M13G: Binary MSP in Globular Cluster M13

• M13G is a binary millisecond pulsar in globular cluster M13 with a 4.32 ms period and an extremely low-mass companion typical of black widow systems.
• Its phase-connected timing solution over 6.4 years reveals a circular 2.89 hr orbit and parameters affected by cluster gravitational acceleration.
• The discovery employed advanced FFT acceleration and overlapping segmented searches under scintillation-enhanced states to overcome its intrinsic faintness.

J1641+3627G, commonly designated M13G, is a binary millisecond pulsar in the globular cluster M13. It was reported from Five-hundred-meter Aperture Spherical radio Telescope (FAST) observations as one of two binary millisecond pulsars uncovered in a sensitive search of the cluster, and it is the only one of the pair for which a phase-connected timing solution was obtained. The system has a spin period of $4.3235653959122(2)\times 10^{-3}$ s and a $0.1205237188(4)$-day circular orbit with an extremely low-mass companion, placing it in the black widow class (Yin et al., 8 Aug 2025). In earlier Chandra and Hubble Space Telescope studies of M13 millisecond pulsars, M13G was not part of the analyzed sample; those observations were restricted to pulsars A–F, and therefore no source-specific X-ray or optical/UV results were reported for J1641+3627G (Zhao et al., 2021).

1. Discovery in FAST observations

M13G was discovered in a deep FAST search of 84 observations of M13 spanning 2018–2025. The detection occurred during a scintillation-brightened state, with the authors emphasizing that the system would otherwise have remained undetected. The search strategy combined Fast Fourier Transform acceleration searches using PRESTO’s accelsearch, searches on both full-length data and segmented data, a deliberately low candidate threshold of $2\sigma$, and an “overlapping coherent segmented acceleration search” intended to improve sensitivity to compact binaries and intermittent sources (Yin et al., 8 Aug 2025).

For M13G specifically, the first detection came from the longest FAST tracking observation on 2023 November 8. That observation was split into eight 2250 s segments, for a total integration of about 18000 s. In the discovery dataset, the pulsar had a spin period of approximately 4.32 ms and a dispersion measure of $30.75\ {\rm pc\ cm^{-3}}$. Folding the full observation with the preliminary ephemeris covered about 1.7 orbital cycles, and no significant short-timescale scintillation or eclipse was seen in that dataset (Yin et al., 8 Aug 2025).

The discovery paper explicitly states that earlier FFT-based searches missed M13G because it is intrinsically weak and affected by binary motion, so its signal fell below earlier sifting thresholds. Within the local discovery sequence of M13 pulsars, this is significant because it frames M13G not as a bright addition to an already complete census, but as an object whose detectability depends sensitively on search methodology and propagation effects (Yin et al., 8 Aug 2025).

2. Timing solution and measured parameters

The published timing solution for M13G is phase-connected over a 6.4-year baseline, from MJD 58397.302 to 60731.003, and was obtained with TEMPO and Dracula. The fit used the BT binary model, 249 times of arrival, the Solar system ephemeris DE438, the time standard UTC(NIST), and time units TDB. The reference epoch is MJD 6(0256.22853)8, and the RMS residual is $24.27\ \mu{\rm s}$ (Yin et al., 8 Aug 2025).

Astrometrically, the pulsar is located at right ascension $16{:}41{:}42.9541(1)$ and declination $+36{:}29{:}21.717(2)$ in J2000 coordinates. Its measured spin frequency is $231.29059200665(1)\ {\rm s^{-1}}$, with $\dot f = 3.548(2)\times 10^{-16}\ {\rm s^{-2}}$. The corresponding spin period is $4.3235653959122(2)\times 10^{-3}$ s, and the observed spin-period derivative is $0.1205237188(4)$0 (Yin et al., 8 Aug 2025).

Quantity	Value
Right Ascension (J2000)	$0.1205237188(4)$1
Declination (J2000)	$0.1205237188(4)$2
Spin frequency $0.1205237188(4)$3	$0.1205237188(4)$4
Spin frequency derivative $0.1205237188(4)$5	$0.1205237188(4)$6
Spin period $0.1205237188(4)$7	$0.1205237188(4)$8
Spin-period derivative $0.1205237188(4)$9	$2\sigma$0
Number of TOAs	249
RMS residual	$2\sigma$1

The negative observed $2\sigma$2 is interpreted not as intrinsic spin-up, but as the effect of cluster gravitational acceleration. This interpretation is central to the system’s physical reading, because it means the measured secular period evolution is dominated by the line-of-sight dynamical environment of M13 rather than by the intrinsic torque of the recycled neutron star (Yin et al., 8 Aug 2025).

3. Orbital architecture and black widow classification

The orbital solution gives a projected semi-major axis of $2\sigma$3 lt-s and an orbital period of $2\sigma$4 days, equivalent to approximately 2.89 hr. The eccentricity is fixed to $2\sigma$5, the longitude of periastron is fixed to $2\sigma$6, and the epoch of periastron passage is $2\sigma$7 (Yin et al., 8 Aug 2025).

The companion constraints were derived from the standard binary mass function,

$2\sigma$8

using an assumed pulsar mass of $2\sigma$9. For M13G, the reported mass function is $30.75\ {\rm pc\ cm^{-3}}$0, the minimum companion mass for $30.75\ {\rm pc\ cm^{-3}}$1 is $30.75\ {\rm pc\ cm^{-3}}$2, and the median companion mass for $30.75\ {\rm pc\ cm^{-3}}$3 is $30.75\ {\rm pc\ cm^{-3}}$4 (Yin et al., 8 Aug 2025).

These values are the basis for the source’s classification as a black widow system. The discovery paper’s reasoning is explicit: the companion is of very low mass, the orbital period is very short, the orbit is compact and circular, and the companion mass is small enough to resemble the evaporated or ablated companions typical of black widows. In this sense, M13G is not merely a generic binary millisecond pulsar in a globular cluster, but a member of the “spider” population with parameters at the extreme low-companion-mass end (Yin et al., 8 Aug 2025).

The system is also notable for the absence of detected eclipse events. The paper interprets this absence as consistent with the low mass function and a likely low-inclination, more face-on geometry. It further notes that spider binaries with higher inclination angles typically show eclipses and larger mass functions, so the non-eclipsing behavior of M13G is treated as supporting, rather than contradicting, the inferred geometry (Yin et al., 8 Aug 2025).

4. Cluster location and dynamical constraints

Within M13, M13G lies relatively far from the cluster center. The reported offsets are $30.75\ {\rm pc\ cm^{-3}}$5 arcmin in right ascension and $30.75\ {\rm pc\ cm^{-3}}$6 arcmin in declination, corresponding to a total angular offset of 1.8034 arcmin. This translates to a projected distance from the globular-cluster center of 2.9087 pc, or 3.2314 core radii (Yin et al., 8 Aug 2025).

The discovery paper notes that this is the second-largest projected angular offset among known M13 pulsars. It also places the pulsar beyond the cluster half-light radius and outside the usual FAST central-beam sweet spot. A plausible implication is that the system’s sky location contributes to its intermittent detectability, since off-axis attenuation compounds the intrinsic faintness and scintillation dependence already emphasized by the timing study (Yin et al., 8 Aug 2025).

The observed negative $30.75\ {\rm pc\ cm^{-3}}$7 is analyzed in the context of the cluster’s and the Galaxy’s gravitational fields. The paper quotes an independent acceleration upper limit from the observed $30.75\ {\rm pc\ cm^{-3}}$8 of $30.75\ {\rm pc\ cm^{-3}}$9. It also constrains the intrinsic spin-period derivative to $24.27\ \mu{\rm s}$0, yielding a derived surface magnetic field $24.27\ \mu{\rm s}$1 and a characteristic age $24.27\ \mu{\rm s}$2 (Yin et al., 8 Aug 2025).

The paper explicitly remarks that the characteristic age exceeds the cluster age, and therefore these derived quantities are not very tightly constrained. In standard pulsar-population terms, this is a familiar consequence of using an observed $24.27\ \mu{\rm s}$3 that is heavily contaminated by external acceleration, but in M13G the effect is especially visible because the measured $24.27\ \mu{\rm s}$4 is negative (Yin et al., 8 Aug 2025).

5. Scintillation, flux variability, and detectability

M13G is presented as a case study in how interstellar scintillation can intermittently reveal otherwise hidden pulsars in globular clusters. Its flux density varies strongly across epochs, with an estimated range from $24.27\ \mu{\rm s}$5 to $24.27\ \mu{\rm s}$6 and a median of $24.27\ \mu{\rm s}$7. The pulsar was found during a scintillation-enhanced state, and this is used to explain why it was missed in some earlier searches and epochs (Yin et al., 8 Aug 2025).

This detectability problem is not attributed to scintillation alone. The FAST analysis links three effects: intrinsic weakness, compact-binary acceleration, and variable propagation gain from scintillation. The combined effect is that a source can remain below conventional search thresholds for long intervals and then become detectable only in favorable orbital and propagation states. That framework is consistent with the specific details of the discovery observation, in which segmented acceleration searches recovered a pulsar whose full-length signal would otherwise have been diluted by orbital motion (Yin et al., 8 Aug 2025).

The broader inference drawn in the paper is that additional M13 pulsars may remain undiscovered because they are intrinsically faint, reside in compact binaries with large accelerations, and are only occasionally brightened enough by scintillation for detection. The authors therefore argue that more sensitive or more sophisticated search methods could still uncover additional M13 pulsars. M13G functions as a concrete demonstration of that incompleteness argument rather than merely as an isolated discovery (Yin et al., 8 Aug 2025).

6. Multiwavelength status and nomenclatural ambiguities

The 2021 Chandra and HST study of M13 millisecond pulsars did not analyze M13G. That paper states that six known MSPs in M13 were known at the time and lists A, C, E, B, D, and F; its focus is explicitly on those six. By omission, no Chandra counterpart is reported for M13G, no HST optical/UV counterpart is reported for M13G, and no astrometric match, offset, count rate, flux, luminosity, spectral fit parameters, orbital constraints, or companion constraints are given for J1641+3627G in that work (Zhao et al., 2021).

This absence is chronologically informative. The Chandra/HST paper detected five of the six pulsars it studied, with A only marginally detected and quoted as an upper limit, and found optical/UV counterparts only for D and F. None of those conclusions can be assigned to M13G, because M13G was not part of that sample (Zhao et al., 2021). For multiwavelength catalog work, this is an important corrective: the literature does not yet provide source-specific X-ray or HST counterpart information for M13G in the same way it does for several earlier M13 pulsars.

A separate ambiguity appears in the supplied corpus through the claim that “J1641+3627G (M13G)” is the same object as Garro01 / VVVX-GC-140900-653712, a newly discovered low-luminosity globular cluster at $24.27\ \mu{\rm s}$8 with $24.27\ \mu{\rm s}$9 kpc and $16{:}41{:}42.9541(1)$0 (Garro et al., 2020). However, the FAST timing paper uses J1641+3627G (M13G) for a millisecond pulsar in M13 at $16{:}41{:}42.9541(1)$1 (Yin et al., 8 Aug 2025). This suggests a nomenclatural conflation in the provided material rather than a single astrophysical source. In the pulsar literature on M13, the designation M13G refers to the FAST-discovered binary millisecond pulsar.