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Determination of pulsar's binary parameters
Alessandro Corongiu Joseph Foy Vladislav Kondratiev аngel G. MuЯoz S. Tutor: Paulo C.C. Freire INAF ­ Oss. Astr. di Cagliari, Italy Arizona State University, USA York University, Canada Univ. de Zulia, Venezuela

NAIC, Arecibo Observatory

Arecibo Observatory, July 15th, 2005

Pulsars
Pulsars are highly magnetized rotating neutron stars. The magnetic field is responsible for: - The radio emission itself - The beaming of the emmitted radiation The observed pulsed behaviour is due to the misalignement of the magnetic axis respect to the spin axis.

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The Search of a pulsar
The search for a pulsar is the search for periodicities in the observed signal. In order to increase the signal to noise ratio, wide band observations are usually performed. Wide band observations are, how ever, so strongly affected by interstellar dispersion that is not possible to sum the signal across the bandw idth and, at the same time, mantain the signatures of the periodicities in the signal. So it's compulsory to dedisperse the signal before adding together all frequency channels.

The Search of a pulsar
Once the dedispersed time series is obtained, a Fourier transformation is performed. The peaks in the power spectrum indicate the presence of periodicities, which may or may not be a pulsar. The time series is then folded at the frequency of any obtained peak in the power spectrum and the obtained profile is visually inspected. If you're lucky, you may find a pulsar.

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Binary parameters
The orbit of a pulsar, as well as any object, in a binary system is determined in its geometrical characteristics, space displacement and syncronised in time by the following parameters: Semimajor axis Eccentricity Longitude of periastron Binary period Time of ascending node

a e PB T0

True spin period and observed spin period
The pulsar is in motion with respect to the Earth, so w e don't observe the TRUE spin period, accordingly to DЖppler effect laws:

V POBS = P RUE 1 + R T c
But we know the pulsar is in a generally elliptical orbit, so we can express the radial velocity VR in terms of the geometrical features of the orbit and, of course, time (circular orbit):

1 2 2 POBS = PTRUE 1 + c P a sin i cos P (t - t0 ) B B
Because w e deal with VR, we are not able to derive the semimajor axis of the orbit, but only its projection on the plane containing the line of sight and the line of nodes.

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The observed pulsar and the data set
We observed PSR J1738+0333, a 5.8ms pulsar in a 8 hr binary system, during the nights of July 13th and 14th. Each observation lasted one hour, the total bandwidth was 400 MHz at a central frequency of 1.4 GHz, and the sampling time was 64 µs. We also analysed 13 observations already present in the Arecibo observations' archive, so w e got a total of 15 measurements of the observed period, covering a data span between MJD 52872 and MJD 53566.

Data reduction
Each dataset has been processed in this way: 1) 2) 3) Dedispersion at the already known dispersion measure Scrunched in frequency Fourier transormed

After the Fourier transformation has been performed, w e picked up the period wich could be effectively the pulsar period at the binary phase w e observed it. Because of the Earth motion around the Sun, an additional contribution to the radial velocity was still present in our measurement, so we had to correct the observed pulsar periods for the Earth's orbital motion.

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Data analysis
Because of the high number of fit parameters, w e started from reasonable initial values, obtained from a pulsar catalogue. We put them in the DЖppler formula and introduced variation parameters as follow s:

POBS = в PTR

UE

+в

1 2PTR c PB

UE

2 2 a sin i cos в t - в t0 PB PB

The obtained values for the fitted parameters are: = = = = 1 1 1.0002 1.0008

Orbital parameters and more
Combining the initial guess values with the fitted variation parameters, we derived the physical parameters of the system:

PTRUE = 5.8500959185 ms PB = 0.3547806 d a sin i = 0.343392ls T0 = 52902.418037
We also derived the value for the mass function:

f(MC) = 3.429 x 10-4 M
And finally, asuming an inclination of 60° and a pulsar mass MP = 1.35 M , we estimated the mass of the companion:

MC = 0.104 M

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Conclusions
We analysed the data of the binary pulsar PSR J1738+0333. Our data come from the Arecibo archive. We also analysed two observations done by ourselves during this week. The reduction process has been the same that is used for searching for new pulsar or solve recently discovered ones. We obtained an orbital solution for this pulsar, and calculated an estimate for the companion mass, which tells us that PSR J1738+0333 is likely orbiting around a light white dwarf.

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