Abstract
We report the discovery of PSR J0952−0607, a 707
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1. Introduction
The discovery of the first millisecond pulsar (MSP), PSR B1937+21 with a spin frequency of 642
It is striking that, since the discovery of PSR B1937+21, only one faster-spinning MSP has been found (PSR J1748−2446ad, in the globular cluster Terzan 5, spinning at 716
Physical effects such as decoupling of the Roche lobe (Tauris 2012), transient accretion (Bhattacharyya & Chakrabarty 2017), and gravitational-wave emission (Chakrabarty et al. 2003) have been put forward to explain the observed spin frequency cutoff. Observationally, there are additional challenges in detecting submillisecond pulsars, compared to canonical MSPs with spin frequencies between 200 and 500
Watts et al. (2015) suggest that a possible bias against finding rapidly spinning pulsars, and hence energetic MSPs, may be the irradiation-driven mass loss from the binary companion, which can lead to eclipses of the radio signal during large parts of the orbit (Stappers et al. 2014; Roy et al. 2015). Similar considerations were previously presented by Tavani (1991), motivated by the discovery of the first eclipsing black widow pulsar binary system, PSR B1957+20, in which the low-mass, bloated companion star is irradiated by the pulsar wind (Fruchter et al. 1988). Indeed, there is evidence that the eclipsing MSP systems—both the black widows with very-low-mass companions and the redbacks with higher-mass ( ) companions—are on average spinning faster than "classical" MSPs with white dwarf companions (Hessels 2008; Papitto et al. 2014). For eclipsing systems, there is again an advantage toward observing at higher radio frequencies, where the eclipse durations are typically lower (Archibald et al. 2009), but also the disadvantage that the intrinsic pulsar spectrum is generally falling off rapidly toward higher frequencies.
Recent results by Kuniyoshi et al. (2015), Kondratiev et al. (2016), and Frail et al. (2016) indicate that the fastest-spinning MSPs tend to have the steepest radio spectra (), pointing to another possible bias against finding fast-spinning MSPs in ongoing surveys, which focus on central observing frequencies around 350 MHz (Deneva et al. 2013; Stovall et al. 2014) and 1.4 GHz (Cordes et al. 2006; Keith et al. 2010; Barr et al. 2013). As a result, radio pulsation searches at frequencies below 300 MHz have the potential of opening up a so far largely unexplored parameter space, in the cases where IISM scattering is low and eclipsing does not hinder detection either.
Here, we present the discovery of PSR J0952−0607, a very-steep-spectrum MSP, which is now the fastest-spinning neutron star known in the Galactic field (outside of a globular cluster). PSR J0952−0607 was found in a radio pulsation survey using the Low-Frequency Array (LOFAR; Stappers et al. 2011; van Haarlem et al. 2013) to target unassociated Fermi
2. Observations and Analysis
2.1. Radio
PSR J0952−0607 was discovered as part of an ongoing LOFAR survey at 135 MHz, continuing on the pilot survey by Pleunis et al. (2017). Unassociated
The
PSR J0952−0607 was discovered blindly at high significance in four of the seven tied-array beams at a spin frequency of 707
Follow-up observations (10 minute integration times) were obtained with the HBAs from 23 LOFAR core stations (longest baseline of 3.5 km) using 7 tied-array beams with 39 MHz of bandwidth centered at 135 MHz on 2017 January 4 (initial follow-up gridding observation) and a single beam with the full HBA band (78 MHz at 149 MHz) for all subsequent observations. These observations allowed us to refine the position of the pulsar and start the timing program. A 3 hr HBA integration was obtained on 2017 January 28/29 to constrain the orbital parameters. To determine the radio spectrum of PSR J0952−0607, we obtained a 2 hr integration with the LOFAR low-band antennas (LBAs) between 30 and 90 MHz on 2017 February 5/6 and a 47 minute observation at 350 MHz (100 MHz bandwidth) on 2017 March 1 with GUPPI (DuPlain et al. 2008) at the Green Bank Telescope (GBT). The pulsar was not detected in the LOFAR LBA observation, but was easily seen in the GBT 350 MHz observation.
The complex voltage data of the discovery and follow-up LOFAR HBA observations were coherently dedispersed and folded with dspsr (van Straten & Bailes 2011) and analyzed using psrchive (Hotan et al. 2004) tools. Pulse profiles for two-minute sub-integrations were referenced against an analytical pulse profile template to obtain time-of-arrival (TOA) measurements. A phase-connected timing solution, accounting for every rotation of the pulsar, was determined from these TOAs using tempo2 (Edwards et al. 2006; Hobbs et al. 2006).
2.2. Optical
We observed the field of PSR J0952−0607 using the Wide Field Camera (WFC) on the 2.54 m Isaac Newton Telescope at the Roque de Los Muchachos on La Palma. A dithered set of 240 two-minute exposures with a Sloan filter were obtained on 2017 January 17 and 18 under good conditions with seeing. The WFC consists of four pixel CCDs, sampled at pix−1. In the following, we use data from the center chip, which contains the location of PSR J0952−0607. All images were bias-subtracted and flat-fielded using dome flats and subsequently registered using integer pixel offsets. To improve the signal-to-noise ratio, we co-added between 5 and 20 images that were consecutive in time.
We determined instrumental magnitudes through point-spread-function (PSF) fitting using DAOphot II (Stetson 1987) and calibrated against -band photometry from Pan-STARRS 1 DR1 (Chambers et al. 2016; Magnier et al. 2016). Astrometric positions from the GAIA DR1 catalog (Gaia Collaboration et al. 2016) were used for the astrometric calibration. A total of 58 GAIA stars overlapped with an subsection of a co-added image of 10 time consecutive two-minute integrations. To correct for the considerable distortion in the WFC camera, cubic polynomials were used to relate pixel positions to R.A. and decl. After iteratively removing two outliers, the astrometric calibration yielded rms residuals of in R.A. and in decl.
2.3. X-Ray
We obtained a 4.6 ks Swift/XRT observation of PSR J0952−0607 on 2017 March 14 in photon-counting mode. The HEASOFT tools were used for standard calibration and extraction of events from a circular region with a radius of 71'' and an annulus with inner and outer radii of 71'' and 142'', centered on the position of the optical counterpart (see below). Using standard response and exposure map calibration files, we find that the count rate at the position of PSR J0952−0607 is consistent with background noise, and that the X-ray counterpart to PSR J0952−0607 is not detected.
3. Results
The phase-connected timing solution models the rotation and orbit of PSR J0952−0607. As the timing solution has a time baseline of approximately a third of a year, the spin parameters (
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Standard image High-resolution imageThe binary companion to PSR J0952−0607 is located at and . The positional uncertainty quoted is the quadratic sum of the uncertainty in the astrometric calibration and the positional uncertainty of the companion on the co-added image (of order ). To estimate the impact of the uncertainty in the optical position of the binary companion on the parameters of the timing solution, we performed a Monte Carlo simulation, drawing positions (, ) from normal distributions with appropriate means and widths. For each of these positions, the remaining parameters in the timing solution were fitted to generate distributions from which the parameters and their uncertainties were determined. These values are listed in Table 1. Taking into account the positional uncertainties yields a 3
Table 1. Parameters for PSR J0952−0607
Parameters | Value |
---|---|
Timing Parameters | |
R.A., | |
Decl., | |
Spin frequency, |
|
Spin frequency derivative, (s−2) | |
Epoch of timing solution (MJD) | 57800 |
Dispersion measure, DM (pc cm−3) | |
Binary model | ELL1 |
Orbital period, Pb (day) | |
Projected semimajor axis, x (s) | |
Time of ascending node passage, Tasc (MJD) | |
Solar system ephemeris model | DE421 |
Clock correction procedure | TT(BIPM2011) |
Time Units | TCB |
Timing Span (MJD) | 57747.1–57851.9 |
Number of TOAs | 164 |
Weighted rms post-fit residual ( |
5.6 |
Reduced value | 1.11 |
Note. The astrometric parameters ( and ) are kept fixed at the position of the optical counterpart. The eccentricity is kept fixed at e = 0, implicitly assuming that the orbit is circular. For the ELL1 binary model (Lange et al. 2001), this means and .
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Models for the electron distribution in our Galaxy along the line-of-sight to PSR J0952−0607 (, ) constrain the distance through the observed DM. The NE2001 model by Cordes & Lazio (2002) predicts a distance of , while the YMW16 model (Yao et al. 2017) places it significantly farther away at . At either distance, the Galactic extinction model by Green et al. (2014, 2015) estimates the same reddening of , leading to an extinction of (Schlafly & Finkbeiner 2011).
The orbital parameters from the timing solution (Table 1) show that PSR J0952−0607 is in a 6.42 hr binary around an ultra-low-mass companion. The mass function is , setting the minimum companion mass at 0.019 M for a 1.4 M pulsar. These properties are consistent with PSR J0952−0607 being a black widow system, where matter from the companion is ablated by the energetic pulsar wind (e.g., Fruchter et al. 1988; see Roberts 2013 for a review).
The black widow nature of PSR J0952−0607 is confirmed by the sinusoidal optical light curve, which is consistent with irradiation of the companion hemisphere facing the pulsar. We use the Icarus software (Breton et al. 2012) to model the -band light curve. As the absence of color information precludes a full parameter fit, we make the following assumptions to estimate system parameters. We assume that the companion is co-rotating and that its base temperature (that of the unirradiated hemisphere) is 2500 K—in line with what is seen in other black widows (see, e.g., Stappers et al. 2001; van Kerkwijk et al. 2011; Romani et al. 2016)—and hence contributes minimally to the flux of the irradiated hemisphere. The reddening is kept at (see above), and the pulsar mass is fixed at 1.4 M⊙. Finally, we require the dayside temperature to be such that the implied irradiation represents of order 10% of the spin-down luminosity for an assumed credible range from 5 × 1034 to erg s−1 (Breton et al. 2013).
We find that the observed light curve is mostly inconsistent with models that assume a filling factor of unity (i.e., where the companion fills the Roche lobe), as it leaves the orbital inclination largely unconstrained, though leaning toward edge-on (), with tightly correlated dayside temperatures and distances in the range of 4500–5800 K and 2.3–5.3 kpc, respectively. The goodness of fit improves significantly for models with an assumed filling factor of 0.5, providing a well-defined inclination of . The correlation between dayside temperature and distance is weaker, yielding similar dayside temperatures and slightly smaller distances (1.7–3.8 kpc). Models with the filling factor as a free parameter prefer slightly smaller filling factors while the overall goodness of the fit is not significantly increased. These models provide similar constraints on the inclination, dayside temperature, and distance, with even weaker correlations due to the extra free parameter.
We conclude that PSR J0952−0607 is almost certainly not close to Roche-lobe filling, with an orbital inclination in the intermediate range. The predicted model distances are at the high end of those estimated from the DM, which may suggest Roche-lobe filling factors of 0.5 or less, or lower dayside temperatures, indicating spin-down luminosities of a few 1034 erg s−1 or that the conversion of spin-down into heating is less than 10% efficient. Upcoming multi-color photometry will be able to confirm these values.
The low Roche-lobe filling factor and low inclination are consistent with the absence of eclipses of the radio signal in the observations obtained so far. Eclipses are seen in the majority of black widow systems, and eclipses are generally most pronounced at low observing frequencies (e.g., Stappers et al. 1996; Archibald et al. 2009). Besides eclipses, ionized matter passing through the line-of-sight leads to increases in the DM near orbital phase , resulting in delays in the TOAs. The TOA residuals in Figure 3 do show systematic delays at –0.28, possibly hinting at the presence of ionized material in the line-of-sight. The ongoing LOFAR timing observations will constrain whether material is ablated from the companion of PSR J0952−0607.
We use the Hamaker (2006) model for the LOFAR HBA beam together with the radiometer equation and the method as detailed in Kondratiev et al. (2016) to obtain flux density measurements for PSR J0952−0607 over the HBA band between 110 and 188 MHz. Measurements from five different observations, totaling 1 hr of integration time, were averaged. The flux density at 350 MHz was measured from the single GBT observation, using the radiometer equation with gain, system temperature, and bandwidth values from Stovall et al. (2014). We obtain , 32, 21, 9, and 1.5 mJy at frequencies of 119.6, 139.2, 158.7, 178.2, and 350 MHz. Following Bilous et al. (2016), we conservatively estimate 50% uncertainties in the flux density measurements. Modeling the spectrum with a power law over frequency
Figure 1 shows the cumulative pulse profile of PSR J0952−0607 at different frequencies, revealing significant evolution with observing frequency. The pulse profile evolves from two double-peaked components at an observing frequency of 350 MHz to two scatter-broadened components at LOFAR frequencies. To estimate the scattering timescale, we approximate scatter broadening as a convolution with a truncated exponential, appropriate for a thin scattering screen (Williamson 1972), and assume that scatter broadening can be neglected in the 350 MHz pulse profile such that it can be treated as the intrinsic profile. The four components are modeled with von Mises functions and the amplitude of the four components was allowed to vary with frequency, while positions and widths are kept fixed. Using this model we find scattering times of 47 and 113
These scattering timescales indicate that the scatter broadening exceeds the pulse period for observing frequencies below 70 MHz, assuming scattering scales as . As the LBA sensitivity peaks near 60 MHz, where the pulsed signal will be scattered out completely, it is not surprising that PSR J0952−0607 is not detected with the LOFAR LBA.
The Swift/XRT X-ray non-detection of PSR J0952−0607 translates to a flux limit in the 0.3–10 keV band of erg s−1 cm−2 for absorbed blackbody ( keV) and power-law () spectra. Here, we assumed cm−2 estimated from the optical reddening through the relation by Güver & Özel (2009). The resulting X-ray luminosity limits (0.3–10 keV) are erg s−1 at a distance of 0.97 kpc and erg s−1 at 1.74 kpc. These limits are consistent with the observed relation between the X-ray luminosity and spin-down luminosity of radio MSPs (Possenti et al. 2002).
4. Discussion and Conclusions
PSR J0952−0607 has a spin frequency . This makes it the fastest-spinning neutron star known in the Galactic field (outside of a globular cluster), surpassing the 35 year record set by the first MSP to be discovered, PSR B1937+21, which spins at 642
For PSR J1748−2446ad it is not possible to determine the intrinsic of the neutron star because the observed change in spin rate with time is dominated by acceleration in the gravitational potential of Terzan 5 (Prager et al. 2016). Conversely, it will be possible to measure PSR J0952−0607's intrinsic spin-down rate and the inferred surface magnetic field, once a full timing solution is available. These measurements will shed light on the question of whether the fastest-spinning radio MSPs also typically have the lowest magnetic fields. The current limit of G already qualifies PSR J0952−0607 as one of the most weakly magnetized pulsars known.
Including PSR J0952−0607, there are 14 Galactic radio MSPs with , of which 5 are in black widow systems, 4 are isolated pulsars, 3 are in redback systems, and 2 have white dwarf companions. The abundance of black widow and redback systems among the fastest-spinning MSPs may hint at an evolutionary origin, possibly related to the accretion process and the amount of accreted matter (Hessels 2008; Papitto et al. 2014).20 We note that radial velocity measurements and light curve modeling of the black widow companions to PSR B1957+20 ( Hz) and PSR J1301+0833 ( Hz) indicate that the MSPs are heavy, with masses of 2.40 ± 0.12 M (van Kerkwijk et al. 2011) and (Romani et al. 2016), respectively. Future photometric and spectroscopic observations of the companion of PSR J0952−0607 could test this hypothesis.
Besides the short spin period, PSR J0952−0607 is remarkable due to its steep radio spectrum. At , its spectral index is among the steepest known compared to recent studies by Kuniyoshi et al. (2015), Kondratiev et al. (2016), and Frail et al. (2016). Our LOFAR and GBT observations should be robust against scintillation, as the bandwidths and integration times used substantially exceed the scintillation bandwidth and timescale toward PSR J0952−0607 (Cordes & Lazio 2002).
The steep spectrum of PSR J0952−0607 adds to the emergent picture where the fastest-spinning MSPs tend to have the steepest spectra, but also that the steepest spectra MSPs tend to be detected by Fermi in
The discovery of PSR J0952−0607 and the previous LOFAR discovery of PSR J1552+5437 (Bassa et al. 2017; Pleunis et al. 2017) demonstrate the potential of MSP searches at unconventionally low radio observing frequencies. Such searches are more sensitive to the population of ultra-steep-spectrum radio MSPs () and can explore whether even faster-spinning, potential submillisecond pulsars can be formed in nature but have previously been missed at higher observing frequencies. Unfortunately, low-frequency searches still suffer from limitations due to IISM scattering and eclipses. However, recent results have demonstrated the power of selecting such sources in low-frequency radio interferometric imaging surveys, where such effects do not affect the detectability of the source, and then following up with deep time-domain searches (Frail et al. 2016). Both imaging-led and direct time-domain search approaches should continue to be exploited.
While there is currently no clear theoretical expectation that the radio spectral index should depend on spin rate, we note that the shrinking size of the light cylinder km could plausibly play a role in spectral steepening because the magnetospheric size becomes comparable to, or smaller, compared to the typical emission height. Furthermore, it is interesting to consider whether the radio emission from the fastest-spinning MSPs is dominated by giant pulse emission from a region co-located with the high-energy
We thank LOFAR Science Operations and Support for their help in scheduling and effectuating these observations. We also thank Caroline D'Angelo, Gemma Janssen, and Alessandro Patruno for useful discussions. C.G.B. and J.W.T.H. acknowledge support from the European Research Council (ERC) under the European Union's Seventh Framework Programme (FP/2007–2013)/ERC grant agreement No. 337062 (DRAGNET; PI: Hessels). R.P.B. had received funding from the ERC under the European Union's Horizon 2020 research and innovation programme (grant agreement No. 715051; Spiders). This Letter is based on data obtained with the International LOFAR Telescope (ILT) under projects LC7_002, DDT7_002 and LT5_003. LOFAR is the Low Frequency Array designed and constructed by ASTRON. It has facilities in several countries, that are owned by various parties (each with their own funding sources), and that are collectively operated by the ILT foundation under a joint scientific policy. The Isaac Newton Telescope and its service programme are operated on the island of La Palma by the Isaac Newton Group of Telescopes in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofísica de Canarias. 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. 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 was performed in part under DOE Contract DE-AC02-76SF00515.
Facilities: LOFAR - , ING:Newton - , Swift - , GBT - , Fermi. -
Software: cdmt, PRESTO, PSRCHIVE, Astropy, ESO-MIDAS, HEASOFT.
Footnotes
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- 20
Furthermore, it has been suggested that the isolated MSPs represent the outcomes of extreme black widow systems, in which the pulsar wind has successfully evaporated the companion star entirely (Fruchter et al. 1988).