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Full-Text Articles in Physical Sciences and Mathematics
Tdcosmo - Xii. Improved Hubble Constant Measurement From Lensing Time Delays Using Spatially Resolved Stellar Kinematics Of The Lens Galaxy, Anowar J. Shajib, Pritom Mozumdar, Geoff C.-F. Chen, Tommaso Treu, Michele Cappellari, Shawn Knabel, Sherry H. Suyu, Vardha N. Bennert, Joshua A. Frieman, Dominique Sluse, Simon Birrer, Frederic Courbin, Christopher D. Fassnacht, Lizvette Villafaña, Peter R. Williams
Tdcosmo - Xii. Improved Hubble Constant Measurement From Lensing Time Delays Using Spatially Resolved Stellar Kinematics Of The Lens Galaxy, Anowar J. Shajib, Pritom Mozumdar, Geoff C.-F. Chen, Tommaso Treu, Michele Cappellari, Shawn Knabel, Sherry H. Suyu, Vardha N. Bennert, Joshua A. Frieman, Dominique Sluse, Simon Birrer, Frederic Courbin, Christopher D. Fassnacht, Lizvette Villafaña, Peter R. Williams
Physics
Strong-lensing time delays enable the measurement of the Hubble constant (H0) independently of other traditional methods. The main limitation to the precision of time-delay cosmography is mass-sheet degeneracy (MSD). Some of the previous TDCOSMO analyses broke the MSD by making standard assumptions about the mass density profile of the lens galaxy, reaching 2% precision from seven lenses. However, this approach could potentially bias the H0 measurement or underestimate the errors. For this work, we broke the MSD for the first time using spatially resolved kinematics of the lens galaxy in RXJ1131−1231 obtained from the Keck Cosmic …
Updated Analysis Of An Unexpected Correlation Between Dark Matter And Galactic Ellipticity, D. M. Winters, Alexandre Deur, X. Zheng
Updated Analysis Of An Unexpected Correlation Between Dark Matter And Galactic Ellipticity, D. M. Winters, Alexandre Deur, X. Zheng
Physics Faculty Publications
We investigate a correlation between the dark matter content of elliptical galaxies and their ellipticity ϵ that was initially reported in 2014. We use new determinations of dark matter and ellipticities that are posterior to that time. Our data set consists of 237 elliptical galaxies passing a strict set of criteria that selects a homogeneous sample of typical elliptical galaxies. We find a relation between the mass-to-light ratio and ellipticity ϵ that is well fitted by M/L = (14.1 ± 5.4)ϵ, which agrees with the result reported in 2014. Our analysis includes 135 galaxies that were not in …
The Bulge–Disc Decomposed Evolution Of Massive Galaxies At 1 < Z < 3 In Candels, V. A. Bruce, J. S. Dunlop, R. J. Mclure, M. Cirasuolo, F. Buitrago, R. A. A. Bowler, T. A. Targett, E. F. Bell, D. H. Mcintosh, A. Dekel, S. M. Faber, H. C. Ferguson, N. A. Grogin, W. Hartley, Dale D. Kocevski, A. M. Koekemoer, D. C. Zoo, E. J. Mcgrath
The Bulge–Disc Decomposed Evolution Of Massive Galaxies At 1 < Z < 3 In Candels, V. A. Bruce, J. S. Dunlop, R. J. Mclure, M. Cirasuolo, F. Buitrago, R. A. A. Bowler, T. A. Targett, E. F. Bell, D. H. Mcintosh, A. Dekel, S. M. Faber, H. C. Ferguson, N. A. Grogin, W. Hartley, Dale D. Kocevski, A. M. Koekemoer, D. C. Zoo, E. J. Mcgrath
Physics and Astronomy Faculty Publications
We present the results of a new and improved study of the morphological and spectral evolution of massive galaxies over the redshift range 1 < z < 3. Our analysis is based on a bulge–disc decomposition of 396 galaxies with M* > 1011 M⊙ uncovered from the Cosmic Assembly Near-infrared Deep Extragalactic Legacy Survey (CANDELS) Wide Field Camera 3 (WFC3)/IR imaging within the Cosmological Evolution Survey (COSMOS) and UKIRT Infrared Deep Sky Survey (UKIDSS) UDS survey fields. We find that, by modelling the H160 image of each galaxy with a combination of a de Vaucouleurs bulge (Sérsic index n = 4) and an exponential disc (n = 1), we can then …
The Decomposed Bulge And Disc Size–Mass Relations Of Massive Galaxies At 1 < Z < 3 In Candels, V. A. Bruce, J. S. Dunlop, R. J. Mclure, M. Cirasuolo, F. Buitrago, R. A. A. Bowler, T. A. Targett, E. F. Bell, D. H. Mcintosh, A. Dekel, S. M. Faber, H. C. Ferguson, N. A. Grogin, W. Hartley, Dale D. Kocevski, A. M. Koekemoer, D. C. Koo, E. J. Mcgrath
The Decomposed Bulge And Disc Size–Mass Relations Of Massive Galaxies At 1 < Z < 3 In Candels, V. A. Bruce, J. S. Dunlop, R. J. Mclure, M. Cirasuolo, F. Buitrago, R. A. A. Bowler, T. A. Targett, E. F. Bell, D. H. Mcintosh, A. Dekel, S. M. Faber, H. C. Ferguson, N. A. Grogin, W. Hartley, Dale D. Kocevski, A. M. Koekemoer, D. C. Koo, E. J. Mcgrath
Physics and Astronomy Faculty Publications
We have constructed a mass-selected sample of M* > 1011 M⊙ galaxies at 1 < z < 3 in the CANDELS UKIDSS UDS and COSMOS fields and have decomposed these systems into their separate bulge and disc components according to their H160-band morphologies. By extending this analysis to multiple bands, we have been able to conduct individual bulge and disc component SED fitting which has provided us with stellar-mass and star formation rate estimates for the separate bulge and disc components. Having utilized the new decomposed stellar-mass estimates, we confirm that the bulge components display a stronger size evolution than the discs. The median sizes of the bulge components is 3.09 ± 0.20 times smaller than similarly massive local galaxies over the …
The Violent Youth Of Bright And Massive Cluster Galaxies And Their Maturation Over 7 Billion Years, B. Ascaso, B. C. Lemaux, L. M. Lubin, R. R. Gal, Dale D. Kocevski, N. Rumbaugh, G. Squires
The Violent Youth Of Bright And Massive Cluster Galaxies And Their Maturation Over 7 Billion Years, B. Ascaso, B. C. Lemaux, L. M. Lubin, R. R. Gal, Dale D. Kocevski, N. Rumbaugh, G. Squires
Physics and Astronomy Faculty Publications
In this study, we investigate the formation and evolution mechanisms of the brightest cluster galaxies (BCGs) over cosmic time. At high redshift (z ∼ 0.9), we selected BCGs and most massive cluster galaxies (MMCGs) from the Cl1604 supercluster and compared them to low-redshift (z ∼ 0.1) counterparts drawn from the MCXC meta-catalogue, supplemented by Sloan Digital Sky Survey imaging and spectroscopy. We observed striking differences in the morphological, colour, spectral, and stellar mass properties of the BCGs/MMCGs in the two samples. High-redshift BCGs/MMCGs were, in many cases, star-forming, late-type galaxies, with blue broad-band colours, properties largely absent amongst …
Cold Gas Dynamics In Hydra-A: Evidence For A Rotating Disc, S. L. Hamer, A. C. Edge, A. M. Swinbank, J. B. R. Oonk, R. Mittal, B. R. Mcnamara, H. R. Russell, M. N. Bremer, F. Combes, A. C. Fabian, N. P. H. Nesvadba, C. P. O'Dea, S. A. Baum, P. Salomé, G. Tremblay, M. Donahue, Gary J. Ferland, C. L. Sarazin
Cold Gas Dynamics In Hydra-A: Evidence For A Rotating Disc, S. L. Hamer, A. C. Edge, A. M. Swinbank, J. B. R. Oonk, R. Mittal, B. R. Mcnamara, H. R. Russell, M. N. Bremer, F. Combes, A. C. Fabian, N. P. H. Nesvadba, C. P. O'Dea, S. A. Baum, P. Salomé, G. Tremblay, M. Donahue, Gary J. Ferland, C. L. Sarazin
Physics and Astronomy Faculty Publications
We present multifrequency observations of the radio galaxy Hydra-A (3C218) located in the core of a massive, X-ray luminous galaxy cluster. Integral field unit spectroscopy is used to trace the kinematics of the ionized and warm molecular hydrogen which are consistent with an ∼5 kpc rotating disc. Broad, double-peaked lines of CO(2–1), [C II] 157 μm and [O I] 63 μm are detected. We estimate the mass of the cold gas within the disc to be Mgas = 2.3 ± 0.3 × 109 M⊙. These observations demonstrate that the complex line profiles found in the cold …
The Progenitors Of The Compact Early-Type Galaxies At High Redshift, Christina C. Williams, Mauro Giavalisco, Paolo Cassata, Elena Tundo, Tommy Wiklind, Yicheng Guo, Bomee Lee, Guillermo Barro, Stijn Wuyts, Eric F. Bell, Christopher J. Conselice, Avishai Dekel, Sandra M. Faber, Henry C. Ferguson, Norman A. Grogin, Nimish Hathi, Kuang-Han Huang, Dalibor D. Kocevski, Anton M. Koekemoer, David C. Koo, Swara Ravindranath, Sarah Salimbeni
The Progenitors Of The Compact Early-Type Galaxies At High Redshift, Christina C. Williams, Mauro Giavalisco, Paolo Cassata, Elena Tundo, Tommy Wiklind, Yicheng Guo, Bomee Lee, Guillermo Barro, Stijn Wuyts, Eric F. Bell, Christopher J. Conselice, Avishai Dekel, Sandra M. Faber, Henry C. Ferguson, Norman A. Grogin, Nimish Hathi, Kuang-Han Huang, Dalibor D. Kocevski, Anton M. Koekemoer, David C. Koo, Swara Ravindranath, Sarah Salimbeni
Physics and Astronomy Faculty Publications
We use GOODS and CANDELS images to identify progenitors of massive (M > 1010 M ☉) compact early-type galaxies (ETGs) at z ~ 1.6. Because merging and accretion increase the size of the stellar component of galaxies, if the progenitors are among known star-forming galaxies, these must be compact themselves. We select candidate progenitors among compact Lyman-break galaxies at z ~ 3 on the basis of their mass, star-formation rate (SFR), and central stellar density, and we find that these account for a large fraction of, and possibly all, compact ETGs at z ~ 1.6. We find that …
Dynamical Masses Of Early-Type Galaxies: A Comparison To Lensing Results And Implications For The Stellar Initial Mass Function And The Distribution Of Dark Matter, J. Thomas, R. P. Saglia, R. Bender, D. Thomas, K. Gebhardt, J. Magorrian, E. M. Corsini, G. Wegner, S. Seitz
Dynamical Masses Of Early-Type Galaxies: A Comparison To Lensing Results And Implications For The Stellar Initial Mass Function And The Distribution Of Dark Matter, J. Thomas, R. P. Saglia, R. Bender, D. Thomas, K. Gebhardt, J. Magorrian, E. M. Corsini, G. Wegner, S. Seitz
Dartmouth Scholarship
This work aims to study the distribution of the luminous and dark matter in Coma early-type galaxies. Dynamical masses obtained under the assumption that mass follows light do not match with the masses of strong gravitational lens systems of similar velocity dispersions. Instead, dynamical fits with dark matter haloes are in good agreement with lensing results. We derive mass-to-light ratios of the stellar populations from Lick absorption line indices, reproducing well the observed galaxy colours. Even in dynamical models with dark matter haloes the amount of mass that follows the light increases more rapidly with the galaxy velocity dispersion than …
Herschel Photometry Of Brightest Cluster Galaxies In Cooling Flow Clusters, A. C. Edge, J. B. R. Oonk, R. Mittal, S. W. Allen, S. A. Baum, H. Böhringer, J. N. Bregman, M. N. Bremer, F. Combes, C. S. Crawford, M. Donahue, E. Egami, A. C. Fabian, Gary J. Ferland, S. L. Hamer, N. A. Hatch, W. Jaffe, R. M. Johnstone, B. R. Mcnamara, C. P. O'Dea, P. Popesso, A. C. Quillen, P. Salomé, C. L. Sarazin, G. M. Voit, R. J. Wilman, M. W. Wise
Herschel Photometry Of Brightest Cluster Galaxies In Cooling Flow Clusters, A. C. Edge, J. B. R. Oonk, R. Mittal, S. W. Allen, S. A. Baum, H. Böhringer, J. N. Bregman, M. N. Bremer, F. Combes, C. S. Crawford, M. Donahue, E. Egami, A. C. Fabian, Gary J. Ferland, S. L. Hamer, N. A. Hatch, W. Jaffe, R. M. Johnstone, B. R. Mcnamara, C. P. O'Dea, P. Popesso, A. C. Quillen, P. Salomé, C. L. Sarazin, G. M. Voit, R. J. Wilman, M. W. Wise
Physics and Astronomy Faculty Publications
The dust destruction timescales in the cores of clusters of galaxies are relatively short given their high central gas densities. However, substantial mid-infrared and sub-mm emission has been detected in many brightest cluster galaxies. In this letter we present Herschel PACS and SPIRE photometry of the brightest cluster galaxy in three strong cooling flow clusters, A1068, A2597 and Zw3146. This photometry indicates that a substantial mass of cold dust is present (> 3×107 M⊙) at temperatures significantly lower (20–28 K) than previously thought based on limited MIR and/or sub-mm results. The mass and temperature of the dust appear …
Herschel Observations Of Fir Emission Lines In Brightest Cluster Galaxies, A. C. Edge, J. B. R. Oonk, R. Mittal, S. W. Allen, S. A. Baum, H. Böhringer, J. N. Bregman, M. N. Bremer, F. Combes, C. S. Crawford, M. Donahue, E. Egami, A. C. Fabian, Gary J. Ferland, S. L. Hamer, N. A. Hatch, W. Jaffe, R. M. Johnstone, B. R. Mcnamara, C. P. O'Dea, P. Popesso, A. C. Quillen, P. Salomé, C. L. Sarazin, G. M. Voit, R. J. Wilman, M. W. Wise
Herschel Observations Of Fir Emission Lines In Brightest Cluster Galaxies, A. C. Edge, J. B. R. Oonk, R. Mittal, S. W. Allen, S. A. Baum, H. Böhringer, J. N. Bregman, M. N. Bremer, F. Combes, C. S. Crawford, M. Donahue, E. Egami, A. C. Fabian, Gary J. Ferland, S. L. Hamer, N. A. Hatch, W. Jaffe, R. M. Johnstone, B. R. Mcnamara, C. P. O'Dea, P. Popesso, A. C. Quillen, P. Salomé, C. L. Sarazin, G. M. Voit, R. J. Wilman, M. W. Wise
Physics and Astronomy Faculty Publications
The question of how much gas cools in the cores of clusters of galaxies has been the focus of many, multiwavelength studies in the past 30 years. In this letter we present the first detections of the strongest atomic cooling lines, [Cii], [Oi] and [Nii] in two strong cooling flow clusters, A1068 and A2597, using Herschel-PACS. These spectra indicate that the substantial mass of cold molecular gas (> 109 M⊙) known to be present in these systems is being irradiated by intense UV radiation, most probably from young stars. The line widths of these FIR lines …
The Noao Fundamental Plane Survey - Iii. Variations In The Stellar Populations Of Red-Sequence Galaxies From The Cluster Core To The Virial Radius, Russell J. S. Smith, Michael J. Hudson, John R. Lucey, Jenica E. Nelan, Gary A. Wegner
The Noao Fundamental Plane Survey - Iii. Variations In The Stellar Populations Of Red-Sequence Galaxies From The Cluster Core To The Virial Radius, Russell J. S. Smith, Michael J. Hudson, John R. Lucey, Jenica E. Nelan, Gary A. Wegner
Dartmouth Scholarship
We analyse absorption line-strength indices for ~3000 red-sequence galaxies in 94 nearby clusters, to investigate systematic variations of their stellar content with location in the host cluster. The data are drawn from the NOAO Fundamental Plane Survey. Our adopted method is a generalization of that introduced by Nelan et al. to determine the global age-mass and metallicity-mass relations from the same survey. We find strong evidence for a change in galaxy properties, at fixed mass, over a range from the cluster centre to the virial radius, R_200. For example, red-sequence galaxies further out in the clusters have weaker Mgb5177 (at …
Structural Properties Of Discs And Bulges Of Early-Type Galaxies, Roelof S. De Jong, Luc Simard, Roger L. Davies, R. P. Saglia, David Burstein, Matthew Colless, Robert Mcmahan, Gary Wegner
Structural Properties Of Discs And Bulges Of Early-Type Galaxies, Roelof S. De Jong, Luc Simard, Roger L. Davies, R. P. Saglia, David Burstein, Matthew Colless, Robert Mcmahan, Gary Wegner
Dartmouth Scholarship
We have used the EFAR sample of galaxies to investigate the light distributions of early-type galaxies. We decompose the two-dimensional light distribution of the galaxies in a flattened spheroidal component with a Sérsic radial light profile and an inclined disc component with an exponential light profile. We show that if we assume that all galaxies can have a spheroidal and a disc component, then the brightest, bulge-dominated elliptical galaxies have a fairly broad distribution in the Sérsic profile shape parameter nB, with a median of approximately 3.7 and with σ∼ 0.9. Other galaxies have smaller nB values. …
Spatially Resolved Spectroscopy Of Coma Cluster Early-Type Galaxies - Iii. The Stellar Population Gradients, D. Mehlert, D. Thomas, R. P. Saglia, R. Bender, G Wegner
Spatially Resolved Spectroscopy Of Coma Cluster Early-Type Galaxies - Iii. The Stellar Population Gradients, D. Mehlert, D. Thomas, R. P. Saglia, R. Bender, G Wegner
Dartmouth Scholarship
Based on Paper I of this series (Mehlert et al. 2000), we derive central values and logarithmic gradients for the Hβ, Mg and Fe indices of 35 early-type galaxies in the Coma cluster. We find that pure elliptical galaxies have on average slightly higher velocity dispersions, lower Hβ, and higher metallic line-strengths than galaxies with disks (S0). The latter form two families, one comparable to the ellipticals and a second one with significantly higher Hβ, and weaker metallic lines. Our measured logarithmic gradients within the effective radius are ⟨△Mg b⟩ ≈ −0.037, ⟨△⟨Fe⟩⟩ ≈ −0.029, ⟨△Hβ⟩ ≈ +0.017 and ⟨△σ⟩ …
Spatially Resolved Spectroscopy Of Coma Cluster Early-Type Galaxies - Ii. The Minor Axis Dataset, G. Wegner, E. M. Corsini, R. P. Saglia, R. Bender
Spatially Resolved Spectroscopy Of Coma Cluster Early-Type Galaxies - Ii. The Minor Axis Dataset, G. Wegner, E. M. Corsini, R. P. Saglia, R. Bender
Dartmouth Scholarship
We present minor axis, offset major axis and one diagonal long slit spectra for 10 E and S0 galaxies of the Coma cluster drawn from a magnitude-limited sample studied before. We derive rotation curves, velocity dispersion profiles and the H3 and H4 coefficients of the Hermite decomposition of the line of sight velocity distribution. Moreover, we derive the line index profiles of Mg, Fe and Hβ line indices and assess their errors. The data will be used to construct dynamical models of the galaxies and study their stellar populations.
The Peculiar Motions Of Early-Type Galaxies In Two Distant Regions -- Vii. Peculiar Velocities And Bulk Motions, Matthew Colless, R. P. Saglia, David Burstein, Roger L. Davies, Robert K. Mcmahan Jr, Gary Wegner
The Peculiar Motions Of Early-Type Galaxies In Two Distant Regions -- Vii. Peculiar Velocities And Bulk Motions, Matthew Colless, R. P. Saglia, David Burstein, Roger L. Davies, Robert K. Mcmahan Jr, Gary Wegner
Dartmouth Scholarship
We present peculiar velocities for 85 clusters of galaxies in two large volumes at distances between 6000 and 15 000 km s−1 in the directions of Hercules-Corona Borealis and Perseus-Pisces-Cetus (the EFAR sample). These velocities are based on Fundamental Plane (FP) distance estimates for early-type galaxies in each cluster. We fit the FP using a maximum likelihood algorithm which accounts for both selection effects and measurement errors, and yields FP parameters with smaller bias and variance than other fitting procedures. We obtain a best-fitting FP with coefficients consistent with the best existing determinations. We measure the bulk motions of …
Spatially Resolved Spectroscopy Of Coma Cluster Early–Type Galaxies, D. Mehlert, R. P. Saglia, R. Bender, G. Wegner
Spatially Resolved Spectroscopy Of Coma Cluster Early–Type Galaxies, D. Mehlert, R. P. Saglia, R. Bender, G. Wegner
Dartmouth Scholarship
We present long slit spectra for a magnitude limited sample of 35 E and S0 galaxies of the Coma cluster. The high quality of the data allowed us to derive spatially resolved spectra for a substantial sample of Coma galaxies for the first time. From these spectra we obtained rota- tion curves, the velocity dispersion profiles and the H3 and H4 coefficients of the Hermite decomposition of the line of sight velocity distribution. Moreover, we derive the radial line index profiles of Mg, Fe and Hβ line indices out to R ≈ 1re − 3re with high signal-to-noise ratio. We …
Fundamental Plane Distances To Early-Type Field Galaxies In The South Equatorial Strip. I. The Spectroscopic Data, K. R. Müller, G. Wegner, S. Raychaudhury, W. Freudling
Fundamental Plane Distances To Early-Type Field Galaxies In The South Equatorial Strip. I. The Spectroscopic Data, K. R. Müller, G. Wegner, S. Raychaudhury, W. Freudling
Dartmouth Scholarship
Radial velocities and central velocity dispersions are derived for 238 E/S0 galaxies from medium-resolution spectroscopy. New spectroscopic data have been obtained as part of a study of the Fundamental Plane distances and peculiar motions of early-type galaxies in three selected directions of the South Equatorial Strip, undertaken in order to investigate the reality of large-scale streaming motion; results of this study have been reported in M\"uller $et$ $al.$ (1998). The new APM South Equatorial Strip Catalog (−17.5 < δ < +2.5) was used to select the sample of field galaxies in three directions: (1) 15h10 – 16h10; (2) 20h30 – 21h50; (3) 00h10 – 01h30. The spectra obtained have a median S/N per ̊A of 23, an in- strumental resolution (FWHM) of ∼ 4 ̊A, and the spectro- graph resolution (dispersion) is ∼ 100 km s−1. The Fourier cross-correlation method was used to derive the radial ve- locities and velocity dispersions. The velocity dispersions have been corrected for the size of the aperture and for the galaxy effective radius. Comparisons of the derived radial velocities with data from the literature show that our values are accurate to 40 km s−1. A comparison with results from Jørgensen et al. (1995) shows that the derived central velocity dispersion have an rms scatter of 0.036 in log σ. There is no offset relative to the velocity dispersions of Davies et al. (1987).
The Peculiar Motions Of Early-Type Galaxies In Two Distant Rregions — Ii. The Spectroscopic Data, Gary Wegner, Matthew Colless, R. P. Saglia, Robert K. Mcmahan
The Peculiar Motions Of Early-Type Galaxies In Two Distant Rregions — Ii. The Spectroscopic Data, Gary Wegner, Matthew Colless, R. P. Saglia, Robert K. Mcmahan
Dartmouth Scholarship
We present the spectroscopic data for the galaxies studied in the EFAR project, which is designed to measure the properties and peculiar motions of early-type galaxies in two distant regions. We have obtained 1319 spectra of 714 early-type galaxies over 33 observing runs on 10 different telescopes. We describe the observations and data reductions used to measure redshifts, velocity dispersions and the Mgb and Mg2 Lick linestrength indices. Detailed simulations and intercomparison of the large number of repeat observations lead to reliable error estimates for all quantities. The measurements from different observing runs are calibrated to a common …
The Peculiar Motions Of Early-Type Galaxies In Two Distant Regions -- V. The Mg-- Relation, Age And Metallicity, M. Colless, D. Burstein, R. L. Davies, R. K. Mcmahan, R. P. Saglia, G. Wegner
The Peculiar Motions Of Early-Type Galaxies In Two Distant Regions -- V. The Mg-- Relation, Age And Metallicity, M. Colless, D. Burstein, R. L. Davies, R. K. Mcmahan, R. P. Saglia, G. Wegner
Dartmouth Scholarship
We have examined the Mg—σ relation for early-type galaxies in the EFAR sample and its dependence on cluster properties. A comprehensive maximum likelihood treatment of the sample selection and measurement errors gives fits to the global Mg—σ relation of Mg b′=0.131 log σ −0.131 and Mg2=0.257 log σ −0.305. The slope of these relations is 25 per cent steeper than that obtained by most other authors owing to the reduced bias of our fitting method. The intrinsic scatter in the global Mg— σ relation is estimated to be 0.016 mag in Mg b′ and 0.023 …