4–8 GHz Fourier-domain Searches for Galactic Center Pulsars

The central parsec of our galaxy hosts a dense nuclear star cluster (NSC; Schödel et al. 2007) surrounding the supermassive black hole (SMBH), Sgr A* of mass M_SgrA* ≈ (4.30 ±0.01) × 10⁶ M_⊙ (GRAVITY Collaboration et al. 2022). The Galactic NSC, while primarily containing old, late-type stars (≥10 Gyr, Schödel et al. 2020), is home to a large population of neutron star and black hole (BH) progenitors, including young, massive main-sequence stars (Ghez et al. 2005; Genzel et al. 2010) and Wolf–Rayet stars (Paumard et al. 2001). Recent detections of numerous X-ray binaries (Hailey et al. 2018; Zhu et al. 2018) and compact steep-spectrum radio sources (Hyman et al. 2005, 2009; Chiti et al. 2016; Zhao et al. 2020; Hyman et al. 2021; Zhao et al. 2022) further indicate a likely abundance of neutron stars and stellar-mass BHs in the NSC. Considering multiwavelength constraints on the known neutron star population, Wharton et al. (2012) argued for the existence of ∼10³ radio pulsars actively beaming toward the Earth from the inner parsec of our galaxy. Several of these pulsars may potentially reside in binaries, analogous to the profusion of millisecond pulsars ⁸ (MSPs) seen in globular clusters (Ransom 2008). Additionally, a substantial MSP population (Brandt & Kocsis 2015; Lee et al. 2015; Bartels et al. 2016; Fragione et al. 2018) in the NSC has been postulated as a plausible explanation for the observed diffuse γ-ray excess around Sgr A* (Ackermann et al. 2014; Ajello et al. 2016), another being dark matter annihilation (Abazajian et al. 2014; Calore et al. 2015) at the Galactic Center (GC).

Enabling powerful strong-field tests of gravity (Wex & Kopeikin 1999; Kramer et al. 2004; Liu et al. 2012; Wex 2014; Psaltis et al. 2016), the discovery and timing of even a canonical pulsar ⁹ (CP) in a binary with a BH will allow rigorous tests of the Cosmic Censorship Conjecture (Penrose 1969, 1999) and the BH No Hair theorem. Furthermore, if orbiting close enough (binary orbital period, P_b ≲1 yr) to Sgr A*, regular pulsar timing efforts will permit accurate measurements of SMBH mass (anticipated precision ≃1–10 M_⊙ with weekly observing cadence over five years, Liu et al. 2012), spin, and quadrupole moment. Finally, radio observations of pulse dispersion, scattering, and Faraday rotation will provide unique probes of the turbulent, magnetoionic central interstellar medium (ISM) of our galaxy.

Motivated by the rich rewards of GC pulsar timing, numerous extensive surveys of the GC have been previously undertaken over a broad range of radio frequencies (e.g., Johnston et al. 2006; Deneva et al. 2009; Macquart et al. 2010; Bates et al. 2011; Eatough et al. 2013a, 2013b; Siemion et al. 2013; Eatough et al. 2021; Liu et al. 2021; Torne et al. 2021, etc.). To date, these endeavors have revealed a single magnetar, namely PSR J1745−2900 (Eatough et al. 2013b) at 24 offset from Sgr A*, and five pulsars, all located ≳10′ away from Sgr A*. The hitherto nondetection of pulsars within a 10′ radius of Sgr A*, termed the “missing pulsar problem,” is often attributed to hyperstrong interstellar scattering in the direction of the GC (Cordes & Lazio 1997; Lazio & Cordes 1998a, 1998b; Cordes & Lazio 2002). While pulse-broadening measurements of PSR J1745−2900 suggest otherwise (Spitler et al. 2014), it is unclear if a single line of sight toward the GC magnetar is representative of a possibly complex scattering structure at the GC (Cordes & Lazio 2002; Schnitzeler et al. 2016; Dexter et al. 2017). Alternatively, an abundance of highly magnetized massive stars in the NSC may preferentially produce magnetars over spin-driven pulsars (Dexter & O’Leary 2014).

Aside from scattering, additional obstacles to GC pulsar discovery include the Galactic background temperature (T_GC(ν); Law et al. 2008), free–free absorption by the ionized central ISM, and orbital motion (if in multiobject systems). While observations at high radio frequencies (ν ≳10 GHz) help mitigate T_GC (ν) and free–free absorption, pulsar emission also significantly weakens with increasing ν (period-averaged flux density, S_ν ∝ ν^−1.4±1.0; Bates et al. 2013). Weighing various chromatic challenges to GC pulsar discovery, Rajwade et al. (2017) recommended 9–13 GHz as the optimal observing band for GC pulsar surveys. However, the observed broad spread of pulsar spectral indices (Bates et al. 2013) mandates continued broadband monitoring to detect elusive GC pulsars.

Orbital motion limits pulsar detection by smearing harmonics of the pulsar rotational frequency (f₀ = 1/P₀) in the power spectrum. Standard Fourier-domain algorithms attempt to correct for this smearing, assuming either a constant or linearly changing radial pulsar acceleration. Such implementations work for integration times, T ≲ 0.10 P_b and T ≲ 0.15P_b , respectively (Ransom et al. 2002; Andersen & Ransom 2018). While acceleration and jerk searches favor shorter T to counter orbital motion, the sensitivity to a single harmonic in the power spectrum also drops with decreasing T. Integration times in Fourier-domain pulsar searches must therefore strike a delicate balance between maximizing the single harmonic sensitivity and mitigating power smearing from orbital motion.

Here, we leverage T ∈ {5, 30, 60} minutes in the 4–8 GHz Breakthrough Listen (BL) GC survey (Gajjar et al. 2021) to conduct sensitive searches for pulsars orbiting Sgr A* or stellar-mass BHs. Section 2 describes our observations and data preprocessing. In Section 3, we present our pulsar search methodology and results. We estimate our survey sensitivity to periodic signals in Section 4. Ultimately, we summarize our key findings and discuss their physical significance in Section 5.

The BL GC survey is an extensive 0.7–93 GHz search of the GC and neighboring Galactic bulge fields for radio technosignatures, pulsars, bursts, spectral lines, and masers (see Gajjar et al. 2021 for the full survey description, data products, and early technosignature and burst science results). The 4–93 GHz component of the survey utilizes the Robert C. Byrd Green Bank Telescope (GBT), whereas the 0.7–4 GHz portion uses the Parkes radio telescope. Figure 1 shows the 4–8 GHz survey field, wherein a 625 radius of the GC is covered by 19 distinct GBT pointings arranged in three concentric hexagonal rings. From inner to outer, these rings are labeled A, B, and C, with 1, 6, and 12 pointings per ring, respectively. All pointings used the single-beam C-band receiver, yielding a half-power beamwidth, at 6 GHz. As illustrated in Figure 1, our central pointing A00 contains the GC magnetar. We refer readers to Suresh et al. (2021) for a 4–8 GHz study of the GC magnetar using our A00 data.

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Table 1 presents an overview of our 4–8 GHz observations ¹⁰ distributed across four epochs during 2019 August–September. Our observing program consists of eleven deep integrations (≥30 minutes) on A00, two 5 minute scans on C10, and three 5 minute cadences on each of the remaining pointings. In addition, we observed test pulsars at three epochs, and confirmed their respective detections to verify our system integrity. To identify and reject radio frequency interference (RFI) via position switching, we conducted alternating observations of pairs of pointings in rings B and C. Pointing pairs were chosen such that the beam centers of grouped pointings were separated by at least 2θ_HPBW on the sky.

To accommodate various science cases, baseband voltages gathered during our observations were channelized to different spectral and temporal resolutions using the Breakthrough Listen Digital Backend (MacMahon et al. 2018; Lebofsky et al. 2019). Here, for our pulsar searches, we worked with total intensity filterbank data (no coherent dedispersion performed) having ≈43.69 μs time sampling and ≈91.67 kHz channel bandwidth. These data contain 53,248 channels spanning 3.56–8.44 GHz, which covers the 3.9–8.0 GHz instantaneous response of the C-band receiver.

2.1. Data Preprocessing

2.2. Red Noise Removal

Slow pulsar discovery (P₀ ≥ 1 s) in long time series (T ≥ 5 minutes) often suffers from the presence of low-frequency noise in Fourier-domain spectra. To alleviate the adverse impact of red noise on our pulsar searches, we detrended our dedispersed time series using a running median window of width W_med.

For deciding on an optimal value of W_med, we visually inspected the effect of different trial W_med on power spectra of barycentric GC magnetar time series (DM = 1776 pc cm⁻³, ; Suresh et al. 2021). Starting at W_med = 4 s, we successively lowered W_med by factors of 2 until a further reduction in W_med brought no concomitant increase in the number of harmonics of f₀ ^mag seen in the power spectrum. In doing so, we settled at W_med = 0.25 s for removing slow baseline fluctuations in our dedispersed time series.

Figure 2 shows the result of time series detrending on the power spectrum of a barycentric DM = 1776 pc cm⁻³ time series from a 30 minute A00 scan. The power spectrum of the detrended time series evidently reveals significant peaks at f₀ ^mag and its first seven harmonics. Without detrending, these peaks remain buried within red noise in the power spectrum of the original time series.

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Finally, to limit the false-positive count in our pulsar searches, we masked periodic RFI in the power spectra of our detrended time series. Looking at power spectra of topocentric DM = 0 pc cm⁻³ time series, we identified and flagged significant spikes at frequencies of 1.2, 6, and 60 Hz (US electric power line frequency), and their first five harmonics. The resulting cleaned power spectra constituted the basis of our Fourier-domain periodicity searches.

Consider a regular pulse train (insignificant pulse jitter) from an isolated pulsar of barycentric rotational frequency, f₀ = 1/P₀. For an effective pulse duty cycle δ_eff, the energy in the pulse train gets distributed over N_h ≃1/2δ_eff independent harmonics in the power spectrum. Consequently, standard periodicity searches perform harmonic summing in power spectra of dedispersed time series to increase the significance of a pulsar detection (Ransom et al. 2002). In a blind search, the pulsar DM, f₀, and δ_eff are unknown apriori. Searches for isolated pulsars, hence require sampling of the three-dimensional parameter space DM–f–N_h .

Binary orbital motion complicates pulsar detection by introducing a time-dependent Doppler drift that smears harmonics in the power spectrum. Conventional search algorithms attempt to retroactively correct for this smearing by presuming a constant or linearly evolving line-of-sight pulsar acceleration (Ransom et al. 2002; Andersen & Ransom 2018).

Figure 3 shows a binary pulsar orbit and its Keplerian orbital elements, including its projected semimajor axis a_p = a sin i (orbital semimajor axis a and inclination i), argument of periapsis ω, and true anomaly A_T . In the Newtonian regime, the line-of-sight pulsar acceleration (a_l ) and jerk (j_l ) are respectively given by Bagchi et al. (2013); Liu et al. (2021):

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In the above equations, e denotes the eccentricity of the pulsar orbit. Casting a_l and j_l in dimensionless units, and introducing the harmonic number h, we have

Here, h = 1 labels the fundamental frequency f, and c is the vacuum speed of light. Following Andersen & Ransom (2018), we define the dimensionless Fourier frequency, r = fT. The quantities z and w thus represent the number of bins of signal drift in r and over time T. In Equations (3) and (4), we note that both z and w scale linearly with h. Therefore, orbital motion lowers the detection significance of all harmonics in the power spectrum, with greater deleterious effects for higher harmonics. The most minimal regime of pulsar detection then occurs when only the fundamental survives with adequate significance in the power spectrum, while all higher harmonics have been smeared into the continuum by orbital motion.

3.1. Acceleration and Jerk Searches

The accelsearch routine of PRESTO (Ransom 2011) executes a matched filtering scheme that accounts for Fourier-domain power smearing of the highest harmonic up to a Fourier acceleration z_max and a Fourier jerk w_max (Ransom et al. 2002; Andersen & Ransom 2018). Searches for binary pulsars, hence involve sampling over five parameters, i.e., the DM, f, N_h , z_max, and w_max.

We targeted the discovery of pulsars in compact orbits around Sgr A* or stellar-mass BHs. We focused our searches on CPs as we expected most MSPs to fall below our detection threshold (see Section 4). To identify suitable trial parameter values for our binary pulsar searches, we considered a M_p = 2.14 M_⊙ pulsar (highest neutron star mass measured to date; Cromartie et al. 2020) located at A_T = −90°in an edge-on orbit (i = 90°) with ω = 0°. We further envisaged N_h = 1 searches for pulsars in tight binaries with large a_l and j_l .

Assuming T = 30 minutes and P₀ = 1 s, Figure 4 shows contours of constant w_max (top row) and z_max (middle row) for pulsar orbits around Sgr A* (left column) and a M_BH = 9 M_⊙ BH (median BH mass for solar metallicity; Woosley et al. 2020). The condition T ≲ 0.15P_b for jerk searches restricts us to P_b ≳ 3.3 hr for T = 30 minutes. Setting P_b = 10 hr as our target, we sought to cover by uniformly sampling the w_max versus z_max curves shown in the bottom row of Figure 4. For our selected M_BH value, a_p varies inappreciably for known ranges of M_p . Therefore, our chosen (z_max, w_max) tuples encompass all known pulsar masses, including the typical mass of 1.4 M_⊙ (Zhang et al. 2011).

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Table 2 outlines our pulsar search strategy, wherein we also incorporated searches for isolated pulsars and binary pulsar orbits in the T = 5 minute integrations of our B- and C-ring pointings. Again, we identified viable z_max and w_max values considering N_h = 1 searches for binary pulsar orbits. Adopting the same (z_max, w_max) tuples for our N_h = {2, 4, 8} searches, we enhance our sensitivity to slowly orbiting pulsars through harmonic summing. However, since our searches perform matched filtering (Andersen & Ransom 2018) in the Fourier domain, the greatest sensitivity will be had for systems with a_l = (z_max c/N_h f T²) and .

Table 2. Pulsar Search Parameters

Science targets	Pointings	Ta	Pb b	(zmax, wmax)
		(minutes)	(hours)
Isolated pulsars	All	5, 30, 60	⋯	(0, 0)
Pulsars orbiting stellar-mass BHs	B-ring, C-ring	5	1	(2, 0), (6, 20)
	A00	30	10	(2, 0), (8, 20)
Pulsars around Sgr A*	A00	30	10	(100, 20), (200, 160),
				(300, 380), (400, 680),
				(500, 1080)

Notes.

1. 1836 trial DMs explored between 0–5505 pc cm⁻³ (both limits included) with a grid spacing of 3 pc cm⁻³.

2. For a sample interval of ≈349.53 μs in the dedispersed time series, the range of f searched is 0–1430 Hz with a resolution of 1/T.

3. Trial N_h values considered = {1, 2, 4, 8}.

^a Integration time. ^b Target binary orbital period assumed for specified (z_max, w_max) tuples.

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Our pulsar search procedure on data can be described in three independent stages. First, we ran nonaccelerated searches for isolated pulsars on a per-scan basis. Second, at the trial parameter values listed in Table 2, we conducted acceleration and jerk searches on data from our 5 minute and 30 minute scans. Finally, we split our 60 minute A00 scan from epoch 2 into two contiguous halves, and executed jerk searches separately on each half.

Imposing a 6σ_ps detection probability threshold in harmonic-summed power spectra, we used the accel_sift.py script of PRESTO (Ransom 2011) to group hits across adjacent trial DMs and frequencies f into distinct candidates. Here, σ_ps measures the equivalent Gaussian significance of a frequency f in the χ²-distributed power spectrum (assuming Gaussian white noise background in detrended time series).

3.2. Results

Our pulsar searches yielded a total of 16,048 periodicity candidates across 64 scans. Table 3 presents our candidate detection statistics organized by pointings. Since we expect any astrophysical signal of our interest to be localized on the sky, we pruned our detection list by rejecting candidates common to paired pointings within a frequency tolerance Δf and a DM tolerance ΔDM. For an integration time T, we chose Δf = 1/2T, i.e., the maximum error on f for N_h = 1. Given an effective pulse width W_eff = δ_eff P, the DM uncertainty associated with pulse detection across a usable bandwidth B is (Cordes & McLaughlin 2003)

Here, B ≈3.35 GHz, and ν_c ≈ 6.1 GHz is the center frequency of our observations. Conservatively setting W_eff = 3t_samp ≈ 1 ms, we obtain ΔDM ≈ 33 pc cm⁻³. As evident from Table 3, our position-switched observations permit us to eliminate about 5% of candidates in rings B and C, thereby leaving us with 15,560 periodicity detections across 64 scans.

Table 3. Periodicity Detection Statistics

Pointing	Ndetected a	Nrejected b	Ncands c
A00	7039	⋯	7039
B01	454	27	427
B02	487	22	465
B03	495	26	469
B04	460	34	426
B05	414	25	389
B06	485	25	460
C01	481	13	468
C02	456	27	429
C03	489	36	453
C04	437	25	412
C05	554	28	526
C06	596	48	548
C07	458	12	446
C08	423	33	390
C09	555	46	509
C10	370	12	358
C11	413	38	375
C12	982	11	971
Total	16048	488	15560

Notes.

^a Number of distinct candidates detected at or above 6σ_ps equivalent Gaussian significance in χ²-distributed power spectra. ^b Number of candidates rejected via position switching. ^c Number of candidates that pass comparisons between periodicity detections in paired pointings.

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In Figures 5 and 6, we statistically analyze the remaining 15,560 candidates in terms of their DM, period (P = 1/f), and σ_ps distributions. The GC magnetar markedly stands out as a high significance cluster of A00 candidates centered at DM = 1776 pc cm⁻³ and P = 3.7686 s. Furthermore, nearly 90% of candidates fall within a horizontal expanse between P = 2 ms and P = 100 ms in the P–DM plane. We attribute this scatter of candidates partly to a statistical sampling effect (greater number of power spectrum samples across P ∈ [2, 100] ms than that spanning P ∈ [10², 10⁴] ms), and partly to noise and intermittent band-limited periodic RFI in dynamic spectra. Appendix A shows the average profiles of two sample candidates, whose phase-resolved dynamic spectra reveal bright RFI between 4.4–4.9, 5.1–5.2, 6.8–7.0, and 7.5–7.8 GHz. These narrowband structures asynchronously wax and wane during our observations, leading to a horde of nonastrophysical candidates detected at numerous DMs and periods.

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Other notable features in Figure 5 include streaks of A00 candidates at P ∈ [30, 100] ms, and an excess of C-ring candidates at P ≲ 2 ms and DM ∈ [0, 150] ∪ [430, 700] ∪ [1000, 1150] pc cm⁻³. Upon manual visual inspection of their respective folded profiles, we traced the A00 streaks to periodic irregularities occurring near the start and end of individual scans. Further, we associate the surfeit of C-ring candidates with the emergence of bright RFI at 5.8–5.9 and 7.8–7.9 GHz during our C12 scans.

In summary, we report the successful detection of the GC magnetar in periodicity searches of our A00 scans. Setting a 6σ_ps detection threshold for our Fourier-domain searches, we find no statistical evidence of novel periodic astrophysical emissions in the 4–8 GHz BL GC survey data.

Consider the minimal detection of a pulsar, with only its h = 1 harmonic visible in the power spectrum. In such a circumstance, the relevant theoretical detection limit is the single harmonic sensitivity at f₀ given by

Here, S_sys is the system-equivalent flux density (SEFD), and m = 6 is the minimum significance required to claim a detection. Often, S_sys in GC surveys is written as a sum of two terms.

where S_sys ^{off − SgrA*} is the SEFD away from the Sgr A* complex, and S_sys ^SgrA* captures the SEFD contribution from the Sgr A* complex.

Assuming slow pulsar orbital motion in time T, we can lower our sensitivity threshold below S_sh by summing over harmonics in the power spectrum. For δ_eff ≪ 1, the corresponding minimum detectable flux density (Dewey et al. 1985) is then

Appendix B describes various sources of pulse broadening that can widen a pulse from intrinsic width W_int to effective width, W_eff = δ_eff P in a dedispersed time series. We define δ_int = W_int/P as the intrinsic pulse duty cycle. From the ATNF pulsar catalog v1.66 (Manchester et al. 2001) ¹¹ , about 83% of CPs have duty cycles between 1% and 10%, with a median duty cycle of 2.5%.

Assuming negligible instrumental and dispersive pulse broadening,

Here, τ_sc(ν) is the scatter-broadening timescale. In the absence of alternate observational evidence, we take τ_sc toward the GC magnetar to be representative of the central ISM throughout the remainder of our study. From Spitler et al. (2014), we have

for GC magnetar pulses. Thus, scattering inhibits the detection of GC pulsars with P₀ ≤ τ_sc(6.1 GHz) ≃1.35 ms.

Table 4 lists observational parameters and theoretical sensitivity limits of GC pulsar surveys conducted at ν_c between 4–9 GHz. We adopted a GC distance, d_GC = 8.18 kpc (Gravity Collaboration et al. 2019), to convert S_sh and S_min to pseudo luminosities, L_sh and L_min, respectively. To facilitate sensitivity comparison across surveys at different ν_c , we scaled their respective L_min to 6.1 GHz invoking , where α = −1.4 is the mean pulsar spectral index (Bates et al. 2013). This scaling preserves the fraction of known pulsars with spectral pseudo luminosity, for a given survey.

Table 4. Observing Parameters and Sensitivity Thresholds for GC Pulsar Surveys Conducted at 4–9 GHz

Survey	νc	B	T	tsamp	Ssys (νc ) a	Lsh (νc ) b	Lmin (νc ) c	Lmin (6.1 GHz) d
	(GHz)	(GHz)	(min.)	(ms)	(Jy)	(mJy kpc2)	(mJy kpc2)	(mJy kpc2)
Johnston et al. (2006)	8.4	0.864	70	1.0	148	22.1	3.5	5.5
Deneva et al. (2009)	4.8	0.8	60	0.65	57.5 e	9.6	1.5	1.1
Bates et al. (2011)	6.59	0.576	280	0.13	216.7	19.8	3.2	3.5
Eatough et al. (2021)	4.85	0.5	72	0.26	129	24.9	4.0	2.9
	8.35	0.5	144	0.13	93.3	12.7	2.0	3.2
This work f :
A00	6.1	3.35	30	0.35	46.3	5.3	0.9	0.9
Off-Sgr A* pointings g	6.1	3.35	5	0.35	10.7	3.0	0.5	0.5

Notes.

^a . ^b Single harmonic pseudo-luminosity threshold, L_sh = S_sh d_GC ², where d_GC = 8.18 kpc (Gravity Collaboration et al. 2019). ^c Minimum detectable pseudo luminosity, L_min (ν_c ) = S_min (ν_c ) d_GC ² for δ_int = 2.5% and P₀ = 1 s. ^d invoked, where α = −1.4 is the mean pulsar spectral index (Bates et al. 2013). ^e T_GC(ν) ≈ 568 K (ν/1 GHz)^−1.13 (Rajwade et al. 2017) assumed to compute S_sys ^SgrA*. ^f We estimated S_sys ^{off − GC} and S_sys ^SgrA* using Figure 1 and Equation (2) of Suresh et al. (2021). ^g B-ring and C-ring pointings with negligible S_sys ^SgrA* in Figure 1.

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Applying the above power-law scaling and assuming δ_int = 2.5%, Figure 7 shows L_min(6.1 GHz) for various surveys as a function of P₀. Our survey clearly represents the most sensitive 4–8 GHz exploration for GC pulsars conducted to date. For P₀ ≳ 100 ms, our survey reaches down to L_min ≈ 0.9 mJy kpc², i.e., an 18% improvement over Deneva et al. (2009), who also utilized the GBT for their observations. However, at ν_c = 4.8 GHz, scattering limits the Deneva et al. (2009) sensitivity for P₀ ≲ 100 ms, with P₀ ≤ 3.4 ms pulsars rendered undetectable. In contrast, our survey still provides significant sensitivity to P₀ ≥ 1.35 ms, thereby extending our discovery phase space to include potential superluminous MSPs (L_6.1 ≥ 6 mJy kpc², P₀ ≈ 3 ms) residing at the GC.

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4.1. Fake Pulsar Injection and Recovery

Equations (6) and (8) describe our survey sensitivity presuming ideal Gaussian, white noise backgrounds in dedispersed time series. However, real-world data frequently contains RFI and red noise, the latter of which substantially worsens our sensitivity to long P₀ (Lazarus et al. 2015; van Heerden et al. 2017). Therefore, to measure our true survey sensitivity, we injected fake pulsars into our original dedispersed time series and verified their recovery.

Following Section 2.2 of Suresh et al. (2021), we first calibrated 11,016 dedispersed time series from six 30 minute A00 scans at epoch 4 (MJD 58738). To simulate a fake pulsar, we began with an input δ_int, P₀, and a 6.1 GHz pseudo luminosity L_6.1. We chose an initial pulse phase randomly from a standard uniform distribution. We then randomly drew Gaussian single pulse amplitudes and FWHMs W from lognormal distributions with means (L_6.1/ δ_int d_GC ²) and δ_int P₀ respectively. For both distributions, we assumed standard deviations equal to 5% of their respective means. To each W sample, we then added t_samp in quadrature. Utilizing the drawn and updated W samples, we thus generated a periodic Gaussian pulse train that models a discretely sampled signal at the location of a pulsar (pulse jitter neglected). We next incorporated scattering by convolving the simulated Gaussian pulse train with a one-sided, decaying exponential of timescale, τ_sc(6.1 GHz) ≃1.35 ms. Finally, we added the resulting periodic signal to all calibrated time series to complete our fake pulsar injection. In the above exercise, we ignored instrumental and dispersive pulse broadening as these effects are negligible for the parameters of our survey and data processing (see Appendix B).

For every trial δ_int and P₀, we kicked off our pulsar injections at L_6.1 = 0.8L_min. Passing all calibrated time series containing the injected signal through our processing pipeline (including time series detrending), we stepped up L_6.1 in small increments until the detection significance of the artificial pulsar exceeded 6σ_ps. Let L_min ^true denote the minimum recovered L_6.1 for a given trial δ_int and P₀. Averaging L_min ^true over identical fake pulsar injections in 11,016 calibrated time series, we obtained the dotted sensitivity curves shown in Figure 8.

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Noticeably, RFI raises our survey sensitivity above theoretical limits by 3%–7% across all P₀. Moreover, the presence of red noise in our raw data progressively hinders our search sensitivity at longer P₀ and larger δ_int. However, despite the deleterious impact of red noise and RFI on our pulsar searches, our survey crucially retains adequate sensitivity to over 95% of theoretically detectable pulsars for a median CP δ_int of 2.5%.

We have conducted a comprehensive 4–8 GHz search of the central 625 (≈14.9 pc in projection) of our galaxy for pulsars. Utilizing the GBT, our observing program comprised of 11 T ≥ 30 minutes integrations on the GC and 53 T = 5 minutes integrations on nearby Galactic bulge fields. As proof of our survey integrity, we successfully demonstrated the detection of the GC magnetar PSR J1745−2900 in all of our GC scans. Executing Fourier-domain acceleration and jerk searches, we report the nondetection of hitherto unknown periodic astrophysical emissions in our data above a 6σ detection threshold.

Our investigations constitute the most sensitive 4–8 GHz exploration for GC pulsars conducted to date. For δ_int = 2.5% and P₀ ≃ 1 s, our survey reaches down to L_min ^true ≈ 1 mJy kpc², i.e., a sensitivity improvement of at least 18% over past GC pulsar searches conducted at similar radio frequencies. Notably, our observations open the window to discovering potential superluminous MSPs (L_6.1 ≥ 6 mJy kpc², P₀ ≈ 3 ms) at the GC. Though we focused our binary pulsar searches on CP orbits around Sgr A* or stellar-mass BHs, our chosen processing parameters in Table 2 also incorporate searches for bright MSPs with low radial pulsar accelerations (z_max ≲ 0.5P_{0, ms} ⁻¹) and jerks (w_max ≲ 1.1P_{0, ms} ⁻¹).

Studying pulsar demographics in our galaxy, Freire (2013) argued that the globular cluster pulsar population is likely older than its Galactic field counterpart. Analogous to globular clusters, the GC environment, with its high density of ∼10⁶ stars per cubic parsec (Schödel et al. 2018), is predicted to favor MSP production. About 3% of Galactic field MSPs have the L_6.1 ≥ L_min ^true of our survey. Say that GC MSPs follow similar population-level statistics as their Galactic field equivalents. For a beaming fraction f_b = 0.7 (Kramer et al. 1998), our nondetection of GC pulsars therefore constrains the total MSP count in the central parsec of our galaxy to N_MSP ≲ 50. Our N_MSP estimate is a factor of 20 smaller than that derived by Wharton et al. (2012), possibly due to our lack of sensitivity to tight MSP orbits. Sideband searches (Ransom et al. 2003) and coherent full-orbit demodulation algorithms (Allen et al. 2013; Balakrishnan et al. 2022) will both provide enhanced sensitivity to short binary orbital periods (P_b ≪ T), thereby yielding stronger constraints on the GC MSP population in the near future.

Alternatively, our nondetection of GC pulsars can be attributed to complex pulsar orbital dynamics arising from plausible close encounters with other neutron stars, stellar-mass BHs, and intermediate-mass BHs in the dense GC environment. Such proximate compact object flybys can potentially disrupt binaries and scatter pulsars into hyperbolic orbits that lead away from the GC (Jiale et al. 2021). On the other hand, a preference for magnetar formation (Dexter & O’Leary 2014) at the GC may explain the “missing pulsar problem” by virtue of the comparatively shorter magnetar lifetimes (∼10⁴ yr).

Throughout our study, we presumed that interstellar scattering does not limit GC pulsar surveys. While τ_sc(ν) measurements of the GC magnetar support the above premise, observations of pulse broadening along different lines of sight are necessary to build a more complete picture of the turbulent central ISM. Hence, we encourage regular monitoring of the GC for fast transients to obtain robust scattering constraints on the ionized central ISM, and thus better inform future GC pulsar surveys.

A.S. thanks Scott M. Ransom for timely responses to software-related queries. A.S., J.M.C., and S.C. acknowledge support from the National Science Foundation (AAG 1815242). J.M.C. and S.C. are members of the NANOGrav Physics Frontiers Center, which is supported by the NSF award PHY–1430284. Breakthrough Listen is managed by the Breakthrough Initiatives, sponsored by the Breakthrough Prize Foundation. The Green Bank Observatory is a facility of the National Science Foundation, operated under a cooperative agreement by Associated Universities, Inc.

This work used the Extreme Science and Engineering Discovery Environment (XSEDE) through allocations PHY200054 and PHY210038, which are supported by the National Science Foundation grant number ACI−1548562. Specifically, it used the Bridges-2 system, which is supported by NSF award number ACI−1928147, at the Pittsburgh Supercomputing Center (PSC).

Facilities: GBT, XSEDE (Towns et al. 2014).

Software: Astropy (Astropy Collaboration et al. 2013, 2018), NumPy (van der Walt et al. 2011), Matplotlib (Hunter 2007), PRESTO (Ransom 2011), Python 3 (https://www.python.org), SciPy (Virtanen et al. 2020).

Figures A1 and A2 show average profiles of two sample candidates that sit amidst the large scatter of detections between P = 2 ms and P = 100 ms in the P–DM plane of Figure 5. Average profiles were generated using the prepfold routine of PRESTO (Ransom 2011).

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Consider a pulsar emitting single pulses of average intrinsic width W_int. Accounting for instrumental effects, sampling, and propagation-induced broadening, the effective pulse width in a dedispersed time series is

Here, t_samp is the sample interval in the dedispersed time series, and t_R ∼ (Δν_ch)⁻¹ is the receiver filter response time for a channel bandwidth Δν_ch.

The term t_chan represents the intrachannel dispersive smearing given by Cordes & McLaughlin (2003)

Further, t_BW quantifies the residual broadband dispersive delay for a DM error ΔDM.

Finally, τ_sc(ν) is the pulse-broadening timescale from multipath wave propagation through turbulent ionized plasma.

For our observations, ν_c ≈ 6.1 GHz, B ≈ 3.35 GHz, Δν_ch ≈91.67 kHz, and t_samp ≈ 349.53 μs. Working with a DM step size of 3 pc cm⁻³, our trial DMs are at best ΔDM = 1.5 pc cm⁻³ off from the true DM of a source. Collectively, the above numbers imply t_R ∼ 11 μs, t_BW ≈ 184 μs, and t_chan ≈ 6 μs for DM = 1776 pc cm⁻³ of the GC magnetar (Suresh et al. 2021). Assuming the empirical GC magnetar scattering law (Spitler et al. 2014) given in Equation 10, τ_sc ≃1.35 ms at 6.1 GHz.

Since τ_sc ≫ t_chan, t_BW, t_R , Equation B1 can thus be simplified to