Discovering Pulsars in Compact Binaries with a Hidden Markov Model

Abstract Discovering radio pulsars in compact binaries, whose orbital periods P b satisfy P b ≲ 1 day, is computationally challenging, because the time-dependent pulse frequency f p ( t ) is strongly Doppler modulated by the binary motion. Here we present a new, fast, semi-coherent detection scheme based on a hidden Markov model (HMM) combined with a maximum-likelihood matched filter, the Schuster periodogram. The HMM scheme complements traditional acceleration searches by dividing f p ( t ) into piecewise-constant blocks and tracking the block-to-block evolution efficiently using dynamic programming. Monte Carlo simulations show that the new method can detect compact binaries with flux densities S ≥ 0.50 mJy and orbital periods P b ≥ 0.012 day under observing conditions (e.g., cadence) typical of radio pulsar surveys, with and without impulsive, narrowband radio-frequency interference. The new method is fast; it employs the classic Viterbi algorithm to solve the HMM recursively. The central processing unit runtime scales nominally as <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>T</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">run</mml:mi> </mml:mrow> </mml:msub> <mml:mo>≈</mml:mo> <mml:mn>2.8</mml:mn> <mml:mspace width="0.25em"/> <mml:msub> <mml:mrow> <mml:mi>N</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>B</mml:mi> </mml:mrow> </mml:msub> <mml:mo stretchy="false">(</mml:mo> <mml:msub> <mml:mrow> <mml:mi>N</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>T</mml:mi> </mml:mrow> </mml:msub> <mml:mo>/</mml:mo> <mml:mn>1</mml:mn> <mml:msup> <mml:mrow> <mml:mn>0</mml:mn> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> <mml:mo stretchy="false">)</mml:mo> <mml:mo stretchy="false">(</mml:mo> <mml:msub> <mml:mrow> <mml:mi>N</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>Q</mml:mi> </mml:mrow> </mml:msub> <mml:mi>ln</mml:mi> <mml:msub> <mml:mrow> <mml:mi>N</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>Q</mml:mi> </mml:mrow> </mml:msub> <mml:mo>/</mml:mo> <mml:mn>1</mml:mn> <mml:msup> <mml:mrow> <mml:mn>0</mml:mn> </mml:mrow> <mml:mrow> <mml:mn>4</mml:mn> </mml:mrow> </mml:msup> <mml:mi>ln</mml:mi> <mml:mn>1</mml:mn> <mml:msup> <mml:mrow> <mml:mn>0</mml:mn> </mml:mrow> <mml:mrow> <mml:mn>4</mml:mn> </mml:mrow> </mml:msup> <mml:mo stretchy="false">)</mml:mo> <mml:mspace width="0.25em"/> <mml:mi mathvariant="normal">s</mml:mi> </mml:math> for N B subbands, N T coherent segments, and N Q frequency bins.