Prepared for submission to JCAP Search for anomalous alignments of structures in Planck data using Minkowski Tensors Joby P. K. a,b,∗ , Pravabati Chingangbam a , Tuhin Ghosh c , Vidhya Ganesan d , Ravikumar C. D. b a Indian Institute of Astrophysics, Koramangala II Block, Bangalore 560 034, India b Department of Physics, University of Calicut, Malappuram, Kerala 673 635, India c School of Physical Sciences, National Institute of Science Education and Research, HBNI, Jatni 752050, Odissa, India d Department of Physics, Indian Institute of Science, C. V. Raman Ave., Bangalore 560 012, India E-mail: joby@iiap.res.in, prava@iiap.res.in Abstract. Minkowski Tensors are tensorial generalizations of the scalar Minkowski Func- tionals. Due to their tensorial nature they contain additional morphological information of structures, in particular about shape and alignment, in comparison to the scalar Minkowski functionals. They have recently been used [29] to study the statistical isotropy of temperature and E mode data from the Planck satellite. The calculation in [29] relied on stereographic projection of the fields to extract the shape and alignment information. In this work, we cal- culate Minkowski Tensors directly on the sphere and compute the net alignment in the data, based on a recent work that extends the definition of Minkowski Tensors to random fields on curved spaces. This method circumvents numerical errors that can be introduced by the stereographic projection. We compare the resulting net alignment parameter values obtained from the frequency coadded CMB temperature data cleaned by the SMICA pipeline 2 , to those obtained from simulations that include instrumental beam effects and residual foreground and noise. We find very good agreement between the two within ≈ 1σ. We further compare the alignments obtained from the beam-convolved CMB maps at individual Planck frequencies to those in the corresponding simulations. We find no significant difference between observed data and simulations across all Planck frequencies, except for the 30 GHz channel. For the 30 GHz channel we find ≈ 2σ difference between the data and the simulations. This mild disagreement most likely originates from inaccurate estimation of the instrumental beam at 30 GHz in the FFP9 simulations. 1 * Corresponding author. 2 Based on observations obtained with Planck (http://www.esa.int/Planck), an ESA science mission with instruments and contributions directly funded by ESA Member States, NASA, and Canada. arXiv:1807.01306v2 [astro-ph.CO] 7 Jul 2018