By careful measurements of the fluctuations in pulsar pulse periods on time scales of days and longer, researchers determined that these fluctuations are caused by changes in the rotation rate of the stellar crust apparently arising from matter accretion. The study of these fluctuations is a particularly promising way to determine the properties of accreting pulsars, because stellar rotation is relatively simple in comparison to much other X-ray source physics and can be investigated in detail. Rotation rates can be determined precisely

Boynton, Paul E.

Deeter, John E.

English

NASA Technical Reports Server

f .  
UNIVERSITY OF WASHINGTON 
SEATTLE, WASHINGTON 98195 
Department o j  Astronomy, FM-20 
August 17, 1987 
Dr. L. Kaluszienski 
Code EZ 
600 Independence Ave. 
?:ASA Ecadquartzrs 
U’ashington, D.C. 20546 
Subject: Final Technical Report - KASA Grant S A G W  805 
I. Overview 
During the funding period for NAGW 805 we established a working collaboration with 
Profs. Satio Hayakawa and Fumiaki Nagase at  Nagoya University. Our joint program 
involves the analysis and interpretation of observations of X-ray pulsars made with X-ray 
dctectors aboard Japanese and U.S. scientific satellites. Both the Nagoya group and we at  
the IJniversity of Washington in collaboration with Prof. Fred Lamb at the University of 
Illinois have pursued this research topic with the goal of better understanding the physical 
processes associated with matter accretion onto neutron stars. 
By careful measurements of the fluctuations in pulsar pulse periods on time scales 
of days and longer. we have determined that these fiiictiiations ai& caused by changes 
in the rotation rate of the stellar crust apparently arising from matter accretion. The 
study of these fluctuations is a particularly promising way to determine the properties of 
accreting pulsars, because stellar rotation is relatively simple in comparison to much other 
X-ray source physics and can be investigated in detail. Moreover, rotation rates can be 
determined very precisely with the combined capabilities of modern X-ray detectors and 
data analysis techniques. Thus, a direct, quantitative confrontation between theory and 
obscrvation is possible. 
11. Research Coxnpleted 
The collaboration with the group at Kagoya University grew out of an arrangement 
made several years ago which allowed Dr. Noriaki Shibazaki to  first visit us at the Univer- 
sity of Washington for several months, and then Prof. Fred Lamb and his colleagues at the 
University of Illinois. Dr. Shibazaki brought with him the Hakucho observations of Vela 
X-1, allowing us to begin a joint analysis of these data while he was at the University of 
Washington. In the course of this work, we were lead to discuss and compare our methods 
and philosophics of pulse timing with those used by the group at Nagoya University, which 
also examined this same data set. They express a specific interest in seeing the software 
we dcvcloped for our pulse timing studies. Funded by KAGM’ 805, we were able to visit 
Japan for a month in the summer of 1985 and continue these discussions. 
An important element of this visit was a workshop held September 4-6 at Inuyama (near 
Xagoya) attended by us and Japanese astrophysicists interested in pulse timing. Each of 
u5 gave two talks at this meeting, and the Japanese contributed about ten presentations. 
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J.E.D. gave an introductory talk on the uses of the harmonic representation for folded 
pulses, a fundamental aspect of our approach to pulse timing. This representation is the 
natural setting for discussion noise in pulse shape which does not have the character of 
white noise (flat power spectrum), and explaining how noise in pulse shape propagates into 
uncertainty in pulse phase. Using the harmonic representation, we have also been able to 
investigate and resolve questions such as the optimum resolution of the pulse shape for 
the purpose of precise timing. In a second talk, J.E.D. discussed the effect of red noise in 
pulsar rotation on the precision of parameters (such ELS the orbital parameters) estimated 
from pulse timing. This included a description of the method we used to reduce the effect 
of red noise in rotation on the estimated orbital parameters for Vela X-1. 
P.E.B. followed with two presentations. In the first talk,  he discussed the sources of 
noise which affect the precision of pulse timing of X-ray pulsars and of results based on 
such pulse timing. Not only is there noise in pulse shape arising from the discreteness of 
photon detection events (”counting statistics”), but there can also be noise both in pulse 
shape and pulse phase intrinsic to the pulsar. The key point in this distinction is that 
the “counting statistics” noise in pulse shape can be reduced by increasing the area of 
the detecior and hence the couriiirig rate, while the i i o k  soiiices iiitiiiisic io the pulse 
formation process can not be similarly reduced. Thus there seems to  be an fundamental 
constraint to the improvement in pulse timing which can be obtained merely by increasing 
the area of the X-ray detector, at least for strong sources. 
In his second talk, P.E.B. showed that such a conclusion is unnecessarily pessimistic. 
Using the methods we have developed for dealing with non-white shape noise, it is possible 
to substantially improve the precision of pulse timing even in the presence of excess noise 
in pulse shape inherent to the pulse formation process. From an understanding of the 
statistical aspects of this problem has emerged a relationship between the spectrum of the 
pulse shape and the spectrum of noise in pulse shape which may be used to predict noise 
limitations on the observations of a given pulsar. Under certain rather general conditions 
the filtering technique we have developed will allow indefinite improvement in pulse timing 
precision with increasing detector area. Thus, pulse timing projects for certain high count- 
rate pulsars which depend on reducing the counting-statistics noise are feasible with large 
zrez detectors, such as AstrhC, XTE, and the 100 m2 XLA proposal. The problem is to 
determine which pulsars have favorabie properties €or noise suppression through filtering. 
Three of these talks were subsequently written up as papers, and submitted to the 
-_____ Astronomical Journal for publication. Preprints of these papers wee previously submitted 
to KASA headquarters. 
Another major portion of our effort in 1985 was the introduction of the group at  
Nagoya University to our approaches of dealing with noise in pulse shape and pulsar 
rotation. This included a successful installation of part of our software on the computer 
used by the Department of Astrophysics at Nagoya University. 
During our visit in 1985, Profs. Hayakawa and Nagase proposed to two Japanese 
foundations for grants to sponsor return visits in 1986. We were fortunate to  have both 
grants awarded. The Japanese Society for the Promotion of Science provided a grant for 
a one month visit by P.E.B., while the Yamada Science Foundation funded a three month 
stay by J.E.D. This trip was actually extended to over four months (July 15 to  November 
24), while the visit by P.E.B. covered the period from August 15 to September 24. 
The major activity during our 1986 visit was the unification of our earlier, separate 
analyses of the Vela X-1 data from the Hakucho and Tenma satellites into a single. joint 
paper (Deeter et al. 1987 - see attached copy). In this paper, we show that the method 
of pulse filtering significantly improves the precision of pulse timing, particularly for the 
Tenma data. We also report on updated mean orbit for Vela IC-1, based on all available 
pulse-timing studies covering a 10-year interval. In addition, we present the local frequency 
record for Vela X-1 for the Hakucho and Tenma data, and compute a power density 
2 
spectrum of fluctuations in the derivative of the pulse frequency on analysis frequencies 
between 0.5 and 80 days. These results support the phenomenological hypothesis that 
unresolved fluctuations in the angular acceleration of the neutron star, describable as 
random noise, are responsible for the entire history of the observed variation in pulse 
frequency of Vela X-1 on all time scales longer than a few days. 
Submitted by: 
I 
Paul E. Boynton 
Prof. of Physics and Astronom 
Dept. of Astronomy FM-20 
University of Washington 
Seattle, U'A 98195 
John E. Deeter 
Research Associate 
Dept. of Astronomy FM-20 
University of Washington 
Seattle, WA 98195 


Analysis and interpretation of X-ray pulsars

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