Welfare-maximizing monetary policy under parameter uncertainty

This paper examines welfare-maximizing monetary policy in an estimated micro-founded general equilibrium model of the U.S. economy where the policymaker faces uncertainty about model parameters. Uncertainty about parameters describing preferences and technology implies not only uncertainty about the dynamics of the economy. It also implies uncertainty about the model's utility-based welfare criterion and about the economy's natural rate measures of interest and output. We analyze the characteristics and performance of alternative monetary policy rules given the estimated uncertainty regarding parameter estimates. We find that the natural rates of interest and output are imprecisely estimated. We then show that, relative to the case of known parameters, optimal policy under parameter uncertainty responds less to natural-rate terms and more to other variables, such as price and wage inflation and measures of tightness or slack that do not depend on natural rates.Monetary policy

A Very Hot, High Redshift Cluster of Galaxies: More Trouble for Omega_0 = 1

We have observed the most distant (z=0.829) cluster of galaxies in the Einstein Extended Medium Sensitivity Survey, with the ASCA and ROSAT satellites. We find an X-ray temperature of 12.3 +3.1/-2.2 keV for this cluster, and the ROSAT map reveals significant substructure. The high temperature of MS1054-0321 is consistent with both its approximate velocity dispersion, based on the redshifts of 12 cluster members we have obtained at the Keck and the Canada-France-Hawaii telescopes, and with its weak lensing signature. The X-ray temperature of this cluster implies a virial mass ~ 7.4 x 10^14 h^-1 solar masses, if the mean matter density in the universe equals the critical value, or larger if Omega_0 < 1. Finding such a hot, massive cluster in the EMSS is extremely improbable if clusters grew from Gaussian perturbations in an Omega_0 = 1 universe. Combining the assumptions that Omega_0 = 1 and that the intial perturbations were Gaussian with the observed X-ray temperature function at low redshift, we show that the probability of this cluster occurring in the volume sampled by the EMSS is less than a few times 10^{-5}. Nor is MS1054-0321 the only hot cluster at high redshift; the only two other $z > 0.5$ EMSS clusters already observed with ASCA also have temperatures exceeding 8 keV. Assuming again that the initial perturbations were Gaussian and Omega_0 = 1, we find that each one is improbable at the < 10^{-2} level. These observations, along with the fact that these luminosities and temperatures of the high-$z$ clusters all agree with the low-z L_X-T_X relation, argue strongly that Omega_0 < 1. Otherwise, the initial perturbations must be non-Gaussian, if these clusters' temperatures do indeed reflect their gravitational potentials.Comment: 20 pages, 4 figures, To appear in 1 Aug 1998 ApJ (heavily revised version of original preprint

The First Detailed X-ray Observations of High-Redshift, Optically-Selected Clusters: XMM-Newton Results for Cl 1324+3011 at z = 0.76 and Cl 1604+4304 at z = 0.90

We present the first detailed X-ray observations of optically-selected clusters at high redshift. Two clusters, Cl 1324+3011 at z = 0.76 and Cl 1604+4304 at z = 0.90, were observed with XMM-Newton. The optical center of each cluster is coincident with an extended X-ray source whose emission is detected out to a radius of 0.5 Mpc. The emission from each cluster appears reasonably circular, with some indication of asymmetries and more complex morphologies. Similarly to other optically-selected clusters at redshifts of z > 0.4, both clusters are modest X-ray emitters with bolometric luminosities of only Lx = 1.4 - 2.0 x 10^(44) erg/s. We measure gas temperatures of T = 2.88 (+0.71/-0.49) keV for Cl 1324+3011 and 2.51 (+1.05/-0.69) keV for Cl 1604+4304. The X-ray properties of both clusters are consistent with the high-redshift Lx-T relation measured from X-ray-selected samples at z > 0.5. However, based on the local relations, their X-ray luminosities and temperatures are low for their measured velocity dispersions (sigma). The clusters are cooler by a factor of 2 - 9 compared to the local sigma-T relation. We briefly discuss the possible explanations for these results.Comment: 14 pages, 4 figures; accepted for publication in Astrophysical Journal Letters; version with full resolution figures available at http://bubba.ucdavis.edu/~lubin/xmm.pd

The Properties of Poor Groups of Galaxies: II. X-ray and Optical Comparisons

We use ROSAT PSPC data to study the X-ray properties of a sample of twelve poor groups that have extensive membership information (Zabludoff and Mulchaey 1997; Paper I). Diffuse X-ray emission is detected in nine of these groups. In all but one of the X-ray detected groups, the X-ray emission is centered on a luminous elliptical galaxy. Fits to the surface brightness profiles of the X-ray emission suggest the presence of two X-ray components in these groups. The first component is centered on the central elliptical galaxy. The location and extent of this component, combined with its X-ray temperature and luminosity, favor an origin in the interstellar medium of the central galaxy. Alternatively, the central component may be the result of a large-scale cooling flow. The second X-ray component is detected out to a radius of at least 100-300 kpc. This component follows the same relationships found among the X-ray temperature, X-ray luminosity and optical velocity dispersion of rich clusters. This result suggests that the X-ray detected groups are low-mass versions of clusters and that the extended gas component can properly be called the intragroup medium, in analogy to the intracluster medium in clusters. We also find a trend for the position angle of the optical light in the central elliptical galaxy to align with the position angle of the large-scale X-ray emission. (Abridged)Comment: 38 pages, AASLaTeX with 16 PS figures. Figure 1a-1l available in gzipped postscript format at ftp://corvus.ociw.edu/pub/mulchae

The behaviour of dark matter associated with 4 bright cluster galaxies in the 10kpc core of Abell 3827

Galaxy cluster Abell 3827 hosts the stellar remnants of four almost equally bright elliptical galaxies within a core of radius 10kpc. Such corrugation of the stellar distribution is very rare, and suggests recent formation by several simultaneous mergers. We map the distribution of associated dark matter, using new Hubble Space Telescope imaging and VLT/MUSE integral field spectroscopy of a gravitationally lensed system threaded through the cluster core. We find that each of the central galaxies retains a dark matter halo, but that (at least) one of these is spatially offset from its stars. The best-constrained offset is 1.62+/-0.48kpc, where the 68% confidence limit includes both statistical error and systematic biases in mass modelling. Such offsets are not seen in field galaxies, but are predicted during the long infall to a cluster, if dark matter self-interactions generate an extra drag force. With such a small physical separation, it is difficult to definitively rule out astrophysical effects operating exclusively in dense cluster core environments - but if interpreted solely as evidence for self-interacting dark matter, this offset implies a cross-section sigma/m=(1.7+/-0.7)x10^{-4}cm^2/g x (t/10^9yrs)^{-2}, where t is the infall duration.Comment: 15 pages, 9 figure

A Merger Scenario for the Dynamics of Abell 665

We present new redshift measurements for 55 galaxies in the vicinity of the rich galaxy cluster Abell 665. When combined with results from the literature, we have good velocity measurements for a sample of 77 confirmed cluster members from which we derive the cluster's redshift z=0.1829 +/- 0.0005 and line-of-sight velocity dispersion of 1390 +/- 120 km/s. Our analysis of the kinematical and spatial data for the subset of galaxies located within the central 750 kpc reveals only subtle evidence for substructure and non-Gaussianity in the velocity distribution. We find that the brightest cluster member is not moving significantly relative to the other galaxies near the center of the cluster. On the other hand, our deep ROSAT high resolution image of A665 shows strong evidence for isophotal twisting and centroid variation, thereby confirming previous suggestions of significant substructure in the hot X-ray--emitting intracluster gas. In light of this evident substructure, we have compared the optical velocity data with N-body simulations of head-on cluster mergers. We find that a merger of two similar mass subclusters (mass ratios of 1:1 or 1:2) seen close to the time of core-crossing produces velocity distributions that are consistent with that observed.Comment: 30 pages and 7 figures. Accepted by the Astrophysical Journal Full resoultion figures 1 and 3 available in postscript at http://www.physics.rutgers.edu/~percy/A665paper.htm

On the Internal Absorption of Galaxy Clusters

A study of the cores of galaxy clusters with the Einstein SSS indicated the presence of absorbing material corresponding to 1E+12 Msun of cold cluster gas, possibly resulting from cooling flows. Since this amount of cold gas is not confirmed by observations at other wavelengths, we examined whether this excess absorption is present in the ROSAT PSPC observations of 20 bright galaxy clusters. For 3/4 of the clusters, successful spectral fits were obtained with absorption due only to the Galaxy, and therefore no extra absorption is needed within the clusters, in disagreement with the results from the Einstein SSS data for some of the same clusters. For 1/4 of the clusters, none of our spectral fits was acceptable, suggesting a more complicated cluster medium than the two-temperature and cooling flow models considered here. However, even for these clusters, substantial excess absorption is not indicated.Comment: accepted by the Astrophysical Journa

The XMM Cluster Survey: The interplay between the brightest cluster galaxy and the intra-cluster medium via AGN feedback

Using a sample of 123 X-ray clusters and groups drawn from the XMM-Cluster Survey first data release, we investigate the interplay between the brightest cluster galaxy (BCG), its black hole, and the intra-cluster/group medium (ICM). It appears that for groups and clusters with a BCG likely to host significant AGN feedback, gas cooling dominates in those with Tx > 2 keV while AGN feedback dominates below. This may be understood through the sub-unity exponent found in the scaling relation we derive between the BCG mass and cluster mass over the halo mass range 10^13 < M500 < 10^15Msol and the lack of correlation between radio luminosity and cluster mass, such that BCG AGN in groups can have relatively more energetic influence on the ICM. The Lx - Tx relation for systems with the most massive BCGs, or those with BCGs co-located with the peak of the ICM emission, is steeper than that for those with the least massive and most offset, which instead follows self-similarity. This is evidence that a combination of central gas cooling and powerful, well fuelled AGN causes the departure of the ICM from pure gravitational heating, with the steepened relation crossing self-similarity at Tx = 2 keV. Importantly, regardless of their black hole mass, BCGs are more likely to host radio-loud AGN if they are in a massive cluster (Tx > 2 keV) and again co-located with an effective fuel supply of dense, cooling gas. This demonstrates that the most massive black holes appear to know more about their host cluster than they do about their host galaxy. The results lead us to propose a physically motivated, empirical definition of 'cluster' and 'group', delineated at 2 keV.Comment: Accepted for publication in MNRAS - replaced to match corrected proo

Astrophysical reaction rate for α(αn,γ)\alpha(\alpha n,\gamma)9^{9}Be by photodisintegration

We study the astrophysical reaction rate for the formation of $^{9}$Be through the three body reaction $\alpha(\alpha n,\gamma)$. This reaction is one of the key reactions which could bridge the mass gap at A = 8 nuclear systems to produce intermediate-to-heavy mass elements in alpha- and neutron-rich environments such as r-process nucleosynthesis in supernova explosions, s-process nucleosynthesis in asymptotic giant branch (AGB) stars, and primordial nucleosynthesis in baryon inhomogeneous cosmological models. To calculate the thermonuclear reaction rate in a wide range of temperatures, we numerically integrate the thermal average of cross sections assuming a two-steps formation through a metastable $^{8}$Be. Off-resonant and on-resonant contributions from the ground state in $^{8}$Be are taken into account. As input cross section, we adopt the latest experimental data by photodisintegration of $^{9}$Be with laser-electron photon beams, which covers all relevant resonances in $^{9}$Be. We provide the reaction rate for $\alpha(\alpha n,\gamma)^{9}$Be in the temperature range from T$_{9}$=10$^{-3}$ to T$_{9}$=10$^{1}$ both in the tabular form and in the analytical form. The calculated reaction rate is compared with the reaction rates of the CF88 and the NACRE compilations. The CF88 rate is valid at $T_{9} > 0.028$ due to lack of the off-resonant contribution. The CF88 rate differs from the present rate by a factor of two in a temperature range $T_{9} \geq 0.1$. The NACRE rate, which adopted different sources of experimental information on resonance states in $^{9}$Be, is 4--12 times larger than the present rate at $T_{9} \leq 0.028$, but is consistent with the present rate to within $\pm 20$ at $T_{9} \geq 0.1$.Comment: 32 pages (incl 6 figures), Nucl. Phys. in pres