# Likely detection of $\gamma$-ray pulsations of PSR J1717$+$4308A in NGC 6341
and implication of the $\gamma$-ray millisecond pulsars in globular clusters

Pengfei Zhang  Department of Astronomy, School of Physics and Astronomy, Key
Laboratory of Astroparticle Physics of Yunnan Province, Yunnan University,
Kunming 650091, People’s Republic of China<EMAIL_ADDRESS><EMAIL_ADDRESS>Yi Xing Key Laboratory for Research in Galaxies and
Cosmology, Shanghai Astronomical Observatory, Chinese Academy of Sciences, 80
Nandan Road, Shanghai 200030, People’s Republic of China  Zhongxiang Wang
Department of Astronomy, School of Physics and Astronomy, Key Laboratory of
Astroparticle Physics of Yunnan Province, Yunnan University, Kunming 650091,
People’s Republic of China<EMAIL_ADDRESS><EMAIL_ADDRESS>Key
Laboratory for Research in Galaxies and Cosmology, Shanghai Astronomical
Observatory, Chinese Academy of Sciences, 80 Nandan Road, Shanghai 200030,
People’s Republic of China  Wei Wu  Department of Astronomy, School of Physics
and Astronomy, Key Laboratory of Astroparticle Physics of Yunnan Province,
Yunnan University, Kunming 650091, People’s Republic of China;
<EMAIL_ADDRESS><EMAIL_ADDRESS>Zhangyi Chen  Department of
Astronomy, School of Physics and Astronomy, Key Laboratory of Astroparticle
Physics of Yunnan Province, Yunnan University, Kunming 650091, People’s
Republic of China<EMAIL_ADDRESS><EMAIL_ADDRESS>
###### Abstract

We report our analysis results for the globular cluster (GC) NGC 6341 (M92),
as a millisecond pulsar (MSP) J1717$+$4308A has recently been reported found
in this GC. The data used are from the Large Area Telescope onboard the Fermi
Gamma-ray Space Telescope (Fermi). We detect $\gamma$-ray pulsations of the
MSP at a $4.4\sigma$ confidence level (the corresponding weighted H-test value
is $\sim$28.4). This MSP, the fourth $\gamma$-ray pulsar found in a GC, does
not have significant off-pulse emission and has $\gamma$-ray luminosity and
efficiency $1.3\times 10^{34}$ erg s-1 and 1.7% respectively. In order to have
a clear view on the properties of the known GC $\gamma$-ray MSPs, we re-
analyze the Fermi LAT data for the other three ones. These four MSPs share the
properties of either having high $\dot{E}$ ($\sim 10^{36}$ erg s-1) or being
in the GCs that contain only limited numbers of known MSPs. In addition, we
find that PSRs J1823$-$3021A and B1821$-$24, in NGC 6624 and NGC 6626
respectively, have detectable off-pulse $\gamma$-ray emission and PSR
J1835$-$3259B in NGC 6652 does not. Using the obtained off-pulse spectra or
spectral upper limits, we constrain the numbers of other MSPs in the four GCs.
The results are consistent with the numbers of the radio pulsars reported in
them. While at least in NGC 6624 and NGC 6626, the contribution of other MSPs
to their observed $\gamma$-ray emission can not be ignored, our study
indicates that the presence of a bright MSP could be the dominant factor for
whether a GC is detectable at $\gamma$-rays or not.

Gamma-rays(637); Globular star clusters(656); Pulsars (1306)

##  1 Introduction

Thanks to the successful launch of the Large Area Telescope (LAT) onboard the
Fermi Gamma-ray Space Telescope (Fermi; Atwood et al., 2009), it has been
found that the Galactic globular clusters (GCs) can have significant
$\gamma$-ray emissions. The GC 47 Tucanae was the first one reported with the
$\gamma$-ray emission (Abdo et al., 2009), then followed with Terzan 5 (Kong
et al., 2010). Up to now, $\gamma$-ray emissions from approximately 35 GCs
have been reported (Tam et al., 2011; Eger & Domainko, 2012; Zhou et al.,
2015; Zhang et al., 2016; Tam et al., 2016; Abdollahi et al., 2020; Song et
al., 2021; Wu et al., 2022; Yuan et al., 2022b; Fermi-LAT collaboration et
al., 2022). It is generally recognized that millisecond pulsars (MSPs)
contained in the GCs are the sources of the emissions, which is supported by
the facts that there are 257 MSPs (spin period $P\leq 30$ ms) found in 36 GCs
(based on the GC pulsar table111https://naic.edu/$\sim$pfreire/GCpsr.html) and
$\gamma$-ray pulsations of three of them have been detected in the LAT data.

Figure 1: TS maps of a $3^{\circ}\times 3^{\circ}$ region centered at 4FGL
J1716.8$+$4310 in 0.1–500 GeV, where the left was based on 4FGL-DR3, showing a
$\gamma$-ray source located south-east of the center, and the right was
calculated when the new source was considered and removed (while 4FGL
J1716.8$+$4310 was kept). The position of the new source and its $3\sigma$
uncertainty are marked by the green plus and circle respectively, and the
white dashed circle indicates the tidal radius of NGC 6341. The pixel scale of
the both TS maps is $0\fdg 1$ pixel-1.

The first reported $\gamma$-ray–pulsations case was PSR J1823$-$3021A in NGC
6624, which had a significance of $\sim 7\sigma$ (Freire et al., 2011). Then
in NGC 6626 (M28), significances of $\sim 4.3\sigma$ and $5.4\sigma$
$\gamma$-ray pulsations were respectively reported for PSR B1821$-$24 by Wu et
al. (2013) and Johnson et al. (2013). Very recently, Zhang, Xing, & Wang
(2022) reported the detection of $\gamma$-ray pulsations (at a $5.4\sigma$
significance level) of a newly discovered MSP J1835$-$3259B in NGC 6652
(Gautam et al., 2022). The properties of these three MSPs are summarized in
Table 1. They share the similarities of having relatively high spin-down
energies $\dot{E}$, their $\gamma$-ray luminosities being among the brightest
ones of all known $\gamma$-ray MSPs (Zhang et al., 2022), and they probably
contribute a dominant fraction to the $\gamma$-ray emission of each of the
respective host GCs.

More such $\gamma$-ray MSPs may be found in GCs, provided accurate radio
ephemerides are available. We note that Pan et al. (2020) reported the
discovery of PSR J1717$+$4308A in the GC NGC 6341 (M92) from the observations
with the Five-hundred-meter Aperture Spherical radio Telescope (FAST). The
MSP, having $P=3.16$ ms, is in an eclipsing binary system with $\sim$0.2-d
orbital period. While this MSP is the only pulsar thus-far found in the GC,
the $\gamma$-ray emission from the GC has been detected and in the Data
Release 3 (DR3) of the fourth _Fermi_ -LAT source catalog (4FGL-DR3; Fermi-LAT
collaboration et al. 2022), the $\gamma$-ray source is named 4FGL
J1716.8$+$4310\. Given these and the detailed ephemeris available for PSR
J1717$+$4308A (Pan et al., 2020, 2021), we have carried out analysis of the
Fermi-LAT data for finding the $\gamma$-ray pulsations of the MSP. We report
the result, a $4.4\sigma$ significance detection of the $\gamma$-ray
pulsations, in this paper.

Table 1: Properties of GC MSPs with $\gamma$-ray pulsations detected

Name | $P$ | $\dot{P}/10^{-20}$ | $\dot{E}/10^{34}$ | $L_{\gamma}/10^{34}$
---|---|---|---|---
| (ms) | (s s-1) | (erg s-1) | (erg s-1)
J1823$-$3021A | 5.44 | 338 | 83 | $7.0\pm 1.8^{\rm a}$
B1821$-$24 | 3.05 | 161 | 220 | 4.0$\pm 1.0^{\rm b}$
J1835$-$3259B | 1.83 | 6.65 | 43 | $5.04\pm 0.44^{\rm c}$
J1717$+$4308A | 3.16 | 6.11 | 7.7 | $1.30\pm 0.17$

Notes. References for $L_{\gamma}$: a Abdo et al. (2013), b Johnson et al.
(2013), and c Zhang et al. (2022).

In addition, considering that $\gamma$-ray emissions of the GCs arise from
their MSPs, the high-energy studies provide a probe into the population of
MSPs in the GCs besides the regular radio compaigns. The numbers of the MSPs
in the GCs have been estimated by comparing the isotropic $\gamma$-ray
luminosity of a GC with the average $\gamma$-ray luminosity of the MSPs (Abdo
et al., 2009, 2010a; Hui et al., 2011; Lloyd et al., 2018; de Menezes et al.,
2019; Zhang et al., 2020; Song et al., 2021). Recently, Wu et al. (2022) have
added the $\gamma$-ray spectral information of the MSPs into the estimation,
which presumably have provided better constraints on the numbers of MSPs in
more than 20 GCs. The numbers estimated in this latter work indicate that for
approximately 10 GCs, only one MSP may be required in them to explain the
observed $\gamma$-ray emissions. Combined with the likely dominant
contributions of the detected three GC MSPs to the $\gamma$-ray emissions of
their respective host GCs (Freire et al., 2011; Wu et al., 2013; Johnson et
al., 2013; Zhang et al., 2022), an interesting question may be raised as if
the $\gamma$-ray emissions of most GCs are similarly due to the presence of
one bright $\gamma$-ray MSP (i.e., not reflecting the MSP numbers). This
possibility may explain why some of GCs, while with high encounter rates, do
not have detectable $\gamma$-ray emissions (e.g., see Wu et al. 2022); it
would be rather because they do not contain one sufficiently bright MSP. To
investigate this possibility, we also conducted time analysis of the LAT data
for the three known GC $\gamma$-ray MSPs. For each of them, the off-pulse
emission was obtained, so as to set a constraint on the number of other MSPs
in each of the host GCs (see, e.g., Johnson et al. 2013). This part of
analysis and the results are also reported in this paper.

Below we first describe the data analysis for PSR J1717$+$4308A in NGC 6341
(M92) and report the results in Section 2. We describe the analysis for the
three GCs that contain a known $\gamma$-ray MSP and present the results in
Section 3. In Section 4, we discuss the results and implications for MSPs in
GCs and provide a summary.

Table 2: Likelihood analysis results for NGC 6341

Model | Parameter values |
---|---|---
LP | $\alpha$ | $\beta$ |  $E_{b}$ (GeV) | TS
| 2.03(31)∗ | 0.45(24)∗ | 1.17∗ | –
| 1.88(13) | 0.71(11) | 1.17(16) | 63.7
PLEC | $\Gamma$ | $b^{\dagger}$ |  $E_{c}$ (GeV) |
| 1.88(17) | 0.67 | 3.00(52) | 63.9

∗Parameter values of the LP model given in 4FGL-DR3, among which $E_{b}$ does
not have an uncertainty. † Value was fixed at 2/3 in our analysis.

##  2 Data analysis and results for PSR J1717$+$4308A

###  2.1 LAT data selection and best-fit model

We selected 14 year _Fermi_ -LAT Pass 8 _Front+Back_ events (evclass = 128 and
evtype = 3) in a time range of from 2008 August 4 16:29:16.8 (MJD 54682.69) to
2022 September 25 22:22:29.0 (MJD 59847.93) in the energy range of 0.1–500
GeV. The region of interest (RoI) was $20^{\circ}\times 20^{\circ}$ with the
center at the position of 4FGL J1716.8$+$4310 (R. A. = $\rm
17^{h}16^{m}48^{s}.79$, Decl. = $+43^{\circ}10^{\prime}22\farcs 78$). The
events with zenith angles $<90^{\circ}$ were kept to avoid the limb
contamination from the Earth. We used the expression of “DATA_QUAL $>$ 0 &&
LAT_CONFIG == 1” to filter out the events with quality flags of “bad” and to
save high-quality events in the good time intervals. The instrument response
function of “P8R3_SOURCE_V3” and the software package of Fermitools–2.0.19
were used in the analysis.

Based on 4FGL-DR3, we constructed a model file using the script
make4FGLxml.py222https://fermi.gsfc.nasa.gov/ssc/data/analysis/user/. The
model file contained the spectral forms of the catalog sources around 4FGL
J1716.8$+$4310 and the respective parameters. All spectral parameters of the
sources within $5^{\circ}$ of the target were set free, and for the sources
within $5^{\circ}-10^{\circ}$ of the target and those $10^{\circ}$ outside but
identified as variables, their normalization parameters were set free. In
addition, the normalizations of the two diffuse emission components (Galactic
and extragalactic) were also set free. All other parameters of the sources in
the RoI were fixed at the values provided in 4FGL-DR3. The target is described
with a log-parabola (LP) model,
$dN/dE=N_{0}(E/E_{b})^{-[\alpha+\beta\log(E/E_{b})]}$, in 4FGL-DR3. The
catalog parameter values are given in Table 5.

Figure 2: $\gamma$-ray spectrum in 0.1–500 GeV obtained for 4FGL
J1716.8$+$4310\. The best-fit LP and PLEC model spectra are shown as the
yellow dashed and black solid lines respectively.

The binned maximum likelihood analysis was performed to the whole data. In the
results we found a new $\gamma$-ray source that was not previously reported or
listed in the Fermi-LAT catalogs. As shown in the Test Statistic (TS) map
(Figure 1) we calculated for the source region, this source is located south-
east of the target and had a TS value of $\sim$40\. Using tool _gtfindsrc_ ,
its position was determined to be R. A. = 17h18m29s.79, Decl. = +42∘38′37′′.38
(J2000.0). We added a point source with a spectral form of power-law (PL),
$dN/dE=N_{0}(E/E_{0})^{-\Gamma}$, at its position in our model file.
Performing the likelihood analysis again, the source could be well fitted and
removed in the TS map (Figure 1). Detailed analyses and results for this new
source will be reported elsewhere (Zhang et al. in preparation). The best-fit
parameter values for 4FGL J1716.8$+$4310, after adding the new source in our
model file, are given in Table 5. Comparing them with the catalog values,
there are small differences but within the uncertainties.

Figure 3: Timing analysis results for PSR J1717$+$4308A in 0.1-500 GeV. Panel
A: weighted $\gamma$-ray pulse profile. The on-pulse phase ranges, $\rm
P_{on_{1}}$ and $\rm P_{on_{2}}$, and off-pulse range $\rm P_{off}$ are marked
as pink, green, and blue shaded regions respectively. The background counts is
shown as the pink dash-dotted line. Panel B: two-dimensional phaseogram, where
the color bar indicates the probabilities of $\gamma$-ray photons originating
from NGC 6341 (the largest probability value is 85.6%). Panel C: weighted
cumulative H-test curve over the whole time period of the Fermi-LAT data.
Panel D: schematic radio pulse profile of PSR J1717$+$4308A drawn based on
that reported in Pan et al. (2020) for comparison.

As the emission should have an MSP origin, we also considered the typical
pulsar model, a PL with an exponential cutoff (PLEC; Abdo et al. 2013),
$dN/dE=N_{0}(E/E_{0})^{-\Gamma}\exp[-(E/E_{c})^{b}]$. Replacing with this PLEC
in our model file for 4FGL J1716.8$+$4310, the binned likelihood analysis was
performed, in which the parameter $b$ was fixed at 2/3 (Abdo et al., 2013).
The resulting best-fit parameters are given in Table 5. The TS value from this
PLEC model is nearly equal to that from the LP model, and thus this model can
also be used for the emission of the source. The average photon flux obtained
was $2.43\pm 0.31\times 10^{-9}$ photon cm-2 s-1 in 0.1$-$500 GeV, giving an
integrated energy flux of $\rm 1.51\pm 0.19\times
10^{-12}~{}erg~{}cm^{-2}~{}s^{-1}$. Using a distance of 8.50$\pm 0.07$ kpc for
NGC
6341333https://people.smp.uq.edu.au/HolgerBaumgardt/globular/fits/ngc6341.html,
the $\gamma$-ray luminosity $L_{\gamma}\simeq 1.30\pm 0.17\times 10^{34}$ erg
s-1 (assuming isotropic emission).

###  2.2 Spectrum extraction

We extracted a spectrum of 4FGL J1716.8$+$4310 from the whole LAT data. The
energy range of 0.1–500 GeV was divided into 12 equal logarithmically spaced
energy bins, and the likelihood analysis was performed to the data of each
bins. In this analysis, only the normalizations of the sources within 5∘ of
the target, which included the new nearby source we have found, were set as
free parameters, while all other parameters were fixed at their values
obtained in the above likelihood analysis. The obtained spectrum is shown in
Figure 2, for which we kept the spectral data points that have their values 2
times greater than their uncertainties and otherwise showed 95% flux upper
limits. Comparing the best-fit LP and PLEC model to the spectrum, the latter
model appears to be able to fit the spectrum as well. Given this and the
nearly equal TS values from the two models, we adopted the PLEC model in the
following data analysis.

Figure 4: TS maps in 0.1–500 GeV calculated from the data in two on-pulse
(left and middle panels) and one off-pulse (right panel) phase ranges. The
tidal radius region of NGC 6341 is marked as the white dashed circle, and the
new $\gamma$-ray source is also indicated as that in Figure 1. The pixel scale
of the TS maps is 0$\fdg$1 pixel-1.

###  2.3 Timing Analysis

Since the $\gamma$-ray emission from NGC 6341 is weak (TS$\simeq$64) and there
are nearby sources with comparable brightnesses, we followed Abdo et al.
(2010b) and selected the events within an aperture radius of
$max[6.68-1.76\log_{10}(E_{MeV}),1.3]^{\circ}\simeq 3\fdg 16$ in 0.1-500 GeV
so as to maximize the signal-to-noise ratio. The selected $\gamma$-ray photons
were assigned with the weights, which were the probabilities of originating
from NGC 6341 given by tool _gtsrcprob_. The weighted photons were then phase-
folded using the ephemeris for PSR J1717+4308A provided in Pan et al. (2020,
2021) by employing Tempo2 (Hobbs et al., 2006) with _Fermi_ plug-in (Ray et
al., 2011). The folded pulse profile in 16 phase bins is shown in Panel A of
Figure 3, for which the counts and uncertainties of the phase bins were
calculated using the method described in Abdo et al. (2013). The two-
dimensional phaseogram is shown in Panel B of Figures 3, and the largest
probability value of the photons was 85.6%.

Following the method described by Kerr (2011), H-test statistic was calculated
using the probabilities as the weights. The curve of the cumulative H-test
value over the whole Fermi-LAT data time period is shown in Panel C of Figure
3. The maximum H-test value was $\sim$28.4, corresponding to a $p$-value of
$1.17\times 10^{-5}$ ($\simeq 4.4\sigma$). It can be noted that the H-test
curve is flat and close to zero before year 2014\. We suspect that since the
ephemeris for the MSP was derived from the FAST observations conducted from
2017 October and the MSP is in a redback binary (Pan et al., 2020), the type
showing high and random orbital variability (see, e.g., Ridolfi et al. 2016),
the phases of the photons before year 2014 could not be accurately given.

###  2.4 Phase-resolved Analysis

Given the folded pulse profile, we divided it into the on-pulse and off-pulse
regions. For the former, two peak phase regions, $P_{\rm on_{1}}$ and $P_{\rm
on_{2}}$, were chosen as in phase ranges of 0.62–0.88 and 1.00–1.12
respectively. The latter, $P_{\rm off}$, was chosen in a phase range of
0.44–0.62. The likelihood analysis was performed to the data in the three
phase ranges respectively, in which the PLEC model was used. In $\rm
P_{on_{1}}$, the resulting parameters were $\Gamma=2.05\pm 0.28$ and
$E_{c}=3.00\pm 0.66$ ($b=0.67$ was fixed), consistent with those from the
whole data (Table 5); the photon flux was $6.6\pm 1.3\times 10^{-9}$ photon
cm-2 s-1 with a TS value of $\sim$49\. In $\rm P_{on_{2}}$, the TS value was
only $\sim$25 (the photon flux was $4.6\pm 1.4\times 10^{-9}$ photon cm-2
s-1), and in $\rm P_{off}$, TS$\sim$1 was obtained. The nearly zero TS value
in $\rm P_{off}$ is expected as the counts in the phase bins are close to the
background value (=32.8; cf., Figure 3); the latter was estimated from diffuse
sources and neighbor point sources following Abdo et al. (2013).

We calculated the corresponding TS maps for the three phase intervals, which
are shown in Figure 4. The TS maps support the timing analysis results. A
simple direct comparison is that while the phase intervals of $\rm P_{on_{2}}$
and $\rm P_{off}$ are 0.12 and 0.18, the TS values are 25 and 1 respectively.
The $\gamma$-ray emission from NGC 6341 thus seems to originate, within
current measurement precision, exclusively from PSR J1717+4308A. In the future
as more data are collected, which improves the sensitivity, it would become
clear if there is significant off-pulse emission from this GC (see the case of
NGC 6624 below in Section 3.2).

##  3 Data analysis for three known GC $\gamma$-ray MSPs

In order to separate a known pulsar’s emission from that of the host GC, we
carried out the similar data analysis for NGC 6624 and NGC 6626 as for NGC
6341. The analysis results for NGC 6652 were taken from that reported in Zhang
et al. (2022).

Figure 5: Pulse profiles and two-dimensional phaseograms obtained for PSRs
J1823$-$3021A (left) and B1821$-$24 (right) respectively. Based on the pulse
profiles, the on-pulse ($\rm P_{on}$) and off-pulse ($\rm P_{off}$) phase
ranges are defined.

For each of the two target GCs, the LAT data of similar time periods in the
same energy range (0.1–500 GeV) were selected. Likelihood analysis was
performed to the whole data to determine the best-fit parameters, in which a
PLEC model was used. We then updated the model files for each of them.

###  3.1 Timing Analysis

To construct the pulse profiles of PSRs J1823$-$3021A (Biggs et al., 1994) and
B1821$-$24 (Lyne et al. 1987; in NGC 6624 and NGC 6626 respectively), we
selected photons within an aperture radius of 6∘ centered at each of the
positions given in Fermi-LAT collaboration et al. (2022). The ephemerides of
the two MSPs are provided by the Fermi Science Support
Center444https://fermi.gsfc.nasa.gov/ssc/data/access/lat/ephems/. The weights
of the photons were the probabilities of originating from a target calculated
using tool _gtsrcprob_ , and the pulse phases of them were assigned by
employing Tempo2 with the Fermi plug-in. Given the $\sim$14-yr long time
period of the data, the ephemerides were updated from running Tempo2 by us.
The resulting folded pulse profiles and two-dimensional phaseograms for PSRs
J1823$-$3021A and B1821$-$24 are shown in Figure 5. The weighted H-test values
were $\sim$1240 and $\sim$213 for J1823$-$3021A and B1821$-$24 respectively.

###  3.2 Phase-resolved analysis

Based on the pulse profiles we obtained, which are very similar to those shown
in Freire et al. (2011) and Johnson et al. (2013), we defined the on-pulse
($\rm P_{on}$) and off-pulse ($\rm P_{off}$) phase ranges: $\rm
P_{on}\simeq$0.56–1.13 and 0.94–1.63, $\rm P_{off}\simeq$0.13–0.56 and
0.63–0.94 respectively for the MSPs in NGC 6624 and NGC 6626. Binned
likelihood analysis was performed to the data sets respectively, where the
PLEC model was used. The results are given in Table 3. Significant off-pulse
emissions from each of the GCs were detected, while we note that in the
initial discovery of $\gamma$-ray pulsations of PSR J1823$-$3021A that used
2-yr Fermi LAT data, no off-pulse emission was detected from NGC 6624.

Table 3: Pulse-phase resolved analysis results for NGC 6624 and NGC 6626

GC | $F_{\gamma}/10^{-11}$ | $L_{\gamma}/10^{34}$ | $\Gamma$ | $E_{c}$
---|---|---|---|---
| (erg cm-2 s-1) | (egr s-1) |  | (GeV)
NGC 6624 |  |  |  |
$\rm P_{on}$ | 2.2(0.3) | 16.8(3.0) | 1.9(0.4) | 3.0(0.3)
$\rm P_{off}$ | 0.5(0.1) | 4.2(0.9) | 1.5(0.2) | 3.0(0.1)
NGC 6626 |  |  |  |
$\rm P_{on}$ | 2.6(0.2) | 9.0(0.7) | 1.4(0.1) | 1.0(0.2)
$\rm P_{off}$ | 1.1(0.4) | 3.8(1.4) | 1.4(0.5) | 1.3(1.1)

Notes. NGC 6624 at $8.02\pm 0.11$ kpc and NGC 6626 at $5.37\pm 0.10$ kpc
(Baumgardt & Vasiliev, 2021) are used.

Figure 6: TS maps in 0.1–500 GeV calculated from the off-pulse phase ranges
for NGC 6624 (PSR J1823$-$3021A; left), NGC 6626 (PSR B1821$-$24; middle), and
NGC 6652 (PSR J1835$-$3259B; right). In each panel, the center and the region
of the tidal radius for the GC are marked by the green plus and dashed circle
respectively. The pixel scale of the maps is 0$\fdg$1 pixel-1. For the off-
pulse emission of NGC 6626, its position and 2$\sigma$ uncertainty are marked
by the black cross and dash-dotted circle respectively.

Figure 7: $\gamma$-ray spectra in 0.1–500 GeV obtained for NGC 6624 (left
panel) and NGC 6626 (right panel) and those during the on-pulse phase range of
PSRs J1823$-$3021A and B1821$-$24 respectively. In each panel, the best-fit
PLEC model spectra are shown as the gray dashed and blue solid lines
respectively.

We calculated the 0.1–500 GeV TS maps to examine the appearances of the off-
pulse emissions, which are shown in Figure 6. Within NGC 6624, TS$\sim$50
emission is present, while there is also some residual emission (TS$\sim$30)
north-east of the GC. The best-fit parameters determined for the off-pulse
emission are consistent with those obtained for the on-pulse one, although
with large uncertainties. As already illustrated by Johnson et al. (2013) in
their analysis for NGC 6626, we also found off-pulse emission similarly
appearing off the GC (Figure 6). Using tool _gtfindsrc_ , we determined its
position: R. A. = 18h25m07s.0, Decl. = $-$24∘46′05′′.9 (J2000.0), with a
2$\sigma$ uncertainty of 0$\fdg$11\. This position, consistent with that
obtained by Johnson et al. (2013) within the uncertainties, is $\sim$0$\fdg$11
away from the center of NGC 6626 while within the GC’s tidal radius. Johnson
et al. (2013) discussed the possible origin for the emission. Since our
purpose is to constrain the number of other MSPs in the GC, we performed the
binned likelihood analysis to the off-pulse data with the position used. The
results (where TS$\simeq 139$) are given in Table 3, and it can be noted that
the cutoff energy $E_{c}$ was poorly constrained. We tested to use a PL model
in the analysis, and obtained a TS value of $\simeq$132 (photon index
$\Gamma\simeq 2.35\pm 0.08$). Comparing the results from the PLEC and PL
model, the spectral curvature of the emission had a significance of only
$\sim$2.6$\sigma$. In any case given our study purpose and the source spectrum
(below we extracted), we adopted the results from the PLEC model.

Figure 8: Left panels: off-pulse $\gamma$-ray spectra of PSR J1823$-$3021A
(upper) and B1821$-$24 (lower). The best-fit models, which take the number of
MSPs into account, are shown as red curves. In the lower panel, an example is
shown when the addition of one more MSP causes the model spectrum (blue dashed
curve) greater than an upper-limit data point. Right panels: $\chi^{2}$ values
from 1000 runs of spectral fitting, among which the 5% smallest values are
marked as golden data points. The 5% limits (black lines) give a range of 1–5
and 1–6 respectively for the numbers of MSPs in NGC 6624 (upper) and NGC 6626
(lower).

Pulse-phase resolved analysis for the emission of NGC 6652 was conducted by
Zhang et al. (2022), and in a small off-pulse phase range they defined, no
emission was detected (TS$\simeq$1). Using the results, we calculated a TS map
in 0.1–500 GeV and include it in Figure 6. The TS map confirms the non-
detection of any emission in the off-pulse phase range.

We extracted spectra of NGC 6624 and NGC 6626 from the whole data and those
from the data in the on-pulse and off-pulse phase ranges of PSRs J1823$-$3021A
and B1821$-$24 respectively. For NGC 6652, we obtained its spectral upper
limits in the off-pulse phase range. The energy range of 0.1–500 GeV was
divided into 12 equal logarithmically spaced energy bins. The maximum
likelihood analysis was performed to the data in each energy bin. The obtained
spectra of NGC 6624 and NGC 6626, as well as the on-pulse ones, are shown in
Figure 7, and those off-pulse ones of NGC 6624 and NGC 6626 and spectral upper
limits of NGC 6652 are shown in Figures 8 & 9. For the spectra, we only kept
the flux data points with TS$\geq$4, and the otherwise upper limits were at a
95% confidence level.

Figure 9: Constraints on the numbers of MSPs in NGC 6652 (left) and NGC 6341
(right) from their spectral upper limits. The blue dashed line in each panel
shows an example when the model spectrum is greater than some upper-limit data
points; the constraints on the numbers of MSPs are thus obtained.

##  4 Discussion and Summary

###  4.1 PSR J1717$+$4308A in the GC NGC 6341

Given the discovery and timing results for the MSP J1717$+$4308A in the GC NGC
6341 reported by Pan et al. (2020, 2021), we have conducted detailed analysis
of the _Fermi_ -LAT data. A new $\gamma$-ray source close to the GC has been
found. With this new source included in our analysis, we have studied the
emission of the GC and found that it can be fitted with the PLEC model, one
typically used for describing pulsars’ emission. A $4.4\sigma$ pulsational
signal has been detected at PSR J1717$+$4308’s spin period, although the
H-test curve indicates that the early data before approximately year 2014 did
not contribute to the significance of the signal. This problem is likely
caused by that the ephemeris of the MSP has been established in recent radio
observations. When more Fermi-LAT data are collected in the near future, the
significance would be expected to increase accordingly and the detection of
the pulsational signal will be more highly confirmed.

Based on the pulse profile of the MSP we have obtained, phase-resolved
analysis of the $\gamma$-ray data has been conducted. No significant emission
has been detected in the off-pulse phase range, and the TS maps calculated
from the on-pulse and off-pulse phase ranges support the detection of the
pulsations of the MSP.

Considering that there is negligible emission in the off-pulse phase range,
the phase-averaged luminosity of the MSP is $L_{\gamma}\simeq 1.3\times
10^{34}$ erg s-1. The derived spin-down energy of the MSP is
$\dot{E}=7.7\times 10^{34}$ erg s-1, giving a $\gamma$-ray efficiency $\eta$
of 0.17. This efficiency value is typical for $\gamma$-ray MSPs (e.g., Wu et
al. 2022). In Figure 10, we show this pulsar’s value along with the other
three known GC $\gamma$-ray MSPs, in which the luminosities in the $\rm
P_{on}$ phase ranges of PSRs J1823$-$3021A and B1821$-$24 (Table 3) and the
phase-averaged luminosity of PSR J1835$-$3259B (given no significant off-pulse
emission from this pulsar) are used. In addition in the figure, we also show
all the other radio pulsars in 27 GCs whose $\dot{E}$ values can be
calculated, i.e., positive $\dot{P}$ values given in the GC pulsar table (note
that the observed $\dot{P}$ values are mostly caused by dynamical effects and
thus the $\dot{E}$ values are rough estimates; see, e.g., Freire et al. 2017
and references therein). Among the GCs, 16 have reported $\gamma$-ray
emissions and the other 11 do not. To plot the radio pulsars in the figure, we
assume 1) the off-pulse $\gamma$-ray luminosities for each of NGC 6624 and NGC
6626 (Table 3) as the luminosities for other known radio pulsars respectively
in the two GCs (Abbate et al. 2022; Douglas et al. 2022; and references
therein), and 2) the $\gamma$-ray luminosity of each 12 GCs (in which no
$\gamma$-ray pulsars are identified) as that of each of their radio pulsars
(where the values are from Wu et al. 2022). In NGC 6652, PSR J1835$-$3259B is
the only pulsar with $\dot{E}$ (DeCesar et al., 2015; Gautam et al., 2022). As
can be seen, while the previous three MSPs are among the ones with the highest
$\dot{E}$, PSR J1717+4308A has comparably low $\dot{E}$. One common feature
may be noted for the four $\gamma$-ray pulsars are that they are either
supposed to be bright given high $\dot{E}$ (cf., PSR B1821$-$24), or their
host GCs are observed at radio or predicted at $\gamma$-rays (Wu et al., 2022)
to contain only several pulsars (i.e., possibly less contamination from other
pulsars when searching for pulsational signals). This feature could be the
reason for the detectability of the $\gamma$-ray pulsations of these four
pulsars.

Figure 10: $\gamma$-ray efficiencies of PSRs J1823$-$3021A, B1821$-$24,
J1835$-$3259B, and J1717+4308A. Other known radio pulsars in the GCs are
included; for those in the GCs with $\gamma$-ray emissions, the $\gamma$-ray
luminosities of the GCs (but for NGC 6624 and NGC 6626, the $\gamma$-ray
luminosities in the $\rm P_{off}$ phase ranges given in Table 3) are used, and
for those in the GCs without $\gamma$-ray emissions (marked by downward
arrows), a flux upper limit of $10^{-12}$ erg s-1 cm-2 is used. The
$\gamma$-ray luminosities and flux upper limit are derived and given in Wu et
al. (2022).

###  4.2 Implication for $\gamma$-ray emissions of GC MSPs

With the likely $\gamma$-ray detection of PSR J1717+4308A, we take these four
MSPs as the representative cases and investigate the implication for the MSPs
that would exist in the four host GCs. We use the off-pulse spectra of NGC
6624 and NGC 6626 and the spectral upper limits for NGC 6652 and NGC 6341
(since the latter two have not been found with significant off-pulse
$\gamma$-ray emissions) and perform the fitting to the spectra or upper
limits. The method and related MSP samples used have been fully described in
Wu et al. (2022) and the parameters for the four GCs are given in Table 4.
From fitting the off-pulse spectra, the numbers of other MSPs in NGC 6624 and
NGC 6626 are constrained to be 1–5 and 1–6 respectively (Figure 8). The
numbers well match those of the known radio pulsars (cf., Figure 10; Abbate et
al. 2022; Douglas et al. 2022; and references therein), while it should be
noted that several pulsars in the two GCs do not have the spin-down rate
information555https://www.naic.edu/$\sim$pfreire/GCpsr.html (i.e., not shown
in Figure 10). Further, there is a caveat that the off-pulse emissions are
assumed not containing any of the two MSPs, which may not be true and possibly
lead to over-estimates for the numbers of other MSPs in the two GCs. The
numbers of other MSPs in NGC 6652 and NGC 6341 are constrained to be $\leq$2
and $\leq$1 respectively. The constraints match the numbers of known pulsars
in the two GCs also well as they have thus-far been reported to contain 2 and
1 pulsars respectively (including PSR J1835$-$3259B and PSR J1717+4308A;
Gautam et al. 2022; Pan et al. 2020).

Table 4: Numbers of other $\gamma$-ray MSPs ($N^{\gamma}_{\rm MSP}$) estimated
from the off-pulse spectra or upper limits for the four GCs

Name | Age∗ | Dist† |  $\chi^{2}$/N | $N^{\gamma}_{\rm MSP}$ | $N^{5\%}_{\rm MSP}$
---|---|---|---|---|---
| (Gyr) | (kpc) |  |  |
NGC 6624 | 11.7 | 8.0 | 2.6/5 | 1 | 1–5
NGC 6626 | 14.0 | 5.4 | 4.3/5 | 4 | 1–6
NGC 6652 | 11.3 | 9.5 |  |  $\leq$2 |
NGC 6341 | 12.8 | 8.5 |  |  $\leq$1 |

Notes. $N^{5\%}_{\rm MSP}$ provides a range given by 5% lowest $\chi^{2}$
values in 1000 fitting runs (see Wu et al. 2022 for details). ∗Ages of NGC
6624 and NGC 6626 are from Oliveira et al. (2020) and Kerber et al. (2018)
respectively, and those of NGC 6652 and NGC 6341 from VandenBerg et al.
(2013). † Distances are from Baumgardt & Vasiliev (2021).

Thus for the four GCs, the estimated MSP numbers roughly match the observed
ones (which may suggest that the detectable pulsars in them have likely been
found completely from radio and $\gamma$-ray surveys). The results help
indicate that while the emission from one bright MSP can be dominant in the
observed $\gamma$-ray emission of the host GC, the contribution from other
MSPs (at least for NGC 6624 and NGC 6626) is not negligible. The estimation
for the number of $\gamma$-ray MSPs in a GC should be carried out with
caution, probably on a case-by-case basis by taking into account the
information provided from radio observations. We have also learned from the
four GCs that the presence of one bright MSP can be the dominant factor for
whether a GC has detectable $\gamma$-ray emission or not.

We might extend the thinking to all the GCs, that is the pulsars found in them
are close to be complete, given the particular effort that has been made
towards finding GC pulsars in the past with different facilities (e.g., Pan et
al. 2021; Abbate et al. 2022; Douglas et al. 2022; Gautam et al. 2022). Then
according to Figure 10, for which a companion table (Table 5) is made to
provide more detailed information, we should make an effort to search for
$\gamma$-ray MSPs in Terzan 5, NGC 6266, NGC 6440, 47 Tuc, and probably NGC
5904 and NGC 6752 as well; the latter two contain known MSPs with $\dot{E}$
similar to that of PSR J1717+4308A. Here we consider those pulsars falling in
the range of $\eta\sim$0.1–1. Also presented in Figure 10 (as well as in Table
5) are 11 GCs containing known radio pulsars but not having detectable
$\gamma$-ray emissions, where a flux upper limit of $10^{-12}$ erg cm-2 s-1 is
used (estimated from the work in Wu et al. 2022). It can be seen that there is
one MSP, PSR J1312+1810E, in NGC 5024 with $\dot{E}>$1035 erg s-1. No emission
has been found from this GC (e.g., Yuan et al. 2022a), while it can be noted
that the distance to the GC is large, $\sim$18 kpc (Harris, 1996; Baumgardt &
Vasiliev, 2021), which may explain the non-detection at $\gamma$-rays of the
GC (or the MSP). In any case, this MSP is of interest as its $\eta$ already
reaches $\sim 10^{-3}$.

###  4.3 Summary

We have detected the $\gamma$-ray pulsations of PSR J1717+4308A in the GC NGC
6341 (M92) at a 4.4$\sigma$ confidence level. No significant off-pulse
emission from the MSP has been found, which suggests that the MSP’s emission
likely contributes dominantly to the observed $\gamma$-ray emission of the GC.
The detection has added the fourth one to the group of GC $\gamma$-ray MSPs.
Based on the four cases, we may suggest that the detectability of a
$\gamma$-ray MSP in a GC relies on sufficiently high $\dot{E}$ (maybe greater
than $10^{35}$ erg s-1) and probably low number of other pulsars as well.

We have re-analyzed the Fermi-LAT data for the three previously known GC
$\gamma$-ray MSPs and obtained their off-pulse spectra and spectral upper
limits. Fitting the spectra or upper limits with the method used in Wu et al.
(2022), which include the spectral upper limits on NGC 6341, we have
constrained the numbers of other MSPs respectively in the four GCs. The
numbers are in consistency with those of known radio pulsars in the four GCs,
suggesting that probably most of pulsars in them have already been found.
While at least in NGC 6624 and NGC 6626, the $\gamma$-ray emission from other
pulsars is not negligible, the four GCs show that a bright MSP can be a
dominant factor for whether a GC is detectable at $\gamma$-rays or not. Our
study has also suggested a few targets for finding more GC $\gamma$-ray MSPs.

Table 5: Detailed information for the estimated numbers of $\gamma$-ray MSPs
and the numbers of reported radio MSPs in 23 GCs shown in Figure 10

GC name | $L_{\gamma}/10^{34}$ | $N^{\gamma}_{\rm MSP}$ | $N_{\rm MSP}$ | MSP name | $P$ | $\dot{P}/10^{-19}$ | $\dot{E}/10^{34}$
---|---|---|---|---|---|---|---
(erg s-1) | (ms) | (s s-1) | (erg s-1)
47 Tucanae | 6.5 | 1–11 | 29 | J0024–7205E | 3.54 | 0.99 | 8.8
|  |  |  | J0024$-$7204F | 2.62 | 0.65 | 14.1
|  |  |  | J0024$-$7204O | 2.64 | 0.30 | 6.5
|  |  |  | J0024$-$7204R | 3.48 | 1.48 | 13.9
NGC 5139 | 3.5 | 1–6 | 18 | — |  |  |
NGC 5904 | 1.7 | 1–3 | 7 | B1516+0204C | 2.48 | 0.26 | 6.7
NGC 6266 | 10.8 | 1–13 | 9 | J1701$-$3006D | 3.42 | 1.26 | 12.4
|  |  |  | J1701$-$3006E | 3.23 | 3.10 | 36.2
|  |  |  | J1701$-$3006F | 2.29 | 2.22 | 72.6
NGC 6402 | 3.3 | 1–6 | 5 | J1737$-$0314A | 1.98 | 0.95 | 48.5
NGC 6397 | 0.3 | 1–1 | 2 | J1740$-$5340(A) | 3.65 | 1.68 | 13.6
Terzan 5 | 45.0 | 9–38 | 41 | J1748$-$2446P | 1.73 | 2.60 | 199.0
|  |  |  | J1748$-$2446Y | 2.05 | 1.50 | 68.9
|  |  |  | J1748$-$2446ak | 1.89 | 0.88 | 51.7
NGC 6440 | 12.9 | 1–11 | 7 | J1748$-$2021H | 2.85 | 1.90 | 32.5
NGC 6441 | 24.4 | 4–20 | 7 | — |  |  |
NGC 6752 | 0.7 | 1–2 | 9 | J1910$-$5959D | 9.04 | 9.63 | 5.2
|  |  |  | J1910$-$5959F | 8.49 | 7.41 | 4.8
NGC 6838 | 0.8 | 1–2 | 3 | J1953+1846A | 4.89 | 0.49 | 1.64
|  |  |  | J1953+1846E | 4.44 | 0.60 | 2.72
NGC 7078 | 5.5 | 1–5 | 5 | B2127+11E | 4.65 | 1.78 | 6.98
NGC 1851 | 0.02a | —b | 14 | J0514$-$4002A | 4.99 | 0.01 | 0.04
NGC 5024 | 0.04a | —b | 4 | J1312+1810E | 3.97 | 7.05 | 44.5
NGC 5272 | 0.01a | —b | 6 | J1342+2822B | 2.39 | 0.19 | 5.4
|  |  |  | J1342+2822F | 4.40 | 0.32 | 1.5
NGC 6205 | 0.006a | —b | 6 | J1641+3627C | 3.72 | 0.01 | 0.1
|  |  |  | J1641+3627E | 2.49 | 0.18 | 4.5
|  |  |  | J1641+2627F | 3.00 | 0.14 | 2.0
NGC 6342 | 0.009a | —b | 1 | — |  |  |
NGC 6517 | 0.01a | —b | 16 | J1801$-$0857B | 28.96 | 21.91 | 0.4
|  |  |  | J1801$-$0857D | 4.22 | 0.06 | 0.4
|  |  |  | J1801$-$0857H | 5.64 | 0.34 | 0.8
NGC 6522 | 0.007a | —b | 5 | J1803$-$3002A | 7.10 | 0.40 | 0.4
NGC 6539 | 0.007a | —b | 1 | B1802$-$07 | 23.10 | 4.70 | 0.2
NGC 6544 | 0.001a | —b | 3 | J1807$-$2500B | 4.19 | 0.82 | 4.4
NGC 6656 | 0.001a | 1–1 | 4 | J1836$-$2354A | 3.35 | 0.02 | 0.2
NGC 7089 | 0.015a | —b | 6 | J2133$-$0049D | 4.22 | 0.78 | 4.1

Notes. $N^{\gamma}_{\rm MSP}$ is the number of $\gamma$-ray MSPs in a GC
estimated in Wu et al. (2022), and $N_{\rm MSP}$ is the number of MSPs ($P\leq
30$ ms) listed in the GC pulsar table, while the MSPs with $\gamma$-ray
efficiency $\eta\leq 1$ (cf., Figure 10) are specifically listed as potential
$\gamma$-ray sources. aLuminosity upper limits, where for the GCs with no
detected $\gamma$-rays, a flux upper limit of $10^{-12}$ erg s-1 cm-2 is used.
b GCs not appearing in Wu et al. (2022).

We thank the anonymous referee for helpful comments. This work is supported in
part by the National Natural Science Foundation of China No. 12163006 and
12233006, the Basic Research Program of Yunnan Province No. 202201AT070137,
and the joint foundation of Department of Science and Technology of Yunnan
Province and Yunnan University (202201BF070001-020). Z. W. acknowledges the
support by the Basic Research Program of Yunnan Province (No. 202201AS070005),
the National Natural Science Foundation of China (12273033), and the Original
Innovation Program of the Chinese Academy of Sciences (E085021002).

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