Observing the Pulsar B0329+054 with the Dwingeloo 25m Radio Telescope

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Observing the Pulsar B0329+054 with the Dwingeloo 25m Radio Telescope

Author Frits Sweijen

s2364883

Supervisor J. McKean

Version Januari 09, 2015

Abstract

The goal of this observation was to learn about the pulsar B0329+054 located at RA=03h32m59.347s; DEC=+54d34m43.25s (J2000)[1]. We observed this radio source with the Dwingeloo radio telescope at an ob- serving frequency of 420 MHz. The data was the analyzed in an attempt to determine the period of this pulsar along with the dispersion mea- surement, which gives an indication for the electron density between us and the source. The period is first estimated using purely the signal and the dynamic spectrum. This estimate is further improved by doing a Fourier transform of the signal and determining the period from that. Fi- nally some additional fine-tuning was done to arrive at the results. This method has given us a period of 0.71452 s. The dispersion measure was found by fitting the data with a straight line and then determining the slope. This resulted in a value of 27.28±0.29 cm−3pc.

1 Introduction

Pulsars are remnants of a type II su- pernova. At the end of their lifetime, massive stars collapse in a supernova and can form a neutron star. The neu- tron star that is left behind is then spinning with a period varying from one to a couple of seconds to very fast spinning ones with periods of millisec- onds. This fast rotation comes from conservation of angular momentum. A rotating body will therefore speed up if it gets smaller. Because the magnetic flux is conserved, the neutron star will have a strong magnetic field due to its small surface area. Typical magnetic field strengths range from 104− 109 T.

Because of the strong magnetic fields, pulsars emit radiation. The radiation we detect is only a narrow beam. This beam comes from regions with open magnetic field lines, called polar caps. This narrow beam then

has a lighthouse effect on the signal.

We receive it as pulses with a certain duration in between.

As pulsars age they lose energy through their rotation. Hence pulsars slow down over time. The older a pul- sar gets the slower it rotates, until the rotation becomes so slow that it no longer emits detectable radiation.[4]

2 Observations

We observed this pulsar November 28, 2014 with the 25m Dwingeloo radio telescope. We observed the source at a frequency ν = 420 MHz (λ = 0.71 m).

The telescope is an alt-az mounted dish made of a mesh. The detector is lo- cated in a focusbox at prime foucs. In the detector two antennas are present.

One for receiving signals from 21-23 cm (1.4 GHz) and one for signals of 70 cm (430 MHz). The observation itself took

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Figure 1: Dynamical spectrum from 26 to 28 seconds in the observation. Note:

not clearly visible on printed version

8 minutes and gave us around 1 GB of data.[3]

3 Results

After collecting the data it was pro- cessed using software provided by ASTRON[2]. Processing the data con- sisted of two parts. First the period was determined and second the disper- sion measure.

3.1 Period

The first step in finding the period is looking at the dynamical spectrum.

The dynamical spectrum is a visual representation of the signals coming into the telescope. The dynamical spectrum of this observation is shown in Figure 1. In this image several features can be distinguished: there are bright bands throughout the en- tire spectrum, solid black lines, general noise and the pulsar signal.

The use of phones, the radio and other similar sources all broadcast ra- dio signals into the sky. The an- tenna also detects these signals. These unwanted signals are called radio- frequency interference (RFI). On top

of the pulsar signal we thus have ex- tra signals interfering with it. Some of the RFI degrades the data so badly that it becomes unusable. The bands for which this is the case have been automatically removed from the spec- trum to ease the data reduction. This leaves solid black lines in the spectrum as there is no information left in those frequency bands anymore. Besides the RFI there is also a small amount of noise coming from other sources like background radiation coming other ra- dio sources in the sky and noise from the instruments on the telescope it- self. This shows itself as a fuzzy green haze and is present at almost every fre- quency.

The signal from the pulsar itself, a pulse, shows as a slightly tilted line go- ing vertically down. Since the signal is periodic this line repeats itself over a certain time. In Figure 1 there are two pulses visible around 26.8 s and 27.5 s.

The first step in determining the period is making an approximation us- ing the spectrum itself. For this the two bright dots at a frequency of ν = 415.15 MHz are used. These are lo- cated at t1 = 26.73842 s and t2 = 27.45102 s respectively. This then

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yields an approximate period of P ≈ t2− t1= 0.7126 s (1)

Figure 2: Fourier transform of the sig- nal at ν = 415.15 MHz.

To get a better estimate, a Fourier transform (FT) of the data is done to pick out any periodicity. In order to get a good transform we need a fre- quency band that has as little noise and RFI as possible as this degrades the signal. We chose the 415.15 MHz band to do the transform. It had some RFI some time into the observation, but it had a couple of clearly visible pulses especially in the beginning that made it look promising. The result- ing transform can be seen in Figure 2.

The first peak is the actual frequency of the signal. The subsequent peaks are harmonics of this signal, i.e. inte- ger multiples for the actual frequency.

In our estimate directly from the dy- namical spectrum we used only two pulses. With the Fourier transform we can now make a better estimate for the period because we can find an average frequency based on multiple data points. The first peak is located at ν1 = 1.39969 Hz and the 21st at ν = 29.39346 Hz. There are 20 in- tervals between these peaks, so we can calculate an average frequency of

ν ≈ ν2− ν1

20 = 1.39969 Hz (2)

The period can then be found from P = 1

ν ≈ 0.71444 s (3) The final step involves fine-tuning the period. In Figure 3 we can see two pulse profiles. The red line is from pulses at the beginning of the data set and the blue line is from pulses at the end of the data set. If the period de- termined earlier is correct, these pro- files should overlap each other. This is clearly not the case, so we need to change the period slightly. Increasing the period will move the blue line to the left and decreasing it will make the blue line move to the right. In this case the it needs to be moved to the left, so the period estimated earlier is too long. This is a process of trial and error which in the end resulted in a pe- riod of

P ≈ 0.71452 s (4) Using this new period to recreate the pulse profiles seen in Figure 3 gives the ones shown in Figure 4.

Figure 3: Folded profile of a pulse at the beginning (red) and the end (blue) of the data set.

Figure 4: Folded profile of a pulse at the beginning (red) and the end (blue) of the data set. This time with the new period.

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3.2 Dispersion Measure

Not all signals from the pulsar arrive at the same time. Lower frequencies ar- rive later than higher frequencies. This is caused by dispersion by the interstel- lar medium (ISM). The ISM consists of gas, dust and charged particles like electrons. These electrons scatter the radio waves, causing a small time de- lay. This delay is called dispersion and by measuring it we can calculate a dis- persion measure (DM). For a frequency ν in MHz the delay τ is[4]:

τ = DM

2.410 × 10−4ν2MHz s (5)

We determine the DM for this pul- sar by looking at the arrival times of five different frequencies. This is shown in Figure 5 and Table 1. From Equation 5 it is seen that there is a lin- ear relation with respect to 1/ν2. Plot- ting the delay τ versus 2.410 × 10−4· 1/ν2 gives a straight line with the DM as the slope. We did this numerically using Python and a fitting function from SciPy. We found for this pulsar a DM of

DM = 27.28 ± 0.29 cm−3pc (6) The result of the fit can be seen in Fig- ure 8.

Figure 5: Arrival time of 5 different frequencies. See Table 1.

Figure 6: The 5 different frequencies after de-dispersion.

With a value for the dispersion measure we can now de-disperse the signal. Doing this allows us to compen- sate for the delay of lower frequency bands so that we can use a larger range of frequencies for the signal and add them up to get a stronger total signal.

We use again the software provided by ASTRON. The result is plotted in Fig- ure 6. Finally all these signals can be added together to get a stronger signal from the pulse. Summing these signals gives a total pulse as shown in Figure 7.

Figure 7: Signals of all 5 frequencies added together.

The dispersion measure itself is a measure of the electron density and is defined as

DM = Z d

0

nedl (7)

where ne is the electron density in cm−3 and d the distance to the source

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in pc. If we assume a constant electron density between us and the pulsar, can related the electron density to the DM as

ne= DM

d (8)

The distance to PSR 0329+054 is 1.06 kpc[5]. This gives an electron density of ne= 0.026 cm−3.

4 Conclusion

After processing the data we found the pulsar PSR 0329+054 to be a bright pulsar. This can be seen in Figure 1. The period was determined to be 0.71452 s. Most pulsars have a period in the order of one second. The pul- sar PSR 0329+054 thus has a relatively normal rotation period.

The dispersion measurement was found to be 27.28 pc cm−3. From this dispersion measure we can infer an electron density of the ISM, assuming it is constant. This tells us that the ISM is ionized to some extend and con- tains free electrons.

5 Discussion

Observing this object revealed some in- formation about the conditions near pulsars. Pulsars emit a stable, periodic signal. The most common pulsars have periods of the order of a second. This makes PSR 0329+054 a normal pul- sar. These rotation periods however are still relatively fast for an object of such a size. This is an indication of the extreme conditions around pulsars.

The signal was clearly visible in the dynamic spectrum, having pulses which are easy to distinguish from the background. This may indicate that it is one of the more brighter radio sources on the sky.

We made an estimate of the elec- tron density between us and the pulsar.

This resulted in a density of 0.025 elec- trons per cubic centimeter. This was determined assuming a constant elec- tron density. Even so, this is not a re- alistic approximation. Some areas will have more electrons while others will have less. The ISM is thus partially ionized and as such there are free elec- trons causing dispersion of the signal.

Improvements of this estimate can be made by better determining the disper- sion measure.

The period and dispersion measure could be better determined by multi- ple changes to the observation. The most simple one would be to observe the source for a longer time to get more data. This could improve the period, because there is more data.

A second, harder change would be to observe at a different location with less RFI. This increases the qualtity of the data and signal to noise ratio.

Finally a better dispersion measure could be found by using more than five frequencies.

References

[1] Nasa extragalactic database.

[2] ASTRON. Dwingeloo-live. http:

//www.astron.nl/onderwijs/.

[3] ASTRON. Pulsars. Manual with general information about pulsars and the telescope.

[4] Bernard F. Burke; Francis Graham-Smith. An Introduction to Radio Astronomy. Cambridge, 2014.

[5] Wang, N. and Yan, Z. and Manch- ester, R. N. and Wang, H. X. Daily observations of interstellar scintil- lation in PSR B0329+54. mnras, 385:1393–1401, April 2008.

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Color Frequency (MHz) Arrival time (s) Delay (s)

Cyan 428.959 0.28336 0.00000

Blue 427.045 0.28892 0.00556

Green 421.986 0.30337 0.02001

Red 418.978 0.31337 0.03001

Black 415.970 0.32226 0.03890

Table 1: Different frequencies and their graphs, arrival times and delays.

Figure 8: Data points fitted with a straight line using least squares fitting. The delay is measured in seconds.

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Appendix A: Fitting Code

#!/ u s r / b i n / env python

from f u t u r e i m p o r t d i v i s i o n

from m a t p l o t l i b . p y p l o t i m p o r t f i g u r e , show i m p o r t math

i m p o r t numpy a s np

i m p o r t s c i p y . s t a t s a s s p s

nu = np . a r r a y ( [ 4 2 8 . 9 5 9 , 4 2 7 . 0 4 5 , 4 2 1 . 9 8 6 , 4 1 8 . 9 7 8 , 4 1 5 . 9 7 0 ] )

t = np . a r r a y ( [ 0 . 2 8 3 3 6 , 0 . 2 8 8 9 2 , 0 . 3 0 3 3 7 , 0 . 3 1 3 3 7 , 0 . 3 2 2 2 6 ] )

t a u = t − t [ 0 ] x , y = 1/ nu ∗ ∗ 2 , t a u

# F i t a s t r a i g h t l i n e f o r t h e DM, y = ax + b

s l o p e , i n t e r c e p t , r , p , s t d e r r = s p s . l i n r e g r e s s ( x , y ) DM = s l o p e ∗ 2 . 4 1 0 e−4

DM err = s t d e r r ∗ 2 . 4 1 0 e−4 p r i n t s l o p e

p r i n t ’ D i s p e r s i o n Measure : ’ , DM p r i n t ’ St a nd ar d D e v i a t i o n : ’ , DM err

# P l o t t h e r e s u l t s f i g = f i g u r e ( )

f i g . s u p t i t l e ( ’ Delay a s f u n c t i o n o f $1 /\\ nu ˆ2 $ ’ , f o n t w e i g h t =’ bold ’ )

ax = f i g . a d d s u b p l o t ( 1 1 1 )

ax . s e t x l a b e l ( ’ $ \\ nu ˆ { − 2 } / ( 2 . 4 1 0 \ c d o t 1 0 ˆ{ −4})$ ’ ) ; ax . s e t y l a b e l ( ’ $ \\ tau$ ’ )

ax . p l o t ( 1 / ( 2 . 4 1 0 e−4 ∗ nu ∗ ∗ 2 ) , tau , ’ bo ’ , l a b e l =’Data ’ ) ax . p l o t ( 1 / ( 2 . 4 1 0 e−4 ∗ nu ∗ ∗ 2 ) , s l o p e /nu ∗∗2 + i n t e r c e p t , ’ r

’ , l a b e l =’ F i t ’ )

ax . l e g e n d ( l o c =’ upper l e f t ’ ) show ( )

Figure

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