Einstein@Home discovery of four young gamma-ray pulsars in Fermi LAT data
We report the discovery of four gamma-ray pulsars, detected in computing-intensive blind searches of data from the Fermi Large Area Telescope (LAT). The pulsars were found using a novel search approach, combining volunteer distributed computing via Einstein@Home and methods originally developed in gravitational-wave astronomy. The pulsars PSRs J0554+3107, J14226138, J15225735, and J1932+1916 are young and energetic, with characteristic ages between and kyr and spin-down powers in the range – erg s. They are located in the Galactic plane and have rotation rates of less than Hz, among which the Hz spin frequency of PSR J0554+3107 is the slowest of any known gamma-ray pulsar. For two of the new pulsars, we find supernova remnants coincident on the sky and discuss the plausibility of such associations. Deep radio follow-up observations found no pulsations, suggesting that all four pulsars are radio-quiet as viewed from Earth. These discoveries, the first gamma-ray pulsars found by volunteer computing, motivate continued blind pulsar searches of the many other unidentified LAT gamma-ray sources.
Subject headings:gamma rays: stars – pulsars: general – pulsars: individual (PSR J0554+3107, PSR J14226138, PSR J15225735, PSR J1932+1916)
The Large Area Telescope (LAT; Atwood et al., 2009) aboard the Fermi Gamma-ray Space Telescope has established pulsars as predominant Galactic gamma-ray sources at GeV energies (Abdo et al., 2013). Most LAT-detected gamma-ray pulsars have been unveiled indirectly. In these cases, known radio pulsar ephemerides are used to assign rotational phases to gamma-ray photons and probe for pulsations. Additionally, dedicated radio searches at positions of unidentified gamma-ray sources as in the Fermi-LAT Second Source Catalog (2FGL; Nolan et al., 2012) discovered many new radio pulsars, likewise providing ephemerides for gamma-ray phase-folding (e.g., Guillemot et al., 2012; Abdo et al., 2013).
For the first time, pulsars have also been detected in direct searches for periodicity in the sparse LAT gamma-ray photons (Abdo et al., 2009). In fact, many pulsars found in such “blind” searches are undetected at radio wavelengths (Ray et al., 2012; Abdo et al., 2013). Blind searches are computationally challenging, because the relevant pulsar parameters are unknown in advance (e.g., Chandler et al., 2001). The challenge is to search a dense grid covering a multidimensional parameter space (for isolated systems: sky location, frequency , and spin-down rate ). The number of grid points to be individually tested increases rapidly with coherent integration time (e.g., Brady et al., 1998): for observations spanning multiple years the finite computing power available makes blind searches with fully coherent (“brute-force”) methods unfeasible, and much more efficient methods are essential.
During the first year of the Fermi mission pioneering blind searches revealed 24 pulsars in LAT data (Abdo et al., 2009; Saz Parkinson et al., 2010) through a clever time-differencing technique (Atwood et al., 2006; Ziegler et al., 2008) that exploits that sparsity of the LAT data. Increasing data time spans intensify the computing burden, and only two more pulsars were found in the second year (Abdo et al., 2013). However, hundreds of unidentified LAT sources with pulsar-like properties (Ackermann et al., 2012; Lee et al., 2012) probably harbor undiscovered pulsars.
The blind-search problem is analogous to searches for continuous gravitational waves (GWs) emitted from spinning neutron stars (Brady et al., 1998), also called “GW pulsars”. This similarity has motivated us to use data-analysis methods originally developed for GW-pulsar detection (Brady & Creighton, 2000; Cutler et al., 2005; Pletsch & Allen, 2009; Pletsch, 2010, 2011) to significantly enhance the sensitivity of blind searches for gamma-ray pulsars.
Using these methods to search LAT data has led to the discovery of new gamma-ray pulsars (Pletsch et al., 2012b, c) on the Atlas computing cluster in Hannover. While these discoveries were isolated young pulsars (with spin frequencies of - Hz), the ongoing searches also cover the higher-frequency range of millisecond pulsars (MSPs). With partial orbital constraints from optical data (Romani, 2012), these methods also discovered a binary MSP via gamma-ray pulsations (Pletsch et al., 2012a).
Searching for fast spinning isolated MSPs dominates the overall computing cost of this survey. To enlarge the available computational resources we have recently moved the survey onto the volunteer computing system Einstein@Home111 http://einstein.phys.uwm.edu/. Here, we present the Einstein@Home discovery and key parameters of four young, energetic pulsars, PSR J0554+3107, PSR J14226138, PSR J15225735, and PSR J1932+1916, detected in the ongoing blind survey of unidentified LAT sources. These are the first gamma-ray pulsars discovered using volunteer computing.
2. Survey and Pulsar Discoveries
The survey targets unidentified 2FGL sources with properties reminiscent of known pulsars. Such selection criteria include significantly curved emission spectra and low flux variability over time (Ackermann et al., 2012), leading to a list of 109 2FGL sources (Pletsch et al., 2012b). Further details on source selection and data preparation are described in Pletsch et al. (2012b).
For each selected target source, a blind search for isolated gamma-ray pulsars has been carried out in three years of LAT data. The parameter space of the search is four-dimensional (sky position, spin-frequency , and ). In the sky, a circular region is searched, centered on the 2FGL-catalog source location having a radius 20% larger than the semi-major axis of the 95% confidence elliptical error region. The survey covers an range up to kHz, in order to be sensitive to MSPs. For Hz, spin-down rates in the range 110 Hz s are searched (see Figure 1). To maintain sensitivity to young pulsars, for Hz the search range is extended down to characteristic ages kyr, comparable to that of the Crab pulsar.
The data-analysis strategy employed in the blind search follows a hierarchical (multistage) approach, outlined in Pletsch et al. (2012b). The first stage explores the full parameter space with an efficient semi-coherent method: coherent Fourier powers computed with a 6 day window are incoherently summed as the window slides along the entire data set. A parameter-space metric (Pletsch & Allen, 2009; Pletsch, 2010; Pletsch et al., 2012b) is used to build an efficient search grid. In the second stage, only significant semi-coherent candidates are followed up via a fully coherent analysis. A third stage further refines coherent pulsar candidates by using higher signal harmonics (adopting the -test of de Jager et al., 1989).
The Einstein@Home volunteer supercomputer does the bulk of the computational work. Einstein@Home was launched in 2005 to search for GW pulsars in detector data from the LIGO-Virgo Collaboration (Abbott et al., 2009a, b; Aasi et al., 2013). Since 2009, Einstein@Home has also been analyzing radio telescope data, finding several new radio pulsars (Knispel et al., 2010, 2011, 2013; Allen et al., 2013). In parallel, Einstein@Home is now also searching for gamma-ray pulsars as described here. This extends the radio and GW efforts with a third distinct search for new neutron stars.
To sign up for Einstein@Home, members of the general public download free software for their Windows, Apple, or Linux computers or Android device. Working in the background, the software automatically downloads work units (executables and data) from the Einstein@Home servers, carries out a search when the host machine is idle, and reports back results. Returned results are automatically validated by comparison of the outcome for the same work unit produced by a different volunteer’s host. With more than 300,000 individuals already contributing, the sustained computing capacity achieved ( PFlop/s) is comparable with the world’s largest supercomputers.
The Einstein@Home results for the formerly unidentified LAT sources, 2FGL J0553.9+3104, 2FGL J1422.5-6137c, 2FGL J1521.8-5735, and 2FGL J1932.1+1913, indicated significant pulsations. All but one of these sources also have counterparts in the Fermi LAT First Source Catalog (1FGL; Abdo et al., 2010), denoted by 1FGL J0553.9+3105, 1FGL J1521.8-5734c, and 1FGL J1932.1+1914c. A dedicated follow-up investigation to further refine the parameters and properties of the newly discovered pulsars is described below.
|Parameter||PSR J0554+3107||PSR J14226138||PSR J15225735||PSR J1932+1916|
|Right ascension, (J2000.0)|
|Galactic longitude, (°)|
|Galactic latitude, (°)|
|Spin frequency, (Hz)|
|Frequency 1st derivative, ( Hz s)|
|Frequency 2nd derivativeaaParameterizes timing noise (and glitch recovery where applicable) rather than pulsar intrinsic spin-down., ( Hz s)|
|Weighted -test (single-trial false alarm probability)|
|Epoch of glitch 1 (MJD)||-||-|
|Permanent increment, ( Hz)||-||-|
|Permanent increment, ( Hz s)||-||-|
|Decaying increment, ( Hz)||-||-||-|
|Decay time constant, (days)||-||-||-|
|Epoch of glitch 2 (MJD)||-||-||-|
|Permanent increment, ( Hz)||-||-||-|
|Permanent increment, ( Hz s)||-||-||-|
|Characteristic age, (kyr)|
|Spin-down power, ()|
|Surface magnetic field strength, (G)|
|Light-cylinder magnetic field strength, (kG)|
|Estimated maximum distancebbAssuming 100% efficiency () and , gives rise to ., (kpc)|
|Estimated “heuristic” distanceccAssuming a “heuristic” luminosity erg s erg s and , yields ., (kpc)|
|Cutoff energy, (GeV)|
|Photon flux above 100 MeV, ( photons cm s)|
|Energy flux above 100 MeV, ( erg cm s)|
|Peak to separation||-||-|
|Peak to separation||-||-||-|
|Radio-flux-density upper limit at 1.4 GHz, (Jy)||66||60||34||75|
Note. – The data time span is – MJD. The JPL DE405 Solar System ephemeris has been used; times refer to Barycentric Dynamical Time (TDB). Numbers in parentheses are statistical 1 errors in the last digits.
3. The Four Gamma-ray Pulsars
For follow-up analysis, we extended the original data sets to include LAT photons recorded from 2008 August 4 until 2013 April 1. We used the Fermi Science Tools222http://fermi.gsfc.nasa.gov/ssc/data/analysis/scitools/overview.html (STs) to select “Source”-class photons according to the P7_V6 instrument response functions (IRFs), with reconstructed directions within 15°of the pulsars, energies above 100 MeV, and zenith angles °. We excluded photons recorded when the LAT’s rocking angle exceeded 52°, or when the LAT was not in nominal science mode. We assigned each photon a weight measuring the probability of having originated from the pulsar (as was also done for the search). These weights (Kerr, 2011) were computed with gtsrcprob based on a spectral model of the region (described below) and the LAT IRFs. This photon-weighting scheme improves the signal-to-noise ratio of the pulsations, providing better background rejection than simple angular and energy cuts.
With these LAT data sets, we refined the initial pulsar parameters after discovery, using the methods by Ray et al. (2011). We subdivided the data sets into segments of about equal length and produced pulse profiles for all segments by folding the photon times with the initial parameters. These pulse profiles were correlated with “template” profiles to obtain pulse times of arrival (TOAs). Using Tempo2 (Hobbs et al., 2006) we fitted the TOAs to a timing model with sky position, frequency and frequency derivatives. Table 1 presents the best-fit timing solutions.
For two of the pulsars, PSRs J14226138 and J15225735, the timing analysis reveals the presence of glitches, manifested as abrupt changes of the stars’ rotation rates. These significantly complicate the timing procedure: if not additionally accounted for, they can lead to loss of phase-coherence.
In dedicated studies, we examined the spin-parameter changes associated with the glitches. For each of the two pulsars, we fixed the sky position to the pre-glitch timing solution, and scanned ranges in on a dense grid around the pre-glitch spin parameters. At each grid point we computed the weighted -test statistic (Kerr, 2011) using photons within a fixed time window. This window was slid over the entire data set with 90% overlap between subsequent steps. The results are shown in Figure 2. The choice of time-window size balances signal-to-noise ratio and time resolution, being just long enough to still accumulate a detectable signal-to-noise ratio. These results enabled us to estimate values for the spin-parameter changes and glitch epochs for PSRs J14226138 and J15225735. We then iterated the timing procedure including a corresponding glitch model. The inferred glitch parameters are given in Table 1. In addition to permanent changes in and , the glitch model for J15225735 also includes a frequency increment that decays exponentially on the timescale (Hobbs et al., 2006). Thus, the net effect after this spin-up glitch recovery is a spin-down, as shown in Figure 2(b).
Figure 3 shows the integrated pulse profiles and phase-time diagrams obtained from the full timing solutions. To characterize the profiles we fitted the observed gamma-ray light curves with combinations of Lorentzian and/or Gaussian lines. The complex pulse profile of PSR J0554+3107 was fitted using asymmetric Lorentzian lines for the first two peaks, and a simple Gaussian for the last component. For PSR J14226138 the best fit is based on two simple Gaussian lines. For PSRs J15225735 and J1932+1916 we modeled the light curves with asymmetric Lorentzian lines. Table 1 shows the resulting peak separations and FWHMs.
We measured the pulsars’ phase-averaged spectral properties through a binned likelihood analysis, using pyLikelihood of the STs. We constructed spectral models including all sources found within 20°of the pulsars from an internal catalog of gamma-ray sources based on three years of LAT data, where the parameters only of point sources within 5°were left free. Each pulsar spectrum was modeled as an exponentially cutoff power law, , where denotes the spectral index and is the cutoff energy. The source models included contributions from the Galactic diffuse emission (using model gal_2yearp7v6_v0), the extragalactic diffuse emission, and the residual instrumental background (using template iso_p7v6source 333http://fermi.gsfc.nasa.gov/ssc/data/access/lat/BackgroundModels.html). For PSR J14226138, the phase-averaged analysis could not constrain . Excluding “off-pulse” photons with phases between and (Figure 3) slightly improved the fit quality. The best-fit values for , , and the derived photon and energy fluxes are given in Table 1. These are in line with and values of other young LAT pulsars (Abdo et al., 2013), apart from PSR J14226138’s low which is currently not well constrained. Future LAT-event-reconstruction enhancements (Atwood et al., 2013) and more photon data may improve the latter measurement.
4. Radio Counterpart Searches
We searched for radio pulsations from the new gamma-ray pulsars with the Effelsberg and Parkes Telescopes. PSRs J0554+3107 and J1932+1916 were observed with the Effelsberg Telescope at GHz for hr, using the new Ultra Broad Band (UBB) receiver (R. Keller et al. 2013, in preparation), as part of the commissioning of the instrument. For PSR J14226138, we used four -minute pointings taken during the High Time Resolution Universe survey (Keith et al., 2010), which we combined and searched coherently for increased sensitivity. Finally, for PSR J15225735 we analyzed a -hr Parkes observation. We used the gamma-ray pulsar ephemerides (Table 1), valid for each radio observation, to fold the radio data and searched in dispersion measure up to pc cm.
We found no significant detection and provide upper limits on the radio flux density, derived with the modified radiometer equation (Lorimer & Kramer, 2005) assuming a detection signal-to-noise-ratio threshold of and a % duty cycle. Configuration details for the Parkes observations are found in Table 5 of Pletsch et al. (2012b). The observation of PSR J15225735 pointed 1.5′ away from the pulsar. This implies only a small sensitivity loss, because the beam’s half-width at half-maximum is 7′ at this frequency. We accounted for this loss as in Pletsch et al. (2012b). For the GHz Effelsberg observations, we assumed , , and a system equivalent flux density Jy, as measured from preliminary UBB performance estimates444UBB performance estimates may evolve as commissioning continues. from continuum observations of 3C 48. After removal of radio-frequency interference, the nominal frequency bandwidth of MHz was reduced to and MHz for PSRs J0554+3107 and J1932+1916, respectively. Table 1 lists the resulting radio-flux-density limits at GHz, which are at the higher end compared to other LAT-discovered pulsars (e.g., Abdo et al., 2013). Although, assuming “heuristic” distances (Table 1), the luminosities are lower than for the vast majority of known pulsars, deeper radio searches are possibly warranted to confirm the present picture.
The measured spin parameters of all four new gamma-ray pulsars classify them as young and energetic (Figure 1). Their spin-down powers, , range from to erg s, for an assumed neutron-star moment of inertia of g cm. With characteristic ages between and kyr, they are among the youngest 4% of pulsars known (Manchester et al., 2005)555http://www.atnf.csiro.au/research/pulsar/psrcat/.
The distances to the four new objects are difficult to constrain without detected radio pulsations providing a dispersion measure. However, an estimated upper bound for the distance to each pulsar can be obtained from relating and the gamma-ray luminosity, , where is a beam correction factor (Watters et al., 2009). Assuming 100% conversion efficiency () as an upper limit, and , typical of gamma-ray pulsars (Watters et al., 2009), the above relation can then be solved for distance, which we denote by . The resulting upper limits for the four pulsars are between and kpc. More realistically, if instead a “heuristic” gamma-ray luminosity (as in Abdo et al., 2013), erg s erg s is assumed, distances between and kpc result (Table 1), suggesting that the pulsars are rather close.
Pulsars are believed to form in supernovae, so the discovery of a young pulsar prompts us to look for an associated supernova remnant (SNR). From Green (2009), we find a co-located SNR for two of the newly discovered pulsars. Care should be taken to establish genuine pulsar/SNR associations, because a chance superposition on the sky has a non-negligible probability (e.g., Gaensler & Johnston, 1995; Kaspi, 1998).
The sky position of PSR J0554+3107 lies about from the geometric center of SNR G, which has an angular size of (Fuerst & Reich, 1986). The low surface brightness reported by Fuerst & Reich (1986) suggests a large SNR age of – kyr, which is compatible with the pulsar’s characteristic age kyr. This is a good estimator of the pulsar’s true age if (1) the present spin period ( ms) is much larger than at birth and (2) the spin-down is dominated by magnetic dipole braking. From the -diameter relation (Milne, 1979), an SNR size of pc yields a distance of kpc. This has a large uncertainty, but is compatible with our estimated maximum pulsar distance kpc. Depending on the estimated age and distance of the SNR, the required transverse velocity of PSR J0554+3107 is between and km s, which is within the typical range of other pulsars (e.g., Hobbs et al., 2005). Thus it appears plausible that PSR J0554+3107 and G are associated.
The ms pulsar J15225735 is located about from the centroid of SNR G, which has an extension of . Caswell et al. (1975) provide an estimated distance of kpc, compatible with our kpc estimated upper limit for PSR J15225735. Their SNR age estimate of – kyr is also compatible with the kyr characteristic age of PSR J15225735, given the same caveats as above. From the possible values of the estimated SNR age and distance, the necessary transverse speed of PSR J15225735 is between and km s, which is also reasonable. Thus, a genuine association between PSR J15225735 and G is plausible and merits further study.
We have reported the Einstein@Home discovery and follow-up study of four gamma-ray pulsars found in a novel blind-search effort using Fermi-LAT data. The inferred parameters characterize the pulsars as energetic and young, likely relatively nearby. Young neutron stars are rare, and nearby ones in particular (e.g., Keane & Kramer, 2008). As such, these four discoveries contribute toward a more complete understanding of the young pulsar population and neutron-star birthrates (Watters & Romani, 2011). For two of the new pulsars, we have shown that associations with positionally coincident SNRs are possible. However, confirmation requires further work (e.g., measuring pulsar proper motion, a difficult task using LAT data alone).
All four gamma-ray pulsars lie close to the Galactic plane and remained
undetected in subsequent targeted radio searches.
In part, this is not unexpected, as argued by Camilo et al. (2012),
since the vast majority of Galactic-plane (non-MSP) radio pulsars
detectable by current radio telescopes and producing
gamma-ray fluxes observable at Earth are likely already known.
In turn, this demonstrates the importance of continued blind pulsar searches
of gamma-ray data: it is the only way to discover such neutron stars.
It is also remarkable that PSRs J14226138 and J15225735 have been detected in the
blind search despite their prominent glitch activity.
These facts, plus the combination of improved search techniques and
massive Einstein@Home computing power leaves us optimistic that we can find
more pulsars among the LAT unidentified sources.
- Aasi et al. (2013) Aasi, J., et al. 2013, Phys. Rev. D, 87, 042001
- Abbott et al. (2009a) Abbott, B., et al. 2009a, Phys. Rev. D, 79, 022001
- Abbott et al. (2009b) Abbott, B., et al. 2009b, Phys. Rev. D, 80, 042003
- Abdo et al. (2009) Abdo, A. A., et al. 2009, Science, 325, 840
- Abdo et al. (2010) Abdo, A. A., et al. 2010, ApJS, 188, 405
- Abdo et al. (2013) Abdo, A. A., et al. 2013, ApJS, 208, 17
- Ackermann et al. (2012) Ackermann, M., et al. 2012, ApJ, 753, 83
- Allen et al. (2013) Allen, B., et al. 2013, ApJ, 773, 91
- Atwood et al. (2006) Atwood, W. B., Ziegler, M., Johnson, R. P., & Baughman, B. M. 2006, ApJ, 652, L49
- Atwood et al. (2009) Atwood, W. B., et al. 2009, ApJ, 697, 1071
- Atwood et al. (2013) Atwood, W. B., et al. 2013, arXiv:1303.3514
- Brady & Creighton (2000) Brady, P. R., & Creighton, T. 2000, Phys. Rev. D, 61, 082001
- Brady et al. (1998) Brady, P. R., Creighton, T., Cutler, C., & Schutz, B. F. 1998, Phys. Rev. D, 57, 2101
- Camilo et al. (2012) Camilo, F., et al. 2012, ApJ, 746, 39
- Caswell et al. (1975) Caswell, J. L., Clark, D. H., Crawford, D. F., & Green, A. J. 1975, AuJPh, 37, 1
- Chandler et al. (2001) Chandler, A. M., Koh, D. T., Lamb, R. C., et al. 2001, ApJ, 556, 59
- Cutler et al. (2005) Cutler, C., Gholami, I., & Krishnan, B. 2005, Phys. Rev. D, 72, 042004
- de Jager et al. (1989) de Jager, O. C., Raubenheimer, B. C., & Swanepoel, J. W. H. 1989, A&A, 221, 180
- Fuerst & Reich (1986) Fuerst, E., & Reich, W. 1986, A&A, 154, 303
- Gaensler & Johnston (1995) Gaensler, B. M., & Johnston, S. 1995, MNRAS, 275, L73
- Green (2009) Green, D. A. 2009, Bull. Astron. Soc. India, 37, 45
- Guillemot et al. (2012) Guillemot, L., et al. 2012, ApJ, 744, 33
- Hobbs et al. (2005) Hobbs, G., Lorimer, D. R., Lyne, A. G., & Kramer, M. 2005, MNRAS, 360, 974
- Hobbs et al. (2006) Hobbs, G. B., Edwards, R. T., & Manchester, R. N. 2006, MNRAS, 369, 655
- Kaspi (1998) Kaspi, V. M. 1998, Adv. Space Res., 21, 167
- Keane & Kramer (2008) Keane, E. F., & Kramer, M. 2008, MNRAS, 391, 2009
- Keith et al. (2010) Keith, M. J., Jameson, A., van Straten, W., et al. 2010, MNRAS, 409, 619
- Kerr (2011) Kerr, M. 2011, ApJ, 732, 38
- Knispel et al. (2010) Knispel, B., et al. 2010, Science, 329, 1305
- Knispel et al. (2011) Knispel, B., et al. 2011, ApJ, 732, L1
- Knispel et al. (2013) Knispel, B., et al. 2013, ApJ, 774, 93
- Lee et al. (2012) Lee, K. J., Guillemot, L., Yue, Y. L., Kramer, M., & Champion, D. J. 2012, MNRAS, 424, 2832
- Lorimer & Kramer (2005) Lorimer, D. R., & Kramer, M. 2005, Handbook of Pulsar Astronomy (Cambridge: Cambridge Univ. Press)
- Manchester et al. (2005) Manchester, R. N., Hobbs, G. B., Teoh, A., & Hobbs, M. 2005, AJ, 129, 1993
- Milne (1979) Milne, D. K. 1979, Australian Journal of Physics, 32, 83
- Nolan et al. (2012) Nolan, P. L., et al. 2012, ApJS, 199, 31
- Pletsch (2010) Pletsch, H. J. 2010, Phys. Rev. D, 82, 042002
- Pletsch (2011) Pletsch, H. J. 2011, Phys. Rev. D, 83, 122003
- Pletsch & Allen (2009) Pletsch, H. J., & Allen, B. 2009, Phys. Rev. Lett., 103, 181102
- Pletsch et al. (2012a) Pletsch, H. J., et al. 2012a, Science, 338, 1314
- Pletsch et al. (2012b) Pletsch, H. J., et al. 2012b, ApJ, 744, 105
- Pletsch et al. (2012c) Pletsch, H. J., et al. 2012c, ApJ, 755, L12
- Ray et al. (2011) Ray, P. S., et al. 2011, ApJS, 194, 17
- Ray et al. (2012) Ray, P. S., et al. 2012, arXiv:1205.3089
- Romani (2012) Romani, R. W. 2012, ApJ, 754, L25
- Saz Parkinson et al. (2010) Saz Parkinson, P. M., et al. 2010, ApJ, 725, 571
- Watters & Romani (2011) Watters, K. P., & Romani, R. W. 2011, ApJ, 727, 123
- Watters et al. (2009) Watters, K. P., Romani, R. W., Weltevrede, P., & Johnston, S. 2009, ApJ, 695, 1289
- Ziegler et al. (2008) Ziegler, M., Baughman, B. M., Johnson, R. P., & Atwood, W. B. 2008, ApJ, 680, 620