PULSE BROADENING MEASUREMENTS FROM THE GALACTIC CENTER PULSAR J1745–2900

The recent discovery of radio pulsations from a magnetar with an angular separation of 3 arcsec from Sagittarius A* (Sgr A*) provides an unparalleled tool for probing the ionized interstellar medium (ISM) toward the Galactic center (GC; Eatough et al. 2013a). SGR J1745-29 was first identified at X-ray wavelengths by the Swift observatory (Kennea et al. 2013). Targeted follow-up observations by the NuSTAR observatory revealed pulsed emission with a period of 3.76 s and a high period derivative (Mori et al. 2013). The inferred magnetic field of ∼10¹⁴ G, X-ray spectral properties, and sudden increase in flux suggests that the object is a transient magnetar (Mori et al. 2013).

Radio follow-up observations of SGR J1745-29 (hereafter PSR J1745-2900) have confirmed the high spin down rate, (6.82  ±  0.03) × 10⁻¹², and measured a dispersion measure (DM) of DM = 1778 ± 3 pc cm⁻³ (Eatough et al. 2013a), the highest DM of any known radio pulsar. The projected minimum physical separation of PSR J1745–2900 from Sgr A* at a GC distance of 8.3 kpc is ∼0.1 pc. The NE2001 model for the distribution of Galactic electrons (Cordes & Lazio 2002) estimates a DM distance for the magnetar that is consistent with the distance of Sgr A*, although the actual electron distribution in the GC is likely more complex. Eatough et al. (2013a) measure a high rotation measure (RM) of RM = −66960  ±  50 rad m⁻² (see also Shannon & Johnston 2013). This RM is an order of magnitude larger than other RMs measured within a few tens of parsecs of Sgr A* (see, e.g., Law et al. 2011, and references therein), and Eatough et al. (2013a) postulate that the Faraday rotation is caused by a magnetized hot gas component (≳8 mG) from which Sgr A* accretes. Furthermore, Mori et al. (2013) find that the column density inferred from the X-ray spectrum measured by NuSTAR is consistent with the magnetar being at the distance of the GC, and Rea et al. (2013) compare the column densities measured from X-ray spectra of Sgr A* and PSR J1745-2900 from the Chandra X-ray Observatory and infer an upper limit to their physical separation of ≲2 pc.

The scatter broadening of PSR J1745–2900 is much lower than expected for a source in the GC. The NE2001 model predicts a large pulse broadening time scale of ∼2300 s at 1 GHz for a source at the distance of Sgr A*. Previously, the lack of pulsars observed in the GC, despite strong evidence for their existence in this region (see, e.g., Wharton et al. 2012), was explained by extreme scattering within ∼150 pc of Sgr A* (Lazio & Cordes 1998), which renders pulsar periodicity searches at typical observing frequencies (∼1 GHz) ineffective.

In this letter, we present multi-frequency measurements of the temporal broadening from PSR J1745–2900 and discuss their implications. In Section 2 we give a brief description of the observational phenomena of pulse and angular broadening. Our observations and data analysis are given in Section 3. The results are presented in Section 4. We discuss our results and summarize in Sections 5 and 6 respectively.

A pulse propagating through the non-uniform, ionized ISM will be scattered, leading to the multi-path propagation effects of angular broadening and pulse broadening. A point source is broadened to a typical observed angular size θ_o, and an impulse-shaped pulse is broadened to a characteristic time scale τ_d. These two quantities, θ_o and τ_d are geometrically related and depend on the properties of the scattering screen (see, e.g., Williamson 1972; Rickett 1990).

Mathematically, temporal scattering is described by the pulse broadening function (PBF). The observed pulse shape is the convolution of the intrinsic pulse shape and the PBF. A commonly assumed geometry is a thin screen with infinite transverse extent dominated by the smallest spatial scale, which has a one-sided exponential PBF (Cronyn 1970):

$$\begin{equation} {\rm PBF_e}(t) = \Theta (t) e^{-t/\tau _{\rm d}}, \end{equation} \tag{ 1 }$$

where Θ(t) is the unit step function. Thick scattering screens have PBFs with slower rise times than PBF_e (e.g., Williamson 1972; Bhat et al. 2004). Kolmogorov media have PFBs that decay more slowly than an exponential (Lambert & Rickett 1999; Cordes & Rickett 1998). Other possible geometries include scattering screens with limited transverse extent or filaments (Cordes & Lazio 2001).

Pulse and angular broadening are also highly dependent on observing frequency (ν) with a typical spectral index α proportional to ∼ν⁻⁴ and ∼ν⁻² respectively. Bhat et al. (2004) measured a mean spectral index of α = −3.9 ± 0.2 for a large ensemble of pulsars with low to moderate DMs. Löhmer et al. (2001) measured the spectral index of nine pulsars with large DMs (∼400–1000 pc cm⁻³) and determined a shallower frequency scaling of α = −3.44 ± 0.13.

The magnetar was observed with the Effelsberg radio telescope at observing frequencies ranging from 1.35 to 18.95 GHz, the Nançay radio telescope from 1.5 to 3.2 GHz, and the Jodrell Bank Lovell telescope at 1.5 GHz. A full list of observing frequencies, bandwidths, observing dates, and observing durations is given in Columns 1–4 of Table 1. In Column 6 the telescope name is abbreviated as follows: "EFF", "NCY", and "JB" refer to Effelsberg 100 m Radio Telescope, Nançay Decimetric Radio Telescope, and Jodrell Bank Lovell Telescope.

3.1. Effelsberg

3.2. Nançay

3.3. Jodrell Bank

The single pulse analysis revealed that the emission profile of the magnetar consists of one or more narrow pulses with widths of ∼1 ms. These single pulses vary stochastically in phase over a range that is roughly an order of magnitude larger than their intrinsic widths. The integrated pulse profile is therefore dominated by jitter, a behavior seen in other magnetars (Camilo et al. 2006; Kramer et al. 2007; Levin et al. 2012). Figure 1 shows integrated pulse profiles (top panels) and pulse profiles from individual rotations (bottom panels) for Effelsberg data at 4.85 and 8.35 GHz. The shapes of the integrated profiles are also Gaussian-like, which is important for our pulse profile fitting technique described in Section 4.2.

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The pulse profiles of PSR J1745-2900 are characterized by three time scales. The shortest is the intrinsic width of the single pulses. The phase jitter time scale is longer and dominates the widths of integrated pulse profiles at frequencies above ∼2 GHz. The third time scale is the pulse broadening caused by interstellar scattering and dominates the integrated profiles at frequencies below ∼2 GHz.

4.1. Model for Pulse Shape

We model both single pulses and average profiles as scattered Gaussian pulses, i.e.,

$$\begin{equation} P_{\rm g}(t) = \displaystyle A e^{-\left(\frac{t-t_0}{\sigma }\right)^2}, \end{equation} \tag{ 2 }$$

where σ is the 1σ pulse width, A is the amplitude, and t₀ is the epoch of the pulse peak. For single pulses the parameter σ is a measure of the intrinsic width, while for the average profiles it measures the jittered width.

The scattered pulse profile P_s(t) is the intrinsic profile convolved with PBF_e, i.e.,

$$\begin{eqnarray} P_{\rm s}(t) &=&P_{\rm g}(t) * {\rm PBF_e}(t)\nonumber \\ &=&\frac{A\sqrt{\pi }}{2}\sigma e^{ \frac{\sigma ^2-4 t \tau _{\rm d}}{4\tau _{\rm d}^2}} \left[1+{\rm erf}\left(\frac{2 (t-t_0)\tau _{\rm d}-\sigma ^2 }{2 \tau _{\rm d}\sigma }\right)\right]. \nonumber\\ \end{eqnarray} \tag{ 3 }$$

The instrumental response further modifies the pulse profile. The observed pulse profile is thus

$$\begin{equation} P_{\rm obs}(t) =P_{\rm s}(t) * S(t) +b\,, \end{equation} \tag{ 4 }$$

where b, the profile baseline level, models any residual DC offset, and S is the integration-sampling function, i.e.,

$$\begin{equation} S(t)=\left\lbrace \begin{array}{@{}c c@{}}1 & -\tau _{\rm s}\le t\le 0, \\ 0 & {\rm otherwise}, \end{array} \right. \end{equation} \tag{ 5 }$$

where τ_s is the sampling time of the pulse profile. For incoherently dedispersed data P_obs(t) should also include a factor for the residual DM smearing across a frequency channel (e.g., Cordes & McLaughlin 2003), but at 18.95 GHz the dedispersion smearing across a frequency channel (16.9 μs) is much less than the sampling time (128 μs) and can be ignored.

4.2. Pulse Profile Fitting

We fit the observed single pulse profiles and the integrated pulse profiles independently at each frequency with the models described above. The pulse profile is parameterized by {t_i, p_i, _i}, where t_i, p_i, and _i are the time, pulse flux and pulse flux error of the ith profile bin. The error _i is estimated via the off-pulse rms level. The reduced χ² for the five parameter fit is

$$\begin{equation} \chi ^2=\frac{1}{N_{\rm b}-6} \sum _{i=1}^{N_{\rm b}} \left[\frac{P_{\rm obs}(t_i; A, t_0, \sigma, b, \tau _{\rm d})-p_i}{\epsilon _i}\right]^2. \end{equation} \tag{ 6 }$$

The least squares solution for the parameters was found by minimizing the χ² using a down-hill simplex method. We seed the initial fitting parameters randomly and repeat for 100 unique trials in order to find the global minima. Our error convention follows Bates & Watts (2007), the 1σ error is defined as the square root of diagonal terms of the covariance matrix for the fitting residuals.

We fit the single pulse profiles at 4.85–18.95 GHz, and the integrated pulse profiles at 1.19–8.35 GHz. The best-fit parameters of all profile fits are given in Columns 5 and 6 of Table 1. We did not fit for the scattering time scale in the 14.6 GHz and 18.95 GHz averaged profile, since it is nearly 1000 times smaller than the pulsar jitter time scale. No systematical structure is found in the fitting residuals, which indicates that the Gaussian modeling for the intrinsic profile is sufficient. Examples of observed pulse profiles from frequencies of 1.19–8.34 GHz (blue lines) and their best-fit model profiles are given in Figure 2.

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Figure 3 shows the scattering time scale (τ_d) versus frequency (left) derived from both the integrated profiles and single pulses and the intrinsic pulse width (σ) versus frequency (right) for the integrated profiles. The lowest frequency measurement from Effelsberg shows a greater than 1σ deviation from the expected scattering value. This could be an instrumental effect (e.g., baseline variations) or a real increase in scattering, but with a single data point we cannot draw any solid conclusions. The apparent deviation of τ_d at 18.95 GHz likely reflects the finite sampling time of the data, as the dejittered average profile is just two sampling intervals wide.

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A least squares fit of all of the scattering time scales given in Table 1 versus frequency yielded a scattering spectral index of α = −3.8 ± 0.2, which is consistent with the statistical values determined by Bhat et al. (2004) and Löhmer et al. (2001) from ensembles of pulsars (see Section 2). The measurement is also consistent with the standard α = 4.0 value but is inconsistent with the value of α = −4.4 expected for a Kolmogorov spectrum (Lambert & Rickett 1999).

The Gaussian widths of the average pulse profiles for PSR J1745–2900 do show scatter but no clear frequency evolution. Magnetar pulse profiles can vary significantly in time and frequency; XTE J1810-197, arguably the most thoroughly studied radio magnetar, exhibits epochs with significant profile variation across frequency and epochs with little profile variation (Kramer et al. 2007). PSR J1745-2900 may be more stable, but an epoch-to-epoch profile variability analysis was outside the scope of this paper.

PSR J1745-2900 is the first object in the GC with both angular and pulse broadening measurements, which constrains the location of a single thin scattering screen (Cordes & Lazio 1997). The angular size of PSR J1745–2900 measured by Bower et al. (2014), submitted and scaled to 1 GHz is θ_1 GHz = 1075 ± 50 mas. Combined with our measurement of τ_1GHz = 1.3 ± 0.2 s, this places the thin screen at a distance of ≈6 kpc from the GC (see Bower et al. 2014). While it is plausible that an H ii region in a spiral arm along the line of sight could cause strong scattering, it also implies the GC contribution to scattering is negligible. If this is true, then many pulsars should have been detected by previous GC surveys (Kramer et al. 2000; Johnston et al. 2006; Deneva et al. 2009; Macquart et al. 2010; Eatough et al. 2013b).

One possible resolution to this apparent contradiction is that the thin screen scattering model is invalid for sources in the GC. Lazio & Cordes (1998) present a more realistic two-component model with a central spheroid of hot gas and a scattering screen located ∼150 pc from Sgr A*. The NE2001 model (Cordes & Lazio 2002) also describes the GC scattering region as an ellipsoid exponential. The physical origin of the scattering screen is likely ionized outer layers of molecular clouds (Lazio & Cordes 1998; Lazio et al. 1999, and references therein), implying that the scattering material is patchy and more complex than a single thin screen. An analog to GC scattering may be the time-variable scattering of the Crab pulsar due to the complex spatial structure of the Crab nebula, which imparts rapid changes in the scattering time scale (Karuppusamy et al. 2010) and, in extreme cases, anomalous dispersion events (Backer et al. 2000).

Alternatively, the magnetar may be at a larger radial distance from Sgr A* (∼10–100 pc) but viewed through a magnetized filament that causes the high DM and RM but low scattering, but this is unlikely. The filament would need an optimistically strong magnetic field, be oriented along the line of sight, and lie in front of PSR J1745-2900. The probability of such an alignment is low. Furthermore, the angular broadening size of PSR J1745-2900 measured by Bower et al. (2014) is consistent with the angular size of Sgr A*, suggesting they are behind the same scattering screen. If the magnetar is in front of the GC scattering region, then Sgr A* and PSR J1745-2900 would have different scattering sizes. Continued high precision monitoring of the DM and RM of PSR J1745−2900 may show whether the source is moving near or within an extended screen boundary.

An alternative scenario is a real paucity of pulsars in the GC, as suggested earlier by Johnston (1994). Newer results, including the discovery of PSR J1745-2900, contradict this possibility. Based on population and multi-wavelength studies, reviews of the physical conditions, and considerations of the stellar population and indications of their formation history, the number of pulsars expected in the GC is in fact high (Lorimer & Kramer 2005). Wharton et al. (2012) predict as many as 100 canonical pulsars and 1000 millisecond pulsars (MSP) in the interesting central parsec of the GC. Because radio magnetars are a rare class of pulsar (1 in ∼500 radio pulsars), this detection suggests there is a large GC pulsar population. From this population PSR J1745-2900 is precisely the type of pulsar we expect to detect in a strong scattering region through selection effects viz. high luminosity, long period, flat spectrum. If the scattering properties of the PSR J1745-2900 is indicative of the entire GC region, then previous surveys should have detected canonical pulsars. MSPs will not be detectable at low frequencies, even with the small scattering time measured here for the magnetar, but high frequency searches could have had the chance to discover the sources with sufficiently large flux density (Eatough et al. 2013b). Still, no discovery was made before the observations of the magnetar. This apparent contradiction between the low pulse broadening measured for PSR J1745-2900 and the lack of other pulsar detections suggests that the scattering environment in the GC requires a more complicated spatial model than a single thin scattering screen, and hyperstrong scattering still dominates most lines of sight.

As future searches of the GC with more sensitive telescopes (e.g., with the Square Kilometre Array, Atacama Large Millimeter Array) are made, and monitoring of the magnetar continues, the question of whether or how we can find pulsars closely orbiting Sgr A* will eventually be answered.

We observed the magnetar PSR J1745-2900 at radio frequencies ranging from 1.2 to 18.95 GHz. Like other radio-emitting magnetars, the average pulse profile of PSR J1745–2900 is jitter dominated. Using both average pulse profiles and single pulses, we measured the scatter broadening time scale across an order of magnitude in frequency and found τ_1GHz = 1.3 ± 0.2 s and α = −3.8 ± 0.2. The pulse broadening is several orders of magnitude lower than predicted by models Cordes & Lazio (2002) for a pulsar near Sgr A*. If there are truly as many as 100 canonical pulsars in the inner 1 pc around Sgr A*, then previous pulsar surveys should have detected many sources. The lack of previous discoveries implies that scattering in the GC is more spatially complex than current models.

We thank the referee for useful comments that improved the clarity of the paper. The authors would also like to thank Bill Coles and Dominic Schnitzeler for useful discussions. L. G. S. and R. K. gratefully acknowledge financial support by the European Research Council for the ERC Starting Grant BEACON under contract no. 279702. M. K., K. J. L., and C. G. B. gratefully acknowledge support from ERC Advanced Grant "LEAP," Grant Agreement Number 227947 (PI Michael Kramer).