Detection and Flux Density Measurements of the Millisecond Pulsar J21450750 below 100 MHz
We present flux density measurements and pulse profiles for the millisecond pulsar PSR J21450750 spanning 37 to 81 MHz using data obtained from the first station of the Long Wavelength Array. These measurements represent the lowest frequency detection of pulsed emission from a millisecond pulsar to date. We find that the pulse profile is similar to that observed at 102 MHz. We also find that the flux density spectrum between 40 MHz to 5 GHz is suggestive of a break and may be better fit by a model that includes spectral curvature with a rollover around 730 MHz rather than a single power law.
Millisecond pulsars (MSPs) are thought to be normal pulsars that have been spun up by accretion from a companion star (Alpar et al., 1982). These pulsars show a variety of complex pulse shapes and usually show more components than in the case of normal pulsars. In addition, the magnetic field strengths are typically four orders of magnitude weaker than normal pulsars (Kramer et al., 1998). The flux density spectra of many MSPs can be fit by a single power law flux density spectrum down to frequencies as low as 100 MHz. Below 100 MHz, there is evidence that at least some MSPs show a break in their spectra (Erickson & Mahoney, 1985; Navarro et al., 1995; McConnell et al., 1996; Kuzmin & Losovsky, 2001). In addition to showing the existence of a spectral turnover, the pulse profile evolution over frequency also provides constraints on the emission mechanisms such as the height of emission region and the magnetic field configuration. For example, PSR J21450750 is among the brightest MSPs (Kuzmin & Losovsky, 2001) and shows significant evolution of the pulse profile with frequency (Kuzmin & Losovsky, 1996; Kramer et al., 1999). Above 1 GHz, the primary pulse is strongest with a weak secondary pulse that lags behind the primary by about 3 ms. At lower frequencies, however, the strengths of the two pulses reverse and the secondary becomes dominant. Kuzmin & Losovsky (1996) interpret this evolution in the context of quadrupole terms in the magnetic field and spatial differences between the radiating particles associated with the different components.
Beyond the pulsars themselves, low frequency observations also provide information about the intervening interstellar medium (ISM) through the sensitivity to changes in the dispersion measure (DM) and pulse scattering broadening (Phillips, 1991; Phillips & Wolszczan, 1991). Furthermore, the nature of the turbulence along the lines-of-sight to pulsars can also be explored through how refractive interstellar scintillation alters the observed flux density over a period of weeks (Gupta et al., 1993). This allows for a more complete understanding of the ISM that can help improve timing models used by pulsar timing arrays for the detection of low frequency gravitational waves.
The first station of the Long Wavelength Array (LWA1; Ellingson et al., 2013; Taylor et al., 2012), is an ideal instrument to study pulsars at these low frequencies. LWA1 consists of 256 dual-polarization dipole antennas that are digitally delayed and summed to form four independent beams. Each beam has two passbands that can be tuned to a center frequency between 10 and 88 MHz, each with up to 19.6 MHz of bandwidth, that produce complex voltage data. We have used LWA1 to study the pulsed emission from PSR J21450750 over the frequency range of 37 to 85 MHz in order to provide a better understanding of the emission mechanisms for this pulsar.
2 Observations & Reductions
Data for PSR J21450750 were taken on two occasions using LWA1. The first data capture is a one hour “exploratory” data set taken on 2013 March 16 starting at 17:00 UTC with a single beam with passbands centered at 73 and 81 MHz. The second set of observations were obtained using LWA1 on 2013 April 20 starting at 14:00 UT for two hours using three beams. The first beam had passbands centered on 41 and 49 MHz while the second beam had passbands centered on 57 and 65 MHz. The final beam used center frequencies of 73 and 81 MHz. For both data sets, raw complex voltage data output at 9.8 Msamples s was recorded for each beam so that the data could be coherently dedispersed. The useable bandwidth within each of the passbands was approximately 8 MHz.
The data were dedispersed using the coherent dedispersion functions that are part of the LWA Software Library (Dowell et al., 2012). These functions follow the dedispersion procedure outlined in §5.3 of Lorimer & Kramer (2005). The dedispersion was carried out with a DM of 9.000 pc cm (Bailes et al., 1994) on the LWA User Computing Facility cluster, a cluster of six nodes with 32 GB of RAM each. This cluster was used to help manage the large amount of memory required to coherently dedisperse such a large fractional bandwidth. For reference, the dispersion delay across the 41 MHz passband is about 10.9 seconds. Unfortunately, the available cluster memory was not enough to process the 41 MHz passband and therefore the coherent dedispersion for this passband was performed using a computer located at the University of New Mexico containing 128 GB of RAM.
After the individual data streams had been dedispersed, a filter bank was synthesized using a fast Fourier transform with 1,024 channels and applied to the data. Then the two linear polarizations were summed. The resulting spectra were written to the PSRFITS data format (Hotan et al., 2004). This yielded spectra with a temporal resolution of 104 s and a spectral resolution of about 9.6 kHz. This temporal resolution is approximately one-third of the pulse width at 50% of peak of 337 s at 1400 MHz (Manchester et al., 2005, 2013) for this pulsar. The data were then flagged for radio frequency interference and folded at the pulsar period of 16.0524 ms with PRESTO (Ransom, 2001) using the pulsar’s spin and orbital parameters. Figure 1 shows an example of the detection for the passband centered on 49 MHz.
After folding, the data were calibrated using a system equivalent flux density (SEFD) estimate derived from drift scans of Virgo A taken at the same elevation as the transit of PSR J21450750 (48). The drift scans of the calibrator were fit with a Gaussian in order to estimate the on and off-source power. These estimates were then combined with the flux density of Baars et al. (1977) to calculate the SEFD for each center frequency. The LWA1 SEFD is dependent not only on the pointing direction but also on the local sidereal time due to the sky noise dominance of the system temperature. To estimate the systematic uncertainty arising from this, we also measured the SEFD from drift scans of Cygnus A. Cygnus A is not an ideal source for determining the SEFD due to its proximity to the Galactic plane and the large size of the LWA1 beam (2 at 74 MHz) but it can be used to provide an upper limit on the SEFD and pulsar flux.
These SEFDs were then used to determine the flux density of the pulsar via:
where is the observed power averaged over the pulsar’s period combined with the observed power from the sky, and is the observed power from the sky when the pulsar is off. For the motivation behind this approach, see Ellingson et al. (2013). The results from the two calibration sources were then combined with a weighted average at each frequency to yield the flux densities presented in Table 1. The 1 uncertainties listed in this table give both the random and systematic uncertainties. The random error arises from the uncertainty in the SEFD values and the observed sky power, and the systematic error is associated with approximating the SEFDs appropriate for PSR J21450750 at the time of the observations with those of Virgo A and Cygnus A.
In addition to our data, we also used values for the flux density of PSR J21450750 gathered from the literature for frequencies between 102 and 4850 MHz (Kuzmin & Losovsky, 2001; Malofeev et al., 2000; Kijak et al., 1997; Kramer et al., 1999; Stairs et al., 1999; Toscano et al., 1998; Bailes et al., 1994). The flux densities of Stairs et al. (1999) and Bailes et al. (1994) do not report uncertainties and for these we have adopted a 10% random uncertainty and a 10% systematic uncertainty.
3.1 Dispersion Measure Variation
As part of the folding process described in §2, a separate DM search was carried out on each passband. Averaging the DMs estimated from each passband, we find a DM for the pulsar of 9.0050.002 pc cm. Keith et al. (2013) present a six year study of the DM of this pulsar and find noise-like fluctuations about a mean value of 8.9980.001 pc cm (M. Keith, 2013, private communication). The data of this study end approximately one year before our observations begin, and such a large change in the DM over that period (0.007 pc cm yr) would be unusual given the behavior shown. A more likely explanation is that the difference in the DM arises from frequency dependent effects, such as intrinsic pulse profile evolution and scattering (see §3.3), although we cannot rule out a change in the DM based on the current data.
3.2 Flux Density Spectrum
Figure 2 plots the LWA1 flux densities along with values from the literature mentioned in §2. For the LWA1 data the random and systematic components of the uncertainty have been added in quadrature for plotting. The plot shows good agreement between the March and April measurements at 73 and 81 MHz. Fitting a power law of to our data we find the best-fit spectral index, , of –1.20.3 with a flux density of 63080 mJy at 41 MHz. The two closest literature values to our frequency range, Kuzmin & Losovsky (2001) at 102 MHz and Malofeev et al. (2000) at 102.5 MHz, bracket our flux densities. At low frequencies the observed flux densities of pulsars vary over time as a result of scattering and refractive scintillation by the ISM. For example, Gupta et al. (1993) made observations of nine pulsars at 74 MHz over a period of 400 days. They found typical variations in the flux densities on the order of tens of percent with maximum variations between the faintest and brightest flux densities on the order of two to three. It is possible that the discrepancy between the LWA1 data and the 102/102.5 MHz data could be a result of scintillation. However, additional observations are needed in order to verify this. It should also be noted that if we extrapolate the LWA1 power law to 102 MHz we find a flux density of 210 mJy, which is within 3 of both literature values.
Kuzmin & Losovsky (2001) report that the spectrum of PSR J21450750 is consistent with a single power law with over the range of 102 MHz to 5 GHz. In contrast, our data are suggestive of a break in the power law at 730 MHz. Indeed, if the measurements of Kijak et al. (1997) and Kramer et al. (1999) are taken at face value and a power law is fit using only data above 400 MHz, the spectral index steepens to a value of –1.90.1, supporting the idea that there is a break in the power law. Therefore we fit the available data with a power law that includes spectral curvature of the form:
where is the spectral curvature and is the rollover frequency. We adopted a rollover frequency of 730 MHz, which is approximately where the power law fits for the LWA1 data and literature above 400 MHz cross. Using this, we find best-fit values of and . To test whether or not this more complicated spectral curvature model describes the literature data better than a single power law, we used an -test to compare the values. The resulting -statistic rejects the null hypothesis that the spectral curvature model does not describe the data better than a single power law at a significance level of 0.5%. Thus, we suggest that the data are better described by the more complicated model. However, additional flux density measurements in the 100 to 700 MHz range and below 40 MHz are needed to further test the robustness of this conclusion and to average out variations introduced by interstellar scintillation that may contribute to the observed scatter in the data toward lower frequencies.
3.3 Pulse Profile Evolution
Figure 3 shows the integrated pulse profiles over one period (16.0524 ms) for the six center frequencies along with Gaussian fits to the profiles. The pulses shown likely correspond to component \@slowromancapii@ in the 102 MHz profile presented in Kuzmin & Losovsky (1996) since this particular component dominates the profile at this frequency. Accordingly, the pulses at each center frequency have been aligned with the phase of component \@slowromancapii@. We also tried fitting the profiles with two Gaussians but the resulting improvements were only significant at the 0.5% level for the 49, 57, and 73 MHz passbands. Interestingly, for the 57 and 73 MHz passbands, the second Gaussian leads the main pulse by 10 to 20 degrees which is consistent with component \@slowromancapiv@ of Kuzmin & Losovsky (1996). However, since the majority of the profiles are not well modeled by two Gaussians we have adopted the single Gaussian fits for all six frequencies for our analysis. We find that the full width at half maximum of the primary pulse in the LWA1 data increases from 17 degrees at 81 MHz to 56 degrees at 41 MHz (Figure 4). At the upper end of the frequency range this is narrower than the 24 degrees reported for component \@slowromancapii@ at 102 MHz.
Besides an intrinsic increase, there are a variety of factors that could contribute to the increasing pulse width toward the lower frequencies. For example, dedispersing at 9.000 pc cm instead of the best-fit DM value given in §3.1 introduces broadening due to DM smearing. However, this should not contribute significantly to the observed pulse width. For the 41 MHz passband, the expected DM smearing across one channel is degrees (6 s). Another factor that contributes to the pulse width is the limited temporal resolution of the profiles presented in Figure 3 that have a resolution of approximately 6 degrees. Finally, scatter broadening can be a factor in the pulse width evolution, particularly at low frequencies. Johnston et al. (1998) report a scintillation bandwidth of 1.48 MHz for this pulsar at a frequency of 436 MHz. This corresponds to a pulse broadening time of 210 degrees (0.11 s) at 436 MHz. Since the broadening time scales as this translates to two degrees at 81 MHz and 31 degrees at 41 MHz. If we adopt a thin screen model for scattering and assume no evolution of the pulse profile, the observed width at 41 MHz corresponds to a width of approximately 34 degrees at 102 MHz. This is larger that reported by Kuzmin & Losovsky (1996) and does not explain the narrower width found at 81 MHz. In addition, scattering would manifest as a significant asymmetry towards the trailing edge of the pulse profile, which is not observed. Higher signal-to-noise ratio profiles are needed to further investigate the pulse evolution below 100 MHz.
We present the first flux density spectrum and pulse profiles of the MSP PSR J21450750 below 100 MHz using data obtained from the LWA1 radio telescope. We have coherently dedispersed observations at 41, 49, 57, 65, 73, and 81 MHz, each with approximately 8 MHz of usable bandwidth and detect the pulsar over the frequency range of 37 to 85 MHz. We find that the flux density spectrum is best fit by a model that includes a spectral curvature with , , and a rollover frequency of 730 MHz. However, additional measurements below 700 MHz are needed to confirm this conclusion. We also find that the pulse profile is similar to that previously reported at 102 MHz although only component \@slowromancapii@ is detected. Finally, these observations also serve as a proof-of-concept for future observations of MSPs with LWA1. In addition, we hope to extend observations down to lower frequencies and to higher bandwidths.
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Note. – The two uncertainties listed for are for the random and systematic components, respectively. See §2 for details.