Astro-Ph/9608086 13 Aug 96

astro-ph/9608086 13 Aug 96 Steward galaxies at galaxies We an correction lifetime galaxy b etween interaction First star of the companion ab out spiral the m the satellite Lopsided symmetric large upper We We The interpretation time conrm observations formation galaxies we to Univ formation distortions conjecture present growth Observatory estimate radii in by Gyr in lopsidedness obtain since UCOLick show limit to a terms Walker we Gyr the We magnitude Spiral ago the of galaxies R for that episo de that on a derive of two California use previous are survey for measurement 1 for of that of galaxies the are companion The interaction lopsided Mihos stellar The the indep endent Observatory the lopsidedness consistent galaxies Galaxies Univ and an with erased accretion disk that this gas limited azimuthal volume correlation principal upp er result photometric p opulations through Santa and scalelengths consumption the lopsidedness of was galaxies through that masses Arizona of sample with same Hernquist limit Rix Second that triggered rate and estimates and Cruz lopsidedness uncertainty the HansWalter are m Dennis mass ABSTRACT b etween a and of have dep ends on H a Board Introduction phase lopsided observed hypothesized exhibit mo dels measures Tucson CA small I Limit we the is and problem accretion Zaritsky linewidth by Fourier an Zaritsky caused of use current of mixing parent lopsidedness an excess the galaxies on in signicant Bruzual for Astronomy at on Rix the frequency AZ interaction of this the to lifetime amplitude for the by the and the EMail Nb o dy recent galaxy estimate companion of which tidal increase Both tidal latetype limit stellar blue mergers We and Galaxy that lopsidedness and interaction of of star and interactions approaches mass arises we level EMail b etween luminosity exploit simulation dennisucolickorg Charlot these such how disks A in M attribute 1 galaxies Astrophysics formation accretion is B luminosity from that By of Accretion fast distortions an m of the rixasarizonaedu the the combining integral that of lies tidally ambiguities indicate relative h of and correlation A Kennicutt stellar to galaxy eld eld 1 rate distortions an Zaritsky in A o ccurred to a during calculate the infalling recent 0 spiral estimate induced part spiral and i of Rate to light that and this range eld that a of an in a

Tamblyn Congdon the ongoing interaction b etween the Milky Way and

the Sagittarius dwarf Ibata Gilmore Irwin and the eventual infall of the

Magellanic Clouds onto the Milky Way galaxy Tremaine all suggest that mass

accretion and infall onto disks o ccurs at the current time Placing quantitative limits

on the rate of such events will further our understanding of galaxy evolution and

provide constraints on cosmological mo dels Great interest was generated by the claim

that the vertical thinness of the stellar disks of most spiral galaxies places a stringent

limit on recent accretion and hence argues against high mo dels Toth Ostriker

However recent Nb o dy simulations suggest that this conclusion is complicated

by the absorption of the satellites orbital energy and angular momentum by the halo

rather than by the disk Navarro Frenk White Walker Mihos Hernquist

Huang Carlb erg and so the accretion rate remains unknown

Infalling and merging comp onents presumably span a wide range of masses

Mergers involving comparably sized progenitors which are often called ma jor

mergers pro duce gross morphological distortions such as large tidal tails Toomre

Toomre and are known to signicantly increase the star formation rate in the

participants Larson Tinsley Lonsdale Persson Matthews Kennicutt

et al Sanders et al Lavery Henry Extrap olating from ma jor

mergers it is plausible to assume that the two clearest interaction signatures a

disturb ed morphology and an elevated star formation rate should b e present at lower

levels in the less dramatic but presumably more common minor mergers There is

no degeneracy b etween an evolved ma jor merger where the strength of the signatures

has faded with time and a minor merger b ecause the former will resemble an elliptical

rather than a spiral galaxy Toomre Schweizer

Global loworder m or asymmetries in spiral galaxy disks the much

lower amplitude analogs of tidal tails or bridges are candidate signatures of mergers

and interactions Baldwin LyndenBell Sancisi rst drew attention to

the common phenomenon of lopsided neutral hydrogen distributions in galaxies

Richter Sancisi studied a much larger sample of galaxies by connecting

lopsidedness in the spatial distribution of neutral hydrogen to asymmetries in the

cm line prole They concluded that at least of the galaxies in H I surveys have

signicant asymmetries Rix and Zaritsky hereafter RZ found and quantied

signicant lopsidedness in the stel lar distribution of spiral galaxies Lopsidedness is

usually not as dramatic in the stars as in the neutral hydrogen but its presence in

the stellar distribution demonstrates that the asymmetry in these cases is not the

result of an interaction with the gaseous intergalactic medium as seen for example

in NGC Pho okun Mundy Furthermore the stellar asymmetry o ccurs

at smaller radii than the H I counterpart and hence has a shorter dynamical time and

lifetime Consequently lopsidedness in the stellar distribution may prove to b e a ner

chronometer of the interaction phenomenon Finally if interactions generate a burst of

star formation then the sp ectral energy distribution of the stellar p opulation provides

an external test of the kinematicallyderived chronology The ability to derive two

indep endent timelines for the interaction allows us to crosscheck estimates of lifetimes

and corresp onding accretion rates

We wil l estimate the minormerger rate by identifying a possible signature of

interaction and measuring both its frequency and lifetime The interaction signature

we choose to use is the m distortion of disk galaxies A numerical simulation

Walker Mihos Hernquist x demonstrates that the infall of a small

satellite can pro duce a large m distortion Observationally we need to determine

the distribution of m amplitudes for a fair sample of galaxies Theoretically we

need to calibrate the m amplitude as a function of p erturb er mass orbital

parameters and time since the interaction and determine what other mechanisms

such as an internal disk instability might contribute to this measure There is some

theoretical work on m distortions and instabilities Sellwoo d Merritt

Weinberg Syer and Tremaine but it is yet unclear whether longlived

m mo des can arise and b e sustained in real disks with or without the aid of a

p erturbing companion An estimate of the accretion rate by attributing al l of the

lopsidedness to recent accretion and mergers wil l lead to an upper limit to the accretion

rate In this study we fo cus on the observational task and p eripherally treat the

theoretical task

We measure the distribution of lopsidedness in eld spiral galaxies from a

mo derately sized sample of nearby galaxies new galaxies and from RZ

and develop a simple measurement of asymmetry based on the azimuthal Fourier

decomp osition of the galaxy light In x we describ e the sample the observations and

the numerical analysis of the data In x we discuss the frequency and amplitudes of

asymmetries the search for nearby p erturbing companions lifetime estimates of the

asymmetry using b oth stellar p opulation synthesis mo dels Bruzual Charlot

and a numerical simulation of the infall of a satellite galaxy from Walker Mihos

Hernquist Finally we convert these results into an upp er limit on the current

satellite accretion rate for eld spiral galaxies In x we summarize our results

The Data

Our sample of nearly faceon target galaxies consists of galaxies of Hubble type S

or later at declinations b etween h RA h brighter than m

with redshifts v km s and with kinematic inclinations less than

cos i The kinematic inclination is determined from the inverse TullyFisher

where W is the observed H I linewidth v M is the mean relation sin i

20 c B

2v (M )

circular velocity for galaxies of absolute magnitude M determined from more edgeon

systems and M is calculated using a smo oth Hubble ow mo del with H km

B 0

1 1

s Mp c The data necessary to compile such a sample was drawn from the H I

catalog of Huchtmeier and Richter and the RC de Vaucouleurs et al

Both the I m and K m observations were obtained with the Las

Campanas m Swope telescop e The Iband images were taken with a thick

Tektronix CCD which has a spatial scale of arcsec pix during the nights of

and February The exp osure times for all of the I frames were sec and

the sky was nearly photometric with only slight o ccasional cirrus The K band images

were taken with a NICMOS IR array reimaging optics provided a spatial

scale of arcsec pix These data were obtained during four photometric nights

February Typical K exp osure times were sec on ob ject with an

equal amount of time o ob ject There are some slight variations in exp osure times

due to scheduling constraints and mechanical or software problems

The observed galaxies are listed in Table One galaxy in Table NGC

do es not satisfy the previous selection criteria b ecause of slight dierences in galaxy

classications b etween the H I catalog Huchtmeier Richter which was used

for the selection and the RC catalog de Vaucouleurs et al which was used

to compile the Table In addition several galaxies have inclinations listed in

Table b ecause their kinematic inclinations dier from their photometric inclinations

as given in the H I catalog and Table The inclinations in the Table for NGC

and ESO G are estimated from our images using the disk axial ratios rather

than b eing drawn from the Huchtmeier Richter compilation b ecause the cataloged

inclinations were grossly dierent from the apparent inclinations

0 1

Both the I and K data were reduced using IRAF The Iband images were bias

subtracted and at elded using twilight sky ats Photometric calibration was done

with Landolt standards observed typically at the b eginning and end of each

night The K band data were reduced as describ ed by RZ We use the RZ analysis

software to measure the disk scalelengths and azimuthal Fourier comp onents of the

light distribution at b oth I and K The center is dened to b e the brightest p oint

near the center of the image the galaxies all have welldened nuclei This choice

can b e justied a p osteriori by the lack of large measured asymmetries in the central

regions cf RZ and by the agreement b etween the values derived from the I and K

images see x

Our choice for a quantitative measure of lopsidedness is the average of the ratio

of the m to m Fourier amplitudes A b etween and scalelengths We

refer to this quantity as hA i and calculate it from b oth our I and K galaxy images

The uncertainty in hA i is set to b e the rms variation of the value of A within the

1 1

radial interval To reduce the eect of foreground stars on the measurement of hA i

IRAF is distributed by the National Optical Astronomical Observatories which are op erated by AURA Inc

under contract to the NSF

we have replaced all pixel values ab ove a selected threshold which is set to b e roughly

equivalent to the central surface brightness of the galaxy with the sky value We

have also reanalyzed the data presented by RZ except for NGC which is a

strongly ringed galaxy in order to calculate hA i for those galaxies see Table Our

measurements of hA i range from to and we dene galaxies with hA i

1 1

as signicantly lopsided

We present hA i rather than A the uncertainty corrected value b ecause A is

1 1 1

a p ositive denite quantity errors bias the measurement upward and a correction is

necessary see RZ for details b ecause the correction to A dep ends on the uncertainty

in A which we do not know precisely for each galaxy If the uncertainty in hA i is

1 1

a conservatively large estimate see b elow then an observed value of hA i of

implies a true value of Evidently this correction is small for the lopsided galaxies

of most interest ie hA i

Estimating Uncertainties

We now demonstrate that although the true uncertainties in hA i are likely to b e

larger than the formal uncertainties they are unlikely to b e signicantly larger than

Therefore as discussed ab ove the uncertainties will not signicantly aect hA i

First to estimate the error in hA i due to incompletely masked stars in the Iband

images we reanalyze the images of two symmetric ie small hA i galaxies NGC

and ESOG to which we have added random stellar elds drawn from

the corners of four other images Except for the three cases out of in which an

extremely bright star landed near the galaxy the average increase in the measured

hA i is for NGC and for ESOG

Second we compare the results for the galaxies with b oth I and K data

Figure The standard deviation of hA i measured in I and K ab out a line of

unit slop e is which again suggests that the hA i uncertainties are likely to b e

somewhat larger than those estimated from the variance of A b etween and

scalelengths However this estimate of the uncertainty in hA i includes wavelength

dep endent variations in morphology The b est t line to the data in Figure has

slop e if the line is forced through the origin The agreement of this t

with a line of unit slop e indicates that there is no systematic dep endence of A with

wavelength b etween the I and K bands We concentrate on the Iband data b ecause

they extend to fainter surface brightness levels and span a larger sample of galaxies

Third we compare the two galaxies NGC and IC that were observed

b oth for this study and by RZ For NGC the measurement of hA i from the

current sample data is in the Iband and is from the K data

of RZ The results for IC are and from the current I

and K band data resp ectively and from the reanalyzed RZ data The

average of the K measurements of hA i is which agrees with the Iband

can have value although the dierence in the K measurements suggest that hA i

uncertainties We exp ect the K measurements to have larger uncertainties than

the Iband measurements b ecause the disk b eyond two scalelengths is weakly detected

in our K data

These various tests demonstrate the basic reliability of the hA i measurements

although they suggest that the true uncertainties in hA i range from to

rather than the formal value We adopt the formal uncertainties for the

Tables and Figures but caution that the true uncertainties may b e to times larger

than those quoted

Results and Discussion

The Distribution of hA i

The distribution of hA i is shown in Figure for b oth the new and the RZ samples

Despite the diering wavelengths of the observations m for the current sample

and m for the previous sample the two distributions are similar and conrm the

general corresp ondence b etween I and K measurements of lopsidedness Because we

mo died our measure of lopsidedness and removed the ring galaxy NGC from the

RZ sample there are now fewer highly lopsided galaxies hA i by the present

denition in the RZ sample than shown in their Figure Even so three of

ob jects in their sample have hA i The results from the present sample conrm

the RZ result that ab out of or of normal eld spirals in a magnitude

limited sample are signicantly lopsided In the combined sample of galaxies or

are signicantly lopsided If we have no implicit preference for selecting lopsided

galaxies then these numbers represent the characteristics of eld spiral galaxies In

x we discuss why lopsided galaxies may b e overrepresented by up to a factor of four

in our sample Figure Plate presents Iband images for some of the more lopsided

galaxies in our sample As can b e seen from these images the lopsidedness is due to

extended features rather than to lo calized cites of recent star formation

Nearby Companions

If lopsidedness lasts a relatively short time Gyr as suggested by winding

arguments RZ and by the numerical simulations discussed b elow then the asymmetry

is not a relic from the main galaxy formation ep o ch but is instead due to a later

interaction or merger For example the stellar disk of M is lopsided as a consequence

of the current interaction with its companion Rix and Rieke None of the

galaxies in our sample are clearly interacting so where are the companions Either

the companion galaxy has merged with the primary or it is sp eeding away from from

the primary By assuming a companion velocity of km s relative to the primary

cf Zaritsky et al by adopting a mean age of Gyr for the distortions

and by averaging over all viewing angles we estimate that the typical p erturb er in a

hyperb olic encounter has a pro jected separation of arcmin from its primary at the

average primary distance Mp c Therefore most escaping p erturb ers should lie

within our CCD images which are arcmin on a side

For the companion galaxy search we used the SExtractor package Bertin

to identify galaxies with total Iband apparent magnitude within our images

Because redshifts are unavailable for most of the pro jected neighbors we dep end on

the pro jected separation to estimate their distance from the primary galaxy We nd

no signicant correlation b etween the pro jected density of galaxies with M

absolute magnitudes are calculated assuming the pro jected companions are at the

same distance as the primary and hA i However this lack of a correlation with

projected density do es not exclude a correlation of lopsidedness with true local density

As shown by sp ectroscopic surveys for satellite galaxies Zaritsky et al satellite

galaxies are a small fraction of all pro jected neighbors at these magnitudes

We identied a total of candidate satellites which implies that ab out eight of the

candidates are true satellites Because the counting statistics generate uncertainties

that are larger than the unknown eight satellites it is dicult to determine any

prop erty related to the true satellites Furthermore we selected against obviously

interacting systems by selecting galaxies with normal morphological classications

One conclusion that we can draw from our images is that signicant lopsidedness

do es not require a close current interaction cf Figure If lopsidedness arises from

interactions then either the lopsidedness lasts a suciently long time for p erturb ers

to have drifted away from the primary or the p erturb ers have b een accreted by the

parent galaxy Mo dels for the generation of lopsidedness must include b oth accretion

and nearby passages By assuming that the lopsidedness we observe is due to accretion

rather than nearby passages we wil l obtain an upper limit on the disk accretion rate

The Star FormationLopsidedness Connection

By analogy to the starbursts found in ma jor mergers one might susp ect that there

should b e enhanced star formation in strongly lopsided galaxies cf Zaritsky

hereafter Z To examine this hypothesis we combine the current data with those

of RZ to maximize our sample size As discussed in Z a massnormalized color is

the most appropriate measure of the star formation activity for this work b ecause it

minimizes the dep endence of the color measurement on morphology and luminosity

We dene the mass normalized color via the TullyFisher relationship Tully Fisher

hereafter TF which predicts the absolute blue magnitude of the galaxy from

its neutral hydrogen linewidth We adopt the Bband TF relationship given by Pierce

i i

and Tully M log W where W is H I linewidth

R R

corrected for internal turbulence and inclination as outlined by Tully The

dierence b etween the observed and predicted blue magnitudes assuming pure Hubble

1 1

ow and H km s Mp c is taken to b e the excess blue light from the galaxy

and indicative of the current and recent few Gyr star formation activity We refer

to this quantity as B or the p eculiar luminosity Negative values of B indicate that

the galaxy is more luminous than exp ected for its rotation sp eed

To search for a correlation b etween lopsidedness and recent star formation we plot

hA i versus B for the combined sample in Figure We have applied a mag

oset to the magnitudes from the RC de Vaucouleurs et al relative to those

from the ESOLV catalog Laub erts Valentijn to place all of the magnitudes

on the same system This oset is derived from the comparison of the magnitudes

for galaxies in the current sample drawn from the two sources A Sp earman rank

correlation test indicates that hA i and B are correlated with condence

R If instead the magnitude oset b etween the two samples is set so the

average value of B is equal in the two samples then the Sp earman test indicates that

a correlation is present at the condence level R The clear outlier at

the top of Figure ESO G is retained b ecause it has no other particularly

distinguishing characteristic although it is one of the two galaxies in the sample with

the latest type Sdm

Because several factors may increase the observational scatter the underlying

correlation is probably tighter than it app ears in Figure we have combined

data from the I and K band we have inferred distances from a smo oth Hubble

ow mo del the blue magnitudes dier b etween RC de Vaucouleurs et al

used for the RZ sample and the ESOLV catalog Laub erts Valentijn used

for the current sample hA i can b e underestimated in more inclined galaxies

the inclination corrections to H I linewidths for the nearly faceon sample members

principally galaxies from the RZ sample are large and for galaxies there is

only a single H I linewidth measurement

The apparent correlation b etween hA i and B can arise for two reasons the

measurement of B is aected by the asymmetry ie errors in the linewidth or

inclination measurement are created by the asymmetry and then pro duce correlated

errors in B or the physical mechanism that is resp onsible for the lopsidedness

also aects the stellar p opulations As we discuss b elow errors in linewidth or

inclination app ear unable to account for the observed correlation

Systematic underestimates of the true H I linewidth in asymmetric galaxies will

lead to erroneously small ie negative Bs and pro duce a correlation b etween

hA i and B in the observed sense For the typical coherent radial motions induced 1

by lopsidedness km s RZ and the nature of the proles classied as strongly

asymmetric by Richter and Sancisi their Figure the errors in the

linewidth necessary to generate jB j distortions app ear unlikely Warps in systems

with strong lopsidedness would widen the velocity prole of these nearly faceon

galaxies and cause B to increase opp osite to what is needed to account for the

correlation

Systematic overestimates of the inclination will also lead to a correlation in

the observed sense Lopsidedness may though need not lead to a nonzero m

amplitude in the stellar disk For illustration compare a mere displacement of the outer

isophote center relative to the nucleus which introduces no error into the ellipticity

measurement but a strong m signal to the addition of mass or luminosity along

one axis which generates a strong m and m signal In the latter case whether

the apparent inclination is increased or decreased relative to the true inclination

dep ends on whether the mass is added along the apparent ma jor or minor axis

We examine a worstcase scenario of the inclination bias by mo deling the

asymmetry as a stretching of the galaxy along one of the principal directions We

assume that the kinematic inclination is the true disk inclination ie intrinsically B

and that the p osition angle of the stretching is randomly oriented in azimuth

After averaging over all angles Figure shows the average induced B and its

disp ersion for the sample galaxies

Only a weak trend in the exp ected sense is generated ab out mag over the entire

range of hA i and the eect on B is small and nearly symmetric ab out B

for the ma jority of the sample The eect is large for a small subset of the sample In

fact the eect is much larger than the observed spread in B The galaxy with the

most negative B IC is well mo deled by the inclination bias but otherwise the

generated distribution of B do es not resemble that seen in Figure We conclude

that while errors in the inclination may account for a few of the most extreme observed

values of B they do not account for the observed correlation b etween B and

hA i and hence that the correlation b etween hA i and B principally reects real

1 1

variations in the stellar p opulations of these galaxies

There are three additional arguments in supp ort of this conclusion First the

disk ellipticities measured by RZ were small typically less than despite the

inclusion of several strongly lopsided galaxies in their sample This fact and the large

negative values of B predicted for some galaxies in our sample by our worstcase

mo del indicates that this mo del for the inclination errors is overly p essimistic

Second there is a correlation with condence see Figure b etween hA i and

luminositynormalized color ie B R another indicator of the eective age of a

stellar p opulation However b ecause galaxy color and mass correlate cf Rob erts

Haynes this result might reect in part a dep endence of hA i on Hubble type

although none is seen in Figure or on massluminosity which is seen in Figure

To remove the impact of the masscolor relationship we examine a restricted

luminosity range M and nd that even for this subsample the

correlation of hA i and B R is detected with condence Third Z found

a correlation b etween B and abundance gradients in the sense that galaxies with

negative B have steep er gradients If B decreases systematically with later type

or lower mass as needed to pro duce the hA iB R relationship the opp osite

trend b etween hA i and abundance gradient slop e is exp ected b ecause smaller galaxies

tend to have atter abundance gradients VilaCostas Edmunds Zaritsky

Kennicutt Huchra

In summary the data suggest that B is principally a measure of p eculiar

luminosity although other interpretations cannot b e entirely eliminated We pro ceed

by attributing B to stellar p opulation variations and return to this issue after our

mo deling of the interaction phenomenon

Lopsidedness the TF Relationship and the Volume Correction

If B variations among galaxies are related to lopsidedness then there will

b e systematic biases in measured TF relationships and morphology statistics of

magnitudelimited galaxy samples

The quoted scatter in TF studies eg Bernstein et al is often much less

than the mag seen in Figure It is unclear to what extent the small scatter in

TF studies is a result of their use of longer wavelength photometry their smaller

inclination errors due to a higher average galaxy inclination or their selection criteria

and reduction pro cedures which indirectly eliminate the most lopsided galaxies for

example Bernstein et al require the ellipticity measurement for each of their galaxies

to converge at large radii This is an imp ortant issue as such culling may not b e

p ossible with higher redshift samples

These diculties are exacerbated in magnitude limited samples if B and hA i are

correlated Lopsided galaxies will b e overrepresented b ecause they are overluminous

For example if the signicantly lopsided galaxies in our sample are on average brighter

by one magnitude than the undisturb ed galaxies then the lopsided galaxies are drawn

from a volume that is four times larger than that from which the undisturb ed galaxies

are drawn If so the observed fraction of galaxies in our sample with hA i

implies that ab out of eld spirals galaxies are signicantly lopsided Such a

correction is critical b ecause the inferred accretion rate assuming a lifetime of Gyr

for signicant lopsidedness see b elow for a sizable satellite drops from Gyr to

Gyr The volume correction will remain uncertain until the correlation b etween

B and hA i is b etter understo o d 1

Chronology from Galaxy Colors

The spread in B suggests that there are stellar p opulations variations among

these galaxies and the correlation b etween B and hA i suggests that these variations

are related to the morphological disturbance Using the stellar p opulation synthesis

mo dels of Bruzual Charlot we calculate the magnitude and duration of color

changes for several starburst scenarios

Our mo dels consist of a star formation burst sup erp osed on an existing p opulation

The initial mass function is a MillerScalo function with upp er and lower mass

cutos of and M resp ectively but our broad conclusions are indep endent

of these details We consider two sets of mo dels Our red mo dels have an old

underlying stellar p opulation that formed entirely during the galaxys rst Gyr and

a young p opulation that forms during a short sudden burst Gyr afterwards Our

blue mo dels have an underlying p opulation with a constant star formation rate for

the last Gyr plus a young p opulation from a sudden short burst In b oth sets of

mo dels the burst forms as many new stars as were present b efore the burst This

fraction of new stars is meant to mimic the accretion of a satellite with of the

primarys mass and the subsequent episo de of increased star formation We assume

that the parent and satellite have similar preexisting stellar p opulations and that

the parent relaxes to its masslinewidth relationship instantly after the accretion We

present calculations for three blue and red mo dels with burst durations of

and Gyr

We compile M which is essentially a stellar mass normalized blue color b ecause

the mo del galaxies have the same mass and B R as functions of the time since

the b eginning of the starburst Results from the red mo dels which show the more

extreme color changes are shown in Figure Some of the mo dels span the observed

range in magnitudes roughly a mag variation in B with several of the mo dels

spanning the mag range seen in the bulk of the galaxy p opulation in Figure

Assuming that B a conservative choice for the rightmost edge of the B

distribution shown in Figure corresp onds to the plateau in the M proles shown

in Figure then we can use p opulation synthesis mo dels to estimate the age since

the starburst for galaxies with B In the upp er panel of Figure we show the

estimated ages as a function of B along a line tted to the data in Figure based

on two of the red mo dels the and Gyr bursts We conclude from the top

panel of Figure that galaxies with signicant lopsidedness probably exp erienced an

interaction well within the last years

The blue mo dels show much smaller color and luminosity evolution and do

not repro duce the full observed range of B If the blue mo dels are appropriate

then B do es not reect stellar p opulation changes and the volume correction to the

frequency of lopsidedness is negligible The correct mo del presumably lies b etween the

red and blue extremes

Chronology from Merger Simulations

Although the exhaustive theoretical work necessary to establish a dynamical

interaction chronometer is b eyond the scop e of this pap er we present one simulation

to demonstrate that minor mergers can create asymmetries comparable to those

observed in our sample Walker Mihos Hernquist have generously provided the

results from their fully selfconsistent stellar dynamical simulation of the accretion of

a satellite galaxy which has of the disk mass of the primary galaxy ab out

of the total mass of the primary for details see Walker Mihos Hernquist

The satellite b egins the simulation at six disk scalelengths from the center of the disk

galaxy in a prograde circular orbit with an inclination of to the disk plane

We convert their numerical data to images that are comparable in size and scale

to the K images Smo othing and addition of noise is done within IRAF We take

snapshots of their simulated galaxy at times of and Gyr after the start

of their simulation see their Figure for images of the galaxy at the rst two of these

time steps Their simulation concludes after Gyr We apply the same analysis

algorithm to these images as we apply to our images We identify the center of the

simulated spiral in the last snapshot the most dynamically relaxed state and x the

p osition of the center for the other two images The values of hA i are

and for the three times resp ectively These results demonstrate

that large infalling satellites create m distortions that are entirely consistent

with those observed The lifetime of lopsidedness will dep end on many details of the

interaction eg mass ratio disk orientaion orbital parameters so the values given

ab ove are strictly only valid for the particular case considered We are currently

examining a range of interaction parameter space in order to b etter estimate the

lifetime of lopsidedness

The simulated measurements of hA i as a function of time were used to date

galaxies along the line tted to the data in Figure cf b ottom panel of Figure

The exact relationship b etween the morphological and stellar p opulation timescales is

unclear b ecause we do not know when the star formation rate b ecomes elevated during

an interaction Nevertheless the age estimates from the two metho ds are roughly

consistent oset by Gyr at a B of If the star formation burst b egins a

time T after the initial conguration of the Nb o dy simulations at which time the

satellite is at six disk scalelengths from the parent then the ages in the upp er panel

of Figure should b e increased by T Requiring synchronicity b etween the kinematic

and photometric age estimates sets T Gyr although given the uncertainties this

agreement is not required These dynamical mo dels also suggest that galaxies with

signicant lopsided have had an interaction within the last Gyr

We combine the p opulation synthesis mo dels with the results from the dynamical

simulation to predict the evolution of recent minor mergers in the B hA i and

B R hA i planes Figure shows the evolutionary tracks for b oth the red and 1

blue mo dels for a choice of T Gyr and a burst duration of Myr The curves

trace the evolution from the b eginning of the Nb o dy simulation hA i is extrap olated

b eyond Gyr and are sup erp osed on the data In b oth planes the mo dels are in

gross agreement with or span the existing data The appropriate mo dels app ear to b e

a combination of our red and blue extreme mo dels Figure demonstrates that

color and symmetry variations during accretion events should b e observable and in the

range necessary to explain the data

Constraining

It is well known that the current satellite accretion rate dep ends on the cosmic

density parameter eg Toth Ostriker From analytic expressions for

the number of mergers of certain masses as a function of time Carlb erg Toth

Ostriker we calculate that the probability for the accretion of a lump with

of the primarys mass for a normal spiral galaxy M Zaritsky White

over the last Gyr is Therefore we would exp ect to see hA i in

of the galaxies if the signature of such an accretion is lopsidedness with hA i

as indicated by the simulation we ignore the very massive interactions

that disrupt disks b ecause the number of infalling ob jects is dominated by those of

lower mass we estimate based on our two chronometers that the lifetime of the

accretion signature is Gyr and we p ostulate that an ob ject accreted by the halo

as calculated by Toth Ostriker is also accreted by the disk Because the observed

frequency of lopsidedness is not that large the mo dels and that data can b e

reconciled by p ostulating that only a fraction of the halo accretion events b ecome disk

accretion events at most a fraction of to dep ending on the adopted volume

correction Such fractions are now not dicult to justify cf Navarro Frenk

White Huang Carlb erg Interestingly low mo dels may have diculty

repro ducing the upp er end of our accretion frequency ie assuming no volume

correction esp ecially if only a small fraction of halo mergers b ecome disk mergers

It is premature to draw inferences on from the present data and interpretations

However Figure illustrates the p otential that observations along these lines have

to provide information on the accretion rate to clarify the connection b etween star

formation and morphological disturbances and to constrain mo dels of merging and

accretion

The rough agreement b etween the theoretical merger rates and those derived from

our assumption that lopsidedness arises from mergers of satellites that have ab out a

tenth the mass of the parent suggests that our assumption may not b e grossly incorrect

Nevertheless we cannot yet eliminate the p ossibility that other mechanisms such as

internal disk instabilities are contributing signicantly or even predominantly to the

observed lopsidedness Therefore we stress that the derived merger rates are upp er

limits

Conclusions

The principal result of this work is the measurement of the m azimuthal

distortion in the stellar disks of galaxies and a comparison of the distortions

measured at I m and K m for galaxies Our conclusion is that hA i

the average of the ratio of the amplitudes of the m to m azimuthal Fourier

comp onents over the radii from to disk scalelengths is greater than for

ab out of our magnitude limited sample hA i is evenly distributed b etween and

Based on the examination of our Iband images we conclude that a close current

interaction is not necessary to pro duce the large lopsidedness that we observe in some

of our galaxies We conjecture that either the companion has merged with the primary

or has receded suciently far away from the primary that the interaction is no longer

evident

We compared the measurement of lopsidedness hA i to a measurement of recent

star formation activity the massnormalized color B B measures the excess B

magnitude of a galaxy relative to the exp ected B magnitude for a galaxy of that

circular velocity where the luminosity is estimated using a TullyFisher relationship

We nd that there is a correlation condence b etween hA i and B which

suggests that the mechanism by which a galaxy b ecomes lopsided also aects its

luminosity After examining the p ossibility that the correlation is due to the eect of

lopsidedness on the measures of rotation velocity and inclination we conclude that the

correlation is at least partly due to a real luminosity change that reects dierences in

stellar p opulations among the galaxies

If lopsided galaxies are systematically brighter than their symmetric counterparts

then they are overepresented in a magnitude limited sample and the true fraction of

signicantly lopsided galaxies may b e several times less than the observed For

a mag dierence b etween lopsided and undisturb ed galaxies as might b e inferred

from our sample cf Figure the fraction of lopsided galaxies is lower than that

observed by a factor of four Until the B hA i correlation is understo o d large

uncertainties in the interaction frequencies will remain

The correlation b etween lopsidedness and star formation activity provides two

avenues with which to map the timeline of the interaction phenomenon These lifetime

estimates are the critical step in converting the observed frequency of lopsidedness into

an estimate of the accretion rate which can then b e used to constrain mo dels of galaxy

evolution and cosmology From p opulation synthesis mo dels Bruzual Charlot

with a variety of burst durations and underlying p opulations we conclude that galaxies

that exhibit B which corresp onds to hA i along the b estt line to the 1

data exp erienced a burst of star formation by mass within the last Gyr We

indep endently estimate the timescale since the hypothesized accretion of a satellite

galaxy using a simulation from Walker et al and conclude that lopsidedness

at the level of hA i and so a B also implies the infall of a

satellite less than Gyr ago Combining our estimate for the lifetime of asymmetries

with hA i Gyr with the observed frequency of such asymmetries in eld

spirals b etween if no volume correction is included and if one includes

the volume correction for a mag brightening of lopsided galaxies we conclude that

the average infall rate of companions that create such asymmetries in eld spirals is

at most b etween every and every Gyr For a particular choice of the lifetime

of lopsidedness these estimates are upp er limits on the accretion rate due to our

assumption that lopsidedness arises only from accretion events The volume correction

currently introduces at least a factor of several uncertainty in this limit

To rene this estimate of the accretion rate further work on b oth the observational

and theoretical fronts is necessary Understanding the luminosityagehA iinfalling

mass relationships is key in using the observational results to place limits on the

disk accretion rate Volume and absolute magnitude limited samples would remove

uncertainties arising from the volume correction and the p ossible correlation b etween

hA i and luminosity Sp ectral information additional colors or H imaging would

also help discriminate b etween a stellar p opulation origin for B and inclination biases

Further observations involving larger samples will enable us to use the distribution of

hA i rather than simply the number b eyond a chosen threshold as the observational

constraint on the accretion rate Theoretical work is necessary to understand all

p ossible sources of lopsidedness in disk galaxies The current work suggests that

lopsidedness in disk galaxies is a promising technique with which to constrain the

accretion rate of galaxies and thereby constrain the mass evolution of normal galaxies

although signicant progress is necessary on several issues b efore denitive conclusions

can b e reached

Acknowledgments DZ acknowledges discussion with Ann Zabludo ab out analogous

interaction chronometers for EA galaxies The authors thank Ian Walker Chris

Mihos and Lars Hernquist for the use of their simulation DZ acknowledges partial

nancial supp ort from the California Space Institute and supp ort provided by NASA

through grant number ARA from the Space Telescope Science Institute

which is op erated by AURA under NASA contract NAS We acknowledge

the Astrophysical Research Consortium for its supp ort of the NICMOS detector

used in this work We thank the Ro ckwell scientists for their eorts in developing

these excellent HgCdTe arrays and the NSF for supp ort These data were also in part

obtained with a chargecoupled device developed by Tektronix for the STIS program

for the Hubble Space Telescope

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TABLE

Galaxy Sample

f a b c i d e e f

Name D TType i W m m B hA i hA i

B R I K

R T T

Mp c km s mag

NGC

NGC B

ESOG

NGC

ESOG

NGC

NGC E

NGC

ESOG

NGC

UGCA

ESOG

NGC

ESOG

NGC D

ESOG

NGC

UGCA

NGC

ESOG

UGCA

NGC

ESOG

NGC

ESOG

NGC

ESOG

Distances from pure Hubble ow mo del with H km sec Mp c Velocities taken from Huchtmeier and

Richter with the exception of those for NGC and which were taken from Zcat Huchra

TTypes from RC de Vaucouleurs et al

Inclinations from Huchtmeier and Richter and references therein

Velocity widths from Huchtmeier and Richter and references therein corrected for inclination and internal

velocity disp ersion as describ ed by Tully

Total apparent magnitudes from the ESOLV catalog Laub erts Valentijn

The formal uncertainties listed here are probably underestimates of the true uncertainties see x

TABLE

Galaxy Sample From Paper I

f a b c i d e

Name D TType i W m B hA i

B K

R T

Mp c km s mag

NGC

NGC A

NGC

ESOG

Distances from pure Hubble ow mo del with H km sec Mp c Velocities taken from Huchtmeier and

Richter with the exception of those for NGC and which were taken from Zcat Huchra

TTypes from RC de Vaucouleurs et al

Inclinations from Huchtmeier and Richter and references therein

Velocity widths from Huchtmeier and Richter and references therein corrected for inclination and internal

velocity disp ersion as describ ed by Tully

Total apparent magnitudes from the ESOLV catalog Laub erts Valentijn

The formal uncertainties listed here are probably underestimates of the true uncertainties see x

Figure Captions

Figure A comparison of the hA i measurements from I and K images As suggested

in the text the uncertainty estimates from the standard deviation of A b etween

and scalelengths app ears to underestimate the true uncertainty Nevertheless there

is a go o d corresp ondence b etween the measurements at the two wavelengths and no

systematic dierence the slop e of the b est t line is if it is constrained to

pass through the origin

Figure The distribution of hA i for the current sample is presented in the upp er

panel from Iband measurements and that for the RZ sample is in the lower panel

from K measurements

Figure Plate Two panels of Iband images of six galaxies with hA i from

the current sample The upp er panel presents the galaxies at a contrast level surface

brightness level to what might b e seen on a sky survey photographic plate and the

lower panel shows the low surface brightness morphology of the galaxies The galaxies

in the upp er row from left to right are NGC IC and ESO G and in

the lower row they are UGCA IC and ESO G In the lower panel

the white dots represent the nuclei of the galaxies Each image is nearly arcmin on a

side

Figure An examination of the correlation b etween hA i and massnormalized color

B In the lower left panel we plot B vs hA i for the combined sample of galaxies

our new sample and the RZ sample Note that the measurements of the new sample

are based on Iband images and those of the RZ sample are based on K images A

magnitude adjustment was made to the RC blue magnitudes for the RZ sample

based on a comparison of the ESOLV and RC blue magnitudes for the new sample of

galaxies The two sets of p oints connected by lines represent the galaxies in common

b etween the current study and RZ In the upp er panel we plot the distribution of

Ttypes morphological type with late type galaxies having larger corresp onding

values of the Ttype as a function of B In the lower right panel we plot hA i as a

function of Ttype

Figure The eect of inclination errors due to hA i The axes are the same as in the

main panel of Figure The gure shows the mean and the disp ersion represented

by the error bars of the inferred B that could arise for each galaxy solely due to an

incorrectly inferred inclination as calculated for the worst case scenario see Section

Figure The correlation b etween hA i and other photometric prop erties In the lower

left panel we plot hA i vs B R for the present sample B R colors are unavailable 1

for the RZ sample In the upp er panel we plot the distribution of M as a function of

B R and in the lower right panel the distribution of hA i versus M

1 R

Figure Changes in color and M predicted from the red p opulation synthesis

mo dels Three red mo dels are plotted a Gyr burst mo del lled circles a

Gyr burst mo del lled squares and a Gyr burst mo del lled triangles

Figure Estimated chronology based on B from the Bruzual and Charlot

stellar p opulation synthesis mo dels upp er panel and on hA i from the Walker et al

simulation of the infall of a mass satellite onto a disk galaxy In the upp er

panel the ages ab ove the line in units of Gyr come from the Gyr burst red

mo del and the ages b elow the line come from the Gyr burst red mo del

Figure The evolutionary tracks in the B hA i and B R hA i planes are

1 1

plotted for the Gyr burst red solid lines and blue dashed lines mo dels

The starburst is assumed to b egin when the satellite is six scalelengths away from the

galaxy nucleus the b eginning of the Nb o dy simulation see text for details The data

are sup erp osed for comparison