Finding (or not) New Gamma-ray Pulsars with GLAST
Finding (or not) New Gamma-ray Pulsars with GLAST
Scott M. Ransom
National Radio Astronomy Observatory, 520 Edgemont Rd., Charlottesville, VA, 22901, USA
Abstract. Young energetic pulsars will likely be the largest class of Galactic sources observed by GLAST, with many
hundreds detected. Many will be unknown as radio pulsars, making pulsation detection dependent on radio and/or x-ray
observations or on blind periodicity searches of the gamma-rays. Estimates for the number of pulsars GLAST will detect
in blind searches have ranged from tens to many hundreds. I argue that the number will be near the low end of this range,
partly due to observations being made in a scanning as opposed to a pointing mode. This paper briefly reviews how blind
pulsar searches will be conducted using GLAST, what limits these searches, and how the computations and statistics scale
with various parameters.
Keywords: pulsars, gamma rays, data analysis
PACS: 95.75.Wx, 95.85.Pw, 97.60.Gb
INTRODUCTION
Pulsar emission mechanism(s) from radio to gamma-rays are poorly understood after 40 yrs of work. Yet despite this
fact, pulsars are high-precision tools that probe a variety of topics in both fundamental physics and astrophysics.
EGRET detected pulsed emission from at least 6, and probably 7−9, young pulsars at energies >∼ 100 MeV [1]. In
addition, several tens of the (primarily Galactic) unidentified EGRET sources are likely pulsars [e.g. 2, 3, 4]. With its
much larger effective area and improved angular resolution, GLAST will almost certainly detect hundreds of pulsars.
The majority of those pulsars will remain unidentified though (and useless as physics tools), unless pulsations are
detected through 1) “folding” of the events using timing ephemerides for known radio pulsars; 2) searches of associated
x-ray sources to find radio-quiet Geminga-like pulsars [5], or very faint radio pulsars [6, 7]; or 3) “blind” searches of
the gamma-ray events [8]. This paper discusses the latter, and perhaps most difficult, option.
The known gamma-ray pulsars have similar characteristics [for a review, see 1]. They are mostly non-variable
sources with fairly flat energy spectra in the gamma-ray regime, but with spectral cutoffs around or just above 1 GeV.
The flat energy spectra imply that most of the photons detected by the Large Area Telescope (LAT) will be in the
∼100-300 MeV range, where the point spread function has a width >∼ 1
◦. The gamma-ray pulse shapes are complex
with two relatively sharp pulses which provide higher harmonic content in searches and make their detection easier.
Most of the GLAST mission will be spent in sky survey mode, where the whole sky is scanned every ∼3 hours1.
On average, a point in the sky will be within the LAT field of view ∼ 1/6 of the time. Pointed observations would
increase this fraction to ∼ 1/2 (with Earth occultations preventing higher on-source efficiency). This loss in efficiency
due to scanning (more specifically, the resulting decrease in the number of source events Ns during a particular viewing
period Tview) will make coherent pulsation searches considerably more difficult and less sensitive.
BLIND SEARCHES FOR GAMMA-RAY PULSARS
Blind searches of low count rate event data are typically conducted using either Fourier techniques (i.e. binning events
into a time series, computing one or more FFTs, and analyzing the resulting amplitude and possibly phase spectra;
[e.g. 9, 8]) or via brute-force epoch folding (i.e. assembling a pulse profile by determining the pulse phase of each
event from a trial ephemeris and then computing a probability of non-uniformity for the profile; [e.g. 10, 11]). Optimal
sensitivity to pulsations comes from searches that treat all of the data in a “coherent” fashion, meaning that the pulsar’s
rotational phase is accurately tracked over the full observation or analysis duration Tview, from first event to last.
1 For details, see the GLAST mission website: http://glast.gsfc.nasa.gov
http://arxiv.org/abs/0704.1131v1
http://glast.gsfc.nasa.gov
5−sig
10−sigm
> 15−sigma detection
non−detection
Pointing
Scanning
FIGURE 1. Left) The number of independent Fourier “bins” (i.e. 1/Tview in Hz) a signal with frequency derivative ḟ (bottom) and
frequency 2nd derivative f̈ (top) would drift in an observation of duration Tview. To preserve sharp features in pulse profiles, search
codes need to account for signal drift to a small fraction (1−10%) of a Fourier bin. Right) The 95% confidence-level detectability
of a blind event-folding search with Tview=20 days for a pulsar with a Gaussian pulse profile with FWHM=15% in pulse phase.
The “sigmas” represent Gaussian significance in standard deviations after accounting for the number of trials searched. The arrow
(representing a factor of ∼3 increase in accumulated events during Tview and which can be translated anywhere on the plot) shows
how the significance improves for pointed observations (which are still affected by Earth occultations) as opposed to scanning
observations. In this case, a 20-day pointing results in an ∼8-σ detection, whereas 20-days of scanning gives a non-detection.
The real problem with gamma-ray pulsation searches comes from the fact that the sources have very low count
rates of 10−7−10−8 photons(>100 MeV) cm−2 s−1, which for the LAT corresponds to roughly 0.2−2 events per
hour. Therefore, very long observations lasting from weeks to years are required to make significant detections. And
unfortunately, young pulsars are notoriously badly behaved over such timescales.
Ideally, we would only need to search over the unknown spin frequency f of a pulsar. However, young pulsars
rapidly spin-down (i.e. have large frequency derivatives ḟ ), they exhibit timing noise which manifests itself in searches
as significant frequency 2nd derivatives f̈ (and for the noisiest pulsars, many higher order derivatives as well), and they
occasionally, on month or year timescales, “glitch” and instantaneously change their observed f and ḟ . Figure 1 shows
the number of independent frequency bins of width 1/Tview in Hz, corresponding to an accumulated phase error of
one rotation, over which a pulsar signal will “drift” during a coherent search for a variety of realistic values of f and
f̈ . Pulsar spin-down becomes important for energetic young pulsars in a day or two, and so all gamma-ray searches
must account for an unknown ḟ . Timing noise can become important after a few weeks or months. Since gamma-ray
pulse profiles contain sharp features, and therefore their pulsed signals contain many harmonics, search codes must
significantly oversample the ∼ 1/Tview or ∼ 1/T
view spacings in f and ḟ to maintain optimal sensitivity.
A potentially bigger problem, as shown by Chandler et al. [8], are positional errors or uncertainties ε , which
cause apparent changes in the observed spin frequency δ f ∼ 10−6εmrad f10 sinθ Hz, frequency derivative δ ḟ ∼ 2×
10−13εmrad f10 cosθ Hz s−1, and frequency 2nd derivative δ f̈ ∼ 4 × 10−20εmrad f10 sinθ Hz s−2, where εmrad is the
position error in milliradians, f10 is the spin frequency in tens of Hz, and θ is the time varying angle between the
Earth’s velocity vector and the line of sight to the pulsar. For candidate GLAST pulsar sources, ε will be milliradians
(arcminutes) in size, making the blind detection of even stable Geminga-like pulsars much more difficult.
The intrinsic ḟ , timing noise, glitch frequency, and position error effects place upper limits on the useful Tview for
coherent pulsation searches to durations as short as ∼10 days for the most energetic and active pulsars, or a few
months for older, slower, and more stable pulsars. Because of the scanning nature of the GLAST mission, there will
be fewer counts accumulated for a particular source over the specified Tview by a factor of ∼3 as compared to a pointed
observation. This decrease in accumulated counts per unit time greatly impacts coherent search sensitivity and is the
reason why scanning is not the optimal observing mode for pulsar studies.
Pulsation Detection and Computational Considerations
The power P in a periodic gamma-ray signal is P∼ 1+αN2s /Nt , where α is a pulse-shape dependent factor (0.4−0.9
for the known gamma-ray pulsars)[e.g. 12]. The total number of events Nt is the sum of the source (pulsed) events
Ns and background (unpulsed) events Nb. The probability that noise fluctuations produce a certain search power Po is
exponentially related to the power: Prob(P ≥ Po) ∝ exp(−Po)Ntrials, where Ntrials is the number of independent trials
searched. Ntrials is proportional to the range of f and ḟ searched, but more importantly, to T
view.
In general then, to optimize search sensitivity, we want large Ns to maximize P, yet a relatively short Tview
(appropriate for the limits discussed in the last section) to reduce Ntrials and the computational complexity. This rule
exposes another problem for scanning-mode observations of pulsars: if Tview is increased by a factor of ∼3 to recover
the events “lost” compared to a pointed observation (assuming the pulsations remain well-behaved over the longer
Tview), a detected signal will have the same power as from the shorter pointed observation, yet the probability that the
signal is significant will decrease by a factor of ∼ 33 = 27 due to the larger Ntrials searched.
Computationally, the complexity of epoch-folding searches scales roughly as T 4view (i.e. Nt ×Ntrials), while FFT-
based techniques fare slightly better and scale as T 3view logTview. Moderate sized computer clusters can currently handle
epoch-folding searches of hundreds to thousands of events for viewing periods of up to several weeks (see Figure 1).
For longer Tview or more limited computing resources, one can use evolutionary [14] and/or heirarchical [13] tech-
niques to greatly reduce the computational burden of coherent searches without greatly impacting the overall sensi-
tivity, if the average pulsation flux is time invariant. Coherent searches with GLAST with Tview <∼ 1−2 months should
be sensitive to pulsars with photon fluxes (>100 MeV) of a few times 10−8 to a few times 10−7 photons cm−2 s−1 for
scanning-mode observations, or as low as ∼2×10−8 photons cm−2 s−1 for pointed observations.
Finally, incoherent searches are possible where the absolute phase of pulsations is not tracked over the full Tview, but
only over much shorter “windows” Twin. Incoherent searches are less sensitive than coherent ones for the same Tview,
but they use many fewer computing resources and enable searches with much longer Tview [9, 15]. The basic idea limits
the duration of the coherently processed intervals Twin such that a signal with any reasonable ḟ or f̈ stays within a single
independent frequency bin (of width 1/Twin Hz) or fraction thereof. These windowed analyses are then combined
without phase information, but with corrections for ḟ and/or f̈ effects occurring between the intervals, and analyzed.
Initial simulations show that one might detect relatively stable pulsars with photon fluxes (>100 MeV) as low as
1−2×10−8 photons cm−2 s−1 with Tview ∼ 1 yr and Twin ∼ 1 day. Without phase information, however, the folding of
all events over such long durations to accumulate high-quality pulse profiles may be difficult or even impossible.
In summary, instabilities of young pulsars, source positional uncertainties, and the default survey/scanning mode for
the mission will make blind pulsation searches with GLAST much more difficult than early estimates had predicted.
It is therefore likely that GLAST will blindly discover only tens of new pulsars rather than hundreds.
Acknowledgements: Thanks go to Paul Ray, Julie McEnery, Mallory Roberts, Maura McLaughlin, and Kent Wood
for useful discussions.
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astro-ph/0310748
	Introduction
	Blind Searches for Gamma-ray Pulsars
	Pulsation Detection and Computational Considerations
