Polarized light in high-redshift radio galaxies
HIGH-redshift radio galaxies are characterized by ultraviolet excesses1,2 associated with elongated continuum and emission-line structures aligned along their radio axes3,4. Commonly, these properties are interpreted in terms of jet-induced star formation. However, observations of a blue, polarized continuum knot in the low-redshift radio galaxy PKS2152 — 69 have suggested an alternative beaming/scattering model5,6. To test this model we have obtained imaging-polarimetry observations of two high-redshift radio galaxies: 3C277.2 (z = 0.766) and 3C368 (z = 1.132). We find that both sources are strongly linearly polarized at ultraviolet rest wavelengths, with E-vectors within 25° of perpendicular to the axis of the extended continuum and radio structures. This implies that a large proportion of the ultraviolet light in these objects does not come directly from stars and we suggest it is scattered radiation from the nucleus. These observations also have important implications for beaming models of the active nuclei and for our understanding of the evolution of the host galaxies.
Investigating the nature of the $\mathsf {\vec z}\simeq\mathsf {2.8}$ submillimeter selected galaxy SMM J02399-0136 with VLT spectropolarimetry
We present deep optical spectropolarimetry of SMM J02399-0136 ($z=2.8$) done with the VLT Antu 8.2 m telescope equipped with FORS1. Moderate continuum and emission line polarization are measured ($P\sim5\%$). We do not detect broad lines in scattered flux as would be expected for a type-2 object but rather a polarization behaviour similar to BAL quasars. This classification is confirmed by the detection of both high and low ionization broad absorption troughs and a very red continuum. We argue that this object shares several properties with local ULIGs such as Mrk 231 and other ultraluminous infrared Lo-BAL quasars. However, the fact that the ultraviolet spectrum is dominated by non-stellar radiation does not prove that the dust that is thermally radiating in the far infrared is predominantly heated by the AGN. Since the energy that we get in the far-infrared is precisely that which is removed from the ultraviolet spectrum, this could mean that the starburst is more dust-enshrouded than the AGN due to a peculiar dust distribution. The limits we place on the putative starburst contribution to the restframe ultraviolet continuum together with constraints on the amount of extinction provide an upper limit to the star formation rate of about 2000 $M_{\odot} $yr -1 , consistent with previously claimed high star formation rates level in this object.
FURUTA INEQUALITY AND ITS RELATED TOPICS
This article is devoted to a brief survey of Furuta inequality and its related topics. It consists of 4 sections: 1. From Lowner-Heinz inequality to Furuta inequality, 2. Ando-Hiai inequality, 3. Grand Furuta inequality, and 4. Chaotic order.