The halo masses and galaxy environments of hyperluminous QSOs at z~2.7 in the Keck Baryonic Structure Survey

We present an analysis of the galaxy distribution surrounding 15 of the most luminous (>10^{14} L_sun; M_1450 ~ -30) QSOs in the sky with z~2.7. Our data are drawn from the Keck Baryonic Structure Survey (KBSS). In this work, we use the positions and spectroscopic redshifts of 1558 galaxies that lie within ~3', (4.2 h^{-1} comoving Mpc; cMpc) of the hyperluminous QSO (HLQSO) sightline in one of 15 independent survey fields, together with new measurements of the HLQSO systemic redshifts. We measure the galaxy-HLQSO cross-correlation function, the galaxy-galaxy autocorrelation function, and the characteristic scale of galaxy overdensities surrounding the sites of exceedingly rare, extremely rapid, black hole accretion. On average, the HLQSOs lie within significant galaxy overdensities, characterized by a velocity dispersion sigma_v ~ 200 km s^{-1} and a transverse angular scale of ~25", (~200 physical kpc). We argue that such scales are expected for small groups with log(M_h/M_sun)~13. The galaxy-HLQSO cross-correlation function has a best-fit correlation length r_0_GQ = (7.3 \pm 1.3) h^{-1} cMpc, while the galaxy autocorrelation measured from the spectroscopic galaxy sample in the same fields has r_0_GG = (6.0 \pm 0.5) h^{-1} cMpc. Based on a comparison with simulations evaluated at z ~ 2.6, these values imply that a typical galaxy lives in a host halo with log(M_h/M_sun) = 11.9\pm0.1, while HLQSOs inhabit host halos of log(M_h/M_sun) = 12.3\pm0.5. In spite of the extremely large black hole masses implied by their observed luminosities [log(M_BH/M_sun) > 9.7], it appears that HLQSOs do not require environments very different from their much less luminous QSO counterparts. Evidently, the exceedingly low space density of HLQSOs (< 10^{-9} cMpc^{-3}) results from a one-in-a-million event on scales << 1 Mpc, and not from being hosted by rare dark matter halos.Comment: 15 pages, 6 figures. Accepted for publication in Ap

Graduate teaching assistants use different criteria when grading introductory physics vs. quantum mechanics problems

Physics graduate teaching assistants (TAs) are often responsible for grading. Physics education research suggests that grading practices that place the burden of proof for explicating the problem solving process on students can help them develop problem solving skills and learn physics. However, TAs may not have developed effective grading practices and may grade student solutions in introductory and advanced courses differently. In the context of a TA professional development course, we asked TAs to grade student solutions to introductory physics and quantum mechanics problems and explain why their grading approaches were different or similar in the two contexts. TAs expected and rewarded reasoning more frequently in the QM context. Our findings suggest that these differences may at least partly be due to the TAs not realizing that grading can serve as a formative assessment tool and also not thinking about the difficulty of an introductory physics problem from an introductory physics student's perspective