itself. Among the promising alternatives, usually involving a small-scale suppression in the matter power spectrum, are warm dark matter (Colín et al., 2000;Bode et al., 2001), self-interacting dark matter (Spergel & Steinhardt,2000), self-annihilating dark matter (Kaplinghat et al.,2000) and fuzzy dark matter (FDM) (Turner,1983;Hu et al., 2000;Goodman,2000;Hui et al.,2017).
Pulsars are instrumental in understanding the nature of dark matter. Timing of the Double Pulsar and eccentric binaries have provided stringent constraints on the family of tensor-vector-scalar theories, one of the dark matter alternatives constituting the modication of Newtonian gravity in the weak-eld regime (Freire et al., 2012).
Dark matter in the form of ultracompact minihalos (Clark et al.,2016;Kashiyama &
Oguri, 2018), or primordial black holes (Seto & Cooray, 2007; Blinnikov et al.,2016;
Clesse & García-Bellido,2017) can also be probed with pulsars. In this thesis we focus specically on testing the FDM hypothesis in which dark matter is composed of spin-0 extremely light bosons. For suciently light (10−23−10−20 eV) bosons, the∼pc-kpc de Broglie wavelength smooths the inhomogeneities at sub-galactic scales, whereas on cosmological scales it is indistinguishable from cold dark matter (Sarkar et al.,2016;
Hloºek et al.,2018). As these bosons are extremely light and interact very weakly with baryonic matter, their detection in a laboratory is extremely challenging (Arvanitaki et al.,2010). In the boson mass range3×10−21−3×10−20eV the FDM can be probed via resonant binary pulsars (Blas et al., 2017, Heusgen et al, in prep.). In Chapter6 we explore the possibility of detection of FDM with PTAs in an even more low-mass regime, from ∼10−23 to 10−22 eV.
1.7. Thesis outline 25
• In Chapter5, after subtracting the ionospheric contribution, we attempt to mea-sure the interstellar turbulent magnetic elds, and set an upper limit on the amplitude of any magnetic-eld uctuations.
• In Chapter 6 we discuss one of the viable dark matter candidates, FDM. We investigate the prospects of FDM detection with PTAs, and set an upper limit on the density of dark matter with PPTA Data Release 2.
• Finally, in Chapter 7 we summarise our results and discuss future prospects for ISM and dark-matter investigation with pulsars.
Chapter 2
Practical aspects of pulsar observations: from observables to fundamental results
Contents
2.1 Radio observations of pulsars . . . 27 2.2 Low-frequency pulsar observations with phased arrays . . . 29 2.2.1 German LOFAR stations. German long-wavelength consortium. 31 2.3 Pulsar timing . . . 34 2.4 On probing pulsar polarisation . . . 40 2.4.1 Stokes parameters . . . . 40 2.4.2 Modelling the Faraday eect: RM measurement techniques . . . 42 Since their discovery in the radio band, pulsars have been observed over a wide range of the electromagnetic spectrum, starting at low radio frequencies (10 MHz) up to very high-energy γ-rays (100 TeV). Although the means of data acquisition are dierent in dierent parts of the spectrum, there are several things in common: e.g. weak pulsar signals require huge collecting areas and long integration times; tiny periods of pulsations can be resolved with high time resolution instruments. The most fruitful type of observations, which have signicantly expanded our understanding of pulsars, have been carried out at radio frequencies.
2.1 Radio observations of pulsars
The traditional way of studying pulsars is by observing them with radio telescopes.
The principal scheme of a modern telescope involves two main components: a frontend and a backend. The frontend is the initial receiving system of the telescope, which collects and amplies the signal. For typical single-dish radio telescopes the collecting area is formed by a reecting surface, which usually has the shape of a paraboloid.
The largest steerable parabolic reectors extensively used for pulsar observations are the 100-m Eelsberg radio telescope in Germany, the 76-m Lovell Telescope in the UK, the 105-m Robert C. Byrd Green Bank Telescope in the USA, the 64-m Parkes radio telescope in Australia, and the 64-m Sardinia radio telescope. The largest non-steerable reectors, such as the 300-m Arecibo radio telescope in Puerto Rico and the
brand-new 500-m FAST radio telescope in China, are designed as spherical caps. In some modern observing systems based on phased arrays, the collecting reectors are completely removed from the scheme (see Section 2.2).
The reectors coherently sum the signal in the focus of the antenna, where it is gathered by the receiver feed horn, which converts the incoming radiation into a series of electric voltages. Afterwards, the analogue voltages are driven through a chain of ampliers and bandpass lters. The latter attenuate all the frequencies outside of the band of interest. Commonly, the signal received at radio frequencyf is down-converted to lower frequencies by modulating the original signal with a monochromatic signal of xed frequency fLO by a Local Oscillator. As a result, two new signals with two new intermediate frequencies are produced, fIM=f±fLO, from which the lower one is chosen with a bandpass lter. The main reasons for down-conversion are to facilitate the process of transmission through the hardware and to avoid negative feedback, caused by the amplied signals that can possibly escape from the hardware system.
While the frontend is a general-purpose system developed for a broad variety of ra-dio astronomical applications, the backend is a more special purpose equipment, which is responsible for further digitisation and processing of the data. The digitisation is han-dled by Analogue-to-digital converters (ADCs), which must sample the analogue signal with a sampling frequency two times higher than the resultant bandwidth, following the Nyquist theorem (Nyquist, 1928; Kotelnikov, 1933; Shannon, 1949). Afterwards, the data are channelised with polyphase lter bank (PFB) technique. A PFB produces a power spectrum of the signal, signicantly suppressing the eects of spectral leakage and scalloping loss, which are inherent to classic discrete fourier transforms (DFT).
In order to compensate for the frequency-dependent dispersion of pulsar signals, which was discussed in Section 1.4.1, the data are de-dispersed. The backend applies a proper dispersive delay given by Equation (1.9), corresponding to the best available DM, to each frequency channel, making the signal aligned across the whole band. This method is known as incoherent de-dispersion, and is easy to apply, as well as being computationally inexpensive. Although it is limited by the dispersive smearing within each individual frequency channel.
One can overcome this issue by using another method, called coherent de-dispersion (Hankins & Rickett, 1975). Within this approach the dispersive delay is expressed in terms of the phase shift ∆Ψ (see Equation (1.9)). In the frequency domain this eect can be described by the transfer function H, which is to rst order1:
H= e−i∆Φ'e− e
2 mec
DM f i
. (2.1)
In order to correct for the dispersion, the raw voltages are Fourier transformed with the fast Fourier transform (FFT). The phase of each Fourier component is derotated by an amount that is proportional to the best-known DM of the pulsar, by applying the inverse of the transfer function, H−1. The coherent de-dispersion is very computationally
1The expression can be further expanded as a Taylor series around the central frequencyf0: f1 '
1 f0−f−ff20
0
+(f−f0)2
f03 .
2.2. Low-frequency pulsar observations with phased arrays 29