DISCOVERY OF A MILLISECOND PULSAR IN THE 5.4 DAY BINARY 3FGL J1417.5–4402: OBSERVING THE LATE PHASE OF PULSAR RECYCLING

In Camilo et al. (2015) we reported on a radio survey of 56 unidentified LAT sources using the CSIRO Parkes telescope. We discovered 10 MSPs, in some cases only after multiple observations of each source. Multiple observations increase the chance that an otherwise detectable pulsar will not be missed due to interstellar scintillation, large acceleration at a particularly unfavorable binary phase, or eclipse. We established that 23 of the remaining unidentified sources had gamma-ray properties consistent with those of known pulsars, and therefore were deserving of further radio searches.

During 2015 March–May we performed 28 search observations of 12 of the highest-ranked LAT targets remaining from our original source list (Table 1). Because the analog filterbank used in the original survey had in the meantime been decommissioned, we used instead a digital filterbank (PDFB4, see Manchester et al. 2013) to record data from the central beam of the Parkes 20 cm multibeam receiver, at a center frequency of 1369 MHz. Each of 512 0.5 MHz wide polarization-summed channels was sampled with PDFB4 every $80\;\mu {\rm{s}}$ for approximately 1 hr (see Table 1), and the resulting power measures were written with 2 bit precision to disk for off-line analysis.

Table 1.  New Radio Searches of 3FGL Sources at Parkes

Source Namea	Integration Time (minutes)	${N}_{{\rm{obs}}}$ b
3FGL J0940.6−7609	60, 60, 60, 41	5
3FGL J1025.1−6507	60, 60, 60, 45	5
3FGL J1231.6−5113	60, 80, 98, 52	5
3FGL J1325.2−5411	60	2
3FGL J1417.5−4402	60	2
3FGL J1753.6−4447	60	2
3FGL J1803.3−6706	55	2
3FGL J1831.6−6503	60	2
3FGL J2043.8−4801	45	3
3FGL J2131.1−6625	60, 60, 60	5
3FGL J2200.0−6930	55, 60, 60	4
3FGL J2333.0−5525	60, 60, 60, 38	6

Notes.

^aSource properties, including the positions that we targeted in our searches, are given in Acero et al. (2015). See also Camilo et al. (2015). ^bNumber of radio searches done, including those listed here and in Camilo et al. (2015).

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We analyzed the data using PRESTO (Ransom 2001), exactly as for our earlier searches described in Camilo et al. (2015). In an observation of 3FGL J1417.5–4402 done on 2015 March 28, we discovered a binary pulsar with period P = 2.66 ms and dispersion measure ${\rm{DM}}=55$ pc cm⁻³ (Figure 1(a)). To our knowledge, this is the first pulsar discovered using any of the PDFBs. We then realized that 3FGL J1417.5–4402 was the gamma-ray source in which Strader et al. (2015) had discovered an unusual binary, and sought to determine whether the new pulsar was related.

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We had searched the location of the new pulsar once before (Table 1), unsuccessfully. Following its discovery we began Parkes timing observations at 1.4 GHz. Between 2015 March 28 and 2016 January 14 we have observed PSR J1417–4402 52 times on 46 days for a total of 75 hr, and have detected it for a total of 11 hr on seven days (Figures 1(a)–(c) and (f)–(i)). All of these detections were within orbital phases $0.4\lt {\phi }_{b}\lt 0.65$, which we have observed for 42 hr (see Figure 2; throughout this paper we use the radio phase convention, in which ${\phi }_{b}=0$ is the time of ascending node of the pulsar). Two thirds of these observing sessions, 85% of the observing time, and all of the detections, used the same PDFB4 setup employed in the discovery observation. The remaining timing observations were done with the Berkeley-Parkes-Swinburne Recorder (BPSR), which in effect samples 340 MHz of bandwidth centered on 1352 MHz every $64\;\mu {\rm{s}}$ with 0.4 MHz resolution (for more details, see Keith et al. 2010).

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For the relatively large DM of PSR J1417–4402 we do not expect interstellar scintillation to modulate the detected flux density by more than a factor of ∼2. Some, likely all, of the non-detections are caused by eclipses, as in Figure 1 (panels (c), (g)–(i)). On at least two occasions (see "kinks" lasting for $\approx 500\;{\rm{s}}$ near the beginning/end of the observations in Figure 1(h)/(i)) the pulse arrival is delayed by $\approx 0.15\;P$, presumably due to an ephemeral clump of ionized material. This time delay corresponds to an extra electron column $\delta {\rm{DM}}\approx 0.15$ pc cm⁻³.

In 2015 June we observed PSR J1417–4402 at the Robert C. Byrd Green Bank Telescope (GBT). We did this on three days for a total of 3 hr at a central frequency of 2 GHz, recording a bandwidth of 800 MHz using GUPPI.¹¹ One of these observations resulted in a detection (Figure 1(d)), at ${\phi }_{b}\approx 0.95$ (Figure 2). On the same day we also did a 1 hr observation using the new GBT C-band receiver, centered at 4.8 GHz with 800 MHz bandwidth, and detected the pulsar with an estimated flux density of $\approx 40\;\mu \mathrm{Jy}$ (Figure 1(e)).

Additionally, we observed PSR J1417–4402 during 2015 April–June at Parkes at 0.7 GHz (once for 0.6 hr) and 3.1 GHz (twice for a total of 1.3 hr), and at the GBT at 350 MHz (three times, 0.6 hr). Finally, in a different Parkes survey of Fermi unidentified sources, we had also observed its location at 1.4 GHz in 2014 July (three times, 2.1 hr). None of these observations resulted in detections.

There are currently too few radio detections to obtain a phase-connected timing solution. However, the existing detections (all of which indicated orbital acceleration) were sufficient to determine that PSR J1417–4402 is the neutron star in the Strader et al. (2015) binary: it has the same orbital period and its phase is $180^\circ$ shifted from that of the optical star. In order to obtain the parameters listed in Table 2 we first extracted pulse times of arrival (TOAs) from all detections. Using the TEMPO¹² timing software we fit each day's TOAs to a model including spin frequency and up to two derivatives as needed. We then did a least-squares fit of a circular orbit ($e\lt 0.02$ according to Strader et al. 2015) to the resulting overall set of Doppler-shifted barycentric spin frequencies. We also used TEMPO to directly fit a zero-eccentricity binary model to the TOAs, allowing for an arbitrary offset between daily sets of TOAs (i.e., the resulting solution is not phase connected). The parameters and uncertainties given in Table 2 encompass the sets of values returned by these two independent fits. Our scant detections currently span a narrow range of binary phases (Figure 2), and we expect greatly improved orbital parameters as detections accumulate; nevertheless, our values for P_b and ${T}_{{\rm{asc}}}$ already have 10 times the precision of those obtained from optical observations.

Table 2.  Parameters of PSR J1417–4402

Parameter	Value
Timing Parameters
Right ascension, R.A. (J2000.0)a	${14}^{{\rm{h}}}{17}^{{\rm{m}}}30\buildrel{\rm{s}}\over{.} 604$
Declination, decl. (J2000.0)a	$-44^\circ 02^{\prime} 57\buildrel{\prime\prime}\over{.} 37$
Spin period, P (ms)	2.6642160(4)
Dispersion measure, DM (pc cm−3)	55.00(3)
Binary period, Pb (d)	5.37372(3)
Projected semimajor axis, x1 (l-s)	4.876(9)
Time of ascending node, ${T}_{{\rm{asc}}}$ (MJD)	57111.457(2)
Derived Parameters
Galactic longitude, l	$318\buildrel{\circ}\over{.} 86$
Galactic latitude, b	$16\buildrel{\circ}\over{.} 14$
DM-derived distance, d (kpc)b	1.6
Pulsar mass function, f1 ( M☉)	0.00433

Notes. Numbers in parentheses represent uncertainties on the last digit. See Section 2.2 for a description of the fits.

^aFixed at the optical position (Strader et al. 2015). ^bFrom the electron density model of Cordes & Lazio (2002) (see Section 3.1).

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The Swift X-ray Telescope (XRT, Burrows et al. 2005) observed PSR J1417–4402 in 2015 March and June, for a total of 12.5 ks. The eight observations in March spanned slightly more than one binary orbit (Table 3). We processed all Swift observations using FTOOLS version 6.16.¹³ The 0.3–10 keV spectrum and light curve from the XRT photon counting mode data were obtained with XSELECT. The source events were extracted from a circular aperture of radius 20 pixels (47''), while the background was taken from an annulus with an inner radius of 60 pixels and an outer radius of 110 pixels.

Table 3.  Swift XRT and UVOT Observations of PSR J1417–4402

ObsID	Date	Exposure Time	Binary Phasea	XRT Count Rate	UVOT Filter	Magnitudeb
	(UT)	(ks)	(${\phi }_{b}$)	(0.3–10 keV) (10−2 s−1)
00084749001	2015 Mar 13	0.4	0.89	${1.8}_{-0.7}^{+0.9}$	uvm2	$\gt 18.60$
00084749002	2015 Mar 14	1.8	0.94	${1.2}_{-0.3}^{+0.4}$	uvw1	$18.98\pm 0.11\pm 0.03$
00084749004	2015 Mar 15	1.6	0.33	1.1 ± 0.3	u	$18.22\pm 0.05\pm 0.02$
00084749005	2015 Mar 16	1.8	0.41	2.35 ± 0.45	uvw2	$\gt 20.26$
00084749006	2015 Mar 17	0.5	0.55	4.0 ± 1.0	uvm2	$\gt 19.93$
00084749007	2015 Mar 18	1.4	0.78	${0.8}_{-0.3}^{+0.4}$	uvw1	$\gt 18.22$
00084749008	2015 Mar 19	1.4	0.95	1.3 ± 0.4	u	$17.85\pm 0.04\pm 0.02$
00084749009	2015 Mar 20	1.7	0.09	1.8 ± 0.4	uvw2	$\gt 19.84$
00084749010	2015 Jun 18	2.1	0.82	1.7 ± 0.3	uvw1	$19.28\pm 0.13\pm 0.03$

Notes. All uncertainties represent 90% confidence levels.

^aPhase 0.75 corresponds to companion superior conjunction. These ${\phi }_{b}$ values are based on the radio ephemeris of Table 2. ^bFor measured magnitudes (in the Vega system, Breeveld et al. 2011), the first uncertainty is statistical and the second is systematic.

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The X-ray count rates appear to show variability, with a maximum at binary phase ${\phi }_{b}=0.55$. However, the probability that the observed counts arise from a constant flux distribution is 2.4% (determined from a ${\chi }^{2}$ fit of a model with a constant count rate to the X-ray light curve), so we cannot rule out the null hypothesis that the flux is constant. The combined time-averaged X-ray spectrum is well-fitted using XSPEC by an absorbed power-law with photon index ${\rm{\Gamma }}={1.59}_{-0.20}^{+0.35}$, column density ${N}_{{\rm{H}}}={2.2}_{-1.3}^{+1.7}\times {10}^{21}$ cm⁻², and an unabsorbed 0.3–10 keV flux of $(8.7\pm 1.5)\times {10}^{-13}$ erg cm⁻² s⁻¹ (all uncertainties in this section represent 90% confidence levels). This is consistent with the spectrum measured from a 2011 Chandra observation (Strader et al. 2015), and corresponds to an X-ray luminosity of $\approx 3\times {10}^{32}\;{(d/1.6{\rm{kpc}})}^{2}$ erg s⁻¹, which we scale according to the DM-derived distance (see Section 3.1 for a discussion of this).

Simultaneously with the XRT, PSR J1417–4402 was observed with the Swift ultraviolet and optical telescope (UVOT, Roming et al. 2005), through a variety of filters. The resulting magnitudes and upper limits are also presented in Table 3. The UVOT photometric measurements were obtained using the uvotsource command in FTOOLS. The source flux was obtained from a 5'' circle, while the background was taken from a source-free circular region of radius 20''. There are two detections in u and two in uvw1. The remaining UV observations yield only upper limits. The implications of these will be discussed in Section 3.2.

Strader et al. (2015) estimate that the PSR J1417–4402 system lies at a distance of $d=4.4\;{\rm{kpc}}$ (with a likely uncertainty of at least 20%) based on the magnitude and optical spectrum of the companion, and assuming that it fills its Roche lobe. Given the poor pulsar detectability (generally low signal-to-noise ratio and frequent eclipses), it is unlikely that a parallax will be measured either interferometrically or through timing observations. But we can estimate the distance from the radio pulsar DM. The Cordes & Lazio (2002) electron distribution model (NE2001) gives ${d}_{{\rm{NE2001}}}=1.6\;{\rm{kpc}}$, while the previously most used electron density model gives ${d}_{{\rm{TC93}}}=3.0$ kpc (Taylor & Cordes 1993).

We favor the NE2001 distance because TC93 generally over-predicts distances and fails to account for the DMs of about 10% of pulsars (Cordes & Lazio 2002, and unpublished reanalysis of the ATNF pulsar catalog). Of 66 pulsars with parallax measurements¹⁴ , 17 have DMs between 35 and 75 pc cm⁻³ (compared to 55 pc cm⁻³ for PSR J1417–4402). Of these, 10 have NE2001-estimated distances that are consistent to within 20% of the parallax distance ranges (only one of the 10 had a well constrained distance used to construct NE2001). The remaining seven objects have distances that disagree by more than 20%, in some cases by a factor of 2. Four have NE2001 distances larger than the parallax distances and the opposite is the case for the other three pulsars.

We conclude that there is no identifiable distance bias in NE2001 (as there is for TC93) and that the NE2001 distance is the best provisional DM-based distance estimate. However, due to possible variations in the scale height of the electron density distribution, there is considerable uncertainty in determining DM distances to pulsars at high Galactic latitude when ${\rm{DM}}\;\mathrm{sin}| b|$ is comparable to its maximum value (see Figure 1 of Cordes & Lazio 2003). PSR J1417–4402 falls in this uncertain regime. Also, a recent study reports new MSP parallax distances that in some cases differ from the NE2001 distances by a factor of 2 (Matthews et al. 2016). Therefore, we do not exclude a larger distance such as that derived by Strader et al. (2015). The conflict between these independent distance measurements, 4.4 and 1.6 kpc, extends to the assumptions made by Strader et al. (2015) in modeling the inclination angle of the system and the masses, because the star would only fill a fraction of the Roche lobe if at the smaller DM-based distance. These issues are discussed in Section 3.3.

Strader et al. (2015) concluded that an accretion disk is present, primarily because of the double-peaked Hα emission line, but also because the X-ray luminosity at their preferred distance of 4.4 kpc is consistent with those of transitional MSPs in their disk states. The detection of radio pulsations from PSR J1417–4402 brings that interpretation into question because the transitional MSPs PSR J1023+0038 (Bogdanov et al. 2015) and XSS J12270−4859 (Hill et al. 2011) show no evidence for radio pulsations in their accreting states. Along with the detection of accretion-powered X-ray pulsations in both systems (Archibald et al. 2015; Papitto et al. 2015), this is an indication that the radio pulsar mechanism of these two MSPs is completely quenched by the accretion flow (see also Cordes & Shannon 2008, and references therein).

If the lower DM distance is adopted, the X-ray luminosity of $\approx 3\times {10}^{32}{(d/1.6{\rm{kpc}})}^{2}$ erg s⁻¹ (Section 2.3) is comparable to ∼10³² erg s⁻¹ measured for the nearby redback PSR J1723−2837 (Bogdanov et al. 2014) and lower than the average accreting luminosity of the transitional MSPs (e.g., Linares 2014). Non-thermal X-rays typically observed in redbacks seems to originate from an intra-binary shock driven by the interaction of the pulsar wind and matter from the companion (Arons & Tavani 1993). However, the uncertain distance to PSR J1417–4402 (Section 3.1) and possible X-ray variability (Strader et al. 2015 and Section 2.3) make existing X-ray observations an unreliable discriminator for the presence or absence of accretion.

Even if no accretion flow is reaching the neutron star and the X-rays are not accretion powered, a disk that is truncated at the magnetospheric radius or beyond could still radiate in the ultraviolet and visible. However, the optical and UV continuum data disfavor an accretion disk. While Strader et al. (2015) measured a V₀ magnitude (corrected for extinction) spanning 15.64–15.91, PSR J1417–4402 is much fainter in u and especially in the UV filters (Table 3). Correcting the Swift u magnitudes for an extinction A_u = 0.50 (Schlafly & Finkbeiner 2011), we find u₀ = 17.35 and 17.72 at ${\phi }_{b}=0.95$ and 0.33, respectively. Then $1.7\leqslant {u}_{0}-{V}_{0}\leqslant 1.9$, which is in the correct range for giant stars of spectral type G8–K0, which have $1.5\leqslant {U}_{0}-{V}_{0}\leqslant 1.9$ (Pickles 1998). This is the type inferred by Strader et al. (2015) from the optical spectrum of the companion. Thus, there is no evidence for extra light in the ultraviolet coming from an accretion disk. Also, the ultraviolet flux detections, being higher at ${\phi }_{b}=0.95$ than at ${\phi }_{b}=0.33$, and faintest at ${\phi }_{b}=0.82$, are consistent in magnitude and phase with the observed modulation due to ellipsoidal variations that dominate the optical light curves in Strader et al. (2015).

However, since the companion star is likely a giant or subgiant (see below), it is brighter than the redback companions and could mask an accretion-disk component. We can estimate an upper limit on a mass-transfer rate under the conservative assumption that $\lt 50\%$ of the minimum observed u-band flux is contributed by a standard blackbody disk (Frank et al. 2002) that is truncated at the pulsar corotation radius, ${r}_{{\rm{co}}}=36$ km for a 2 M_☉ neutron star. For an inclination angle of $58^\circ$ (see Section 3.3) and a distance of 1.6 kpc, the limit is $\dot{m}\lt 4\times {10}^{14}$ g s⁻¹. The u-band luminosity of a disk is barely changed even if it is truncated at the light cylinder radius, ${r}_{{\rm{lc}}}=127$ km for PSR J1417–4402.

This can be compared with $\dot{m}\approx 1\times {10}^{15}$ g s⁻¹ estimated by Papitto & Torres (2015) for the demonstrably accreting transitional objects PSR J1023+0038 and XSS J12270−4859 using similar assumptions. And if the distance to PSR J1417–4402 is actually 4.4 kpc, then it could have a similar accretion rate as the transitional pulsars. Note that, in all of these cases, a disk with such a low accretion rate cannot actually reach the corotation radius, and most of the matter is propelled away (Papitto & Torres 2015). This leaves the possibility that the Hα could be emitted either from the outer disk or in a wind.

The current properties of PSR J1417–4402 appear to be most reminiscent of the eclipsing radio MSP J1740−5340 in the globular cluster NGC 6397 (D'Amico et al. 2001), which is bound to a "red straggler"/sub-subgiant companion in a 1.3 day orbit. However this system was likely formed in an exchange interaction in the dense cluster environment (Orosz & van Kerkwijk 2003), with an evolutionary path substantially different from that of PSR J1417–4402. The bolometric luminosity of the PSR J1417–4402 companion, determined by Strader et al. (2015) for a distance of 4.4 kpc, is reduced by a factor of 7.6 at the DM-derived 1.6 kpc, making it comparable to that of subgiants. PSR J1740−5340 exhibits radio eclipses around superior conjunction for 40% of the orbit, as well as random DM variations at all phases. Its X-ray spectrum is non-thermal (with ${\rm{\Gamma }}=1.7$) and possibly modulated at the binary period (Bogdanov et al. 2010), suggestive of an intra-binary shock. Perhaps most importantly, PSR J1740−5340 also exhibits a prominent Hα emission line with complex morphology and strong orbital phase dependence (Sabbi et al. 2003), which can be interpreted as being produced in part by a wind from the secondary star that is driven out of the binary by the pulsar wind. The clear evidence for an active rotation-powered radio pulsar suggests that PSR J1417–4402 is presently in the so-called "radio ejection" regime (Ruderman et al. 1989; Burderi et al. 2002) in which any Roche lobe overflow through the L1 point cannot overcome the barrier imposed by the pulsar wind pressure. A larger orbit actually favors this scenario according to Burderi et al. (2002).

One might also consider the possibility that the system transitions rapidly between accreting and non-accreting states. But Hα emission, as evidence for accretion, was detected by Strader et al. (2015) in more than one dozen observations spanning 1 year through 2015 February, while the first detection of radio pulsations, ruling out accretion onto the neutron star, occurred only one month later (Section 2.1). Given all the available evidence, we favor an interpretation in which the PSR J1417–4402 system was not accreting at the time of the optical and radio observations.

If the mass ratio and the inclination angle of the system can be determined with precision, then the mass of the neutron star can also be measured. This is of particular interest because Strader et al. (2015) concluded that the neutron star is massive, ${M}_{1}=1.97\pm 0.15$ M_☉. Assuming a tidally locked, Roche-lobe filling secondary, they obtained a mass ratio $q\equiv {M}_{2}/{M}_{1}=0.18\pm 0.01$ from a measurement of the projected rotational velocity of the secondary (which has unspecified systematic uncertainties) and its radial velocity semi-amplitude ${K}_{2}=115.7\pm 1.1$ km s⁻¹. They also assumed a Roche-lobe filling star to fit the optical light curves for the orbital inclination angle using an ellipsoidal model, finding $i=58^\circ \pm 2^\circ$.

Using the pulsar projected semimajor axis x₁ (Table 2) we infer that the pulsar radial velocity semi-amplitude is 19.8 km s⁻¹. Along with K₂ this implies $q=0.171\pm 0.002$, limited by the precision on K₂. Figure 3 shows the masses of the neutron star and companion as a function of inclination angle, allowing for the uncertainties on K₂ and x₁. For $56^\circ \leqslant i\leqslant 60^\circ$, M₁ ranges over 1.77–2.13 M_☉, and ${M}_{2}=0.33\pm 0.03$ M_☉. However, if located at the smaller DM-based distance, the radius of the companion is only 0.36 times the Roche-lobe radius; its tidal distortion is reduced, and a larger i would be necessary to fit the ellipsoidal modulation, resulting in smaller masses. The minimum allowed masses (for $i=90^\circ$) are ${M}_{2}\geqslant 0.20$ M_☉ and ${M}_{1}\geqslant 1.15$ M_☉. The Roche lobe radius decreases only slightly, from 4.1 R_☉ at $i=58^\circ$ to 3.5 R_☉ at $i=90^\circ$ according to the formula of Eggleton (1983), so a higher inclination at the smaller distance would not allow the companion to contact the Roche lobe.

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The optical light curves (Strader et al. 2015), dominated as they are by ellipsoidal modulation, show no evidence for heating of the companion's photosphere by the pulsar wind. This is probably because the intrinsic luminosity of the giant/subgiant dominates. We can place an upper limit on the spin-down luminosity $\dot{E}$ of the pulsar, or more precisely, on the product of $\dot{E}$ and an efficiency factor η that includes the physics of reprocessing and any anisotropy of the pulsar wind. A heating effect can be approximated using $\eta \dot{E}{R}_{2}^{2}/4{a}^{2}=2\pi {R}_{2}^{2}\sigma ({T}_{h}^{4}-{T}_{{\rm{eff}}}^{4})$, where ${T}_{{\rm{eff}}}$ is the intrinsic temperature of the unheated star, T_h is the average temperature of the side facing the pulsar, R₂ is the radius of the companion, and a is the orbital separation.

We use ${T}_{{\rm{eff}}}=5000$ K from the optical spectrum of Strader et al. (2015), and assume an upper limit of 5200 K for T_h based on the absence of a heating signature at the level of 0.1–0.2 magnitudes. For $i=58^\circ$, the orbital separation is a = 17 R_☉, and the limit on $\eta \dot{E}$ is $2.1\times {10}^{35}$ erg s⁻¹. If instead we assume as a maximum $i=72^\circ$ (for which M₁ = 1.4 M_☉), then a = 15.2 R_☉ and $\eta \dot{E}\lt 1.7\times {10}^{35}$ erg s⁻¹. Neither of these limits are very restrictive, as η is likely to be less than unity. These limits can also accommodate the gamma-ray luminosity of 3FGL J1417.5–4402, 3 × 10³⁴ erg s⁻¹ at a distance of 4.4 kpc (see Section 4).

With a binary period of 5.4 days, PSR J1417–4402 is on the evolutionary track of low-to-intermediate mass companions that started mass transfer onto a neutron star after they left the main sequence (Podsiadlowski et al. 2002), and have increasing periods. This distinguishes them from the black widows, redbacks, and other low-mass X-ray binaries that have binary periods $\leqslant 1$ day, began mass transfer on the main sequence, and evolve toward shorter periods. For 1 M_☉ secondaries, these classes are separated by a bifurcation period of $\approx 18$ hr at the onset of mass transfer.

With ${M}_{2}\approx 0.3$ M_☉, the companion of PSR J1417–4402 must have already lost most of its initial mass, only a fraction of which, accreting onto the neutron star, is sufficient to spin it up to 2.66 ms. In the models of Podsiadlowski et al. (2002), PSR J1417–4402 is not far from the ends of the tracks that terminate when the binary period is in the range 6–20 days, and the companion is a He white dwarf of 0.2–0.3 M_☉. The neutron stars in these calculations, assumed to begin with 1.4 M_☉, end in the range 1.8–2.2 M_☉. Exactly how far PSR J1417–4402 is along this evolution is difficult to determine, since its companion may or may not be filling its Roche lobe, may or may not be finished accreting onto the neutron star, and may be losing mass mostly through ablation by the pulsar wind, a process that is difficult to model.