Objective Measurement of Morphology
As with the advent of the Hubble Space Telescope and 8 m class
ground-based telescopes galaxies are sampled at fainter magnitudes and higher
redshifts the need arises for a means of objective measurement of galaxy
morphology for the purpose of galaxy evolution studies.
Following Abraham et al.(1994, 1996a,b) we use a quantitative classification
system based on measurements of the rotational asymmetry and central
concentration of galaxian light, to measure the morphologies of 158 galaxies
in the Nearby Field Galaxy Survey (NFGS) in the U, B and
Rc filters (fig.1a-c).
The NFGS galaxy sample is well suited for the calibration of this system in
the local universe. The range in luminosity and type is very large, while
the range in redshift is small
(z=0.01+0.05-0.01; hence the wavelength of
measurement closely approximates the rest-frame wavelength of the emitted
The use of multi-filter data allows us to study directly the dependence of
morphology on rest-frame wavelength (figs.2,3), luminosity and galaxy colour
The Importance of Rest-Frame Wavelength
We find a strong dependence of morphology on wavelength, Hubble type and
galaxy colour: galaxies are more asymmetric and somewhat less concentrated at
shorter wavelengths and/or later types, and get bluer as they get less
concentrated and more asymmetric.
The values of the asymmetry and central concentration (as measured thru a
particular filter) critically depend on galaxy type. The values of central
concentration — and to a lesser extent of asymmetry — are also
sensitive to the cutoff isophote within which the measurement takes place.
The amplitude of the shift in the peak of the distribution of the asymmetries
going from Rc to U sits in an interesting range, as
it is of the same order of magnitude as that observed between measurements in
the Medium Deep Survey and Hubble Deep Field (Abraham et al. 1996a,b) (see
Concentration and Asymmetry
We fit for each galaxy in B an elliptical aperture E(1) with major axis
position angle φ, semi-major and semi-minor axes a and b
and ellipticity ε = (1 − b/a) to the pixels
at a specified isophote μlim.
Concentration index C is then defined by:
Σij in E(α) ( Iij )
C = ------------------ ,
Σij in E(1) ( Iij )
where α is an empirically chosen ``shrinking factor'' (in units of
semi-major axis a for fixed φ and ε. We adopted Abraham
et al.'s optimal choice value α = 0.3.
Rotational asymmetry index A is defined by rotating a galaxy image
about its center and self-subtracting this image from the original one,
using aperture E(1) to define the galaxy pixels:
1 Σij in E(1) | Iij - IRij |
A = - * ----------------------- - k ,
2 Σij in E(1) ( Iij )
where Iij is the intensity in pixel (i,j), and
IRij is the corresponding intensity after the object's
image has been rotated by 180° about its center. The k term is a
small correction accounting for signal introduced into A by noise in
the sky background.
Aperture E(1) is also used in U and Rc, to define
the galaxy pixels.
The Nearby Field Galaxy Survey
The Nearby Field Galaxy Survey (NFGS) is an attempt to remedy the situation
noted by (e.g.) Koo et al. (1993): one of the major problems with the
interpretation of various measurements on distant galaxies is the absence of
a good nearby comparison sample.
We obtained over the last three years U, B and Rc
filter photometry and both nuclear and integrated (luminosity weighted)
spectrophotometry (3600–7200 Angstrom) for a total of close to 200
nearby field galaxies of all types and spanning a wide range in luminosity.
This unique data set will provide us with an accurate description of the
distributions of magnitude, structural parameters, colour and spectral types
in the local universe.
The observed emission line strengths will allow us to measure the star
formation rates; absorption line diagnostics will be used to study the star
formation history of these galaxies, as demonstrated by Caldwell et al. (1993)
for galaxies in the Coma Cluster.
Magnitudes and structural parameters (effective radius, surface brightness,
concentration and asymmetry) will allow us to model detection rates at
increasing redshift. These data will be used as an aid in understanding the
spectra of galaxies at higher redshift, and in measuring the changes in star
formation rates over time.
Because many galaxy properties correlate with magnitude, our sample must span
a broad range in luminosity. Imposing a diameter limit would bias against
low surface brightness galaxies. As a result, we want to avoid a purely
magnitude or diameter limited sample. Instead we impose a luminosity dependent
lower limit on the recessional velocity.
We selected galaxies from the first CfA redshift catalogue, which contains
galaxies to a limiting photographic magnitude of mZ=14.5 (Huchra
et al. 1983), and split up the sample into absolute magnitude bins of width
1 magnitude. For each of these bins we sorted the list by type and
randomly took out galaxies in such proportions as to end up with a total of
198 galaxies with a luminosity distribution approximating the observed local
galaxy luminosity function.
The final sample contains galaxies with the desired range of absolute
magnitudes (−14 < MB < −22), extending
five magnitudes fainter than the chararacteristic luminosity L* ~ −19.2
(de Lapparent et al. 1989).
- Fig.1: Distribution of the 158 measured NFGS galaxies in the asymmetry
versus central concentration plane (for definitions see text) for
a) U, b) B, and c) Rc filters
Point shapes are coded according to Hubble type, point sizes according to
blue luminosity and point colour according to (B−R) colour.
- Fig.2: Average values of asymmetry and central concentration as a
function of wavelength for two cutoff isophotes. Point shapes are coded
according to Hubble type as in Fig.1 .
- Fig.3: Fractional number distributions of asymmetry as a function of
filter of measurement for two cutoff isophotes. For reference, the U
filter distributions have been overplotted in the panels for B and
- Fig.4: Histograms of the asymmetry index A for galaxies in the
HDF (solid line) and MDS (dotted line), reproduced from Abraham et al.
(1996a). The amplitude of the shift between the peaks of the two
distributions is 0.24.
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