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Aperture arrays have been studied extensively for application in the next generation of large radio telescopes for astronomy, requiring extremely low noise performance. Prototype array systems need to demonstrate the low noise potential of aperture array technology. This paper presents noise measurements for an Aperture Array tile of 144 dual-polarized tapered slot antenna (TSA) elements, originally built and characterized for use as a Phased Array Feed for application in an L-band radio astronomical receiving system. The system noise budget is given and the dependency of the measured noise temperatures on the beam steering is discussed. A comparison is made of the measurement results with simulations of the noise behavior using a system noise model. This model includes the effect of receiver noise coupling, resulting from a changing active reflection coefficient and array noise contribution as a function of beam steering. Measurement results clearly demonstrate the validity of the model and thus the concept of active reflection coefficient for the calculation of effective system noise temperatures. The presented array noise temperatures, with a best measured value of 45 K, are state-of-the-art for room temperature aperture arrays in the 1 GHz range and illustrate their low noise potential.