astro-ph/9409071 27 Sep 94 contract with the National Op erated Hubble Fellow The by The Observatories Madingley Road the Contribution Institute of Asso ciation Aeronautics and San Space to Martin Drive Baltimore MD Astronomy University of Cambridge ssmmailastcamacuk Telescope Science Institute of Faint Henry of fergusonstsciedu Stacy Universities Low Galaxy S C SurfaceBrightness Space Administration McGaugh Ferguson Cambridge CB for Counts Research in HA England Galaxies Astronomy Inc under

ABSTRACT

Recent observations have revealed a p opulation of blue galaxies at intermediate redshift

with a space density well in excess of exp ectations from the lo cal luminosity function and

standard cosmology The colors and luminosities of these faint blue galaxies are similar to

nearby low surfacebrightness LSB galaxies Such galaxies are severely underrepresented

in surveys used to dene the lo cal luminosity function but could in principle b e detected

in deep surveys If LSB galaxy density is high enough the faintgalaxy counts could b e

explained without requiring rapid galaxy evolution

To explore the consequences of including LSB galaxies we construct catalogs of simulated

nonevolving galaxies drawn from a multivariate distribution of galaxy luminosities central

surface brightnesses bulgedisk ratios and sp ectralenergy distributions We compare two

mo dels dominated by LSB galaxies to a standard nonevolving mo del Mo del galaxies are

convolved with seeing and selected in a manner that closely matches real surveys For each

mo del we compute the lo cal B band luminosity function HI mass function number counts

J

in the B I and K bands redshift distributions and color distributions

J

We nd it p ossible to include a large p opulation of LSB galaxies and incorp orate a steep

faintend slop e of the luminosity function in our simulations without violating the constraints

on the lo cal eldgalaxy luminosity function or the HI mass function For q the most

favorable mo del matches the counts to B but falls short of the observations at fainter

magnitudes The discrepancy at faint magnitudes is smaller in the I and K bands The

colors and redshift distributions remain roughly consistent with observations to B The

most serious discrepancy with observations is in the distribution of r at faint magnitudes

e

suggesting that the mo del contains to o many LSB galaxies

Nevertheless the results suggest that LSB galaxies could b e a signicant contributor to

faintgalaxy counts reducing the need for such extreme mo dels of galaxy evolution as rapid

merging or bursting dwarf galaxies We prop ose several tests to assess the contribution of

LSB galaxies to faint galaxy counts and to dierentiate mo dels involving mo derate galaxy

evolution from mo dels involving rapid merging or starbursts

Introduction

Counts of very faint galaxies oer a simultaneous prob e of the curvature of the universe

and the evolution of its contents The classic numbermagnitude relation set out by Sandage

as a test of the cosmological mo del has now b een measured to the limits of meter

telescop es and the results are dicult to interpret The counts of faint galaxies in the B

and I bands show numbers are well in excess of cosmological mo dels that do not include

galaxy evolution for any value of the deceleration parameter q Tyson Jarvis Tyson

Lilly Cowie Gardner Metcalfe et al Early attempts to reconcile the

observations to the standard FriedmannLemaitre cosmological mo del p ostulated that the

faintgalaxy excess was primarily due to luminosity evolution galaxies were brighter in the

past b ecause they were forming more stars Tinsley Bruzual Kron Yoshii

Takahara Guiderdoni Ro ccaVolmerange A robust prediction of such mo dels

is that the redshift distribution of faint galaxies should p eak at higher z than in nonevolving

mo dels However deep redshift surveys show a distribution that app ears consistent with the

noevolution prediction to B Broadhurst Ellis Shanks Colless et al

Cowie Songaila Hu Colless et al Furthermore while the B counts show

a strong excess over nonevolving mo dels counts in the K band show no excess Gardner

Cowie Wainscoat

Explanations oered for this discrepancy involve altering cosmology mo difying the stan

dard picture of galaxy evolution or altering prop erties of the lo cal galaxy p opulation

Fukugita et al attempt to t the count and redshift data with standard Yoshii

Arimoto galaxy evolution mo dels and nd that mo dels with a sizable

cosmological constant are favored However gravitational lensing statistics and Lycloud

statistics Fukugita Turner Maoz Rix Fukugita Lahav favor a

small or vanishing cosmological constant Mo dications of galaxy evolution include either

rapid density evolution through merging or selective luminosity evolution To explain the

excess in the B band merger mo dels require triggered bursts of star formation while the

galaxies are still widely separated Guiderdoni Ro ccaVolmerange Broadhurst El

lis Glazebro ok Lacey Silk Lacey et al The required merger rate

is dicult to reconcile with constraints on the fraction of stars that could have formed in

elliptical galaxies in the last Gyr the thinness of spiral galaxy disks or the weak angular

correlation among galaxies at B Toth Ostriker Dalcanton Efstathiou

et al Ro che et al Mo dels involving selective luminosity evolution prop ose that

dwarf galaxies have faded more than giants in the last Gyr Broadhurst Ellis Shanks

Cole Treyer Silk Lilly The most extreme mo dels supp ose that dwarf

galaxy evolution is halted until redshifts z whereup on dwarfs form their stars in rapid

bursts and subsequently fade b eyond detectability Babul Rees For such a high

space density of dwarf galaxies to have b een missed lo cally requires that they have extremely

low surface brightnesses either b ecause of expansion after exp elling their gas in sup ernovae

Dekel Silk or b ecause of a topheavy initial mass function

A more conservative suggestion is that plausible mo dications to the lo cal luminosity

function and distribution of galaxy sp ectral types can bring noevolution NE mo dels much

closer to the data Driver et al present the limiting case of a dwarfdominated no

evolution mo del while Ko o Gronwall Bruzual primarily mo dify galaxy sp ectral

energy distributions Neither mo del fully succeeds Driver et al attempt to match

the counts by adopting a luminosity function with a very steep faintend slop e

The resulting mo del is able to repro duce the faintgalaxy count and color data but predicts

a median redshift well b elow that observed at B for the mo del compared to

from the observations of Colless et al Incompleteness in the combined LDSS survey

Colless et al Colless et al cannot b e the cause of the discrepancy as the survey

is more than complete Ko o et al adopt a set of eleven plausible galaxy sp ectral

types from the evolutionary mo dels of Bruzual Charlot then adjust the luminosity

functions and space densities of the dierent types to provide the b est simultaneous t to

the faintgalaxy counts colors and redshift distributions Postfacto comparison to the lo cal

eldgalaxy luminosity function shows reasonable agreement to the limits of the Loveday

et al survey The success of the mo del is due to the assumption of an op en universe

q and the inclusion of a much larger prop ortion of blue galaxies than typically

seen in lowredshift surveys see Fig Indeed the mo del contains no galaxies redder than

B V with absolute magnitudes M This is equivalent to removing all

B

J



ellipticals and S galaxies brighter than L from the standard NE mo del

Of course within the standard cosmological framework al l galaxies must evolve NE

mo dels are clearly unphysical and are intended only to provide a baseline to isolate the

eects of the cosmological curvature or selection eects from the eects of galaxy evolution

Philosophically we nd the Ko o et al approach which gives large weight to observations

highz galaxies a bit less useful than the standard approach of xing the distribution of

galaxy prop erties to match observations of nearby galaxies In the standard NE mo del it is

easy to turn on evolution adjusting the redshifts of formation starformation timescales

dust content etc to try to match the faintgalaxy observations for an assumed q and

while still repro ducing the prop erties of nearby galaxies If this do es not work as many

argue then more exotic solutions are required In the Ko o et al approach it is not

clear what form the evolution should take There is no physically acceptable way to add

mild evolution to their mo del If one simply turns on evolution of galaxies at some

highz with the starformation timescales given in their Table the luminosity function

and color distribution will b e a strong function of z and the resulting distribution of nearby

galaxy prop erties is unlikely to b e acceptable If one instead adopts their luminosity function

and color distribution at z and evolves the mo dels backwards with the assumed star

formation timescales the predictions for faint galaxy counts and redshift distributions will

change drastically the three bluest classes of galaxies would form at redshifts z and

hence disapp ear at the faint magnitudes where k corrections would otherwise make them the

most numerous p opulation

The mo del presented here is more in the spirit of standard NE mo dels with the exception

that we prop ose a sp ecic selection eect that could account for the discrepancy b etween the

lo cal galaxy prop erties and the deep counts The crux of our mo del is the observation that

the restframe isophotal limits of deep CCD surveys are fainter than the isophotal limits of

the photographic surveys used to dene the lo cal luminosity function McGaugh This

is illustrated in Fig where we show the lo cal and deep survey limits for three galaxies

with the same total magnitude but with dierent scale lengths Hence a large p opulation of

lowsurfacebrightness galaxies could contribute to the counts at faint magnitudes without

violating current limits on the lo cal luminosity function While their lo cal space density is

not well known examples of nearby LSB galaxies have b een found in deep photographic

surveys Bothun et al Davies Phillipps Disney Schombert et al

Schombert et al These galaxies are typically very blue McGaugh Bothun

and app ear to b e weakly clustered Bothun et al Mo McGaugh Bothun

prop erties reminiscent of faint blue galaxies LSB galaxies found in the eld are typically

HIrich disk galaxies with low starformation rates McGaugh Bothun The inferred

color and luminosity evolution of such galaxies is slow enough that a nonevolving mo del is

a reasonable approximation for their app earance at mo derate redshifts

The presentation is as follows In x we briey review the canonical wisdom on diskgalaxy

Figure

This gure shows simulated radial surfacebrightness proles for three exp onential disk galax

Galaxy A has the canonical Freeman central surface brightness ies with M

B

J

B at z Galaxies B and C have scale lengths a factor of and larger

J

00

resp ectively The left panel shows the galaxies viewed in FWHM seeing at z The

horizontal line shows the isophotal threshold of APM survey Loveday et al Galaxy

C would b e missed entirely by the survey while galaxy B would have a measured total

magnitude to o faint by mag if the isophotaltototal correction were based on galaxy A

00

The right panel shows the same three galaxies shifted to z and viewed in seeing

A type II see text SED was assumed giving mag of k dimming The horizontal line

in this panel is Tysons isophotal threshold All three galaxies would b e

B

J

detected ab ove this threshold Isophotaltototal magnitude corrections are and

mag for galaxies AB and C resp ectively

surface brightnesses and show that existing constraints do not rule out the p ossibility of a

large p opulation of LSB galaxies Because the intrinsic distribution of surface brightness of

disks is not well constrained in subsequent sections we adopt three dierent distributions

and compare their predictions for counts redshift distributions colors and the HI mass

function The mo deling is done via a MonteCarlo technique describ ed in x Comparisons

to the observations are presented in x In x we discuss tests that can b e carried out with

highresolution data to assess whether LSB galaxies are indeed a signicant contributor to

faint galaxy counts

The Intrinsic Distribution of Central Surface Brightness of Galaxy Disks

Most determinations of the galaxy luminosity function and number counts predicted

therefrom implicitly assume that the distribution of galaxy surface brightnesses is a

function This is an imp ortant simplication as it allows one to make use of easily measured

isophotal magnitudes without the need for detailed surface photometry and suppresses one

dimension of integration It is observationally supp orted by Freeman who found

that all spiral galaxies had central surface brightnesses B mag arcsec

the scatter b eing consistent with observational error

Disney p ointed out that selection eects could cause the apparent distribution to

app ear sharp even if the intrinsic distribution were broad Allen Shu concurred that

such selection eects could act against surface brightnesses fainter than the Freeman value

but argued that higher surface brightness ob jects would not b e missed Disney Phillipps

developed a formalism to correct the apparent distribution in which a particular value

of the central surface brightness is favored and b oth high and low surface brightness ob jects

can b e missed

That the apparent distribution of central surface brightnesses p eaks at the Freeman

value has b een conrmed by Phillipps et al and van der Kruit who found

and in B resp ectively These authors employed dierent metho ds to

J

recover the intrinsic distribution Phillipps et al applied the metho d of Disney

Phillipps and found a distribution which was broad and asymmetric Davies

mo deled the way in which central surface brightnesses were measured by Phillipps et al

and concluded that deviations from pure exp onential proles caused by even mo dest

bulge comp onents would broaden the distribution still further implying large numbers of

LSB galaxies The VV metho d Schmidt was used by van der Kruit who

max

found that a narrow scatter of mag ab out the Freeman value was recovered if the sample

was restricted to large early type galaxies However the distribution did not approximate

a function for dwarf galaxies

The results of these studies are mutually inconsistent and the situation remains confused

What is really needed is the bivariate distribution of luminosity and surface brightness Since

the surface brightness p ortion of the distribution is not well constrained we adopt two very

dierent forms of the bivariate distribution in order to demonstrate the eects on the pre

dicted counts The rst mo del A increases the normalization of the luminosity function

while the second mo del B steep ens the slop e of the faint end This is accomplished with

out violating constraints on the lo cal luminosity function when the pro cedures of isophotal

measurement and selection are taken into account

In mo del A galaxies exist with equal numbers p er unit magnitude over the range of

central surface brightness in B This is motivated by the existence of large

J

low surface brightness galaxies Bothun et al Schombert Bothun Imp ey

Bothun Schombert et al While the space density of such galaxies is not well

known it no doubt exceeds that exp ected from a Gaussian distrubution of central surface

brightness with a disp ersion mag ab out the Freeman value In order to isolate the

eect of this surface brightness distribution on one parameter of the luminosity function

the normalization it is assumed that there is no correlation b etween surface brightness

and luminosity i e the shap e of the luminosity function is the same for every surface

brightness This is consistent with though not demanded by the similarity b etween the HI

rotation velocity distributions of LSB and other eld galaxies which suggests that they all

have comparable masses Schombert et al

The range of surface brightnesses included in the at distribution of the mo del is dictated

at the faint end by the fact that galaxies fainter than will not contribute signicantly

to the counts even if large and luminous At the bright end the distribution is truncated at

the Freeman value following the results of Allen Shu that very few high surface

brightness galaxies exist If there are many of these then of course cosmological dimming

will bias faint galaxy samples towards high surface brightnesses Phillipps Davies Disney

In mo del B we assume that the narrow distribution of central surface brightnesses found



by van der Kruit eectively holds for giant L L galaxies but that there is a

systematic trend b etween luminosity and surface brightness for fainter galaxies This strongly

aects the slop e of the faint end of the luminosity function when isophotal rather than total

measures are used b ecause intrinsically faint galaxies have their luminosities signicantly

underestimated To illustrate the severity of this aect we assume the following



for L L

and

 

L log LL for L L



The equation for subL galaxies is essentially a constant size relation with some Gaussian

scatter

Finally for comparison we compute a standard NE mo del using a galaxy mix similar

to that adopted by Yoshii Takahara but incorp orating isophotal selection with

disk central surface brightnesses set to the Freeman value with mag Gaussian scatter

These distributions are illustrated schematically in Fig

Mo dels A and B are clearly ad hoc and are intended not to represent reality but to

illustrate the imp ortance of galaxy selection criteria and magnitude estimation techniques in

b oth the lo cal and deep surveys Mo del B is p erhaps closer to the truth in that it includes

the general trend of decreasing surface brightness with decreasing luminosity observed for

Virgo and Fornax Cluster dwarf galaxies Binggeli Sandage Tarenghi Ferguson

Figure Schematic illustration of the centralsurfacebrightness distributions assumed for

galaxy disks in our mo dels In mo del A we assume that surfacebrightness is indep endent

of luminosity In mo del B surface brightness dep ends on luminosity as describ ed in the

text with mag scatter ab out the mean relation The MonteCarlo NE mo del assumes

Freeman disks with mag scatter The analytic NE mo del assumes no scatter

Sandage The surfacebrightnessluminosity relation in mo del B is much steep er

than observed but is dicult to rule out as galaxies with low surface brightness for their

luminosity will always b e preferentially missed in real surveys An intermediate case might b e

one with a shallower trend of surface brightness with luminosity but with broader scatter in

central surface brightness at xed luminosity as found by Imp ey Bothun Malin and

Bothun Imp ey Malin Mo del B is also similar to the mo del of Lacey et al

which included isophotal selection with a surfacebrightnessluminosity relation similar to

that seen in Virgo and a steep luminosity function These prop erties were predicted from

their mo del of tidally triggered galaxy formation that included halo formation galactic

winds sp ectral evolution and extinction The eects of surface brightness are thus dicult

to disentangle from other asp ects of the mo del

Construction of MonteCarlo Mo dels

The simplest way to include intrinsic scatter into the galaxy distribution functions is to

construct simulated galaxies using MonteCarlo techniques For the three mo dels describ ed

ab ove galaxy parameters are chosen at random from the distribution functions describing

space density constant luminosity surface brightness morphological type and bulgedisk

ratio Catalogs of simulated galaxies are constructed and are observed ie they are selected

and their magnitudes are measured in a way that closely matches real surveys

For comparison and as a check on our MonteCarlo technique we compute a second

Table Galaxy Parameters

NE mo del



bulge to Bulge Disk



Type M Mp c total SED SED

B

ES I

S I I

Sab I II

Sb c I III

Sdm III

Mo del A



bulge to Bulge Disk



Type M Mp c total SED SED

B

ES I

S I I

Sab I II

Sb c I III

Sdm III

Mo del B



bulge to Bulge Disk



Type M Mp c total SED SED

B

ES I

S I I

Sab I II

Sb c I III

Sdm III

NE mo del with total magnitude selection using the analytic form of the luminosity func

tion and numerically integrating over the luminosity function to compute N m and N z

distributions The techniques are identical to those used by Yoshii Takahara but

the luminosity function and type distributions are slightly dierent For our comparison we

use luminosity functions identical to those for the isophotal NE mo del The distribution of

sp ectralenergy distributions SEDs is slightly dierent however as the Yoshii Takahara

mo dels do not include separate bulge and disk comp onents

Galaxies are divided into ve broad Hubble types each characterized by the following

a Schechter luminosity function



  LL 

LdL LL e dLL



characterized by a space density a faintend slop e and a characteristic luminosity



L

a ratio of bulgetotal luminosity in the B band Simien de Vaucouleurs and

Gaussian scatter ab out this ratio characterized by a disp ersion dierent for each

type and constrained such that L bul g eL total

B B

surface brightness proles g r given by

n

g r g expa r r

n e

with n for galaxy disks and n for galaxy bulges and co ecients a and

a and

separate luminosity indep endent sp ectralenergy distributions Coleman Wu Weed

man for the bulge and disk comp onents

The parameters describing the dierent mo dels are shown in Table

For the MonteCarlo mo dels we construct simulated catalogs of galaxies for each mor

phological type selecting the parameters for each galaxy at random from the distribution

functions of bulgetotal ratio central surfacebrightness and luminosity The co de uses a

doubleprecision random number generator and has b een extensively tested to ensure that

input distribution functions are prop erly repro duced by the random selection even in the

tails of the distribution Redshifts of the galaxies are selected so as to pro duce a uniform

comoving density using the rejection metho d Press et al with the Euclidean volume

element as the comparison function to the cosmological volume element for q Mag

nitudes are then computed for sp ecied bandpasses by integrating the redshifted sp ectral

energy distributions through the lter bandpasses Dep ending on the survey we are trying to

simulate these catalogs contain anywhere from to galaxies and list for each galaxy

the redshift luminosity in the restframe B band apparent magnitudes in various bands

J

and scale lengths of the bulge and disk comp onents These galaxy catalogs are then fed

to separate programs that observe the galaxies using seeing and selection criteria that

closely match real surveys Distributions of apparent magnitude redshift color etc are

then compiled from galaxies that pass the selection criteria using isophotal ap erture or

total magnitudes as appropriate The resulting distributions are normalized to represent the

correct volume densities of each galaxy type Note that our simulations do not explicitly

include the noise present in any real observations To the extent that the algorthims used

in the deep surveys for detecting galaxies and measuring their magnitudes are unbiased the

eect of noise is simply to increase the scatter in the measured magnitudes Scatter of a few

tenths of a magnitude is unimp ortant over the many decades of the N m diagram and over

the relatively wide magnitude intervals used for N z In any case the b est way to assess

the impact of noise would b e to construct simulated images with noise and analyze them in

the exact same way as the observations While such an exp eriment would b e worthwhile it

is b eyond the scop e of this pap er

Table Assumed Survey Parameters

00 00

Band Observer Magnitude Seeing D

min lim

B Loveday Isophotal

J

B KOS Total

J

B Tyson Isophotal

J

B Colless Isophotal

J

B Cowie Isophotal

AB

I Lilly Nm Hybrid

AB

I Lilly Nz Ap erture

AB

K Cowie Ap erture

AB

Notes

Correction added to isophotal magnitudes

Rough estimates Used to set type fractions

Correction added to isophotal magnitudes

00

Assumed complete to D Isophotal magnitudes used

00 00

Isophotal magnitudes for galaxies with D otherwise used ap erture

00 00

Assumed complete to D ap erture magnitudes used

00

Assumed complete to D Isophotal magnitudes used

The surveys we have chosen to simulate are listed in Table Each is describ ed by the

estimated FWHM of the seeing disk a type of selection diameter or magnitude and a type

of magnitude ap erture isophotal hybrid or total We tune the mo del to match roughly

the canonical distribution of morphologies and total luminosity function in bright surveys

 

Table lines This involves adjusting L and separately for the dierent Hubble

types As an indep endent test of the prop erties of lo cal galaxies in x we predict the color

distributions for a sample of bright galaxies and compare to the observed distribution for

a subsample of the RC catalog de Vaucouleurs et al We then compute the faint

galaxy counts redshifts and colors for the rest of the surveys listed in Table

Cosmological Model

Our mo dels are constructed in the framework of the standard FriedmanLemaitre mo del

with zero cosmological constant The relevant formulae are set out in Yoshii Takahara

and Sandage Briey the apparent magnitudes of sources in a bandpass are

related to their absolute magnitudes M by

m M k z log d

L

where k is the standard k correction that incorp orates the frequency shift and the bandpass

dilation due to redshift and d is the luminosity distance in Mp c The luminosity distance

L

is

q

c

d fq z q q z g

L

H q

where H q and c are the Hubble constant the deceleration parameter and the velocity of

light resp ectively As our aim in this pap er is to elucidate the eects of surfacebrightness

selection rather than to test a particular cosmology we adopt H km s Mp c and

q throughout

The comoving density of galaxies is conserved in our mo del The number of galaxies p er

unit redshift p er steradian dep ends only on the volume element

dV cd

L

p

dz H z q z

Galaxy angular sizes are computed using the angulardiameter distance

d

L

d

A

z

PointSpread Function Convolution

Atmospheric distortions seeing can have a signicant eect on galaxy counts at faint

magnitudes This eect was not included in McGaughs initial consideration of the

counts of LSB galaxies but has b een considered in other contexts by Pritchet Kline

and Yoshii To compare our results to the counts from deep surveys we convolve

our mo del galaxy proles with p ointspread functions that closely match the conditions in

the real surveys Assuming a circular galaxy with a surface brightness prole g where

r r and assuming a circular Gaussian p ointspread function with disp ersion in units

e

of r the convolved onedimensional prole has the form

e

1

Z

g I f d g f

I x is the mo died Bessel function of the rst kind and

f x expx

To sp eed our calculations we have computed the surfacebrightness prole g and the

integrated prole

Z

g d G

separately for bulge and disk proles for a grid of and in steps of in

and For each mo del galaxy we compute r in arcsec for the disk and bulge comp onents

e

using the angulardiameter distance and compute g through the lter bandpass using

the appropriate k corrections To compute an isophotal radius we step through the grid g

using a value of that approximates real observing conditions and summing bulge and disk

comp onents until the ux drops b elow that corresp onding to the limiting isophote

The Distribution of Morphological Types

When isophotal selection is not considered the actual morphologies of galaxies are irrel

evant and all that is imp ortant is their sp ectral energy distributions A typical assumed mix

of Hubble types is ES SaSb and Sc or later Tinsley Shanks et al

Yoshii Takahara This morphological mix is justied on the basis of widearea

surveys of bright galaxies such as those of Tammann Yahil Sandage Kirshner

Oemler Schechter and Peterson et al

As our mo dels include isophotal selection b oth sp ectral energy distributions and galaxy

proles are imp ortant Galaxies in our mo dels are simple entities comp osed of pure r

law bulges and pure exp onential disks We have separated galaxies into ve morphological

classes For each type we x the ratio of bulge to total light in the B band to mean values

J

found by Simien de Vaucouleurs but allow Gaussian scatter ab out this mean

The adopted bulgetotal parameters are shown in Table Sp ectral energy distributions are

sp ecied separately for bulge and disk comp onents see b elow so the ratio of bulgetotal

light will vary with bandpass

The key new feature of our mo del is the inclusion of LSB disk galaxies Matching the

distribution of morphological types in widearea surveys introduces an additional uncertainty

in our mo dels as the selection criteria of those surveys are not well quantied In particular

the fraction of latetype galaxies esp ecially in mo del B is critically dep endent on the limiting

isophote of the surveys As these limits have never b een explicitly quantied for surveys

with go o d morphological resolution we have simply chosen a limit that app ears to us to

b e a go o d approximation of the survey material used by Kirshner et al and Shanks

00

et al Sp ecically we use our co de to simulate a survey in seeing complete to

00

B for galaxies with isophotal diameters D We adjust the space densities

J

of the dierent types to pro duce the prop ortions ESSabSb cSdm in the

nal survey

The Luminosity Function

While each morphological type is characterized by its own luminosity function for the

overall normalization we require that the total luminosity function match that observed lo

cally Kirshner Oemler Schechter Efstathiou Ellis Peterson Loveday et al

Our goal here is to demonstrate that when a realistic mo del for isophotal selection is

included existing observations still allow ro om for a large p opulation of LSB galaxies To

mo del the lo cal luminosity function LF we try to mimic the selection criteria of Loveday

et al herafter LPEM However for comparison to previous faintgalaxy mo deling

we have adopted the Yoshii Takahara LF slop e and normalization



gal Mp c in preference to the b est t found by LPEM Our adopted lo cal

LF is consistent to their b est t to within their errors adopting the LPEM b est t would

increase the discrepancy in N m for all mo dels but would not aect the comparison of

B

J

the dierent mo dels

The LPEM eldgalaxy luminosity function was derived from a redshift survey of galaxies

detected on I I IaJ Schmidt plates by the Automatic Plate Measuring APM machine Kib

blewhite et al An automated stargalaxy separation algorithm was used combined

with visual insp ection of the images to decide whether or not to include an ob ject in the

survey Sources were detected by the APM ab ove an isophote of mag arcsec

B

J

Loveday APM magnitudes are simply a logarithmic scaling of the sum of the lin

earized pixel intensities ab ove this threshold They therefore closely corresp ond to isophotal

magnitudes with the exception that saturation at surface brightnesses may ar

B

J

ticially increase the magnitudes of highsurfacebrightness galaxies Loveday used

CCD images of selected galaxies to compute a constant conversion from APM magnitudes to

total B magnitudes This pro cess makes no correction for the dierent prop ortions of the

J

total galaxy light encompassed for high and low surfacebrightness galaxies ab ove the APM

detection threshold The magnitudes are therefore essentially isophotal with a constant

oset

To simulate this pro cess we compute isophotal magnitudes at for each

B

J

00

of our simulated galaxies assuming FWHM seeing but then add a constant oset of

m mag to simulate the conversion from APM to total magnitudes This is the

conversion appropriate for pure Freeman disks which presumably dominate the calibration

sample We select galaxies from our simulated catalogs with these corrected magnitudes

in the range B and use the standard V V technique Schmidt

J max

to reconstruct the luminosity function We tune the shap es of the typesp ecic luminosity

functions to pro duce an observed luminosity function that matches a Schechter function



with gal Mp c and Figures show the comparison of the

mo dels to our adopted eldgalaxy LF The rather steep intrinsic faint end slop e of the

mo del B luminosity function is consistent with that determined by Bothun Imp ey Malin

from the distribution of scale lengths and surface brightnesses found in the Fornax

Cluster not shown in the gure

Spectral Energy Distributions

We use standard sp ectralenergy distributions SEDs determined from observations of

nearby galaxies as the basis for our magnitude computations Pence Coleman Wu

Weedman While these SEDs undoubtedly do not cover the full range exhibited

by real galaxies we take them as a conservative starting p oint In this resp ect our mo del

is distinctly dierent from that of Ko o et al where much of the increase in counts

comes from galaxies that are bluer than commonly found in lo cal galaxy samples Our

ability to match the counts without pro ducing excess blue galaxies lo cally illustrates that

surfacebrightness selection eects are at least as imp ortant as k corrections in governing the

Though Loveday searched for the p ossibility a surface brightness eect the bright

isophotal limit do es not allow sucient dynamic range for this eect to b e readily apparent

esp ecially when there is large scatter in the calibration data Indeed much of the scatter in

the raw APM magnitudes could b e due to uctuations in the isophotal limit from plate to

plate In an ideal situation correction from isophotal to total magnitudes should b e made on

an individual basis for each galaxy based on prole shap e When a single average correction

is applied instead the most seriously aected ob jects are those asso ciated with large volume

corrections pro ducing a pronounced eect on the luminosity function NE model

Selected by total mag.; measured total mag

Selected by iso. mag.; measured iso. mag

Figure This and the next two gures show the luminosity functions for our mo dels The

solid line shows our ducial observed total luminosity function consistent with the APM

survey of Loveday et al For comparison the dashed line shows a luminosity function



with the same but with The op en symbols show the luminosity function that

would b e recovered from our simulated galaxy catalogs if galaxies could b e selected by

total magnitude The solid symbols show the luminosity function recovered when the APM

selection criteria and magnitude estimation scheme are adopted as describ ed in the text

The luminosity functions of the individual morphological types have b een tuned to match

the ducial total luminosity function and the three panels here show the extent to which

this tuning has b een successful This panel shows the NE mo del Model A

Selected by total mag.; measured total mag

Selected by iso. mag.; measured iso. mag

Figure Mo del A

Model B

Selected by total mag.; measured total mag

Selected by iso. mag.; measured iso. mag

Figure Mo del B

Figure Adopted sp ectral energy distributions

Table Photometric Zero Points

f erg cm s A for m

Band Zerop oint

B

J

B

V

B

AB

I

AB

K

AB

counts

The SEDs adopted are shown in Fig For A we use the compilation

of Coleman Wu Weedman We adopt three of their SEDs lab eling them I I I

and I I I Type I is used for ellipticals bulges and S disks and is taken from their Table

tabulation of the mean M M SED Type II is is taken from their Table and

is used for Sab disks Type III comes from their Table SED for Im galaxies These

SEDs are extrap olated to long wavelengths following Yoshii Takahara and linearly

extrap olated to short wavelengths as shown in Fig The SEDs chosen for the bulge and

disk comp onents of each galaxy type are shown in Table We normalize the ux in each

in the restframe the multiply by SED to pro duce an absolute magnitude M

B

J

the appropriate factor for the absolute magnitude of the disk or bulge We then redshift the

galaxy and compute a weighted mean ux over the lter bandpass to account for k dimming

To convert to magnitudes we use the zero p oints shown in Table

HI Mass Function

A standard argument against a high spacedensity of LSB galaxies is that blind HI surveys

do not nd many optically invisible HI clouds Ferguson Sandage Briggs

We regard this as a serious constraint and devote x to a detailed discussion of the HI

constraints To compare our luminosity function to HI surveys we need a relation b etween

optical luminosities and HI masses We assume E and S galaxies have no HI and adopt for

later types the conversion formula of Briggs

M M LL

HI

M



B

J

for all types regardless of the value of L used for where we adopt LL

the optical luminosity function Comparison to the observed HI mass function is shown in

Fig and discussed in x

Galaxy SurfaceBrightnessLuminosity Relations

The most imp ortant departure of our mo del from others that have considered isophotal

selection is that we adopt nonstandard mo dels for the distribution of central surface bright

ness of spiral galaxy disks for galaxies of type Sa and later Our assumptions are describ ed

in x and illustrated in Fig

The disks of S galaxies are assumed to have regardless of luminosity

Because we are ignoring evolution the prop erties of S disks are not imp ortant for our

mo dels as the k corrections preferentially remove earlytype galaxies from highredshift

samples

For elliptical galaxies and bulges we use the relation from Sandage Perelmuter

M

e B

T

which translates to

log LL

e



In this mo del surface brightness increases with decreasing luminosity for M

B

T

for elliptical galaxies While this app ears to hold for r law ellipticals seen in nearby

clusters it do es not hold for the dwarfellipticals that dominate the counts in those clusters

Binggeli Sandage Tarenghi Ferguson Sandage However dE galaxies do

not app ear to b e abundant in the eld and are in any case bluer than giant Es and have

exp onential surfacebrightness proles Thus to the extent that dE galaxies are included

they are group ed implicitly with lowluminosity LSB galaxies in our mo dels The E and S

galaxy luminosity functions in our mo dels are either at or declining at faint magnitudes

and hence do not predict large numbers of compact highsurface brightness galaxies at low

luminosities Isophotal selection makes very little dierence to the counts of earlytype

galaxies in our mo dels

Galaxy Selection Functions in Deep Surveys

The details of ob ject selection and photometry in faint galaxy surveys are dicult to

mo del precisely and are sometimes not completely sp ecied in the published rep orts Au

tomated galaxy detection algorithms typically catalog pixels ab ove a certain SN threshold

then assign adjacent detected pixels to a single ob ject To increase the detection prob

00

ability for faint galaxies the images are usually convolved with a kernel of FWHM

b efore running the detection algorithm Various stargalaxy separation pro cedures are used

to remove unresolved ob jects but the details of these are unimp ortant at faint magnitudes

where stars are a negligible fraction of the total source counts For the detected ob jects some

surveys rep ort isophotal magnitudes others ap erture magnitudes and still others rep ort a

hybrid of the two

The ultimate test of the mo dels would b e to construct simulated images with signal

tonoise ratios and PSFs that match the real surveys then analyze them with the same

software that was used on the real images This task is b eyond the scop e of our pap er and

in any case is b est done in collab oration with the actual observers For illustrative purp oses

we present in x simulated deep HST WFPC images but for comparison to existing

observations we use the approximations to the surveys describ ed b elow

For the B band counts we compare to Tyson His isophotal threshold was

J

and he rep orts isophotal magnitudes ab ove that threshold The seeing FWHM

B

J

00

was ab out We use the Lilly et al survey for the I band Magnitudes used

for the N m diagram in that study were in the Oke AB system I I

AB

00

and were isophotal ab ove a threshold of for galaxies with D but were

I

AB

00

ap erture magnitudes through a ap erture for smaller galaxies Images were convolved to

00

an eective seeing of The K counts are taken from Gardner Cowie Wainscoat

Details of the galaxy selection and photometry for the deep est K counts have not

b een published We assume following Yoshii that the survey is complete for galaxies

00

with K K isophotal diameters D The seeing FWHM was taken to b e

AB

00

At the faintest levels the published counts include completeness corrections for the num

b er of overlapping sources We have not simulated this pro cess as our mo del galaxies are

all counted if they meet the survey selection criteria

We compare our redshift distributions to three published samples Cowie Songaila

Hu Lilly Colless et al Deep AngloAustralian Telescope AAT

primefo cus plates were used to select galaxies for the LDSS redshift survey Colless et al

The magnitudes measured were essentially isophotal ab ove with

B

J

a constant unsp ecied shift to bring them into agreement with a standard sequence of

00

galaxies measured through a ap erture with a CCD An Sb c Freeman disk observed at

00

z would have a central surface brightness of B In seeing the correction

J

00

from m to m would b e mag which we adopt for all galaxies in the sample The

Lilly sample was compiled from deep CCD imaging with the CanadaFranceHawaii

00

Telescope CFHT in seeing The isophotal selection limits are not sp ecied For our

00

mo dels we assume that the sample is complete for galaxies with D Magnitudes

00

for the detected galaxies are computed through a ap erture and galaxies are required

to have ap erture magnitudes I The deep est redshift survey is that of

AB

Cowie Songaila Hu who published redshifts for a small sample of galaxies to

B selected from the Lilly Cowie Gardner survey The selection criteria of

the nal sample of ob jects are not well dened as only were from the original input

00

sample In our mo dels we assume the survey was diameterlimited at D B

AB

and use uncorrected isophotal magnitudes to decide whether the galaxies are brighter than

the magnitude limit

While the galaxy counts are very sensitive to selection criteria and magnitude schemes in

our mo dels the redshift distributions are not In the NE mo del and mo del A the luminosity

function is not steeply rising so a change in the limiting isophote do es not bring in many low

redshift LSB galaxies The steeply rising luminosity function in mo del B however causes

the redshift distribution to b e progressively skewed toward lower redshifts for fainter limiting

isophotes

Comparison to Observations

The rst test of any mo del that claims to require no evolution is that it match the

observed prop erties of lo cal galaxies Complete samples of lo cal galaxies with HI uxes

colors scalelengths and bulgedisk ratios are nonexistent We are therefore forced to

use incomplete samples and to approximate their selection criteria We have tuned our

typesp ecic luminosity functions as describ ed ab ove to match the lo cally observed total

luminosity function and to b e in rough agreement with prop ortions of morphological types

determined by Pence Tinsley and Shanks et al It is useful to have

an indep endent test that the mo dels repro duce known prop erties of lo cal galaxies To this

end in x and x we compare our mo del predictions to lo cal estimates of the HI mass

function and galaxy B V color distribution

The HI Mass Function

The LSB galaxies that p opulate our mo dels are for the most part visible on skysurvey

plates that is how many of the known examples have b een found and are esp ecially easy to

nd if you know where to lo ok ie from an HI p osition The impressive constraints on the

space density of isolated HI clouds Fisher Tully Briggs are essentially useless

for constraining our mo del as the isophotal limits of the searches for optical counterparts

have not b een quantied Detections of HI emission in the o b eams are not uncommon in

these surveys Briggs but are almost always asso ciated with optically visible galaxies

These galaxies even if they are LSB are removed from the samples b efore the space density

of intergalactic HI clouds is computed This HI cloud density therefore do es not constrain

the LSB galaxy density An HI mass function derived purely from the ob eam detections

without reference to optical counterparts would provide strong constraints on our mo del

but nothing along these lines has b een published The most relevant surveys therefore are

those that allow some comparison b etween the frequency of serendipitous detections and

the galaxy luminosity function Kerr Henning Weinberg et al The surveys

of Schneider et al and Homan et al are in highdensity regions and are

Figure Constraints on the HI massfunction of galaxies The solid curve shows the HI mass

function for normal galaxies derived from the NE mo del as describ ed in the text The dotted

and dashed curves show the predictions for mo dels A and B resp ectively Squares show the

HI mass function from Kerr Henning with dotted lines showing the b ehavior if

the massfunction is normalized to the normalgalaxy HI mass function at M The

triangles are the Weinberg et al mass function normalized to that computed from

the canonical optical luminosity function M M The Arecib o HI cloud limits are

HI

the limits on the spacedensity of isolated HI clouds computed by Briggs

therefore dicult to compare to the exp ectations from the eldgalaxy luminosity function

0

Kerr Henning carried out a blind HI search with the Greenbank telescop e

They observed test directions in the galactic plane and directions out of the plane

detecting a total of ob jects Briggs converts their numbers to an HI mass function

which we show in Fig converted to prop er units for H Comparison of the Kerr

Henning mass function to the optical luminosity function is highly uncertain as we

do not know the density of galaxies b ehind the plane of the Milky Way With our adopted

L to M conversion ob jects with masses M M app ear decient by a factor

B HI HI

of compared to the exp ected HI mass function for normal galaxies This decit was also

noted by Briggs and attributed to the diculty of detecting broad linewidth galaxies

As this diculty is not quantied we do not know how many large linewidth LSB galaxies

could b e lurking in the night sky However the decit may also b e due in part to a dierence

in mean densities of galaxies b ehind the plane If we normalize the Kerr Henning HI mass

function to the eldgalaxy Schechter function at M M as shown by the dotted

HI

lines in Fig our dwarf dominated mo del B is still marginally consistent with the data

Weinberg et al conducted another blind HI survey using the VLA They chose

elds b oth within the PerseusPisces sup ercluster and in a foreground void Seventeen ob jects

were detected in the sup ercluster and none in the void Once again normalization is a

problem and we have chosen simply to normalize the counts in the mass range M

HI

to the eld galaxy M mass function computed from our ducial lo cal luminosity

HI

function This is not strictly prop er as some of the Weinberg et al elds were centered

on bright galaxies If anything however that should lead us to underestimate the relative

prop ortion of low M galaxies The Weinberg et al mass function is shown as triangles in

HI

Fig Weinberg et al nd that their HI mass function is consistent with a at luminosity

function in the mass range M However with only galaxies in

HI

this mass range the constraints on the slop e are not particularly go o d Furthermore their

velocity resolution km s was not optimal for detecting narrow linewidth galaxies and

may lead to some incompleteness at the lowmass limits of their mass function

We conclude that our mo dels are neither supp orted nor ruled out by existing limits on

the HI mass function The steep HI mass function of mo del B shows the largest discrepancy

with the data but is still within the uncertainties of the overall normalization of the observed

HI mass function and the conversion b etween blue luminosity and HI mass As most known

LSB eld galaxies are rich in HI a more complete HI survey would provide a stringent test

of our prop osal

Local B V Colors

The choice of SEDs for the bulge and disk comp onents in our mo del was largely dictated

by the availability of the Coleman et al templates Our pro cedure for tuning the

luminosity typesp ecic functions provides no guarantee that the color distribution of galaxies

will match that seen in lo cal galaxy samples Other investigators Tinsley have used the

B R colors distribution of Kirshner et al to x the distribution of morphological

J F

types However there are diculties in repro ducing the Kirshner et al passbands

Bruzual Instead we selected all galaxies from the RC de Vaucouleurs et al

satisfying the following criteria

00 

B D jbj and v km s

T GSR

To correct for extinction we use the catalogued A values and assume A E B V

B B

We susp ect that the RC is reasonably complete to this limit Of those galaxies satisfying

the ab ove criteria have measured B V sucient for the color distribution to b e

representative of the sample as a whole

We apply the same diameter magnitude and velocity selection criteria to our mo dels

and compare the resulting color distribution to the RC sample in Fig For comparison

we also show the lo cal BV distribution that would b e inferred from the Ko o et al

mo del if galaxies were selected purely by total magnitude

As our mo dels were not tuned to match the observed color distribution we regard the

agreement for mo dels A and B as satisfactory Mo del B shows the b est agreement and also

the b est agreement with the deep survey data see b elow As our NE mo del is very similar

to other NE mo dels found in the literature they would presumably show the same surfeit

of red galaxies if sub jected to the same test Part of the failure of NE mo dels to match the

counts may therefore b e due to p o or assumptions ab out the distribution of z SEDs as 0.81 NE model 300

200

100

0 0.66 model A 300

200

100

0 0.77 model B 300

200

100

0 0.58 Koo et al. (1993) 300

200

100

0 0 0.5 1

B-V

Figure Lo cal B V color distribution for our mo dels and for that of Ko o et al

The comparison sample is selected from the RC catalog as describ ed in the text The mean

B V for the dierent samples are shown in the upp er left The mean for the RC sample

is B V The mo dels have b een normalized to match the number of galaxies in the

RC sample

suggested by Ko o et al However the Ko o et al counterevolution mo del

app ears to skew the distribution to o far to the blue

Number Counts

Having shown that our mo dels are at least consistent with lowredshift observations we

now turn to a comparison with estimates of N m from deep surveys Our assumptions

ab out the surveys are found in Table The results are shown in Fig The NE mo del

with isophotal selection follows quite closely the NE mo del computed with total magnitude

selection In b oth cases our NE mo del agrees closely with that of Yoshii Takahara

and falls short of the observed counts by a factor of four at B Mo del A is a slight

J

improvement but still falls short by a factor of three at B Mo del B b egins to depart

J

from the observed counts at B and is a factor of two short at B

J J

The trends are similar in the I band with mo del B providing an acceptable t down

to I In the K band the agreement b etween the standard NE mo del and the

AB

observations b ecomes worse when isophotal selection is included Once again mo del B

provides the b est t

The turnover at faint magnitudes is of course in part due to the adopted q

cosmology For q not shown in the gures mo del B agrees with the observed counts

to within a factor of two down to B and to within the observational uncertainties down

to the limits of the I and K band observations

NE model

Figure This and the next two gures show number counts in the B I and K bands

AB AB AB

for our mo dels compared to the data from various sources Solid lines show the exp ected

N m for each of our mo dels The dashed lines show the standard nonMonteCarlo no

evolution mo del based on totalmagnitude selection as describ ed in the text This gure

shows the NE Mo del

Model A

Figure Mo del A

Model B

Figure Mo del B

Table Median Redshifts

Magnitude

Survey Band Range NE mo del A mo del B Observed

Colless B

J

Cowie B

AB

Lilly I

A

B

Redshift Distributions

Our mo del redshift distributions are compared to the observations in Fig The

observed median redshifts are z and for the Colless Cowie and Lilly

samples resp ectively The median redshifts predicted by our mo dels are shown in Table

The mo dels predict a slightly higher prop ortion of low redshift galaxies than observed

by Colless et al and slightly more high redshift galaxies than Cowie sees The

most serious discrepancy is in the I band where our mo dels predict a median redshift

higher than observed As the mo dels underpredict the counts in the magnitude ranges

sampled by the Lilly I band and Cowie B band surveys detailed agreement with the

observed redshift distributions is not exp ected The most imp ortant p oint is that none of

the mo dels when prop erly normalized overpredict the numbers of galaxies seen at lowz

This was certainly not a foregone conclusion for mo del B which is dominated by dwarfs

and illustrates the imp ortance of isophotal selection The median redshifts are signicantly

lower for this mo del when galaxies are selected by total magnitude

Color Distributions

Figure This and the next two gures show redshift distributions in the B B and I

J AB AB

bands The histograms show the data The solid curve shows the results of the MonteCarlo

mo dels that simulate the selection criteria of the surveys and the dotted lines show the

result of the standard NE mo del

Figure Redshift distributions for mo del A

Figure Redshift distributions for mo del B

Table B I Colors

AB AB

Sample Mean

Lilly observed

NE mo del

Mo del A

Mo del B

NE model

Figure B I color distributions for the mo dels limited at I compared to

AB AB

the data of Lilly et al The mo dels were binned in mag intervals then smo othed

with a b oxcar lter over bins to simulate photometric errors near the survey limits

Color distributions can provide an additional constraint on the mo dels With only three

SEDs we cannot hop e to match the color distribution in detail however we can at least

test whether the mean and disp ersion of the predicted colors are close to those observed In

Fig we compare the mo del colors to those observed by Lilly Cowie Gardner

00 00

Galaxies were required to have I and B through a ap erture in

AB AB

seeing for b oth the mo dels and the data The mo del color distributions plotted in the gure

are are binned in mag intervals and smo othed with a b oxcar lter over three bins to

simulate photometric errors The means and standard deviations of the B I colors

AB AB

are shown in Table

Diagnostics for HighResolution Imaging

One of the ma jor goals of high resolution imaging with the refurbished Hubble Space

Telescope HST is to reveal the morphologies of highredshift galaxies In this section we

illustrate the dierences b etween mo dels dominated by LSB galaxies and the standard NE

mo del when the faint galaxies are well resolved As neither the standard NE mo del nor the

mo dels dominated by LSB galaxies have b een tuned eg by adjusting q to match the

counts at faint magitudes detailed agreement is not exp ected However neither changing

cosmology nor including mild evolution is likely to change the relative distributions of the

normal galaxy mo dels and LSB galaxy dominated mo dels in the diagrams we present

As we have not simulated mo dels involving evolution we cannot compare our predictions

for faintgalaxy morphology in detail to those of other mo dels The only other mo del to make

quantitative predictions for faint galaxy morphology is that of Lacey et al However

Figure Distribution of intensityweighted axial ratios ba Galaxies for this sample

00

were selected in the I band to have diameters D and magnitudes m

AB iso

The axial ratio is the weighted mean of the bulge and disk axial ratios using the ux ab ove

the limiting isophote as the weighting factor The instrumental PSF FWHM is assumed to

00

b e Smearing by this PSF is included in the mo deling the selection of galaxies but not

in the computation of their axial ratios

a few very general considerations may serve to illustrate the exp ected dierences b etween a

universe dominated by slowlyevolving LSB galaxies and one dominated by merging galaxies

or starforming dwarfs In a mo del dominated by bursting dwarf galaxies for example those

galaxies that have completed their starburst but have not yet faded from view will b e redder

than their bursting counterparts The mo del therefore predicts that lowsurface brightness

galaxies will b e redder than highsurface brightness galaxies Our LSB galaxy mo dels predict

the opp osite trend Mo dels involving merging and triggered star formation predict that the

bluest galaxies will have close neighbors or will b e in the pro cess of merging and therefore

have disturb ed morphologies On the other hand if they are similar to lo cal LSB galaxies

the bluest galaxies in deep surveys should have a dearth of close companions and should

display the morphologies of latetype spirals or irregulars

As most of the galaxies of interest are near the WFPC detection limit for reasonable ex

p osure times ks the task of measuring faintgalaxy morphologies may not b e entirely

straightforward Bulgedisk decomp osition at low SN for example may not provide stable

estimates of the central surface brightnesses of disks In the remainder of this section we

explore several parameters axial ratios eective radii and isophotal magnitudes that can

b e measured in WFPC images without detailed prole tting and that provide a robust

distinction b etween mo dels that are dominated by LSB galaxies and mo dels that are not

Axial Ratio Distribution

Figure Distribution of halflight radii r for the three mo dels Selection criteria are the

e

same as the previous gure The computation of r includes the eect of smearing by the

e

00

PSF

In the LSB galaxy mo dels the counts are dominated by disk galaxies A simple way

of testing whether disk galaxies dominate the counts is to lo ok at the distribution of axial

ratios ba Figure shows the distribution our three mo dels Mo del B is clearly the most

dominated by disk galaxies and would b e easily distinguished from the noevolution case in

the absence of comp eting eects However there are fairly serious comp eting eects Dust

in the disks of LSB galaxies could make edgeon galaxies app ear fainter than their faceon

counterparts We have included no extinction in our mo dels Perhaps equally imp ortant

is the eect of inclination on the selection algorithm Galaxy detection routines such as

FOCAS detect ob jects by recording the number of connected pixels ab ove a xed threshold

In the absence of dust an edgeon LSB galaxy will contain a smaller number of pixels but

each pixel will have a higher ux than the detected pixels in the same galaxy seen face

on Faceon galaxies near the survey limit will tend to break up into many small regions of

unconnected pixels while their edgeon counterparts might not Finally in dwarf galaxies



the stellar velocity disp ersion is a much larger fraction of the rotation velocity than in L

galaxies suggesting that the dwarfs might not b e as at as we have assumed This could b e

an imp ortant eect in the dwarfdominated mo del B

Eective Radii

The distribution of halflight radii provides a much more robust test of mo dels involving

LSB galaxies We have computed r from the onedimensional proles in our catalogs

e

including the eects of seeing Figure shows the predicted r distribution for the three

e

mo dels considered here Lilly et al nd a distribution of r in V images of an I

e AB

00

selected sample that p eaks close to the limit imp osed by seeing The distribution

Figure The variation in the number of galaxies detected brighter than an isophotal

magnitude of I with the limiting isophote The instrumental PSF is assumed to b e

AB

00

FWHM No diameter limit is imp osed on the galaxies

00

for Mo del B to roughly the same I limit p eaks at suggesting that a constantsize

AB



relation for galaxies with L L is probably to o extreme

The Eect of Isophotal Thresholds

Another way to test for LSB galaxies is to examine the eect of imp osing dierent isopho

tal thresholds on the number counts In the standard NE mo del the number of galaxies seen

to a xed isophotal limiting magnitude is not a strong function of the isophotal limit chosen

so long as it is well b elow the Freeman value On the other hand the number of galaxies

detected in LSB galaxy mo dels is quite sensitive to the limiting isophote Figure shows

the surfacedensity of galaxies in our mo dels brighter than an isophotal magnitude I

AB

as a function of the limiting isophote The exp ected number of galaxies rises much more

steeply in mo del B than in the other mo dels

Simulated Images

The tests describ ed ab ove provide a quantitative means of establishing whether LSB

galaxies are a signicant contributor faint galaxy counts The simulated images shown in

Figs provide a more qualitative impression of the approximate morphologies exp ected

in HST images To pro duce the images galaxies were selected at random from the simulated

catalogs with the appropriate relative prop ortions of the dierent morphological types

Image parameters were were fed to the IRAF mkob jects task and the resulting images

IRAF is distributed by Kitt Peak National Observatory National Optical Astronomy

Observatories op erated by the Asso ciation of Universities for Research in Astronomy for the

Figure Simulated WFPC WF image of a standard NE mo del with galaxy densities

00 00

increased by a factor of two The area covered is with a pixel size of In

s through the this and the following images exp osure times were assumed to b e

FW lters A count rate of counts s pixel for the sky background estimated

from the WFPC instrument handb o ok for high ecliptic latitudes Images were convolved

with a mo del WFPC PSF b efore adding noise with the IRAF mknoise task Read noise

was taken to b e e pixel and dark count was assumed to b e counts s pixel

Comparison to gure illustrates the dramatic dierence in morphologies exp ected if LSB

galaxies are the dominant contributor to faint galaxy counts

Figure Simulated WFPC image of mo del A

Figure Simulated WFPC image of mo del B To give an idea of the depth of the

simulated images two galaxies are marked I magnitudes are and for galaxies

AB

and resp ectively

were convolved with a mo del WFPC p ointspread function The NE mo del is shown in

Fig scaled up by a factor of two in density to provide a reasonable number of galaxies

in the image Even at HST resolution many of the galaxies are barely resolved In contrast

mo del B Fig shows a larger number of galaxies as it must to match the counts

and a much larger fraction of resolved galaxies These app ear as as fuzzy patches which

although lacking detailed structures like spiral arms not attempted in the simulations are

clearly distinct from the ma jority of galaxies seen in the standard NE image The larger

fraction of edgeon systems is also readily apparent The distinctions b etween Mo del A Fig

and the NE mo del are more subtle but still readily apparent to the eye Ultimately the

most robust test of the mo dels and assessment the p otential biases in of various detection

algorithms would b e to take such simulations and analyze them in the same way as the real

observations

Conclusions

Our goal in this pap er has b een to construct a set of alternative mo dels of nonevolving

galaxy distributions to test whether LSB galaxies could b e a signicant contributor to faint

galaxy counts and to illustrate the imp ortance of galaxy selection and magnitude measure

ments schemes in intrepreting faintgalaxy counts

We have compared two rather extreme mo dels for the surfacebrightness distribution of

galaxies to a standard nonevolving mo del In mo del A galaxy disks have central surface

brightnesses ranging from the Freeman value of B to B with constant

J J

numbers p er unit magnitude indep endent of luminosity In contrast mo del B incorp orates a



steep surfacebrightnessluminosity relation Disk galaxies brighter than L have B

J



mag while those fainter than L follow a constant size relation with the same

scatter By tuning the typesp ecic luminosity functions we nd that we can include a large

p opulation of LSB galaxies in either mo del A or mo del B without violating the constraints on

the lo cal eldgalaxy luminosity function eg Loveday et al The HI mass function

is not in conict with observations but could b e easily tested with a larger purely HI survey

or with more attention to the selection criteria for identifying the optical counterparts of

existing HI detections

The inclusion of LSB galaxies reduces the discrepancy b etween nonevolving mo dels and

faintgalaxy counts for q For the parameters of Tysons survey the predicted

surfacedensity of galaxies at B for mo del A is only a factor of higher than the

J

NE mo del Mo del B increases the counts by a factor of but is still a factor of two shy

of the observations at B The redshift and color distributions for b oth mo dels match

J

the observations reasonably well Agreement b etween the LSB galaxy mo dels and the faint

galaxy data would improve for lower values of q or for bluer LSB galaxy colors

These results indicate that LSB galaxies could in principle b e an imp ortant comp onent of

the observed faintbluegalaxy p opulation Lo cal examples of LSB galaxies have mo dest star

formation rates and have probably not drastically changed their luminosities or colors in

National Science Foundation

the last Gyr For these galaxies the assumption of no evolution in our mo dels is probably

a reasonable approximation The assumed surface brightness distributions on the other

hand are completely arbitrary The distribution of r predicted by mo del B is probably

e

incompatible with groundbased observations while mo del A is consistent with the available

constraints The true surface brightness distribution probably lies somewhere b etween the

extremes of our two mo dels

Highresolution imaging with HST will allow a quantitative estimate of the contribution

of LSB galaxies Sensitive tests for LSB galaxies include measuring the distribution of r

e

within a limited magnitude range and measuring the variation of N m as a function of

limiting isophote see x Qualitatively our mo dels dier from mo dels involving merging

andor triggered star formation Guiderdoni Ro ccaVolmerange Lacey Silk

Broadhurst Ellis Glazebro ok in predicting that the bluest galaxies within a xed

magnitude will b e the most isolated and have the lowest surface brightnesses Mo dels

involving the late formation of dwarf galaxies Babul Rees also predict that the

bluest galaxies will b e the most isolated However in these mo dels lowsurfacebrightness

galaxies will b e redder on average than highsurfacebrightness galaxies while our mo dels

predict the opp osite trend

If LSB galaxies are a signicant contributor to the counts of faint galaxies then the re

quirements on galaxy evolution mo dels b ecome much less extreme Standard mo dels of

highsurfacebrightness galaxy evolution Bruzual Arimoto Yoshii Ro cca

Volmerange Guiderdoni Bruzual Charlot predict some color and lumi

nosity evolution that must b e included in any selfconsistent mo del We susp ect that

such mo dest evolution coupled with a more realistic surfacebrightness distribution and

surfacebrightnessluminosity relation could restore the agreement b etween galaxy counts

and q mo dels at least to the limits of current redshift surveys

This work was supp orted by the Science and Engineering Research Council and by NASA

through grant HF awarded by the Space Telescope Science Institute which is op erated

by the Asso ciation of Universities for Research in Astronomy Inc for NASA under contract

NAS We thank Arif Babul for stimulating the MonteCarlo mo deling

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