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Millisecond Pulsar Rivals Best Atomic Clock Stability

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Millisecond Pulsar Rivals Best Atomic Clock Stability 41st AnnualFrequency Control Symposium - 1987 MILLISECOND PULSAR RIVALS BEST ATOMIC CLOCK STABILITY by David W. Allan Time and Frequency Division National Bureau of Standards 325 Broadway, Boulder, CO 80303 Abstract pulsar the drift rate is exceedingly constant; i.e., no second derivative of the period has been The measurement time residuals between the observed.[4] The very steady slowing down of the millisecond pulsar PSR 1937+21 and atomic time have pulsar is believed to be caused by the pulsar been significantly reduced. Analysisof data for the radiating electromagnetic and gravitational waves.[5] most recent 865 day period indicates a fractional frequency stability (square KOOt of the modified Time comparisonson the millisecond pulsar require Allan variance) of less than 2 x for the best of measurement systems and metrology integration times of about 113 year.The reasons for techniques. This pulsar is estimated to be about the improved stability will be discussed; these a are 12,000 to 15,000 light years away. The basic result of the combined efforts of several elements in the measurement link between the individuals. millisecond pulsar and the atomic clock are the dispersion and scintillation due to the interstellar Analysis of the measurements taken in two frequency medium, the computationof the ephemeris of the earth bands revealed a random walk behavior for dispersion in barycentric coordinates, the relativistic along the 12,000 to 15,000 light year path from the transformations becauseof the dynamics and pulsar to the earth. This random walk accumulates to gravitational potentials of the atomic clocks about 1,000 nanoseconds (ns) over 265 days. The involved with respect to the reference frame of final residuals are nominally characterized by a interstellar space, the sensitivityof the Arecibo white phase noise at a level of ns. 369 Observatory (AO) radio telescope (area 73,000of m2 OK 18 acres), the accuracy of the Princeton-installed Following improvement of thesignal-to-noise ratio, measurement system, the filter bank and data evidence was found for a residual modulation. processing techniques for determining the arrival Possible explanations for this modulation include: a time of the pulses, the transfer of time from the binary companion (or companions) to the pulsar with Arecibo Observatory atomic clock to the time from the approximate period(s) of 120 da S and with a mass (or international timing centers,and, last the masses) of the order of1 x lo-' that of the pulsar; algorithms for combining the clocks in the world irregular magnetic drag in the pulsar; unaccounted ensemble to provide the atomic clock reference. delay variations in the interstellar medium; modeling errors in the earth's ephemeris; reference atomic New Measurement Techniques clock variations in excess of what are estimated; or gravity waves. For gravity waves, the amplitude of Since the discovery of the millisecond pulsar by the length modulation would be about5 parts in Backer and Kulkarni [2] (14 November 19821, several Further study is needed to determine which is the very significant improvements in the ability to most probable explanation. measure the pulsar have occurred. Figure 1 is a stability plot of the residuals over the first two Introduction years after all the then-knownperturbations were removed. The stability is characterized by al/f Timekeeping has historically evolved with phase modulation (PM) spectral density. The standard astrometry; e.g. the rotation of theearth, the orbit deviation of the time residuals over the first two of the earth around thesun OK the moon around the years was 998 ns. In the fall of 1984 the groupat earth have been fundamental pendula for time keeping.Princeton installed a new data acquisition system in As atomic clockswere shownto be more accurate and conjunction with the filter bank for better stable than those basedon astrometry, the second was determination of the arrival time of the pulses. redefined.[l] It now seems that an astronomical Nearly simultaneously NBS in cooperation with A0 phenomenon [Z] may rival the best atomic clocks installed a GPS common-view receiver for the link currently operating. The current best estimate of between the Arecibo clock and international timing the period of the millisecond pulsar (PSR 1937+21) is centers. The white PM noise of the GPS common-view 1.557 806 451 698 38 ms f0.05 fs as of 6 October 1983 link is less than10 ns. at 2216 UT.[3] This accuracy is such thatwe could wait over 100 years between measurements of the The data from the pulsar included measurements made arrival times of signals fromthe pulsar before being at both 1.4 GHz and 2.38 GHz.[3] The data were concerned with which pulsewe were counting. The unequally spaced with the average sample period period derivativehas been measured as P = (1.051053 varying between about3 and 20 days depending upon f 0.000008) x seconds per second which is the data segment. Figure 2 and Figure 3 are plots of 3.31687 parts in lo1' per year. This frequency drift the raw residuals over the period from theof Fall is less than that aof typical rubidium frequency 1984 to February 1987. Since the data were unequally standard and greater than that a of typical cesium spaced we analyzed the data in two ways. First, frequency standard. However, in the case of the taking the numbersas a simple time series they were analyzed as if they were equally spacedwith the Contribution of theU.S. Government, not subject to assumed spacing T~ equal to the average spacing copyright. between the data points. Second,we used the actual number of points available, but linearly interpolated "US GOVERNMENT WORK IS NOT PROTECTED BY US COPYRIGHT" 2 MILLISECOND PULSRR PSR 1937+21 - UTCCUSNO3 LOG MOD SIGyCTRUl VIR LORRN-C FOR 30 NBV'82 -13 OCT'84 -11 LICKER PM -td. Dev. = 998 ns -i2 - 13 -_ C) -- - 0 -14 - -1s 5 6 7 8 L06 TRU [Seconds) Figure 1. A plot of the square-root of the modified Allan variance,;,.(T) as a functionof integration time, r, for the first two yearsof measurements of the millisecond pulsar timing. LoranC was the time transfer means to relate to UTC(USN0). MILLISECDNO PULSRR PSR 1937+21 - UTCCNBSI TIME Cn83 ORTR'@ 1.4 6HZ MJD'S 45988 - 46851 DAY CMJDI Figure 2. A plot of the residuals of the measurementsof the millisecond pulsar time at1.4 GHz versus UTC(NBS) via the GPS common-view time transfer technique and after installation of the upgraded Princeton measurement system. 3 MILLISECOND PULSRR PSR 3937+23 - UTCCNBBI TIME Cn.3 DATA AT 2.38 6HZ MJO'S 45986 - 46861 DAY CHJOI Figure 3. A plot of the residuals of the measurements of the millisecond pulsar time at2.38 GHz versus UTC(NBS) via the GPS common-view time transfer technique and after installation of the upgraded Princeton measurement system MILLISECOND PULSAR PSR 1937+21 - UTCCNBSI LOG HOD SIGyCTAUl DATA AT 1.4 GHZ HJD'S 46986 - 46851 -13 - 12 -13 -14 -1aI- F 5 6 7 8 LOG TAU CSmoond.1 Figure 4. A plot of the square-rootof the modified Allan variance,a,(.) as a function of integration time,r, for the 1.4 GHz data shown in Figure2. 4 a data value between adjacent actual values to seen--similar to Figure 4. The standard deviation of construct an equally spaced data set.The latter the residuals around a linear regressionon the data approach had the effect of decreasing the amplitudein Figure 3 was 378 ns for the 865 days. Again it is of the higher frequency Fourier components and apparent that the residuals are not random and increasing the amplitude of the lower frequency uncorrelated as the ratio of the classical variance Fourier components. The conclusions drawn from the to the squared white PM level is 1.42 now f 0.17. two different methods of analysis were consistent. The stability plots in Figures4 and 5 are quite Since it is the nature of whitenoise (random similar. uncorrelated deviations) thata measurement is independent of the data spacing, and the modified Since the stability of UTC(NBS) can be determined Allan variance indicated white PM, then that independently of this measurement procedure, a very indication is a necessary but not sufficient totest careful analysisof the data taken over1000 days prove that the measurement noise is white PM.On the covering the pulsar analysis period was performed. hand, M0d.o (T) E uY(x) does not behaveas The stability of UTC(NBS) with coordination entries if Y T , then this is a necessary and sufficient test removed -- denoted AT1 -- was compared in an"N- that the spectrum is something other thana white cornered-hat"[j'] procedure against other primary noise process. As will be shown later, the latter timing centers. This was accomplished using the situation is applicable to our case. international NBSIGPS common-view technique, which supplies data to the BIH for the generation of Pulsar Stability Analysis International Atomic Time(TAI).[7] The measurement noise for allof the time comparisons was less than Figure 4 shows the fractional frequency 10 ns for the white noise PM. Figure6 shows a plot stability plotay(-c), for the 1.4 GHz data against of the estimated frequency stability for the NBS AT1 UTC(NBS). There are several significant differences time scale and indicates that the stability of AT1 is between these data and those taken over the first twotypically less than years using Loran C. First, the spectral density has changed from a l/f PM toa more nearly white PM The following two equations are proposed a asmodel process. Second, the noise level has been reduced of the time residuals for the system.
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