The uGMRT Observations of Three New Gigahertz-peaked Spectra Pulsars

Flux density is one of the main observables of pulsars. The analysis of pulsars' spectra provides information about both the radiation mechanism and the influence of the interstellar medium. The spectra of the majority of pulsars in the frequency range between 100 MHz and 10 GHz are well-characterized by the single power-law function with a mean spectral index of −1.6 (Lorimer et al. 1995; Maron et al. 2000; Jankowski et al. 2018). In recent years Kijak et al. (2007, 2011b) have found that some pulsars have spectra that exhibit turnovers between 0.5 GHz and 1.5 GHz, and they have proposed naming such cases as gigahertz-peaked spectra (GPS) pulsars. The comprehensive study conducted by Jankowski et al. (2018) revealed that 21% of the pulsars' spectra were either broken or curved. ³ However, the recent results of the Green Bank North Celestial Cap pulsar survey show that 99% of the pulsars' spectra are well-described by a simple power-law function ⁴ (McEwen et al. 2020). This discrepancy may be due to the differences in frequency coverage of the surveys, and it may also be related to observations of different parts of the sky. Moreover, McEwen et al. (2020) reported several nondetections that could constitute very faint sources at 350 MHz. In addition to the GPS phenomenon, many recent observations confirm common low-frequency breaks (i.e., below 100 MHz) or turnovers in pulsars' spectra. The LOw-Frequency ARray pulsar census has shown that only 18%–21% of the spectra were well-described by the simple power-law function at low frequencies (Bilous et al. 2020; Bondonneau et al. 2020). The results of the GaLactic and Extragalactic All-sky MWA survey revealed that 52% of the investigated pulsars' spectra above 72 MHz were either broken or curved (see Murphy et al. 2017, and references therein). The reduction of the pulsar flux density in a low-frequency regime could be caused either by some intrinsic mechanism relating to the generation of pulsar emission or by the influence of interstellar matter (see, for example, Sieber 2002).

Previous studies have suggested that the origin of high-frequency spectral turnovers is most probably extrinsic in nature. Kijak et al. (2011b) pointed out that most of the GPS pulsars have interesting environments, such as a supernova remnant (SNR), pulsar wind nebula (PWN), or an H ii region. In the case of PSR B1259−63, which orbits a Be star, Kijak et al. (2011a) observed changes in the pulsar's spectrum during different observation sessions. When the pulsar was far away from the star, its spectrum displayed typical power-law behavior; but as it approached closer to the star, the spectrum apparently changed into a broken type, then finally displayed curved behavior with a turnover. The most probable explanation was that the pulsar's radiation was absorbed in the strong stellar wind of the luminous Be star. This case was key to the formulation of the hypothesis that an observed flux density deficit below GHz frequencies was caused by some external mechanism. Another case strengthening this hypothesis was the flux density variability of the radio magnetar Sagittarius A^* observed after its outburst in 2013, which again suggested that external factors were responsible for the observed high-frequency turnovers (see Lewandowski et al. 2015, and references therein). The low-frequency part of the radio magnetar spectrum showed lower values a week after the outburst compared to the measurements a month later. The spectral shape continued to exhibit a deviation from simple power-law behavior 100 days after the outburst (Pennucci et al. 2015). The observed spectral changes could be explained by the constant absorption of the radio emissions by the matter in the pulsar's vicinity and the additional absorption resulting from the matter released during the outburst. The GPS phenomenon was also visible in two other radio magnetars (for the details, see Kijak et al. 2013). To summarize, we currently know of around 30 GPS pulsars: the majority of them have been classified by Basu et al. (2018), Dembska et al. (2014, 2015), and Kijak et al. (2011b, 2017, 2021; J. Kijak et al. 2021, in preparation); one was discovered by Allen et al. (2013); and three were identified by Jankowski et al. (2018).

Lewandowski et al. (2015) proposed using the free–free thermal absorption model to explain the observed turnovers in pulsars' spectra. They showed that the observed absorption could have been caused by a surrounding medium in the form of dense SNR filaments, bow-shock PWN (where the amount of absorption depends on the geometry of the system), or a relatively cold H ii region. This model has been applied to study the environmental conditions around a number of GPS pulsars (Basu et al. 2016; Kijak et al. 2017; Basu et al. 2018; Rożko et al. 2018, 2020). A similar approach has also been used by Rajwade et al. (2016) to explain turnover behavior.

The main limitation of the previous studies that have estimated the low-frequency spectrum, and thereby constrained the GPS nature, has been the poor coverage of flux density measurements in the low-frequency domain. For some of the GPS candidates, only two narrowband flux density measurements exist in the low-frequency range (below 1 GHz). Near-continuous frequency coverage between 300 MHz and 800 MHz, i.e., around the expected peak frequency, should allow us to better characterize the shape of spectra. This motivated us to use the wideband receivers of the Giant Metrewave Radio Telescope (GMRT) to study the low-frequency spectral nature of the candidate GPS pulsars using the interferometric technique. ⁵ Previous narrowband observations using GMRT have suggested that three pulsars (J1741−3016, J1757−2223, and J1845−0743) are likely to have GPS spectra. We have expanded on these earlier observations and used the wideband receivers to measure the pulsars' flux densities, with the aim of ascertaining the spectral nature of the three sources. In this work, we present the results of both kinds of observations: the narrowband measurements for the central frequencies of 325 MHz, 610 MHz, and 1280 MHz; and the wideband measurements for the spectral bands 250–500 MHz and 550–850 MHz.

The outline of the paper is as follows. In Section 2 we describe the observations and calibration techniques used to estimate the flux density measurement. In Section 3 we present an analysis of the measured spectra in each pulsar and the implications of their respective environments. In Section 4 we summarize the results of the narrowband and wideband observations.

The observations were conducted using GMRT, which is an array of 30 45 m parabolic dishes. For many years, GMRT was strictly a narrowband instrument that allowed observations at five different frequency ranges, centered around 153 MHz, 235 MHz, 325 MHz, 610 MHz, and 1280 MHz, with a maximum bandwidth of 33 MHz (Roy et al. 2010). Its receiver system was recently upgraded and now provides near-continuous coverage at four wide-frequency bands: 120–250 MHz (band-2), 250–500 MHz (band-3), 550–850 MHz (band-4), and 1050–1450 MHz (band-5) (Gupta et al. 2017).

The narrowband observations at 610 MHz were conducted in 2015 August (project code: 28_072), while the 325 MHz and 1280 MHz observations were carried out in 2017 August–September (project code: 32_072). These observations were part of a larger project studying the GPS nature in pulsar spectra, which will be published in J. Kijak et al. (2021; in preparation). Following the initial analysis of these observations, pulsars PSR J1741−3016, PSR J1757−2223, and PSR J1845−0743 were identified as possible GPS candidates. These three sources were selected for the observations using the wideband uGMRT receivers that were conducted in 2018 May–June (project code: 34_027). A total of 2048 spectral channels over the entire frequency band were recorded during the wideband observations at band-3 (250–500 MHz) and band-4 (550–850 MHz). Initial checks were carried out to identify suitable subbands devoid of significant interference for subsequent image analysis and flux measurement. Band-3 was divided into six subbands, each being approximately 30 MHz wide (256 channels), and band-4 was divided into five subbands, each being approximately 50 MHz wide (256 channels). On further inspection, the subbands at the edges of the leading and trailing ends of the band-3 sensitivity profile were excluded, due to their nonlinear shapes. The observation details, together with the central frequency of each subband, are shown in Table 1. The subsequent analysis of the subbands was identical to the narrowband observations, as detailed below.

The flux calibrators 3C 286 and 3C 48 were observed during each observing run to calibrate the flux density scale. The phase calibrator 1822–096 was observed at regular intervals to correct for temporal variations and fluctuations in the frequency band (with the exception of 2015 August 15 and 28, when the phase calibrator 1714–252 was observed). All of the pulsars were observed for around 60 minutes each over two observational sessions, separated by a few weeks, to take into account the possible influence of interstellar scintillations. The flux density scales of 3C 48 and 3C 286 were set using the estimates of Perley & Butler (2013), which were subsequently used to calculate the flux density of the different phase calibrators during each observing session. The observing details, like the observation dates, the measurement frequency, and the estimated flux density levels of the phase calibrators, are summarized in Table 1. There were issues with the flux calibrator measurements during one of the observing sessions, 2018 May 30, at band-3. However, an identical observing setup was also used on 2018 May 2, and the flux calibration from this day was used to set the flux density scale of the earlier observation as well. Additional checks, using flux density levels of background sources similar to those in Rożko et al. (2018), were conducted to ensure the accuracy of the flux scaling within the measurement errors. The removal of bad data, the calibration, and the image analysis were carried out using the Astronomical Image Processing System, as previously described by Dembska et al. (2015), Kijak et al. (2017), and Basu et al. (2018).

In Table 2, we report the measured flux density of the pulsars from the three narrowband observations (325 MHz, 610 MHz, and 1280 MHz), as well as the four subbands in band-3 and the five subbands in band-4. We have used proportional errors of 20% to account for variations in the flux scaling factors relating to the wideband observations.

Figure 1 (top panel) presents the spectrum of PSR J1741−3016, with all of the available flux density measurements. The new measurements confirm the GPS characteristics of this spectrum. The observed discrepancy between the band-3 measurements and the flux density value at 610 MHz is likely due to refractive interstellar scintillation (RISS). The dispersion measure (DM) of PSR J1741−3016 is equal to 382 cm⁻³ pc (Morris et al. 2002). For pulsars with such a high dispersion measure, the timescale of RISS can range from months to years, and a modulation index near 600 MHz should result in around 0.3 (Rickett 1990). Thus, RISS could be responsible for the observed flux density fluctuations for measurements that are separated by a few years, but it should not affect the mean flux density values at two frequencies obtained from two observational sessions separated by only a few weeks. In turn, the diffractive interstellar scintillation (DISS) timescale in this case is very short (in the order of a few minutes), and thus any intensity fluctuations caused by DISS should be completely averaged during each of the observational sessions.

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The middle panel of Figure 1 shows the spectrum of PSR J1757−2223, where, at frequencies lower than 441 MHz, the pulsar flux density was below the detection limits (which are reported in Table 2). These results confirm the GPS classification of the spectrum, and the wideband measurements are consistent with the flux densities obtained from the narrowband observations. The DM of PSR J1757−2223 is 239.3 cm⁻³ pc (Morris et al. 2002), and hence it should be less affected by RISS. This case shows that for pulsars with expected flux density values between 1 mJy and 2 mJy at low-frequency bands, the observing time should be increased in future observations to improve the detection sensitivity.

In the case of PSR J1845−0743 (where DM = 280.93 cm⁻³ pc, as reported by Petroff et al. 2013), both the narrowband and the wideband measurements confirm that the spectrum should be classified as GPS (see the bottom panel in Figure 1). The low-frequency wideband measurements show some fluctuations, but are consistent within the measurement errors.

3.1. Physical Constraints on the Surrounding Medium

In this work, similar to several earlier studies, we have used the free–free thermal absorption model to explain the observed turnovers in pulsars' spectra (for the details, see, e.g., Lewandowski et al. 2015; Kijak et al. 2017). This model was first proposed by Sieber (1973) to explain low-frequency turnovers. In our approach, we used a simplified model of optical depth (Wilson et al. 2009), which gave us the following estimate of flux density (S) as a function of frequency (ν):

$$\begin{eqnarray}&&{S}_{\nu }=A{\left(\displaystyle \frac{\nu }{10\,\mathrm{GHz}}\right)}^{\alpha }{e}^{-B{\nu }^{-2.1}},\end{eqnarray} \tag{ 1 }$$

where A is the intrinsic flux density at 10 GHz, α is the pulsar intrinsic spectral index, and B equals $0.08235\times {T}_{{\rm{e}}}^{-1.35}\,\mathrm{EM}$ (EM is the emission measure and T_e is the temperature of the absorber). Using the Levenberg–Marquardt least squares algorithm (Levenberg 1944; Marquardt 1963), we determined the parameters A, α, and B. We estimated the errors using χ² mapping. Table 3 shows the results of the fits, and Figure 1 shows the fitted model with 1σ envelopes. Due to the lack of low-frequency measurements, all three pulsars' spectra were previously classified as displaying typical power-law behaviors (Jankowski et al. 2018). All of the observed pulsars may now be classified as new GPS sources: the calculated peak frequencies (ν_p), i.e., the frequencies at which the spectra exhibit a maximum, are 620 MHz for PSR J1741−3016, 640 MHz for PSR J1757−2223, and 650 MHz for PSR J1845−0743.

Table 3. Estimating the Fitting Parameters for the GPS Pulsars Using the Thermal Absorption Model

PSR Name	A	B	α	χ2	νp	${\nu }_{{\rm{p}}}^{\mathrm{nb}}$
					(GHz)	(GHz)
J1741−3016	${0.03}_{-0.02}^{+0.05}$	${0.4}_{-0.2}^{+0.2}$	$-{2.2}_{-0.8}^{+0.6}$	1.52	${0.62}_{-0.22}^{+0.27}$	${0.80}_{-0.40}^{+0.40}$
J1757−2223	${0.07}_{-0.04}^{+0.06}$	${0.3}_{-0.1}^{+0.2}$	$-{1.4}_{-0.4}^{+0.3}$	0.23	${0.64}_{-0.25}^{+0.29}$	-
J1845−0743	${0.2}_{-0.2}^{+0.3}$	${0.3}_{-0.1}^{+0.1}$	$-{1.4}_{-0.6}^{+0.4}$	0.85	${0.65}_{-0.21}^{+0.29}$	${0.62}_{-0.13}^{+0.17}$

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The main purpose of the wideband observations was to improve the model's approximation, and thus to determine the maximum energy in the spectrum with greater accuracy. To check how the wideband observations have improved our ability to find the peaks in spectra, we compared the peak frequencies obtained from all of the available flux denisty measurements with those obtained from just the narrowband observations, within their error limits. The high-frequency measurements in each case were obtained from Jankowski et al. (2018) and Johnston & Kerr (2018). The peak frequencies from the purely narrowband estimates are shown as ${\nu }_{{\rm{p}}}^{\mathrm{nb}}$ in Table 3. No spectral turnover can be identified in PSR J1757−2223 from just the narrowband observations, due to the lack of detection at 325 MHz. In the case of PSR J1741−3016, for only the narrowband observations, the constrained peak frequency is ${800}_{-400}^{+400}$ MHz. In comparison, the peak frequency obtained from the wideband data gives a much better peak frequency estimate of ${620}_{-220}^{+270}$ MHz. In the case of PSR J1845−0743, both sets of measurements give similar results (see Table 3).

Since there have been no clear detections of known SNRs or PWN in the vicinities of these pulsars, the discussion of potential absorbers is more speculative. Nonetheless, we decided to follow Basu et al. (2016) and Kijak et al. (2017) by using information from the pulsars' DM to obtain some constraints on the electron density and electron temperature of a potential absorber. Similar to these earlier works, we assumed that half of the contribution to the DM comes from the potential absorber, and we used this to calculate its electron density n_e. Using that information, we then calculated the emission measure for the three likely environments: a dense SNR filament (with a size equal to 0.1 pc), a PWN (with a size of 1.0 pc), and a cold H ii region (with a size of 10.0 pc). In each case, the fitted value of parameter B provided the constraints on the electron temperature. The results are shown in Table 4.

Table 4. The Constraints on the Physical Parameters of the Absorbing Medium

Size	ne	EM	Te
(pc)	(cm−3)	(pc cm−6)	(K)
J1741−3016
0.1	1910 ± 30	3650 ± 114	${4170}_{-1440}^{+1680}$
1.0	191 ± 3	365 ± 11	${760}_{-260}^{+305}$
10.0	19.1 ± 0.3	36.5 ± 1.1	${137}_{-48}^{+55}$
J1757−2223
0.1	1196 ± 2	1431.6 ± 4.8	${2900}_{-1210}^{+1380}$
1.0	119.6 ± 0.2	143.16 ± 0.48	${530}_{-220}^{+250}$
10.0	11.96 ± 0.02	14.316 ± 0.048	${96}_{-40}^{+46}$
J1845−0743
0.1	1404.6 ± 0.1	1973.0 ± 0.3	${3570}_{-1020}^{+1220}$
1.0	140.46 ± 0.01	197.30 ± 0.03	${650}_{-180}^{+220}$
10.0	14.046 ± 0.001	19.730 ± 0.003	${118}_{-34}^{+40}$

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The expected values of the electron density n_e and the electron temperature T_e are:

• 1.  
  n_e ∼ a few thousand cm⁻³ for T_e ∼ 5000 K in the case of a dense SNR filament (see, e.g., Lee et al. 2013);
• 2.  
  n_e ∼ 50–250 cm⁻³ and T_e = 1500 K for a bow-shock PWN (see Bucciantini 2002; Gaensler & Slane 2006, and references therein); and
• 3.  
  n_e ∼ several hundred cm⁻³ and T_e = 1000–5000 K for an H ii region (see Shabala et al. 2006, and references therein).

The wideband observations allow us to determine the shape of the spectrum with greater accuracy, and thus help to eliminate the likelihood of some of the possible absorbers. In all of the cases, the H ii region should be excluded, since the obtained electron temperatures are too low. On the other hand, the electron densities calculated from the DM are too low to sustain a dense SNR filament, and the ages of the pulsars (see Table 5) indicate that any SNRs formed during their births should already have dissipated. Thus, the PWN scenario seems the most plausible here, although there are no clear detections of known PWN around any of these sources. This is not surprising, since the angular size of the structure of a 1 pc diameter at the distance of each pulsar turns out to range from 05 to 09. This is well below the angular size that can be detected using an interferometer like GMRT, which has a minimum angular resolution of around a few arcseconds.

Table 5. The Basic Parameters of Pulsars ^a

PSR Name	Distance	Age	DM	νp
	(kpc)	(Myr)	(pc cm−6)	(MHz)
J1741−3016	3.870	3.34	382	${620}_{-220}^{+270}$
J1757−2223	3.727	3.75	239.3	${640}_{-250}^{+290}$
J1845−0743	7.113	4.52	280.93	${650}_{-210}^{+290}$

Note.

^a All values comes from the ATNF Pulsar Catalogue: https://www.atnf.csiro.au/research/pulsar/psrcat (Manchester et al. 2005).

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Taking into account the basic pulsar parameters, such as age, distance, and DM (see Table 5), together with the observed turnovers in spectra, we believe that these three pulsars are good candidates for the hosting of PWN. Even if they have not been observed so far, future advances in observing techniques, with upcoming instruments like the square kilometer array, may enable their detection.

In this work, we present the results of the wideband observations of three pulsars using GMRT. We identify three new GPS pulsars by taking advantage of dense frequency coverage, which improves the quality of estimations in the low-frequency spectrum. The wideband observations are highly useful for estimating GPS behavior, especially since the frequencies at which we observed were near the turnovers in the spectra. A more precise determination of the peak frequency allows us to better constrain the nature of the surrounding medium, and eliminate several potential absorbers.

Of the three pulsars selected for wideband observations, all were found to exhibit GPS-type spectra, proving our methods and criteria for selecting the potential candidates to be correct. The case of PSR J1757−2223 will also help us to prepare future observational projects relating to wideband observations of GPS pulsars: for a pulsar with an expected flux density between 1 mJy and 2 mJy in band-3, that pulsar should be observed for a longer duration, in excess of the 60 minutes that we used, to improve the detection sensitivity.

The discussion of potential absorbers has shown that all three pulsars are good candidates for the search for PWN. Even if such nebulae have not been discovered in current sky surveys, the improvement of observation techniques, both in the X-ray and radio range, should enable their detection in the future.

We thank the anonymous referee for comments that helped improve the paper. We thank the staff of the GMRT who have made these observations possible. The GMRT is run by the National Centre for Radio Astrophysics of the Tata Institute of Fundamental Research. This work was supported by grant 2020/37/B/ST9/02215 of the National Science Centre, Poland.