secondary γ-ray peak. Johnson et al. (2014) found that Class II MSPs had the shortest spin periods, with five of the six members of this class having spin periods less than 2 ms, while Class I and Class III MSPs had longer spin periods. PSR J0307+7443, with a spin period of 3.2 ms, does not fit that trend.

The close-orbit pulsars are more difficult to classify since nearly all show strong frequency dependence in their radio pulse profiles. At 350 MHz, PSR J1302−3258 is a Class I object, with the main radio peak leading the γ-ray peak. However, we note that an interpulse becomes apparent at 820 MHz, which trails the secondary γ-ray peak and becomes even more prominent at higher radio frequencies. The Fermi-LAT 2PC catalog used the brightest profile peaks (at 2 GHz) of PSRs J0023+0923, J1810+1744, and J2215+5135 when calculating phase lags. However, both PSRs J0023+0923 and J1810+1744 show a narrow “precursor” peak that is not visible at 350 MHz but whose peak brightness begins to approach the main peak’s brightness by 2 GHz, and would presumably become the “main peak” at higher frequencies. At low frequencies, PSR J0023+0923 is Class I and PSR J1810+1744 is Class II, but if measured from the flatter-spectrum precursor peak, the classifications would be reversed. The pulse-profile evolution of PSR J2215+5135 is even more pronounced. At 350 MHz, it has two peaks which are fairly well aligned with the γ-ray peaks, implying this would be a Class II source, but at 2 GHz there is a single peak that is neither of the 350 MHz peaks and which trails the γ-ray peaks, and so would be Class III. Pulse profiles which strongly evolve with frequency seem to be a feature of many black widows and rebacks. We note that this has also been noted in the original black widow pulsar PSR B1957+20 (Johnson et al. 2014) as well as in the rebacks PSR J1048+2339 (Deneva et al. 2016) and PSR J1023+0038 (Archibald et al. 2009). For these systems, at least, classification schemes based on relative phases of γ-ray and radio peaks could break down. The pulse-profile evolution common to these also brings up the possibility that the companion is somehow influencing the radio emission of the pulsar if this frequency dependence is truly more common among these systems than in the general MSP population.

### 4.3. Implications for General Millisecond Pulsar Population Statistics

In the standard theory of MSP formation, a neutron star in a binary system is “recycled” by accreting matter from its companion star (Alpar et al. 1982; Stairs 2004), and consequently, most MSPs are expected to be in binary systems with a white dwarf, the natural end state of the evolution of the light companion following accretion and spinup. However, psrcat currently lists<fnref n="30" /> 52 MSPs in the Galactic field without binary companions, about 23% of the total. The formation of these isolated MSPs is still not well understood, though one possibility is that they ablated their companions with their strong relativistic particle winds (Ruderman et al. 1989). Another ~32 MSPs<fnref n="31" /> in the Galactic field do not have ordinary white dwarf companions but instead have either undermassive companions or nondegenerate companions. Understanding the various subpopulations of MSPs is critical for improving our

view of the pulsar recycling process and whether it proceeds via only one channel or a variety of routes. The rapid rate of MSP discovery is can greatly help in this endeavor by rounding out the population with respect to previous observational biases.

Deep searches targeting γ-ray sources have a very different set of observational biases than shallow, wide-field radio surveys. Due to there being a much stronger correlation between spin-down luminosity and apparent γ-ray luminosity than there is with apparent radio luminosity, a γ-ray targeted survey will be more biased toward nearby, energetic MSPs and less biased toward high radio luminosities. Older low-frequency surveys had much less spectral resolution and were, therefore, more susceptible to DM smearing of the pulse profile, degrading their sensitivity to MSPs. Higher DM and scattering in the Galactic plane would also inhibit the discovery of MSPs. In the past, there were also strong biases against detecting pulsars with short orbital periods since acceleration searches only became common practice after 2000.

Only two out of 18 MSPs (11%) detected in this survey are isolated. 3PC reports 91 MSPs discovered by targeting unidentified Fermi sources, and of these, only 16 are isolated,<fnref n="32" /> about 18%. Both are lower than the roughly 25% isolated fraction of the Galactic plane population found before 2009. Furthermore, eight of the pulsars detected in this survey have orbital periods $P_b < 1$ day. In the same 3PC sample, the fraction of short-period binaries is 54%. In stark contrast, only ~14% of MSPs found before 2009 have such short binary periods. As a result of the Fermi searches, there are now more known MSPs with short orbits than isolated ones. If we compare the Galactic field population of $P_b < 1$ day MSPs to the ones in globular clusters, in both cases, the fraction is now ~25%. This calls into question the importance of binary exchange in the formation of these systems in globular clusters.

Compared to binary MSPs, isolated MSPs could in principle be older or sustain a higher spin-down energy loss ($\dot{E}$) in order to disintegrate their companions fully. To investigate this, we have compared the $\dot{E}$ and characteristic ages of binary and isolated MSPs both in full and restricted to Galactic latitudes $|b| > 5°$. In order to obtain a larger sample, we use values of $\dot{P}$ which have not been corrected for the Shklovskii effect to estimate $\dot{E}$ and the characteristic age. (In addition to this caveat, it is important to note that these are derived quantities of $P$ and $\dot{P}$ and are only rough proxies of the true ages and spin-down luminosities.) The distribution function for these two quantities is shown in Figure 15, the inspection of which indicates that the distributions for isolated and binary MSPs are broadly compatible. We quantitatively compared the distributions using a two-sample Kolmogorov–Smirnov test, finding modest evidence ($p$-value of 5%) that the $\dot{E}$ distributions differ. Further examination indicates that the $|b| > 5$ pulsars have only a 2% probability of being drawn from the same distribution, with isolated pulsars generally having lower values of $\dot{E}$, while the $|b| < 5$ populations are compatible. There is no substantial difference in any of the age distributions. Further work will be necessary to determine if the observed difference in spin-down luminosities is intrinsic or an observational selection effect against low-$\dot{E}$, high-latitude binaries.

<footnote n="30">³⁰ MSP class counts obtained with psrcat use version 1.70 and require period $P < 10$ ms and a well-measured $\dot{P}$.</footnote>

<footnote n="31">³¹ http://astro.umd.edu/~eferrara/pulsars/GalacticMSPs.txt</footnote>

<footnote n="32">³² We exclude two MSPs which were discovered in a targeted search of LAT data (Clark et al. 2018).</footnote>
secondary γ-ray peak. Johnson et al. (2014) found that Class II MSPs had the shortest spin periods, with five of the six members of this class having spin periods less than 2 ms, while Class I and Class III MSPs had longer spin periods. PSR J0307+7443, with a spin period of 3.2 ms, does not fit that trend.

The close-orbit pulsars are more difficult to classify since nearly all show strong frequency dependence in their radio pulse profiles. At 350 MHz, PSR J1302−3258 is a Class I object, with the main radio peak leading the γ-ray peak. However, we note that an interpulse becomes apparent at 820 MHz, which trails the secondary γ-ray peak and becomes even more prominent at higher radio frequencies. The Fermi-LAT 2PC catalog used the brightest profile peaks (at 2 GHz) of PSRs J0023+0923, J1810+1744, and J2215+5135 when calculating phase lags. However, both PSRs J0023+0923 and J1810+1744 show a narrow “precursor” peak that is not visible at 350 MHz but whose peak brightness begins to approach the main peak’s brightness by 2 GHz, and would presumably become the “main peak” at higher frequencies. At low frequencies, PSR J0023+0923 is Class I and PSR J1810+1744 is Class II, but if measured from the flatter-spectrum precursor peak, the classifications would be reversed. The pulse-profile evolution of PSR J2215+5135 is even more pronounced. At 350 MHz, it has two peaks which are fairly well aligned with the γ-ray peaks, implying this would be a Class II source, but at 2 GHz there is a single peak that is neither of the 350 MHz peaks and which trails the γ-ray peaks, and so would be Class III. Pulse profiles which strongly evolve with frequency seem to be a feature of many black widows and rebacks. We note that this has also been noted in the original black widow pulsar PSR B1957+20 (Johnson et al. 2014) as well as in the rebacks PSR J1048+2339 (Deneva et al. 2016) and PSR J1023+0038 (Archibald et al. 2009). For these systems, at least, classification schemes based on relative phases of γ-ray and radio peaks could break down. The pulse-profile evolution common to these also brings up the possibility that the companion is somehow influencing the radio emission of the pulsar if this frequency dependence is truly more common among these systems than in the general MSP population.

### 4.3. Implications for General Millisecond Pulsar Population Statistics

In the standard theory of MSP formation, a neutron star in a binary system is “recycled” by accreting matter from its companion star (Alpar et al. 1982; Stairs 2004), and consequently, most MSPs are expected to be in binary systems with a white dwarf, the natural end state of the evolution of the light companion following accretion and spinup. However, psrcat currently lists<sup>30</sup> 52 MSPs in the Galactic field without binary companions, about 23% of the total. The formation of these isolated MSPs is still not well understood, though one possibility is that they ablated their companions with their strong relativistic particle winds (Ruderman et al. 1989). Another ~32 MSPs<sup>31</sup> in the Galactic field do not have ordinary white dwarf companions but instead have either undermassive companions or nondegenerate companions. Understanding the various subpopulations of MSPs is critical for improving our

view of the pulsar recycling process and whether it proceeds via only one channel or a variety of routes. The rapid rate of MSP discovery is can greatly help in this endeavor by rounding out the population with respect to previous observational biases.

Deep searches targeting γ-ray sources have a very different set of observational biases than shallow, wide-field radio surveys. Due to there being a much stronger correlation between spin-down luminosity and apparent γ-ray luminosity than there is with apparent radio luminosity, a γ-ray targeted survey will be more biased toward nearby, energetic MSPs and less biased toward high radio luminosities. Older low-frequency surveys had much less spectral resolution and were, therefore, more susceptible to DM smearing of the pulse profile, degrading their sensitivity to MSPs. Higher DM and scattering in the Galactic plane would also inhibit the discovery of MSPs. In the past, there were also strong biases against detecting pulsars with short orbital periods since acceleration searches only became common practice after 2000.

Only two out of 18 MSPs (11%) detected in this survey are isolated. 3PC reports 91 MSPs discovered by targeting unidentified Fermi sources, and of these, only 16 are isolated,<sup>32</sup> about 18%. Both are lower than the roughly 25% isolated fraction of the Galactic plane population found before 2009. Furthermore, eight of the pulsars detected in this survey have orbital periods $P_b < 1$ day. In the same 3PC sample, the fraction of short-period binaries is 54%. In stark contrast, only ~14% of MSPs found before 2009 have such short binary periods. As a result of the Fermi searches, there are now more known MSPs with short orbits than isolated ones. If we compare the Galactic field population of $P_b < 1$ day MSPs to the ones in globular clusters, in both cases, the fraction is now ~25%. This calls into question the importance of binary exchange in the formation of these systems in globular clusters.

Compared to binary MSPs, isolated MSPs could in principle be older or sustain a higher spin-down energy loss ($\dot{E}$) in order to disintegrate their companions fully. To investigate this, we have compared the $\dot{E}$ and characteristic ages of binary and isolated MSPs both in full and restricted to Galactic latitudes $|b| > 5°$. In order to obtain a larger sample, we use values of $\dot{P}$ which have not been corrected for the Shklovskii effect to estimate $\dot{E}$ and the characteristic age. (In addition to this caveat, it is important to note that these are derived quantities of $P$ and $\dot{P}$ and are only rough proxies of the true ages and spin-down luminosities.) The distribution function for these two quantities is shown in Figure 15, the inspection of which indicates that the distributions for isolated and binary MSPs are broadly compatible. We quantitatively compared the distributions using a two-sample Kolmogorov–Smirnov test, finding modest evidence ($p$-value of 5%) that the $\dot{E}$ distributions differ. Further examination indicates that the $|b| > 5$ pulsars have only a 2% probability of being drawn from the same distribution, with isolated pulsars generally having lower values of $\dot{E}$, while the $|b| < 5$ populations are compatible. There is no substantial difference in any of the age distributions. Further work will be necessary to determine if the observed difference in spin-down luminosities is intrinsic or an observational selection effect against low-$\dot{E}$, high-latitude binaries.

<footnote n="30"><sup>30</sup> MSP class counts obtained with psrcat use version 1.70 and require period $P < 10$ ms and a well-measured $\dot{P}$.</footnote>

<footnote n="31"><sup>31</sup> http://astro.umd.edu/~eferrara/pulsars/GalacticMSPs.txt</footnote>

<footnote n="32"><sup>32</sup> We exclude two MSPs which were discovered in a targeted search of LAT data (Clark et al. 2018).</footnote>
<figure><img src="image_18.png" /><figcaption>**Figure 15.** The cumulative distribution functions (CDFs) of the spin-down energy loss rates (top) and ages (bottom) for isolated and binary MSPs. The different line styles show the full, low-latitude (dashed) and high-latitude (dotted) samples. These CDFs are broadly compatible, but a Kolmogorov-Smirnov test provides modest evidence that the high-latitude *E* distributions differ. See the main text for details of the sample construction and analysis.</figcaption></figure>

## 5. Conclusion

This work reports on a groundbreaking survey conducted more than 10 yr ago. Although we wish it had been published sooner, much of the delay was due to the success of the project. The MSP discoveries necessitated timing observations, and the discovery of such an unusually—at the time—large number of “spider” pulsars demanded multiwavelength follow up. It was always tempting to acquire more observational data and better understand this growing source class and its relation to γ-rays. The haul of new MSPs also created its own distractions, because it inspired numerous follow-up surveys, many cited above, of different parts of the sky, at different frequency ranges, and with different Fermi source lists. The success of this method continues through the present day, with powerful new instruments like FAST and MeerKAT and finding ever fainter radio pulsars in Fermi sources (Wang et al. 2021; Clark et al. 2023a).

Despite the long gap between observations and report, this work is the definitive record of the radio observations carried out, the follow-up timing observations, and the phase-aligned γ-ray and radio pulse profiles. Together with a synthesis of multiwavelength observations, particularly X-ray but also

benefiting from optical analyses of redback candidates that lack pulsations, we can argue that γ-ray targeted searches correct a long-standing bias in radio surveys, which seem to have overproduced isolated MSPs relative to the general population. And it is only with the benefit of the substantial follow up that we can appreciate how efficient the original target selection was. It is thus fitting that this report finally appear in the literature, and we conclude: better late than never!

## Acknowledgments

This work was partially supported by NASA Fermi Guest Investigator Program grants NNG10PB13P, NNX10AP81G, NNX12AE32G, NNX12AP21G, and NNX13AO96G. The Green Bank Telescope is operated by the National Radio Astronomy Observatory, a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc. The WSRT is operated by ASTRON/NWO. This work makes use of observations from the Las Cumbres Observatory Global Telescope network, with support from New York University Abu Dhabi. This paper includes observations made with the MuSCAT3 instrument, developed by Astrobiology Center and under financial supports by JSPS KAKENHI (JP18H05439) and JST PRESTO (JPMJPR1775), at Faulkes Telescope North on Maui, HI, operated by the Las Cumbres Observatory. We thank Gyula Jozsa for help scheduling the WSRT observations. J.W.T.H. acknowledges funding from an NWO Vidi fellowship and ERC Starting Grant “DRAGNET” (337062). M.S.E.R. acknowledges funding from the NYU Abu Dhabi faculty research fund. Work at NRL is supported by NASA and by ONR 6.1 basic research funding. E.C.F. is supported by NASA under award number 80GSFC21M0002. S.M.R. is a CIFAR Fellow. M.A.M. is supported by NSF award 2009425. M.E.D., E.C.F., M.K., M.A.M., S.M.R., and P.S.R. are members of the NANOGrav Physics Frontiers Center and are supported by NSF award 2020265.

The Fermi-LAT Collaboration acknowledges generous ongoing support from a number of agencies and institutes that have supported both the development and the operation of the LAT as well as scientific data analysis. These include the National Aeronautics and Space Administration and the Department of Energy in the United States, the Commissariat à l'Energie Atomique and the Centre National de la Recherche Scientifique/Institut National de Physique Nucléaire et de Physique des Particules in France, the Agenzia Spaziale Italiana and the Istituto Nazionale di Fisica Nucleare in Italy, the Ministry of Education, Culture, Sports, Science and Technology (MEXT), High Energy Accelerator Research Organization (KEK) and Japan Aerospace Exploration Agency (JAXA) in Japan, and the K. A. Wallenberg Foundation, the Swedish Research Council, and the Swedish National Space Board in Sweden.

Partially based on observations obtained with XMM-Newton, an ESA science mission with instruments and contributions directly funded by ESA Member States and NASA

Additional support for science analysis during the operations phase is gratefully acknowledged from the Istituto Nazionale di Astrofisica in Italy and the Centre National d'Études Spatiales in France. This work performed in part under DOE Contract DE-AC02-76SF00515.

We thank the NANOGrav collaboration for contributing data on PSR J0340+4130 that were used for this paper. We also
thank Duncan Lorimer and Elizabeth Ferrara for maintaining the list of published and unpublished Galactic field MSPs.

*Facilities:* GBT, Fermi, GMRT, WSRT, NRT, Swift, CXO, XMM.

## ORCID iDs

P. Bangale https://orcid.org/0000-0002-3886-3739

B. Bhattacharyya https://orcid.org/0000-0002-6287-6900

F. Camilo https://orcid.org/0000-0002-1873-3718

C. J. Clark https://orcid.org/0000-0003-4355-3572

I. Cognard https://orcid.org/0000-0002-1775-9692

M. E. DeCesar https://orcid.org/0000-0002-2185-1790

E. C. Ferrara https://orcid.org/0000-0001-7828-7708

L. Guillemot https://orcid.org/0000-0002-9049-8716

J. W. T. Hessels https://orcid.org/0000-0003-2317-1446

M. Kerr https://orcid.org/0000-0002-0893-4073

M. A. McLaughlin https://orcid.org/0000-0001-7697-7422

L. Nieder https://orcid.org/0000-0002-5775-8977

S. M. Ransom https://orcid.org/0000-0001-5799-9714

P. S. Ray https://orcid.org/0000-0002-5297-5278

M. S. E. Roberts https://orcid.org/0000-0002-9396-9720

J. Roy https://orcid.org/0000-0002-2892-8025

G. Theureau https://orcid.org/0000-0002-3649-276X

M. T. Wolff https://orcid.org/0000-0002-4013-5650

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Pleunis, Z., Bassa, C. G., Hessels, J. W. T., et al. 2017, *ApJL*, 846, L19

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Ransom, S. M., Eikenberry, S. S., & Middleditch, J. 2002, *AJ*, 124, 1788

Ransom, S. M., Ray, P. S., Camilo, F., et al. 2011, *ApJL*, 727, L16
thank Duncan Lorimer and Elizabeth Ferrara for maintaining the list of published and unpublished Galactic field MSPs.

Facilities: GBT, Fermi, GMRT, WSRT, NRT, Swift, CXO, XMM.

## ORCID iDs

P. Bangale https://orcid.org/0000-0002-3886-3739

B. Bhattacharyya https://orcid.org/0000-0002-6287-6900

F. Camilo https://orcid.org/0000-0002-1873-3718

C. J. Clark https://orcid.org/0000-0003-4355-3572

I. Cognard https://orcid.org/0000-0002-1775-9692

M. E. DeCesar https://orcid.org/0000-0002-2185-1790

E. C. Ferrara https://orcid.org/0000-0001-7828-7708

L. Guillemot https://orcid.org/0000-0002-9049-8716

J. W. T. Hessels https://orcid.org/0000-0003-2317-1446

M. Kerr https://orcid.org/0000-0002-0893-4073

M. A. McLaughlin https://orcid.org/0000-0001-7697-7422

L. Nieder https://orcid.org/0000-0002-5775-8977

S. M. Ransom https://orcid.org/0000-0001-5799-9714

P. S. Ray https://orcid.org/0000-0002-5297-5278

M. S. E. Roberts https://orcid.org/0000-0002-9396-9720

J. Roy https://orcid.org/0000-0002-2892-8025

G. Theureau https://orcid.org/0000-0002-3649-276X

M. T. Wolff https://orcid.org/0000-0002-4013-5650

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