisecond pulsars (Kondratiev et al., 2016). Most recently Frail et al. (2016) made 150 MHz measurements of 200 known pulsars using data from the reprocessed GMRT Sky Survey (TGSS ADR; Intema et al., 2016). In this paper we present Murchison Widefield Array observations of 60 pulsars at frequencies between 72 and 231 MHz.

2 OBSERVATIONS AND DATA REDUCTION

2.1 Observations

The Murchison Widefield Array (MWA; Tingay et al., 2013) is a 128-tile low-frequency radio interferometer located in Western Australia. One of the major MWA projects is the GaLactic and Extragalactic All-sky MWA survey (GLEAM; Wayth et al., 2015). GLEAM is a survey of the radio sky south of declination $+30^{\circ}$ at frequencies between 72 and 231 MHz, conducted between 2013 June and 2014 July. The survey was performed using five instantaneous observing bandwidths of 30.72 MHz, with each band observing the same part of the sky for an integration time of $\sim$2 minutes. The observing bands were further subdivided into four sub-bands with bandwidths of 7.68 MHz during processing. Hence, the GLEAM survey reports twenty flux density measurements between 72 and 231 MHz.

Note that although the entire sky was imaged in the GLEAM survey, the first major GLEAM catalogue release (Hurley-Walker et al., 2017) excludes the Galactic plane region ($|b|<10^{\circ}$). However, in this work we measure flux densities directly from the survey images and hence cover the whole $\delta<30^{\circ}$ sky.

2.2 Data reduction

The data reduction process that was performed is discussed in detail by Hurley-Walker et al. (2017). In summary, the raw visibility data from the MWA observations were processed by Cotter (Offringa et al., 2015) and radio frequency interference (RFI) was excised using the AOFlagger algorithm (Offringa et al., 2012). For the five instantaneous observing bandwidths of 30.72 MHz, an initial model of the sky was used to apply initial amplitude and phase calibration solutions. Imaging was performed using WSClean (Offringa et al., 2014), with a “robust” parameter of $-1.0$ (close to uniform weighting). Uniform weighting weights the visibilities in inverse proportion to the sampling density function. This has the effect of minimising the sidelobe level and hence minimises contamination from diffuse structure and to aid in easily identifying unresolved sources, such as pulsars. Multi-frequency synthesis was applied across the instantaneous bandwidth for each snapshot observation, and cleaned (Högbom, 1974) to the first negative clean component. The observations were then divided into four 7.68-MHz sub-bands and jointly cleaned, resulting in a RMS of $\sim$250 to $\sim$50 mJy beam*-1* for 72 to 231 MHz, respectively. The 7.68 MHz sub-band images were then put through a self-calibration loop, using the initial calibrator images to ensure position and flux density consistency and stability.

An initial flux density scale for the images was then set using the Molonglo Reference Catalogue (MRC; Large et al., 1981, 1991), scaled to the respective frequency, and an astrometric correction was applied using the sources referenced in MRC. The snapshots for an observed declination strip were mosaicked, with each snapshot weighted by the square of the primary beam response. Any residual declination dependence of the flux density scale in the mosaics, due to uncertainties in the primary beam model, was corrected using the VLSSr, MRC, and NRAO VLA Sky Survey (NVSS; Condon et al., 1998) catalogues. We estimate that the flux density calibration is accurate to $8\%$ for sources with $|b|>10^{\circ}$ and up to $20\%$ for sources with $|b|<10^{\circ}$.

A deep wide-band image covering $170-231$ MHz was formed for each mosaic. The deep wide-band image provides a higher signal-to-noise ratio and more accurate source positions than what can be attained for a single 7.68-MHz sub-band image. The Background And Noise Estimator (bane)111https://github.com/PaulHancock/Aegean/wiki/BANE was used to measure the background and noise properties of the deep-wideband images. bane estimates the background and noise of an image as the median and standard deviation of the pixel distribution over a sliding window. Calculating the background and noise properties in this way is biased by the presence of sources. bane mitigates this bias via sigma clipping of the pixel distribution (3 rounds of 3$\sigma$). bane creates maps of the sky of the same dimensions as the input image, with each pixel representing either the background or noise level at a given location. The background and noise maps were then passed to the source finding and characterisation program Aegean v1.9.6 (Hancock et al., 2012) to form a reference catalogue. The positions of the sources in the reference catalogue were then convolved with the appropriate synthesised beam at each sub-band frequency to characterise the flux density of the sources in each of the 20 sub-band images.

2.3 Sample Selection

We selected all sources from the ATNF pulsar catalogue v1.54 (Manchester et al., 2005) that fell within the observed GLEAM region of $\delta<+30^{\circ}$. We excluded globular cluster pulsars, and those with a positional uncertainty of greater than 1 arcmin. This left a sample of 1996 sources. We then searched the GLEAM 170–231 MHz mosaics for $3\sigma$ detections within 2 arcmins of the positions of these sources. We manually inspected postage stamp images of the potential detections, ruling out artefacts and coincident extragalactic sources based on their visual morphology. We also ruled out sources with existing non-pulsar identifications in SIMBAD or the NASA/IPAC Extragalactic Database.

This resulted in a sample of 60 sources with GLEAM detections, as shown in Figure 1. Using a definition of millisecond pulsars as having spin periods of $P<30$ ms and spin-down rates of $\dot{P}<1\times 10^{-16}$ s s*-1*, six sources in our sample are millisecond pulsars and 53 are normal pulsars. One source, PSR J1810$+$1744, has an unknown spin-down rate, but its spin period of 0.00166 s indicates it is a millisecond pulsar. For each of these candidate sources we measured the flux density at the position of the pulsar using the source finding package Aegean v1.9.6 (Hancock et al., 2012). The measured MWA positions agreed well with the positions in the ATNF pulsar catalogue; the mean position offsets are $\Delta\alpha=13^{\prime\prime}$, $\Delta\delta=9^{\prime\prime}$.

2.4 False detection rate

It is possible that some of the matches with ATNF pulsar positions are due to chance coincidences. To estimate what fraction this might be, we can consider the areal density of sources in the GLEAM catalogue. The GLEAM catalogue has 304 894 sources over an area of 24 402 square degrees, or $\sim 12$ sources per square degree. Therefore any given pulsar has a $3\%$ chance of being matched with a background source by chance coincidence. This implies that out of the detections we made, it is possible that $1-2$ of them are false positives.

The actual coincident source rate could be somewhat higher than this, since we searched to a lower flux density cutoff than the published GLEAM catalogue, and we also searched in the Galactic plane where the source density is higher. However, we expect the false detection rate to be of order a few sources.

3 Results and Discussion

We fit and parameterised each of the 60 detected sources in the GLEAM averaged mosaics (centred on 200 MHz) using Aegean’s priorised222Priorised fitting holds the position and shape of a source fixed and only fits for the flux density, thus making it possible to measure the flux densities of sources that are below the nominal detection limit and using prior information to reduce the uncertainties in subsequent measurements. fitting option. The distribution of measured flux densities is shown in Figure 2. We then fit a source at the same position in each of the $20\times 8$ MHz sub-band images. We measured flux densities in each sub-band image if there was a detection above $3\sigma$. We excluded sources that were obviously extended (by visual inspection), and so were able to fit each source with a point source model.

3.1 Comparison with the literature

Fifteen of the sources in our sample have a detection in either the VLSS (Cohen et al., 2007; Lane et al., 2014), LOFAR (Bilous et al., 2016), Slee (1995) or Malofeev et al. (2000) surveys.

The Bilous et al. (2016) LOFAR census provides a good comparison as the mean frequency of the LOFAR High-Band Antennas (HBA) is 149 MHz which aligns well with our GLEAM sub-band centred on 151 MHz. The Bilous et al. (2016) flux densities were measured from the single best observation (each observation covered at least 1000 spin periods), and their comparisons with LOFAR imaging observations suggest there may be up to $40\%$ difference between the flux densities obtained through these different methods. The agreement to our data is roughly within these limits.

Four of our sources are in the Bilous et al. (2016) sample:

• •

J0826$+$2637 (B0823$+$26) has an MWA 151 MHz flux density of $365\pm 48$ mJy. The LOFAR 149 MHz flux density is somewhat higher at $522\pm 261$mJy, but still agrees within the stated errors of both surveys;

• •

J1136$+$1551 (B1133$+$16) has an MWA 151 MHz flux density of $1057\pm 49$ mJy, which agrees well with the LOFAR 149 MHz flux density of $935\pm 467$ mJy;

• •

J1543$+$0929 (B1541$+$09) has an MWA 151 MHz flux density of $371\pm 45$ mJy, which is substantially lower than the LOFAR 149 MHz flux density of $768\pm 384$ mJy, although still within the reported uncertainty of the LOFAR measurement.

We do not have a reliable sub-band flux density measurement for J1932$+$1059 (B1929$+$10) but our 200 MHz averaged band measurement agrees reasonably well with existing literature measurements, including LOFAR (see the plot in Figure 3.2). Inspection of the spectral energy distribution suggests our MWA results are overall in good agreement with the rest of the literature measurements, for example the TGSS ADR1 150 MHz flux density is $368\pm 41$ mJy.

In addition, three of our millisecond pulsars are in the Kondratiev et al. (2016) sample, which presents flux densities, also averaged over the 110–188 MHz band (centred on 149 MHz). Note that the errors quoted in Table 4 of Kondratiev et al. (2016) are much smaller than the actual estimated errors of $50\%$, so for this comparison we have assumed $50\%$ errors on the LOFAR flux densities:

• •

J0034$-$0534 has an MWA 151 MHz flux density of $394\pm 24$ mJy which agrees with the LOFAR 149 MHz flux density of $491\pm 245$ mJy;

• •

J0737$-$3039A has an MWA 200 MHz flux density of $53\pm 8$ mJy and an MWA 143 MHz flux density of $89\pm 25$ mJy, both of which agree with the LOFAR 149 MHz flux density of $64\pm 32$ mJy;

• •

J1810$+$1744 has an MWA 151 MHz flux density of $320\pm 102$ mJy which agrees within the errors with the LOFAR 149 MHz flux density of $563\pm 282$ mJy.

3.2 Spectral energy distributions

In Figures 3.2 and 3.2 we present spectral energy distributions (SEDs) for each of the normal and millisecond pulsars in our sample, respectively. Where it was possible to measure sub-band flux densities with greater than $3\sigma$ significance we have included the individual sub-band flux densities in the SEDs (for example, PSR J0034$-$0721). In other cases the sub-band measurements were either below the noise, or we excluded them due to calibration issues with Galactic plane data (for example, PSR J0630$-$2834). In these cases we only included the 200 MHz flux density measured from the 170–231 MHz mosaics.

It is important to note that the literature fluxes come from many different projects, with different observational setups. In addition, low frequency flux density measurements are more affected by scintillation than higher frequency measurements, and pulsars can also be intrinsically variable. As a result, fluxes measured by different groups at different times may vary by an order of magnitude. We have excluded two sets of recent measurements (Stovall et al., 2015; Frail et al., 2016) from our fits (but included them in the SEDs) as the flux calibration requires further investigation333See discussion of flux density scale at: http://tgssadr.strw.leidenuniv.nl.

We fit each of our pulsar spectral energy distributions with both a single power law of the form:

[TABLE]

where $\alpha$ is the spectral index, and $S_{\nu_{0}}$ is the flux density at a reference frequency $\nu_{0}$; and a broken power law of the form:

[TABLE]

where $\nu_{\rm br}$ is the break frequency, and $\alpha_{\rm lo}$ and $\alpha_{\rm hi}$ are the spectral indices below and above that break frequency, respectively.

Model fits to the SEDs were conducted using a nonlinear least-squares routine that applied the Levenberg-Marquardt algorithm, an iterative procedure that linearizes the function at each step based on a new estimate of the function from the gradient of the previous step. The fitting routine produced a covariance matrix with which 1-$\sigma$ uncertainties on the parameters were taken to be the square-root of the diagonal terms. In the fitting procedure the uncertainties on the data points were assumed to be independent and Gaussian. Initial conditions for the broken power-law fits were selected by random sampling using a Monte Carlo simulation. In cases where there were not enough data points to support a broken power-law fit we chose a single power law. In cases where the reduced $\chi^{2}$ suggested a broken power-law fit was preferred we ran an F-test and rejected the null hypothesis for probability $P<0.01$.

We found that 28 of the pulsars in our sample could be fit by a single power law. The distribution of spectral indices from these fits is shown in Figure 9. The individual fits are shown by the dashed lines in Figures 3.2 and 3.2 and the spectral indices derived from these fits are listed in Tables 3.2 and 3.2. 30 of the remaining sources were fit by a broken power law and the results from these fits are given in Table 3.2. We note that some of these sources show signs of a spectral turnover whereas others have a clear spectral break. The flux density measurements for each GLEAM sub-band are given in Table 4.

One source (PSR J0828$-$3417) has too few points to be fit. Another source (PSR J0437$-$4715) could not be fit by either a single or broken power law. This source is known to scintillate (Bell et al., 2016) and is discussed further in Section 3.4. The GLEAM sub-band points show this clearly, with significant changes in the flux density between neighbouring bands. The GLEAM observations cycle through each of the five major frequency bands, and so the observations at different frequencies are not simultaneous. This variability means the SED can not be well fit.

PSR J0942$-$5657 is not fit well due to several points with higher than expected flux densities at low frequencies. This could be due to the low frequency measurement, which is at relatively low resolution, picking up diffuse emission from a surrounding supernovae remnant or pulsar wind nebula. It is not possible to disentangle these factors with the MWA continuum data alone.

Currently our sample is too small to see if the spectral indices we measure here correlate with any intrinsic parameters of the pulsars (such as spin-period, spin-down age, dipole magnetic field, energy-loss rate), but we expect that with deeper surveys in the near future we can increase the number of pulsars significantly (see Section 4) and will be more sensitive to population-wide trends.

Previous work has shown that approximately $10\%$ of pulsars can not be fit by a single power law (Maron et al., 2000). We found a substantially higher fraction than this ($30/58=52\%$). The higher percentage is probably due to our sample being able to detect sources with low frequency spectral breaks. The distribution of spectral break frequencies for pulsars that were fit by a broken power law is shown in Figure 10: 23 of our sources have $v_{\rm br}\lesssim 400$ MHz. The sources with spectral breaks do not have any obvious intrinsic parameter that would select for this property.