Galaxy rotation curve measurements with low cost 21 cm radio telescope

Abstract

Probing the Universe with atomic hydrogen 21 cm emission is a fascinating and challenging work in astronomy. Radio telescopes play a vital role in detecting and imaging these faint signals. Powerful radio telescopes are complex to construct and operate. We have built a simple, low-cost 21 cm radio telescope primarily for educational training purposes. The design uses a custom horn antenna, ready-to-use radio-frequency components, and a software-defined radio module. The telescope operates efficiently from a rooftop in a city environment. Using this telescope, we have conducted observations and successfully detected the 21 cm line emissions from the different directions of our galactic plane. Based on the Doppler-shift observed in these measurements, we have successfully derived the Galactic rotation velocity (rotation curve) in those directions. The paper presents the details of the telescope construction, 21 cm observation, and the Galactic rotation curve derivation.

Appendix I: Appendix

• 1. Noise figure We used the Friis formula to calculate the total noise figure $NF_{total}$ of the Receiver chain [2]. Every active element in the receiver chain will add noise to the signal.

  $$\begin{aligned} NF_{total} = NF_1 + \frac{NF_2 -1}{G_1} + \frac{NF_3 -1}{G_1 G_2} + ..... + \frac{NF_n -1}{G_1 G_2 ... G_n} \end{aligned}$$

  (A1)

  Here, NF is the noise figure of the individual elements. G is their gain. In this formula the first element decides the noise figure’s maximum value. Therefore we used a low noise amplifier as the first element at the receiver chain. From this formula, we calculated the total noise figure of the receiver chain as 2.1675 dB.

• 2. Minimum detectable signal The minimum detectable signal (MDS) is the minimum power level that can process by a receiver. It is also known as the noise floor of the system. It can also be defined as the input signal power required to give a particular SNR at the output.

  $$\begin{aligned} MDS = 10log_{10} \Big (\frac{kT}{1mW}\Big ) + NF_{total} + 10log_{10}(BW) \end{aligned}$$

  (A2)

  Where, BW is the band width of the receiver. We find that system noise floor for our receiver is -111 dBm.

Figure 15

Horn antenna return loss (S11) performance. The CST software based simulation of the flare extended horn-antenna shows that the antenna can perform well beyond about 1000 MHz. It can also be noted that the antenna would perform poor below 1000 MHz. This poor performance at lower frequencies is desirable, as it will help to block some of the unwanted frequencies, especially the GSM mobile phone signals (around 900 MHz) from saturating the 21 cm receiver. GSM signals are typically very strong in a city environment and would contaminate the sensitive radio telescope when operated nearby. It can also be noted that S11 parameter value around 1420 MHz is better than −13 dB implying that a good performance from the antenna is expected for the 21 cm signal reception.

Figure 16

Construction details and simulated response of the 1420 MHz bandpass of the Micro-strip filter. This filter is a 9th order inter-digital Chebyshev micro-strip bandpass filter, which is implemented on 0.8 mm di-electric thickness high frequency printed circuit board which is popularly known as ULTRALAM-2000, having di-electric constant $\epsilon _r$ of 2.5 and loss tangent of 0.0022. The design of this filter is done in Keysight Genesys 10 CAD software. The inter-digital filter is a compact configuration consists of an array of nine TEM-mode transmission line resonators, each of which has an electrical length of 90$^\circ$ at the mid-band frequency and is short-circuited at one end and open-circuited at the other end with alternative orientation. In general, the physical dimensions of the line elements or the resonators as indicated by the widths W1–W9. Coupling is achieved by way of the fields fringing between adjacent resonators separated by specified spacing. The grounding of micro-strip resonators, which is accomplished via holes. However, because the resonators are quarter-wavelength long using the grounding, the second pass-band of the filter is centred at about three times the mid-band frequency of the desired first pass-band, and there is no possibility of any spurious response in between. The measured frequency response of the implemented filter is shown in the left side. The design criteria for pass band and stop band attenuation are at −2 dB and 30 dB respectively, with the pass-band ripple of 0.01 dB. The optimized −3 dB bandwidth of 110 MHz centred at 1420 MHz. It can be observed that the centre frequency is slightly deviated from 1420 MHz by 1 MHz on the higher side and the −3 dB band width is almost 120 MHz with a downwards slope of 2 dB. The rejection of −30 dB attenuation at 1340 and 1520 MHz frequencies with the bandwidth of 180 MHz has been achieved, which is the indicative of obtained form factor of the filter is in the order of 1.5.