High signal-to-noise ratio observations and the ultimate limits of precision pulsar timing

We demonstrate that the sensitivity of high-precision pulsar timing experiments will be ultimately limited by the broadband intensity modulation that is intrinsic to the pulsar's stochastic radio signal. That is, as the peak flux of the pulsar approaches that of the system equivalent flux density, neither greater antenna gain nor increased instrumental bandwidth will improve timing precision. These conclusions proceed from an analysis of the covariance matrix used to characterise residual pulse profile fluctuations following the template matching procedure for arrival time estimation. We perform such an analysis on 25 hours of high-precision timing observations of the closest and brightest millisecond pulsar, PSR J0437-4715. In these data, the standard deviation of the post-fit arrival time residuals is approximately four times greater than that predicted by considering the system equivalent flux density, mean pulsar flux and the effective width of the pulsed emission. We develop a technique based on principal component analysis to mitigate the effects of shape variations on arrival time estimation and demonstrate its validity using a number of illustrative simulations. When applied to our observations, the method reduces arrival time residual noise by approximately 20%. We conclude that, owing primarily to the intrinsic variability of the radio emission from PSR J0437-4715 at 20 cm, timing precision in this observing band better than 30 - 40 ns in one hour is highly unlikely, regardless of future improvements in antenna gain or instrumental bandwidth. We describe the intrinsic variability of the pulsar signal as stochastic wideband impulse modulated self-noise (SWIMS) and argue that SWIMS will likely limit the timing precision of every millisecond pulsar currently observed by Pulsar Timing Array projects as larger and more sensitive antennae are built in the coming decades.Comment: 16 pages, 9 figures, accepted for publication in MNRAS. Updated version: added DOI and changed manuscript to reflect changes in the final published versio

Introduction to fMRI: experimental design and data analysis

This provides an introduction to functional MRI, experimental design and data analysis procedures using statistical parametric mapping approach

Parameter Estimation from Time-Series Data with Correlated Errors: A Wavelet-Based Method and its Application to Transit Light Curves

We consider the problem of fitting a parametric model to time-series data that are afflicted by correlated noise. The noise is represented by a sum of two stationary Gaussian processes: one that is uncorrelated in time, and another that has a power spectral density varying as $1/f^\gamma$. We present an accurate and fast [O(N)] algorithm for parameter estimation based on computing the likelihood in a wavelet basis. The method is illustrated and tested using simulated time-series photometry of exoplanetary transits, with particular attention to estimating the midtransit time. We compare our method to two other methods that have been used in the literature, the time-averaging method and the residual-permutation method. For noise processes that obey our assumptions, the algorithm presented here gives more accurate results for midtransit times and truer estimates of their uncertainties.Comment: Accepted in ApJ. Illustrative code may be found at http://www.mit.edu/~carterja/code/ . 17 page

NICMOS Observations of the Transiting Hot Jupiter XO-1b

We refine the physical parameters of the transiting hot Jupiter planet XO-1b and its stellar host XO-1 using HST NICMOS observations. XO-1b has a radius Rp=1.21+/-0.03 RJup, and XO-1 has a radius Rs=0.94+/-0.02 RSun, where the uncertainty in the mass of XO-1 dominates the uncertainty of Rp and Rs. There are no significant differences in the XO-1 system properties between these broad-band NIR observations and previous determinations based upon ground-based optical observations. We measure two transit timings from these observations with 9 s and 15 s precision. As a residual to a linear ephemeris model, there is a 2.0 sigma timing difference between the two HST visits that are separated by 3 transit events (11.8 days). These two transit timings and additional timings from the literature are sufficient to rule out the presence of an Earth mass planet orbiting in 2:1 mean motion resonance coplanar with XO-1b. We identify and correct for poorly understood gain-like variations present in NICMOS time series data. This correction reduces the effective noise in time series photometry by a factor of two, for the case of XO-1.Comment: 13 pages, 8 figures, submitted to Ap

Time-Correlated Structure in Spin Fluctuations in Pulsars

We study statistical properties of stochastic variations in pulse arrival times, timing noise, in radio pulsars using a new analysis method applied in the time domain. The method proceeds in two steps. First, we subtract low-frequency wander using a high-pass filter. Second, we calculate the discrete correlation function of the filtered data. As a complementary method for measuring correlations, we introduce a statistic that measures the dispersion of the data with respect to the data translated in time. The analysis methods presented here are robust and of general usefulness for studying arrival time variations over timescales approaching the average sampling interval. We apply these methods to timing data for 32 pulsars. In two radio pulsars, PSRs B1133+16 and B1933+16, we find that fluctuations in arrival times are correlated over timescales of 10 - 20 d with the distinct signature of a relaxation process. Though this relaxation response could be magnetospheric in origin, we argue that damping between the neutron star crust and interior liquid is a more likely explanation. Under this interpretation, our results provide the first evidence independent from pulsar spin glitches of differential rotation in neutron stars. PSR B0950+08, shows evidence for quasi-periodic oscillations that could be related to mode switching.Comment: 25 pages, Final journal version (MNRAS