ELEMENTOS DE UNA BUENA NUTRICIÓN

A quantitative expression of the survey’s sensitivity can be obtained in terms of the minimum detectable flux density, as given by the radiometer equation (see e.g.Lorimer & Kramer,2012): Smin=β S/NminTsys Gp nptobs∆f δ 1₋δ 1₂ , (3.1)

here β = 1.05 is the signal degradation due to 8-bit digitisation, Tsys is the system

temperature of the receiver ( Tsys = Trec+Tsky). In the case of the 7-beam receiver

installed at the Effelsberg telescopeTrec= 21 K for the central beam andTrec= 21−30

K for the outer beams11. G = 1.5 K Jy−1 is the antenna gain of the telescope at 1.36 GHz, δ is the pulse duty cycle, tobs is the observation length, ∆f = 240 MHz is

the effective bandwidth of the receiver and np = 2 is the number of polarisations

summed. The factor S/Nmin is the minimum signal-to-noise ratio (S/N) sufficient

for a confident detection12. In the idealised case of dominating white noise, the false alarm statistics calculations (see e.g. Lorimer & Kramer, 2012) give S/Nmin = 8.

This value is widely used in theoretical estimates of sensitivities of different surveys. For example, the theoretical curves demonstrating the dependence of the minimum detectable flux density on the pulse period for the case of the HTRU-North mid-lat assumingS/Nmin= 8 are plotted in Fig. 3.7. However, in reality the presence of RFI

and non-whiteness of the spectrum raise the threshold.

To estimate the true survey sensitivity, we performed an analysis of known pulsar redetections. For this we used the information from the ATNF pulsar catalogueto create a list of known pulsars that could potentially appear in the mid-lat data taken by that time (all 50%). A pulsar was put on the list if it had:

1) a reported reference pulse width (W50) and a flux density at 1400 MHz (S1400); 2) the sky position within one beamwidth from an observed pointing13.

Using the radiometer equation Eq. 3.1, the HTRU-North parameters, the sky temperature model of Haslam et al. (1982) and the pulsar parameters from the ATNF pulsar catalogue, we calculated the expected S/Ns for the all the sources fulfilling the aforementioned requirements. To account for the flux density scaling with the

11_{The values ofT}

recfor different feed horns used in this work vary by 10–20% as they highly depend on environmental conditions, such as airmass (via elevation) and ground radiation (priv.com. with Benjamin Winkel).

12_{Using the terminology of pulsar astronomy, this is the “folded” S/N which is calculated in the} time domain. It should be distinguished from the so-called “spectral” S/N which is determined by the amplitudes of harmonics in the power spectrum and usually used for building the candidates’ hierarchy. 13_{Theoretically the beam pattern is assumed to be Gaussian within this distance. However, the} beam shape may experience distortions from gaussianity further away from the beam centre.

3.5. Survey’s sensitivity analysis 63 1 10 100 1000 10000

Period (ms)

0.0

0.5

1.0

1.5

2.0

S

(m

Jy)

DM: 0 pc cm

DM: 200 pc cm

DM: 500 pc cm

DM: 1000 pc cm

Figure 3.7: Theoretical dependence of minimum detectable flux density on spin period as calculated from Eq. 3.1 for the mid-latitude region. The curves correspond to different DM values: 0, 200, 500, 1000 pc cm−3_{. Here we assumeT}

sky= 8 K andS/Nmin= 8.

distance from the beam centre, the S/Ns were multiplied by an offset factor assuming a Gaussian beam shape. Of all possible redetections, we chose 202 pulsars with an expected S/Ns higher than 13. This S/N value was chosen empirically to account for possible detrimental influence of RFI.

Next, each survey pointing potentially containing a pulsar (or several pulsars) from the list was checked in two ways:

1) whether the pulsar/pulsars had been detected during the processing of the corre- sponding HTRU-North pointings with the FAST PIPELINE and, if detected, with which signal-to-noise ratio, “S/N FP”;

2) whether the pulsar/pulsars had been detected after separately folding the original filterbank files with the best available ephemerides from theATNF pulsar catalogue

and, if detected, with which signal-to-noise ratio, “S/N refolded”.

We summarize these results in two tables (see Table 3.2 and 3.3) and further analyze the confirmed redetections and non-detections separately.

3.5.1 Known pulsar redetections

A total of 165 known pulsars from the list were redetected in the survey. Among them, 41 pulsars were missed by the FAST PIPELINE (FP-missed) but showed up

in the refolding. The majority of these FP-missed pulsars demonstrated low refolded S/N values, mostly concentrated in the range from 5.7 to 14.2. Thus, in reality, they were either not sufficiently bright for being found in the periodicity search with the FAST PIPELINE and/or the data were of poor quality, with a high degree of RFI contamination. For such data the chances of detection were higher in the case of refolding since all the refolded files were visually inspected and manually cleaned with

pazi utilite from psrchive14, if necessary, whereas during the processing with the FAST PIPELINE only the built-in automatic algorithms of RFI rejection were used. These algorithms could be not sufficiently sensitive to some types of RFI.

A few “just-above-the-threshold” refolded S/N values (from 14.2 to 16.6) were obtained for long-period pulsars (PSR J1851₋0053 with P = 1.409 s, PSR J1839- 1238 with P = 1.911 s and PSR J1830₋1135 with P = 6.221 s) whose detection in the Fourier domain searches may be hampered due to the presence of red noise. This might be one of the reasons why they have been missed despite looking potentially detectable. Another reason is that, for the case of long-period pulsars, a 180-second integration may contain less than a hundred pulses resulting in insufficient power per Fourier bin, if the pulse-to-pulse variability is taken into account. The same is probably true for two bright exceptions PSR J1837₋0045 (P = 0.617 s) and PSR J1852₋0635 (P = 0.524 s) that were missed by the FAST PIPELINE but showed up in the refolding with the S/N close to that expected.

Another 4 pulsars – PSR J1915+0738, PSR J1850₋0026, PSR J1905+061615 and PSR J1839₋0643 – were found with the FAST PIPELINE in their harmonics. The full list of the redetections’ parameters, including the expected and obtained S/Ns (both for the FAST PIPELINE and refolding) are provided in Table3.2. As can be seen, the “S/N FP” in most cases differs a lot from the “S/N expected”. The lowest “S/N FP”= 4.59 is found for PSR J0540+3207 whereas its “S/N expected” is 15.87. Unsurprisingly, “S/Ns refolded”, in general, match better to “S/Ns expected”.

Since all seven beams hosted redetections, we decided to analyze the individual sensitivity provided by each feed horn. For each beam we plotted the ratio of the S/N expected to the S/N refolded (called SNRexp/SNRobs on the plots) as a func-

tion of the pulsar’s positional offset from the beam centre. The plots of individual beams were combined into the Effelsberg 7-beam pattern (see Fig. 3.8). On these plots the black unit line, apparently, represents the one-to-one correspondence between SNRexp and SNRobs. The dashed red line represents the weighted average of the ratio

SNRexp/SNRobscalculated using the statistics from all redetections made in the corre-

sponding beam. As can be seen, for beam 0 and beam 5 the weighted average is close to unity, thus, the sensitivity is close to the theoretically expected one. In the case of beam 1 and beam 4 the weighted average slightly deviates from unity, being around 1.25. For beam 6 it is 1.45. Beam 2 and beam 3 exhibit the highest deviation from the theoretically expected sensitivity with the weighted averages of 1.55 and 1.6 respec-

14_{http://psrchive.sourceforge.net/, (van Straten et al.,2012)}

15_{The pulsar was detected in harmonics at the beam edge of one pointing, and it was also properly} detected at fundamental frequency in another pointing where it was located slightly closer to the beam centre.

3.5. Survey’s sensitivity analysis 65

Figure 3.8: Comparison between the expected and obtained signal-to-noise ratios for a sample of known pulsars blindly redetected in the HTRU-North survey. Here SNRexp

is the expected S/N calculated according to Eq. 3.1, SNR_obs is the S/N obtained after refolding the survey filterbank files with the ephemeris from the ATNF pulsar catalogue. The ratio SNRexp/SNRobs is plotted for each beam of the HTRU-North

7-beam pattern (for a set of pulsars detected in that beam). In each beam plot: the black solid line represents unity, the red dotted line represents the weighted average of SNRexp/SNRobs calculated for the corresponding beam.

tively. Using all these values to calculate the average deviation in sensitivity for the whole system, we get SNRexp/SNR_obssys=1.3. Thus, we can conclude that our system

is 1.3 times less sensitive than we expected.

3.5.2 Missed known pulsars

37 known pulsars were missed both in the FAST PIPELINE and further folding with the ephemeris from theATNF pulsar catalogue. Table3.3contains the detailed infor- mation about this set of sources with a possible explanation for every non-detection. Most of these pulsars (29) appeared to be below our real sensitivity threshold: for some of them the expected S/N values, if taken with the uncertainties, may fall below 13. Moreover, the difficulties with determining Trec and, consequently, Tsys, precisely for

every observation imply underestimated uncertainties. Other reasons for non-detection are likely to be a strong RFI and red noise. These factors may be particularly respon- sible for missing long-period pulsars (P >1 s) whose expected S/Ns exceed 20. A few pulsars with low DMs were not seen, most probably, due to scintillation. Finally, some “non-trivial” sources such as: X-ray pulsars PSR J1809₋1943 and PSR J1832₋0836, a young pulsar in a relativistic binary PSR J1906+0746 and PSR J1916+0748 known to exhibit giant pulses were not expected to show up in the (quick) periodicity search of this survey.