Research Highlight

First measurement of 10kpc scale lensing power spectra toward a lensed quasar (press release)

 

Our research team (K.T. Inoue(PI), T. Minezaki, S. Matsushita, and K. Nakanishi) succeeded in measuring 10 kpc scale lensing power spectra of potential, shift, and convergence toward the lensed quasar MG J0414+0534 (Fig.1) at a redshift of 2.639 using Atacama Large Millimeter/Submillimeter Array (ALMA). The article was published in "The Astrophysical Journal” (Impact Factor 5.521, 2023) at on September 7th.

 

 

Fig1. Plots of measured lensing power spectra of potential, astrometric shift, and convergence toward the lensed quasar MG J0414+0534. The horizontal axis shows the angular wave number in 360 degrees in units of 10^6 and the vertical axis shows the lensing powers. Each color shows results with a particular boundary condition on the measured potential fluctuations. For details see Inoue et al. 2023 (Credit: K.T. Inoue).

 

A lensing power spectrum is the power spectrum (Fourier transformed two-point correlation) of a potential, astrometric shift, or convergence (or equivalently dimensionless projected matter density) of matter fluctuations projected on a two-dimensional surface that is diagonal to line of sight to a light source. So far, lensing power spectra have been measured by using the weak lensing effects: From a large set of observed shapes of galaxies, one can measure shears of bundle of photons, which are related to the convergence, the dimensionless projected matter density. Such measurements have been limited on matter fluctuations on scales larger than those of massive galaxies. However, the lensing power spectra on scales smaller than those of dwarf galaxies have not been measured due to insufficient angular resolution and information of the surface brightness of lensed images.  

 

 

 

Fig.2  Conceptual diagram of the lensed quasar MG J0414+0534 observed by ALMA. The light pathes are perturbed by clumps of dark matter in the lensing galaxy (subhalos) and those in the intergalactic space (Credit: NAOJ, K.T. Inoue).

 

 

As shown in Fig.2, our research team used the strong lensing system MG J0414+0534 that can enhance the weak lensing effect due to dwarf galaxy-sized halos in the line of sight. The corresponding physical scale is ~10 kpc. The magnification at the positions of lensed image is as large as 10-20. Therefore, it can enhance the astrometric shifts due to a number of halos in the line of sight by ~10-20. Moreover, the lensed images of the light source (dust emission) has a spatial extension of ~10 kpc, which is necessary to detect fluctuations on a scale of 10kpc. Using a combination of ALMA and a strong lensing of an extended source, we were able to measure a few milliarcsec astrometric shifts due to dwarf galaxy-sized halos in line of sight.

 

 

Fig.3  An Image of the lensed quasar MG J0414+0534 observed by ALMA (green and red) overlaid with a

best-fitted convergence perturbation due to halos in the lensing galaxy and the intergalactic space. 

Light orange color shows high density region and dark orange color shows low density region (Credit: ALMA (ESO/NAOJ/NRAO), K.T. Inoue). 

 

In order to model the combination of strong lensing (by galaxies) and weak lensing (by dwarf galaxy-sized halos in line of sight), we devised a new analysis method based on the Fourier mode expansion to obtain the lensing powers directly from an observed lens system using a radio interferometer. Our method can be used to any distribution of projected matter density without assuming particular form of matter density profile of halos.  A best-fitted convergence perturbation was shown in Fig.3.

 

In modeling the lens system, we included the positions of lensing galaxies measured by Hubble Space Telescope (HST), mid-infrared flux ratios of multiply lensed images of a bright core of a quasar measured by Subaru and Keck telescopes, and the positions of radio jets emitting from a quasar measured by a millimeter to centimeter wave radio telescope Very Long Baseline Array (VLBA). By combining these data to our submillimeter wave data measured by ALMA, we were able to obtain first upper and lower bounds of the lensing power spectra on a scale of 10 kpc.

 

Although we were not able to distinguish the weak lensing effects due to subhalos in the massive lensing galaxy with those due to halos in the intergalactic space, our measurements are consistent with the theoretically predicted abundance of Cold Dark Matter (CDM) halos in which halos in the intergalactic space dominates the weak lensing effect. Thus, our research is an important step to elucidate the true nature of dark matter.

 

This work was supported by Grants-in-Aids for Scientific Research from the Japan Society for the Promotion of Science (Nos. 17H02868, 19K03937), the National Astronomical Observatory of Japan ALMA Joint Scientific Research Project 2018-07A, the same ALMA J A P A N Research Fund NAOJ-ALMA-256, and Taiwan MoST 103-2112-M-001-032-MY3, 106-2112-M-001-011, 107-2119-M-001-020, 107-2119-M-001-020.

The Atacama Large Millimeter/submillimeter Array (ALMA), an international astronomy facility, is a partnership of the European Organisation for Astronomical Research in the Southern Hemisphere (ESO), the U.S. National Science Foundation (NSF) and the National Institutes of Natural Sciences (NINS) of Japan in cooperation with the Republic of Chile. ALMA is funded by ESO on behalf of its Member States, by NSF in cooperation with the National Research Council of Canada (NRC) and the National Science and Technology Council (NSTC) in Taiwan and by NINS in cooperation with the Academia Sinica (AS) in Taiwan and the Korea Astronomy and Space Science Institute (KASI). ALMA construction and operations are led by ESO on behalf of its Member States; by the National Radio Astronomy Observatory (NRAO), managed by Associated Universities, Inc. (AUI), on behalf of North America; and by the National Astronomical Observatory of Japan (NAOJ) on behalf of East Asia. The Joint ALMA Observatory (JAO) provides the unified leadership and management of the construction, commissioning and operation of ALMA.