The possibility of thermally induced initial density perturbations in inflationary cosmology is examined. The fluctuation dynamics of a scalar field plus thermal bath system during slow roll is described by a Langevin-like equation. Fluctuation-dissipation arguments show that for a wide parameter range within the standard inflation model, the thermal fluctuations of the scalar field can dominate its quantum fluctuations. The initial amplitude of density perturbations is found to lie in a range which is consistent with the recent observations of cosmic temperature fluctuations.Comment: 8 pages, latex, In press Physical Review Letters 199

We present nine color CCD intermediate-band spectrophotometry of a two square degree field centered on the old open cluster M67, from 3890$\rm \AA$ to nearly 1$\mu$. These observations are taken as a part of the BATC (Beijing-Arizona-Taipei-Connecticut) Color Survey of the Sky, for both scientific and calibration reasons. With these data we show that the BATC survey can reach its goal of obtaining spectrophotometry to a zero point accuracy of 0.01 mag, and down to V = 21 with 0.3 mag random error. We fit the color-magnitude diagrams (CMDs) with Worthey's theoretical models. The net result is the excellent fit of the 4.0 Gyr, [Fe/H] = $-0.10$ model to our data, including a good fit to the main sequence (MS) turn-off. Our data are consistent with a toy model with 50\% of the stars in M67 being binaries and a random distribution of binary mass-ratios, although other models with different mass-ratio distributions cannot be ruled out. The spatial distribution and mass function (MF) of stars in M67 show marked effects of dynamical evolution and evaporation of stars from the cluster. Blue stragglers and binary stars are the most condensed within the cluster, with degree of condensation depending on mass.We find M67 to have an elongated shape, oriented at an angle of $15^{\circ}$ relative to the galactic plane. Within its tidal radius, the observed MF of M67 between 1.2 $\rm M_\odot$ and $\rm 0.8 M_\odot$ has a Salpeter slope $\rm \eta = -1.93 \pm 0.66$. For stars of mass below 0.8 $\rm M_\odot$, $\rm \eta \sim 0$. It is plausible that the leveling-off of the MF at lower masses is a result of evaporation of lower mass stars in this mass range at a rate of one every $\sim 10^7$ years. If so, it is plausible that the IMF of M67 has the canonical field value of $\rm \eta = -2.0$.Comment: 74 pages, including 19 ps figures. Accepted for publication in AJ, Aug, 199

Intrigued by the initial report of an extended lumiosity distribution perpendicular to the disk of the edge-on Sc galaxy NGC 5907, we have obtained very deep exposures of this galaxy with a Schmidt telescope, large-format CCD, and intermediate-band filters centered at 6660Å and 8020Å. These two filters, part of a 15-filter set, are custom-designed to avoid the brightest (and most variable) night sky lines. As a result, our images are able to go deeper, with lower sky noise than those taken with broad-band filters at similar effective wavelengths: e.g., 0.6 e − arcsec −2 sec −1 for our observations vs. 7.4 e − arcsec −2 sec −1 for the R-band measures of Morrison et al. In our assessment of both random and systematic errors, we show that the flux level where the errors of observation reach 1 mag arcsec −2 are 29.00 mag arcsec −2 in the 6660Å image (corresponding to 28.7 in R-band) and 27.4 mag arcsec −2 in the 8020Å image (essentially on the I-band system).As detailed in Shang et al., our observations show NGC 5907 has a luminous ring around it that most plausibly is due to the tidal disruption of a dwarf spheroidal galaxy by the much more massive spiral. Here we show that, fainter than 27th R mag arcsec −2 , the surface brightness around NGC 5907 is strongly asymmetric, being mostly brighter on NW (ring) side of the galaxy midplane. This asymmetry rules out a halo for the origin of the faint surface brightness we see.We find this asymmetry is likely an artifact owing to a combination of ring light and residual surface brightness at faint levels from stars that our star-masking procedure cannot completely eliminate. The possible existence of an optical face-on warp in NGC 5907, suggested by our VLA HI observations, is too confused with foreground star contamination to be independently studied. Good agreement with the surface photometry of NGC 5907 by Morrison et al. and other workers lead us to conclude that their data are similarly affected at faint levels by ring light and residual effects from their star masking procedures. Inspection of the images published by Morrison et al. and Sackett et al. confirm this to be the case. Thus, we conclude that NGC 5907 does not have a faint, extended halo.In this paper we present the details of our deep surface photometry of this galaxy, this time paying close attention to the issue of the faint luminosity distribution around this galaxy. Section 2 presents our observations, including details of the data reduction process, which are important for the reader to be able to critically assess the accuracy of our method. In Section 3 we study the faint luminosity distribution around NGC 5907 as it appears in our images, including how the ring, foreground stars, and a possible face-on warp can influence what we see. Our results are compared to those previously published in Section 4, in which we also reassess the likelihood of a halo existing around this galaxy. Section 5 summarizes the main results of this paper. OBSERVATIONS AND DATA REDUCTIONThe phases of data reduction that con...

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