A Search for Pulsars in Steep-spectrum Radio Sources toward the Galactic Center

Given the enhanced gas and stellar densities at the Galactic center (GC), it has long been predicted that a large population of neutron stars would be found in this region (Paczynski & Trimble 1979; Cordes & Lazio 1997; Pfahl & Loeb 2004). There has been some success at identifying X-ray binaries (Zhao et al. 1992; Bower et al. 2005; Hailey et al. 2018) and probable pulsar wind nebulae toward the GC (e.g., Park et al. 2005). Pulsation searches in the GC region have been focused mainly on finding radio pulsars within the star cluster around Sagittarius A* (Sgr A*) and especially in the immediate vicinity of the supermassive black hole at the center of the Galaxy. Johnston et al. (2006) and Deneva et al. (2009) tiled a small (≲1°) area around Sgr A* and discovered a total of five normal (i.e., nonrecycled) pulsars within 10'–15' of Sgr A*. Their dispersion measures (DMs) are 962–1456 pc cm⁻³, corresponding to line-of-sight distances that place these pulsars within the bulge according to the models of the ionized gas in the Galaxy (Cordes & Lazio 2002; Yao et al. 2017). Macquart et al. (2010), Wharton et al. (2012), and Siemion et al. (2013) performed deep pointed observations of the central parsec around Sgr A* itself but did not discover any new pulsars. Mori et al. (2013) serendipitously discovered a magnetar in X-rays only 3'' from Sgr A*. The magnetar was subsequently detected as a radio pulsar at multiple radio frequencies. It has the highest DM of all known pulsars to date, 1778 pc cm⁻³, corresponding to a line-of-sight distance of 8.3 kpc. So far, no millisecond pulsars (MSPs) have been found near Sgr A* (Macquart & Kanekar 2015).

The low pulsar yield in the GC region has been attributed to the hyperstrong scattering occurring within ∼100 pc of Sgr A* (Lazio & Cordes 1998). The effects of this scattering can be seen clearly in the angular broadening of stellar masers (van Langevelde et al. 1992; Frail et al. 1994) and Sgr A* itself (Bower et al. 2006) and implies such strong temporal broadening that pulsations would be difficult to detect at the typical decimeter wavelengths used in searches. By contrast, the observed temporal broadening of the magnetar PSR J1745−3009 near Sgr A* is much smaller (∼1.5 s at 1 GHz) than expected if the enhanced scattering is local to the GC, and the bulk of the scattering is likely occurring along the line of sight in the Scutum spiral arm (Bower et al. 2014). This result suggests either that the distribution of the turbulent, ionized gas is more complex than assumed or that there is a genuine dearth of pulsars at the GC (Spitler et al. 2014; Pynzar' 2015; Rajwade et al. 2017).

Recently, there has been a renewed interest in finding pulsars at the GC. Data from the Fermi spacecraft show that there is a γ-ray emission excess (GRE) coming from a radius of ∼15° around the GC (Vitale & Morselli 2009; Hooper & Goodenough 2011). While these early studies favored an origin in the annihilation signature of dark matter particles, recent analyses of the spatial and spectral properties of the GRE using data from the entire Fermi mission to date argue that the GRE is caused by a population of thousands of MSPs (Ajello et al. 2016; Bartels et al. 2016; Calore et al. 2016; Lee et al. 2016; Gonthier et al. 2018).

Confirming this hypothesis requires direct detection of pulsations. Most MSPs are in binary systems, and searching for MSP pulsations directly in Fermi γ-ray data with no prior knowledge of orbital parameters is still not computationally feasible. Furthermore, blind radio surveys are prohibitively expensive in telescope time, since they have small fields of view at the high frequencies required to mitigate the putative scattering in the GC (Calore et al. 2016). An effective means of overcoming these barriers was recently demonstrated through discovery of an MSP toward the GC (Bhakta et al. 2017). The approach relies on efficient localization of unresolved, steep-spectrum radio sources from wide-field, low-frequency images (see Frail et al. 2018). By way of historical example, the radio source 4C21.53W was intimated to be a fast, highly dispersed pulsar (Erickson 1983) prior to its discovery as the first MSP (Backer et al. 1982) based entirely on an analogy of its steep low-frequency spectrum to the then-fastest-known Crab pulsar.

In this paper, we expand on the original pilot study (Bhakta et al. 2017), increasing the number of candidates approximately fourfold using a deeper low-frequency image and following up potential candidates with higher angular resolution interferometric imaging and single-dish pulsation searches. In Section 2, we introduce this low-frequency monitoring survey (Section 2.1), the method that we use to identify initial pulsar candidates (Section 2.2), the follow-up observations to eliminate false positives (Section 2.3), and the search for pulsations (Section 2.4). Our results are presented in Section 3, and in Section 4, we summarize the challenges and prospects for future GC pulsar searches.

Our observations are done in multiple different steps similar to previous studies (e.g., Bhakta et al. 2017; Frail et al. 2018). We first make a deep, low-frequency, wide-field image (5 deg²) centered on Sgr A* to identify all known radio sources in the field (Section 2.1). Then, using archival data and existing all-sky surveys at other frequencies, we produce continuum spectra for each radio source. We identify the most promising pulsar candidates using compactness and spectral slope criteria (Section 2.2). Next, we follow up this subsample of potential pulsar candidates with high angular resolution interferometric observations in order to eliminate resolved radio sources from further consideration (Section 2.3). Finally, we carry out single-dish observations of the final candidate list to look for pulsations (Section 2.4).

2.1. Wide-field, Low-frequency Imaging

2.2. Initial Pulsar Candidate Selection

For each 320 MHz radio source in Section 2.1 with a signal-to-noise ratio (S/N) of 10 or more, we searched existing all-sky surveys at 1.4 GHz and 843 and 150 MHz (Condon et al. 1998; Bock et al. 1999; Intema et al. 2017) and archival VLA data at other frequencies to produce continuum spectra. From these data, we fit the flux density measurements with a power-law spectral index α of the form F_ν ∝ ν^α, typically over a range from 150 MHz to 1.4 GHz, although in some cases, archival flux densities were available up to 6 GHz.

We selected promising pulsar candidates based on compactness and spectral slope criteria. For our compactness cutoff, we follow Frail et al. (2018) and require only that the ratio of the flux density of the low-frequency radio source to its peak intensity not exceed a value of 1.5. While this definition is not as stringent as the point-source definitions typically used by sky surveys (e.g., Intema et al. 2017), it does allow for anomalous values of this ratio that could occur if the pulsars scintillate strongly during the integration time.

Our second selection criterion is based on the spectral index α. The true distribution of pulsar spectral indices has a mean α = −1.4 ± 1 (Bates et al. 2013), but allowing for the biases that affect low-frequency surveys, the measured distributions are closer to α = −1.8 ± 0.2 (Maron et al. 2000; Frail et al. 2016; Kondratiev et al. 2016). In contrast, the weighted mean spectral index of extragalactic radio sources is α = −0.787 (de Gasperin et al. 2018). Thus, pulsar candidates stand out in low-frequency images. This is dramatically illustrated in the meter and centimeter images from Frail et al. (2016), but the effect is better quantified in Figure 1. Here we plot the cumulative spectral index histograms of a sample of 623 known pulsars from PSRCAT and 447,848 radio sources with spectral index values measured from 150 MHz to 1.4 GHz (de Gasperin et al. 2018) and that satisfy the compactness criterion defined above. From Figure 1, we see that while only 1.5% of the sky survey sources have a spectral index α ≤ −1.4, almost 80% of the known pulsars have measured values of α this steep. In a sample of ∼400 sources such as we have here, we would not expect to find any background radio sources in the field with α ≲ −1.8. For our spectral index cutoff criterion, we chose α ≤ −1.4. This value is equal to the true mean spectral index of pulsars (see above), but it is shallower than the cutoff values adopted in earlier image-based studies (e.g., Kaplan et al. 2000; Frail et al. 2016; Maan et al. 2018). While this value will likely increase the number of false positives, this can be mitigated somewhat because the GC is a region with lots of ancillary multiwavelength data that can be used in evaluating sources.

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Based on the above selection criteria, we chose 12 possible pulsar candidates. From a sample of nearly 400 sources, we would expect that the number of steep-spectrum background radio sources would be approximately six (i.e., 1.5%). The number could be as large as 12, given the long tail of the Poisson distribution for small sample sizes. This fraction of 1.5% is highly uncertain for a number of reasons. To begin with, it refers to compact steep-spectrum (presumably extragalactic) radio sources with a lower flux density cutoff at meter wavelengths of approximately 10 mJy (de Gasperin et al. 2018). Only half of all pulsars with measured spectral indices in PSRCAT have 400 MHz flux densities in excess of 10 mJy, so the comparison in Figure 1 is of two source populations with different flux density distributions. It may be that the fraction of steep-spectrum radio sources increases with decreasing flux density, although we note that the trend for the median spectral index is in the opposite direction (de Gasperin et al. 2018). We have also assumed that the GC is a typical direction for radio source counts. More complete deep radio continuum imaging is needed of the GC to better characterize the source population (Nord et al. 2004; Lazio & Cordes 2008). Given these uncertainties, it is possible that most of the 12 candidates are background radio sources and not pulsars. To increase our confidence, we undertake high-resolution imaging next.

2.3. High-resolution Interferometric Imaging

The list of preliminary pulsar candidates in Section 2.2 was generated from VLA images at 320 MHz having synthesized beams of 14'' × 5'' (A configuration) and 37'' × 14'' (B configuration). With this angular resolution, it is still possible that some resolved radio sources passed through our compactness criterion as false positives. The most significant contaminants are a population of steep-spectrum, luminous high-redshift galaxies (HzRGs; Miley & De Breuck 2008). The size distribution of HzRGs has been studied (Pentericci et al. 2000; Saxena et al. 2018) and suggests that an angular resolution of at least 5'' is needed to separate them from pulsars. The best study for our purposes comes from Pentericci et al. (2000), where, in a sample of 29 HzRGs, only 15% were unresolved at arcsecond resolution.

Accordingly, we targeted all of our candidates with the VLA (Program 16B-322) at the C band (4.5–6.5 GHz) in 2017 January in order to verify their compactness and steep spectra. See Table 1. With the array in its A configuration, we obtained high-resolution (∼05), high-sensitivity images. In addition, we observed another two dozen high-S/N sources that came close to passing our initial criteria but might have steeper spectra or be more compact at higher frequencies. We utilized the VLA automatic CASA pipeline to edit and calibrate the data with 3C48 and J1751–2524 as the flux and phase calibrators, respectively. Imaging and measuring source flux densities was accomplished in AIPS. The ratio of the integrated to peak flux densities was again used as a measure of the compactness of the candidates.

Many candidates were resolved on the high-frequency images into multiple components with a double- or single-lobed radio galaxy morphology. Others with resolved arcsecond structure, such as HzRGs, and those with extensive extended emission were also culled, since pulsars should be unresolved. Moreover, the high-frequency observations had sufficient bandwidth to allow for spectral index measurements within the band. This increased our confidence in our initial spectral index measurements (obtained from archival data at widely spaced epochs), and it allowed us to consider candidates with low-frequency turnovers due to free–free absorption, for example.

Together with our 320 MHz and other published lower-frequency measurements, we refined the spectra, resulting in a final list of seven pulsar candidates with a compactness ratio less than 1.5 and spectral index steeper than α = −1.4. If all of our original sample of 12 were HzRGs, then we would have expected 1.8 compact HzRGs (Pentericci et al. 2000), while the probability of finding seven is 0.2%. Thus, these seven remain compelling pulsar candidates. The high-frequency observations for these sources are summarized in Table 1. The rms noise sensitivity was typically 0.05 mJy beam⁻¹ but ranged from 0.01 to 0.1 mJy beam⁻¹, due mostly to the range of durations required to detect the different candidates.

Figure 2 shows the locations of the seven candidates superimposed on a continuum GC radio image, and Table 3 lists their properties. One of our candidates, C1748–2827, has such a steep spectrum that its extrapolated flux is well below the detection threshold of our C-band observation. We therefore searched for and detected the source in L-band (1–2 GHz), ∼10 resolution VLA observations of the GC region (Program S9145), also made in 2017 January (M. Kerr 2019, private communication). These observations are described in Table 1.

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Table 3.  Pulsar Candidates

Name	R.A.	Decl.	l, b	S320	Spectral Ind.a	${S}_{\mathrm{int}}/{S}_{\mathrm{peak}}$
	(h m s)	(deg arcmin arcsec)	(deg)	(mJy)		(@ 5.5 GHz)
C1742–2722	17:42:09.56	−27:22:06.4	0.94, +1.47	68 ± 6	−1.4 ± 0.1	1.0
C1744–3121	17:44:06.60	−31:21:12.5	357.77, −0.98	56 ± 6	−1.4 ± 0.2	0.9
C1745–2732b	17:45:37.20	−27:32:18.1	1.19, +0.73	38 ± 4	−1.6 ± 0.0	1.1
C1748–2827c	17:48:07.08	−28:27:41.8	0.69, −0.22	27 ± 3	−2.8 ± 0.1	1.2
C1750–2928b	17:50:38.54	−29:28:25.1	0.11, −1.22	56 ± 3	−1.5 ± 0.1	1.4
C1753–2853	17:53:13.53	−28:53:09.8	0.90, −1.40	99 ± 5	−1.4 ± 0.1d	1.0
C1753–2755	17:53:48.57	−27:55:13.8	1.80, −1.02	133 ± 12	−1.5 ± 0.2d	1.5

Notes.

^aSpectral index determined from fits (e.g., see Figure 3) to 320 MHz and 5 GHz (this work) and published multifrequency flux densities (Condon et al. 1998; Lazio & Cordes 1998, 2008; Mauch et al. 2003; White et al. 2005; Intema et al. 2017). ^bPossible extended structure or multiple components. ^cNot detected at 5 GHz (0.09 mJy 5σ upper limit). Spectral index fit and compactness ratio based on detection in 1.5 GHz observations made available by M. Kerr (2019, private communication). ^dThe spectral index based on two points within the 5 GHz band is much steeper than α = −1.5. Possible turnover in spectrum.

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For the candidate C1748−2827, a set of Stokes Q, U, and V images were generated to measure its polarization properties. The VLA observations of C1748−2827 on 2017 January 9–19 were designed to provide high-resolution Stokes I images; consequently, a leakage calibration source was not observed. In order to solve for the antenna leakage (i.e., D-terms), we reduced a separate set of archival L-band observations (VLA Project Code 16B-023) made on 2017 January 10 with the same observational parameters. These observations targeted the calibrator J0713+4349, which is unpolarized at these frequencies. We then transfered the leakage calibration solutions from these data to the January 9–19 data and used the flux calibrator of the latter, 3C 286, to solve for the absolute polarization position angle.

2.4. Single-dish Pulsation Searches

From archival data taken for a GC monitoring campaign, we have identified potential pulsar candidates within an approximately 5 deg² region centered on Sgr A*. A total of 12 candidates were identified initially from a sample of 375 sources at 320 MHz, based on compactness and spectral index criteria. Follow-up observations were conducted at 5 GHz with subarcsecond resolution in order to eliminate false positives (e.g., HzRGs, evolved lobes of radio galaxies, and transients), resulting in seven compelling pulsar candidates (Table 3). Most of the candidates have a spectral index α close to −1.4. Approximately 1%–2% of all compact radio sources have similar spectral index values (de Gasperin et al. 2018). Thus, in a random sample on the sky, we would expect four to eight such sources in the field. These still remain interesting pulsar candidates since the bias-corrected mean spectral index for pulsars also has a mean α = −1.4 ± 1 (Bates et al. 2013).

Our most intriguing candidate is C1748−2827 (Table 3). At Galactic coordinates (ℓ, b) = (069, 022), C1748−2827 lies 43' from Sgr A* and ∼11' from the massive molecular cloud Sgr B2. There is no known X-ray or gamma-ray source at this position, but the SIMBAD database lists two X-ray sources 15'' and 37'' away, as well as the X-ray binary XTE J1748–288 located 53'' to the southwest that was previously detected as a transient at 330 MHz (Hyman et al. 2002). The candidate C1748−2827 is notable for its steep spectrum (Figure 3), detectable from 150 MHz to 2 GHz, but with only an upper limit in the 4–8 GHz band despite our sensitive observations. A power-law fit to these spectral data finds a spectral index α = −2.8 ± 0.1. Thus, C1748−2827 is an excellent pulsar candidate; the fraction of background radio sources with such a steep spectral index is vanishingly small (∼10⁻⁶), while 15% of pulsars in PSRCAT have spectral indices α as steep as that of C1748−2827.

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No linear polarization was detected for C1748−2827, with a 5σ upper limit of 0.4 mJy beam⁻¹. The rms noise for the linear polarization image $P=\sqrt{{Q}^{2}+{U}^{2}}$ was about 2× larger than the total intensity Stokes I of 0.05 mJy beam⁻¹ reported in Table 1 as a result of "bootstrapping" the antenna leakage solutions from another data set to perform polarization calibration (Section 2.3). Only eight of the 12 VLA observations (∼23 minutes of the 36 minutes total on-source) could be calibrated successfully. Lenc et al. (2018) discussed several advantages to performing pulsar searches using circular polarization at low frequencies; however, no circular polarization was detected with a 5σ upper limit of 0.3 mJy beam⁻¹.

There is no obvious detection of C1748−2827 on a 74 MHz VLA image of the GC with 2' × 1' resolution (Brogan et al. 2003) and an rms noise level of approximately 100 mJy beam⁻¹, which is not inconsistent with the source being located at the GC. There are a number of reasons that the source may be undetected, including insufficient sensitivity, free–free absorption, scatter broadening, or an intrinsic turnover common to pulsars. We place an upper limit of 1 Jy on its flux density (Figure 3), and we emphasize that our result is marginal and calls out for improved low-frequency observations.

No pulsations were detected in a search with the GBT (Section 2.4). Based on the sensitivity achieved with the GBT and compared to the flux densities measured from the VLA images (viz. Tables 3 and 4), we conclude that the GBT search was sensitive enough to have detected pulsations from C1748−2827 and the other candidates in Table 3 with high significance. Also, a single pulse search yielded no evidence of isolated dispersed pulses above 6σ from any of the candidates. How, then, could a pulsar be missed in our search? There have been several previous unsuccessful pulsation searches toward steep-spectrum radio sources identified in imaging surveys (e.g., Damico et al. 1985; Crawford et al. 2000; Davoust et al. 2011; Maan et al. 2018). A variety of scenarios have been discussed to explain the nondetections (e.g., de Gasperin et al. 2018; Maan et al. 2018). In this special line of sight, however, it seems likely that scattering broadening is the limiting factor in search sensitivity due to the large and turbulent gas densities toward the GC.

With this hypothesis in mind, we explored the effects of scattering and DM as a function of distance and observing frequency toward C1748−2827, which is closest to the GC, and C1742−2722, which is 17 away from the GC and serves as a proxy for the other candidates in Table 3. The temporal smearing τ_obs for a pulsar is the quadrature sum of several terms—the intrinsic pulse width τ_int, the sampling time dt, the dispersive smearing within a single-channel bandwidth τ_DM, and the temporal scattering τ_scat. The τ_int is measured from the width of the integrated pulsar pulse profile and is usually expressed as a fraction of the pulse period. The single-channel bandwidth and dt come from the observing setup in Section 2.4 and Table 4, while the values for τ_DM and τ_scat must be estimated from a model for the Galactic distribution of ionized gas. We use the Yao et al. (2017, hereafter YMW16) and Cordes & Lazio (2002, hereafter NE2001) models. Multiple components are needed to fully model the electron density, but toward the GC, the thin disk and GC components are the most significant for both NE2001 and YMW16. While both models provide estimates for the gas density along the line of sight, one important difference between NE2001 and YMW16 is that the former provides estimates on τ_scat along the line of sight based on interstellar scattering measurements used as a constraint in their model. In the case of the GC, NE2001 derived the degree of scattering from measurements of the angular broadening of OH/IR masers and Sgr A*. In their model fitting, YMW16 did not incorporate such measurements, preferring to estimate τ_scat using an empirical relationship between DM and τ_scat derived from pulsar observations (Krishnakumar et al. 2015). Another important difference between YMW16 and NE2001 for our purposes concerns the parameters of the GC component. While they derived a similar central density and radial and vertical scale heights for the GC component, the offsets of the center of the distribution differ (Cordes & Lazio 2003). The difference is large enough that the line of sight toward C1748−2827 lies well within the YMW16 GC component, while it passes along the outer edge of the NE2001 GC component. All of the other PSR candidates in Table 3 are sufficiently far away in angular extent that the thin disk dominates over the GC component.

Given an electron density model and the GBT observing parameters from Section 2.4, τ_obs can be derived as a function of distance in any direction and at any frequency. Since most of the sensitivity to pulsations is lost when the pulsar period is below ∼5 × τ_obs (e.g., Macquart et al. 2010), we can straightforwardly derive a minimum detectable period P_min. This is shown in Figure 4 for C1748−2827 and C1742−2722 using both the YMW16 and NE2001 models at an observing frequency of 2 GHz for C1748−2827 and 6 GHz for C1742−2722 and assuming a typical pulsar duty cycle of 5%. For example, for C1748−2827 at d = 8.5 kpc, YMW16 predicted DM = 2230 pc cm⁻³ and τ_scat = 0.57 s, while NE2001 predicted DM = 1268 pc cm⁻³ and τ_scat = 55 s. The different methodology used in how YMW16 and NE2001 estimated τ_scat and the small offsets in the sky position for their GC component lead to a large uncertainty with P_min = 3 and  280 s at d = 8.5 kpc for C1748−2827 using YMW16 and NE2001, respectively. If C1748−2827 were at or near the GC, then our GBT search would have only been sensitive to magnetar periods for the YMW16 model. The minimum period for the NE2001 model rises sharply at this distance to a value that exceeds any known pulsar. Figure 4 shows that if C1748−2827 was along the line of sight, we would have been sensitive to normal pulsars over d < 8 kpc in either model, while for MSPs, the range is approximately d ≤ 4.5 kpc. For C1742−2722 and the other pulsar candidates in Table 3 observed at 6 GHz, we would have been sensitive to any pulsar using the YMW16 model, while only magnetars would be detected further than d = 8.5 kpc using the NE2001 model.

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The detection of pulsations at or near the GC may not be as dire as these models suggest. Bower et al. (2014, 2015) argued, based on the angular and temporal scattering properties of the magnetar PSR J1745−2900, that the bulk of the scattering is occurring along the line of sight (in the Scutum spiral arm) and not at the GC, as posited by NE2001. A more distant scattering screen lowers τ_scat. The reported τ_scat values for those pulsars that are thought to lie in the GC (Johnston et al. 2006; Deneva et al. 2009; Bower et al. 2015) lie in the range of 1.3–2.3 s when scaled to 1 GHz. Thus, for pulsation searches at 2 GHz, we might expect P_min ≃ 0.6 s, or about five times lower that the YMW16 estimate. The strong frequency dependence of scattering, i.e., τ_scat ∝ ν⁻⁴, argues for sensitive high-frequency pulsation searches (Macquart & Kanekar 2015).

The continuum spectrum of C1748−2827 provides some weak constraints on the distance and period. The luminosity of C1748−2827 at 1.4 GHz, if located at d = 8.5 kpc, would be 25 mJy kpc². This value lies at the high end of the normal pulsar luminosity distribution but not extraordinarily so. The lack of a low-frequency spectral turnover in Figure 2 can also be used to put some estimate on the amount of ionized gas toward C1748−2827. Assuming an electron temperature T_e = 5000 K, we find that deviations from the power-law fit occur at 150 MHz at emission measures (EMs) ≳5000 pc cm⁻³. This is identical to the EM value estimated by Pynzar & Shishov (2014) toward this position; thus, there is no useful distance constraint. Finally, we note that recent discoveries of MSPs have reignited an old debate about a possible inverse correlation between the pulsar period and spectral index (e.g., Bassa et al. 2017), suggesting that C1748−2827 with α = −2.8 could be an MSP. However, from an analysis of the spectral properties of 441 pulsars, this period–α correlation is not strong (Jankowski et al. 2018). Instead, there is good evidence that the value of α is correlated with the period derivative, spin-down luminosity, and magnetic field at the light cylinder radius.

We have imaged a 25 radius around Sgr A* at 320 MHz, searching for radio point sources with approximately two times greater sensitivity than previous studies (Nord et al. 2004; Bhakta et al. 2017). After careful vetting, we identify seven compact (θ < 1''), steep-spectrum (α < −1.4) sources as promising pulsar candidates. While some of our candidates could be background extragalactic sources, we argue based on their properties that they are likely pulsars either at the GC or along the line of sight. One of our candidates (C1748−2827) stands out in particular. It lies southeast of the Sgr B2 star-forming region and is 43' from Sgr A*. It has an unusually steep spectral index, α = −2.8.

A single-dish search for pulsations was conducted for all seven candidates (Table 4). For C1748−2827, the search for pulsations was conducted at center frequencies of 1.4 and 2 GHz, while for the other candidates, the search was conducted at 2 and 6 GHz. No pulsations were found from any of the candidates.

We hypothesize that the lack of pulsations for our best candidates is the result of scattering broadening due to the large degree of turbulence for lines of sight toward the GC. We make estimates of the minimum detectable pulsar period P_min as a function of distance using global models for the Galactic electron density distribution. In the GC region, the NE2001 and YMW16 models differ substantially in their estimates of the electron density and temporal scattering, producing a wide range of model-dependent P_min values. Other efforts to use the spectral index and lack of a low-frequency turnover to constrain the distance and period of C1748−2827 are not decisive. Our best constraints come from direct measurements of the τ_scat values for known pulsars at the GC, including the magnetar PSR J1745−2900. They suggest that, if our candidates lie at the GC, we should have been capable of detecting pulsations from magnetars and normal pulsars, but not MSPs.

Demonstrating that C1748−2827 and other steep-spectrum sources are pulsars will be challenging. The detection of a large rotation measure toward C1748−2827, similar in strength to those seen toward Sgr A* and PSR J1745−2900, would convincingly argue for a GC origin. Measuring smaller rotation measure values, such as seen toward other GC pulsars, would provide no useful distance constraints. Using all available data from our VLA observations at 1–2 GHz, we achieve a S/N ∼ 10 in Stokes I, suggesting that it will be difficult to measure large rotation measure values. In order to detect rotation measures comparable to those of Sgr A* and PSR J1745–2900 for such a weak source, methods such as Faraday rotation measure synthesis (Brentjens & de Bruyn 2005) are most practical; however, to be confident in the results, we must first detect linear polarization.

For this reason, we only examined the linear polarization image formed from the Stokes Q and U images using the full 1 GHz bandwidth to determine whether the source is polarized at frequencies of 1–2 GHz. Our inability to detect linearly polarized emission is not inconsistent with our other results. Given the Stokes I detection of S/N ∼ 10 for C1748−2827, if the source is strongly linearly polarized (50%–100%), then the signal would, at best, be a marginal detection at S/N ∼ 2. If we assume that 5σ is an upper limit on the polarization of this source, then we expect that this source is <90% linearly polarized. Since determining the rotation measure of this source would make a strong case for a GC origin, follow-up observations are recommended.

Continuum variance imaging is another promising technique that can identify pulsars by their diffraction interstellar scintillation (Dai et al. 2017). However, in order for the intensity scintillations not to be quenched, the imaging integration time and observing bandwidth must be well matched to the diffractive properties of the medium. Using the nominal parameters of PSR J1745−2900, we estimate that observing bandwidths of sub-Hz to tens of Hz would be required over the frequency range of 0.3–5 GHz. These small values are not feasible for a sensitive detection experiment in existing interferometric back ends.

The foregoing discussion shows the limitation of current image-based searches. Future low-frequency, wide-field imaging surveys of the GC that can achieve sensitivities a factor of 5–10 times better than the images that we used here may be possible. With wide instantaneous bandwidths, it would also be possible to measure "in-band" spectral indices and identify compact steep-spectrum sources from these deep images alone. However, this method must impose a cutoff on the spectral index in order to eliminate contamination from background extragalactic radio sources. The result is that the most promising candidates would have the steepest spectra. For a region like the GC, the push to higher frequencies to overcome the effects of interstellar scattering must be balanced against the rapid drop in S/N for candidates identified using this method. Some of the limitations of this method can be overcome if ancillary data are used at other wavelengths to search for pulsations. For example, we have used the subarcsecond localizations of steep-spectrum radio sources in Fermi error circles to identify MSPs based on their gamma-ray pulsations (Frail et al. 2018). This method, applied to Fermi sources toward the GC, would naturally bypass the temporal broadening that plagues radio-only searches.

The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc. The Green Bank Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc. Portions of this work at NRL were funded by NASA. Basic research in radio astronomy at NRL is supported by the Chief of Naval Research (CNR). The authors thank Dr. Joseph Lazio for his very helpful comments and useful discussions. S.D.H. thanks Dr. Huib Intema for assistance with low-band data reduction and Drs. Matthew Kerr and Subhashis Roy for making available 1.5 GHz JVLA observations and a 254 MHz GMRT image of the GC, respectively, for measurements of pulsar candidate C1748–2827. S.D.H. thanks Ms. Isabel Joyner for her assistance measuring pulsar candidate flux densities. This research has made use of the SIMBAD database, operated at CDS, Strasbourg, France. This research has made use of the NASA/IPAC Extragalactic Database (NED), which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration.

Facilities: Karl G. Jansky Very Large Array (VLA) - , Robert C. Byrd Green Bank Telescope (GBT) - .

Software: AIPS, CASA, PRESTO.