Structural and Photometric Properties of the Andromeda Satellite Dwarf Galaxy Lacerta I from Deep Imaging with WIYN pODI

0.82 MB·

by  Katherine L. Rhode

Draftversion January31,2017
TypesetusingLATEXtwocolumnstyleinAASTeX61
7 STRUCTURAL AND PHOTOMETRIC PROPERTIESOF THE ANDROMEDA SATELLITE DWARF GALAXY
1 LACERTA I FROM DEEP IMAGING WITH WIYN PODI
0
2

n Katherine L. Rhode,1 Denija Crnojevic´,2 David J. Sand,2 Steven Janowiecki,3 Michael D. Young,1 and
a Kristine Spekkens4
J

7
2
1Indiana University Department of Astronomy, 727 East 3rd Street, Swain West 319, Bloomington, IN 47405, USA

A] 2TexasTech UniversityDepartment of Physics, Box 41051, Lubbock, TX 79409-1051, USA
3International Centre for Radio Astronomy Research (ICRAR), University of WesternAustralia, 35 Stirling Highway, Crawley, WA 6009,
G
Australia
h. 4Department of Physics, Royal Military College of Canada, P.O. Box 17000, StationForces, Kingston, Ontario, K7K 7B4, Canada
p
- ABSTRACT
o
r We present results from WIYN pODI imaging of Lacerta I (And XXXI), a satellite dwarf galaxy discovered in the
t
s outskirtsofthe Andromedagalaxy(M31)inPan-STARRS1surveydata. Ourdeep,wide-fieldg,iphotometryreaches
a
∼3 magnitudes fainter than the photometry in the Pan-STARRS1 discovery paper and allows us to trace the stellar
[
population of Lac I beyond two half-light radii from the galaxy center. We measure a Tip of the Red Giant Branch
1
v (TRGB)distanceforLacIof(m−M)0 =24.44±0.11mag(773±40kpc,or264±6kpcfromM31),whichisconsistent
8 with the Pan-STARRS1 distance. We use a maximum-likelihood technique to derive structural properties for the
6 galaxy,and find a half-lightradius(r ) of 3.24±0.21arcmin(728±47pc), ellipticity (ǫ)of 0.44±0.03,totalmagnitude
h
1 MV = −11.4±0.3, and central surface brightness µV,0 = 24.8±0.3 mag arcsec−2. We find no HI emission in archival
8
0 data and set a limit on Lac I’s neutral gas mass-to-light ratio of MHI/LV < 0.06 M⊙/L⊙, confirming Lac I as a
. gas-poor dwarf spheroidal galaxy. Photometric metallicities derived from Red Giant Branch stars within 2 rh yield a
1
median [Fe/H] of −1.68±0.03, which is more metal-rich than the spectroscopically-derived value from Martin et al.
0
7 (2014). Combining our measured magnitude with this higher metallicity estimate places Lac I closer to its expected
1 position on the luminosity-metallicity relation for dwarf galaxies.
:
v
i Keywords: Local Group – galaxies: individual (Lac I) – galaxies: individual (And XXXI) – galaxies:
X
dwarf – galaxies: photometry
r
a
[email protected]
[email protected]
[email protected]
[email protected]
[email protected]
[email protected]
2 Rhode et al.
1. INTRODUCTION area of the thin rotating plane of M31 satellite galax-
ies(Ibata et al. 2013)butMartin et al. (2014)showed
The number, spatial distribution, mass function, and
that it is moving in the opposite sense relative to the
kinematics of the dwarf galaxies in an environment like
disk; Per I and Lac I are located on the far east-
thatoftheLocalGroupprovideimportanttestsforthe-
ern and far western sides of Andromeda, respectively
oreticalideasaboutcosmology,darkmatter,andgalaxy
(Martin et al. 2013a,b).
formation (e.g., Klypin et al. 1999, Moore et al. 1999,
Promptedinpartbytheinstallationandcommission-
Bullock & Johnston 2005, Simon & Geha 2007). Fur-
ingofanewcameraontheWIYN3.5-mtelescope1 dur-
thermore, dwarf galaxies themselves serve as valuable
ing the 2012−2013 observing season, we began a cam-
laboratories for our understanding of the physical pro-
paign to obtain deep, wide-field imaging of these and
cessesinvolvedingalaxyevolution,starformation,feed-
otherselectednearbydwarfgalaxies. Theaimistotake
back,and chemicalevolution(e.g., Mateo 1998,Tolstoy
advantageoftheexcellentimagequalityanddepthmade
et al. 2009. McConnachie 2012 and references therein).
possible by WIYN to study the galaxies’ structure and
Theimportanceofdwarfgalaxiestoalloftheseareasof
stellar populations out to large galactocentric radius.
extragalacticastrophysicsandcosmologyhasmotivated
The first dwarf galaxy we targeted is Lac I, a relatively
anarrayofsurveysandsearchesforadditionallow-mass
luminous dwarf(M ∼ −12)thatlies ∼20◦ (∼275kpc)
galaxies in and around the Local Group (e.g., Willman V
away from Andromeda in projected distance (Martin
et al. 2005; Martin et al. 2006; Belokurov et al. 2007;
et al. 2013a). The photometry of Lac I presented in
Bellet al. 2011;McConnachie et al. 2009;Adams et al.
Martin et al. (2013a) reached i ∼ 22.5 and yielded
2013; Bechtol et al. 2015; Koposov et al. 2015; Kim et
estimates of the distance, size, and metallicity of the
al. 2015, Janesh et al. 2015).
galaxy. The Martin et al. (2014) spectroscopy study
In particular, the regions around the Andromeda
presented the systemic velocity and velocity dispersion
Galaxy(M31)havelatelybeenthe focusofanumberof
(v =−198.4±1.4kms−1,σ =10.3±0.9kms−1)as
dedicated searchesfor satellite dwarfgalaxies,andhave r,helio v,r
well as a refined metallicity estimate and V-band mass-
metwithmuchsuccess. Forexample,searchesforstellar
to-light ratio. In this paper, we present results from
overdensitiesinphotometricobservationsfromtheSloan
imaging of Lac I that reaches ∼24−25 in the g and i
DigitalSkySurvey(SDSS)andthePan-AndromedaAr-
filters, covers a ∼20′ x 20′ area, and allows us to trace
chaeologicalSurvey (PAndAS) have resulted in the dis-
the stellar population beyond two half-light radii.
covery of tens of dwarf galaxies in regions around An-
The paperis organizedas follows. Section2 describes
dromeda (e.g., Zucker 2004, 2007; McConnachie et al.
theobservationsandinitialdatareductionandSection3
2008; Martin et al. 2006, 2009; Bell et al. 2011; Slater
discusses our methods for source detection, photome-
et al. 2011). A recent contribution in this area comes
try, and completeness testing. Section 4 presents the
from the Panoramic Survey Telescope and Rapid Re-
properties we measure for Lac I, including the color-
sponse System 1 (Pan-STARRS1; Kaiser et al. 2010)
magnitude diagram (CMD), distance via the Tip of
3π survey. By searching throughPan-STARRS1 photo-
the Red Giant Branch (TRGB) method, structural pa-
metric sourcecatalogs,Martinetal. (2013a)discovered
rameters, luminosity, limits on the neutral gas content,
twonewdwarfgalaxies,LacertaI(AndXXXI)andCas-
andthephotometrically-derivedmetallicitydistribution
siopeia III (And XXXII), in regionsaroundAndromeda
function. Thelastsectionofthe papergivesasummary
that hadnot been included in other systematic imaging
and our final conclusions.
surveys. In a follow-up paper, Martin et al. (2013b)
described the discovery in Pan-STARRS1 imaging data
2. OBSERVATIONS AND DATA REDUCTION
of a third Andromeda satellite galaxy, Perseus I (And
XXXIII), located in a region with shallow SDSS cov- Observations of Lac I were obtained on 2013 October
erage. All three galaxies were confirmed to be satel- 1 with the WIYN 3.5-m telescope and the One Degree
lite galaxies via a spectroscopic study by Martin et al. Imager with a partially-filled focal plane (pODI; Har-
(2014), who derived systemic radial velocities for each beck et al. 2014). The pODI camera was comprised
system as well as individual metallicity measurements of nine orthogonal transfer arrays (OTAs) arranged in
for member stars (see Section 4.4 for more discussion). a 3x3 configuration, as well as four additional OTAs
All three are located more than 10 degrees away from positioned at various radial locations around the focal
M31 in projection and have relatively faint central sur-
facebrightnesses(µ0 >∼25−26magarcsec−2),properties 1 The WIYN Observatory is a joint facility of the University
which likely contributed to their late discovery (Mar-
of Wisconsin-Madison, Indiana University, the National Optical
tin et al. 2013a, 2013b). Cas III is located within the AstronomyObservatoryandtheUniversityofMissouri.
Properties of Andromeda Satellite Dwarf Lac I 3
plane. Each individual OTA is an 8x8 arrangement of <0.01 magnitude, confirming that the sky conditions
orthogonaltransferCCDdetectorswith480x49612-µm were stable and the night was photometric. The pho-
pixels. The central 3x3 array of OTAs in pODI, which tometric calibration coefficients calculated in this way
provided a field-of-view of ∼24′ x 24′ and a pixel scale were applied to all instrumental magnitudes measured
of 0.11′′ pixel−1, was used to image the target objects via PSF photometry of the Lac I images (see next sec-
and the outlying OTAs were used for guiding during tion). Inaddition,individualreddeningcorrectionswere
the exposure. (Note that pODI was upgraded in 2015 calculated for each star in the Lac I images by apply-
and is now referred to as the ODI camera; new detec- ing the Schlafly & Finkbeiner (2011) coefficients to the
torswereaddedtocreatea 5x6OTAconfigurationthat Schlegel et al. (1998) values for Galactic extinction at
provides a 40′ x 48′ field-of-view.) We obtained nine the position of the star. The median color excess value
700-secondexposuresofthe Lac Ifield ing andanother across the Lac I field-of-view is E(B −V) ∼ 0.14. For
nine 600-second exposures in i with pODI. The tele- the remainder of the paper, we will use final calibrated
scope was dithered between exposures in order to help and dereddened g0 and i0 values.
eliminategapsbetweenthe CCDs andOTAsduringthe
subsequent image stacking process.
3. SOURCE DETECTION AND PSF
The pODI images were immediately transferred from
PHOTOMETRY
WIYN to the ODI Pipeline, Portal, and Archive (ODI-
PPA; Gopu et al. 2014)2 at Indiana University and Point-spread-function-(PSF)-fitting photometry was
performedonthefinalcombinedg−andi−bandimages,
laterprocessedwiththeQuickReducepipeline(Kotulla
using the suite of dedicated programs DAOPHOT and
2014). The pipeline corrects each image for cross-talk,
ALLFRAME(Stetson 1987,1994). Webeganbyselect-
subtracts the overscan signal, corrects the images for
ing ∼300bright,non-saturatedstarsineachimageand
non-linearity and persistence, applies bias, dark, flat-
using them to construct a model PSF. This model PSF
field, and pupil ghost corrections, and removes cosmic
was then used to measure magnitudes of all sources de-
rays. The pipeline-processed images of Lac I were then
tectedineachimagewithpeakcountsatleast3σ above
flattened with a night-sky flat, reprojected to a com-
the background noise level. The final photometry cat-
mon pixel scale, and finally average-combined to cre-
alog was cleaned by retaining sources with χ2 < 1.5
ate a single deep, stacked image in each filter. Areas
(i.e., the goodness-of-fit parameter for the PSF fitting
on the edges of the stacked images with slightly higher
of each source) for i > 21.5, and with a more gener-
noise levels (because of reduced exposure time due to o
ouscutbelow thisvalue; the sharpnesswasadditionally
the dither pattern) were clipped to produce a usable
field ∼20′ x 20′ in size. The mean full-width at half- constrained to be |sharp| < 2 (to remove, e.g., cosmic
rays or resolved background galaxies). These cuts yield
maximum of the point spread function (FWHM PSF)
in the final combined images is 0.84′′ in the g-bandand a total of 33577 bona-fide stars (see Figure 1). The
0.70′′ in the i-band. full photometric catalog for the Lac I g and i images is
presented in Table 1. The catalog includes a sequence
Sky conditions on the night that Lac I was observed
number for each star, the star’s Right Ascension and
were clear. Sloan Digital Sky Survey (SDSS; Ahn et
al. 2012) stars present in various images of other fields Declination, the calibrated, dereddened g0 and i0 mag-
nitudes andassociatedinstrumentalerrors,andthe cal-
taken throughout the night were used to calculate pho-
culatedGalacticextinctionvalues(A andA )thatwere
tometriccalibrationcoefficientsthatcouldbeappliedto g i
applied.
theLacIframes. (AsmentionedintheIntroduction,the
In order to assess the true photometric uncertainties
LacIfieldisnotincludedinthecurrentSDSSfootprint.)
andincompletenessintheimages,weinjected∼650,000
The RMS scatter of the zero points calculated from in-
artificial stars (divided into 26 separate experiments to
dividual SDSS stars within a given image taken that
avoid artificial crowding) distributed evenly across the
night ranged from 0.016−0.021 magnitude. The mean
framesandwithcolorsandmagnitudesintherangecov-
zeropointsforimagestakenofdifferentfieldsandatdif-
ered by real stars. We then performed the same de-
ferent times of the night agreed with each other within
tection, photometry, calibration, and dereddening steps
described above to measure the magnitudes of the fake
2 The ODI Portal, Pipeline, and Archive (ODI-PPA) system stars. The overall color-averaged 50% completeness
isa jointdevelopment projectof the WIYN Consortium, Inc., in limit is reached at g0 = 25.6 and i0 = 24.2, respec-
partnershipwithIndianaUniversity’sPervasiveTechnologyInsti-
tute(PTI)andwiththeNationalOpticalAstronomyObservatory tively. These values change to g0 = 25.3 and ii = 24.0
ScienceDataManagement (NOAOSDM)Program. in the innermost∼3 arcminofLac I due to higherstel-
lar density there. The artificial star tests indicate that
4 Rhode et al.
the photometric uncertainties are ∼0.1 mag at i0 ∼23
and g0 ∼23.5.
4. PROPERTIES OF LAC I
4.1. Color-Magnitude Diagram and Stellar Spatial
Distribution
The first two panels of Figure 2 show the dereddened
CMD for stars within the half-light radius of Lac I (r
h
= 3.24±0.21 arcmin; see Section 4.3). The rightmost
panelofFigure 2 showsa rescaledCMD ofthe field, for
comparison. The field regions are two rectangular ar-
easchosennear the cornersofthe pODI pointing,along
the dwarf galaxy’s minor axis and beyond 3r ; these
h
two regions are marked with solid lines in the left-most
panel of Figure 3. The total area of the field regions is
largerthanthe areausedtoproduce the LacI CMD,so
we constructed the field CMD by randomly extracting
a proportionalnumber of stars from the field regions so
that we were sampling equal areas of sky. The photo-
metricuncertaintiesderivedfromtheartificialstartests
as described in the previous section are shown in all
three panels of the figure.
ExaminationofFigure2showsthatourfollow-uppho-
tometryfrompODIreaches∼3magnitudesfainterthan
the photometry presentedin the Pan-STARRS1 discov-
erypaper(Martin et al. 2013a). Aprominentredgiant Figure 1. Source selection criteria based on the χ2 and
sharpness parameters from the DAOPHOT photometry, as
branch(RGB) is the main feature observedin the Lac I
a function of dereddened i-band magnitude. Red sources
CMD. The RGB coincides in location with 12 Gyr old
are the ones that we retain as genuine stars, black ones are
isochronesrepresentinga range of metallicities; see Sec-
rejected.
tion 4.4 for more discussion. There is no overdensity of
bright, blue ((g−i)0 .0.5) sources in the Lac I CMD, is clear from these two upper panels of Figure 3 that
andneitherarethereluminous asymptoticgiantbranch
there is an obvious overdensityof sources that make up
(AGB)stars,whichwouldappearjustabovetheTRGB.
the mainbody ofLacI,andthatthe galaxyhasa fairly
The absence of these features suggests a predominantly
elliptical shape.
old nature for Lac I’s stellar population. Finally, the
ThedistributionofcontaminatingobjectsintheCMD
detectionofahorizontalbranch/redclump,expectedat
is deduced from the two rectangular field regions. As
i0 & 24.5, is hampered by the rapidly decreasing com- mentioned, the field regions are located beyond 3r (as
h
pleteness at these magnitudes (the 50% completeness
derived in Sec. 4.3), and while we cannot rule out the
level is marked with a dashed line in the leftmost panel
presence of Lac I stars at these radii, their number
of Fig. 2); we are unable to draw any firm conclusions
should be negligible. Examination of the field CMD
about the presence or absence of this feature.
in the rightmost panel of Fig. 2 illustrates that at
ThetoptwopanelsofFigure3showthespatialdistri-
magnitudes fainter than i0 ∼ 22.5, unresolved back-
bution of the RGB stars across the pODI field-of-view.
groundgalaxieswillbethemainsourceofcontaminating
The stars used to create the upper two plots in this fig-
objects. At brighter magnitudes, Galactic foreground
ure arethosethat appearwithin the RGB selectionbox
star sequences are readily apparent. For all subsequent
in the leftmost panel of Figure 2. The dashed line in
analysis in this paper, we take into account the back-
the left-hand panel of Figure 3 is an ellipse centered on
ground/foreground contamination based on the com-
the galaxy that marks the half-light radius derived in
bined CMDofthe twofieldregions. The locationofthe
Section 4.3, and the arrow indicates the direction to-
RGB selection box marked in the CMD was chosen so
ward M31. The right-hand panel of Figure 3 shows a
thatitbeginsatthelocationoftheTRGB,encompasses
smoothed density map of the RGB stars, with the sur-
the full width of the RGB, and cuts off at a faint mag-
face density ofstarsindicatedby the grayscalevalue. It
Properties of Andromeda Satellite Dwarf Lac I 5
Figure 2. Dereddened CMDs of all stars within Lac I’s half-light radius (left and middle panels). The red dashed line in the
left panel indicates the 50% completeness level, and the photometric uncertainties derived from artificial star tests are shown
in all the panels. The numbers of sources are also reported in each panel. In the middle panel, 12 Gyr Dartmouth isochrones
for [Fe/H] = −2.5, −2.0, −1.5, and −1.0 (green lines) from Dotter et al. (2008) are overlaid on the datapoints, and theRGB
selection box is marked (red polygon). The right panel shows the combined CMD of the two field regions marked in Fig. 3,
rescaled tothe area in theleft and middle panels.
nitude limit of i0 = 24 to avoid the region of the CMD consider metal-poor stars and minimize contamination
with both rapidly increasingincompleteness and photo- from foreground Galactic stars. This procedure deter-
metric uncertainties, as well as an increasing number of mines the observed magnitude at which the luminosity
background galaxy contaminants. The magnitudes and functionhasasharptransition,whichisexpectedforold
colorsoftheobjectsthatappearwithinthesetwo“field” andmetal-poorRGBpopulationsattheendofthisevo-
regionsofthe pODI imagesareplottedinthe rightmost lutionary phase (e.g. Salaris et al. 2002). The absolute
panel of Fig. 2. magnitude for this transition is constant, and it is com-
putedtobeM =−3.44±0.10magfortheSDSSi-band
i
4.2. TRGB Distance
(Bellazzini 2008). The uncertainty is computed with a
ThedistancetoLacIisderivedbyapplyingtheTRGB Monte Carlo(MC) approach,byvaryingthe magnitude
method(Lee et al. 1993;Rizzi et al. 2007)toourdata. of the observedstars within the photometric uncertain-
To accomplish this we adopt the method introduced by ties and re-fitting the model luminosity function. From
Makarov et al. (2006),modifiedfollowingtheapproach this analysis we derive a best-fit TRGB luminosity of
ofWu et al. (2014). First,amodelluminosityfunction i = 21.00±0.05 mag, which translates to a distance
o
is convolvedwith completeness, uncertainty andbias as modulus of (m−M)0 = 24.44±0.11 mag, fully con-
derivedfromourartificialstartests; then,we fittedthis sistent with the (m−M)0 =24.40±0.12 mag estimate
model function to Lac I’s luminosity function (see Fig- givenintheMartin et al. (2013a)discoverypaper. The
ure 4), which is derived for RGB stars within 2rh and physical distance to Lac I is thus 773±40 kpc, which
with a color cut of 1.2 < (g − i)0 < 1.8 in order to
6 Rhode et al.
0.15 420
0.1
300
)
es) 0.05 2002min
degre -0 /arc
η(-0.05 120 ars
t
s
(
-0.1 60
-0.15
20
0.2 0.15 0.1 0.05 -0 -0.05 -0.1
ξ (degrees)
Figure 3. Top left panel. Spatial distribution of RGB stars across the pODI field-of-view (see selection box in the CMD
presented in Fig. 2), in standard coordinates centered on Lac I. The dashed ellipse is drawn at the half-light radius, the
rectanglesarethechosenfieldregionsandthearrowindicatesthedirectiontowardsM31. Toprightpanel. DensitymapofRGB
starsinLacI(thegrayscalekeyisshownontheright). Bottom panel. SurfacedensityprofileofRGBstarsinLacIasafunction
of elliptical radius. The exponential profile and background level, as derived from our maximum likelihood computation, are
indicated as described in the legend. Error bars are Poisson errors on the numberof objects in each radial bin.
is consistent with M31’s distance. Combining this with Figure2,whichincludesalimitingmagnitudeofi0 =24
thedistancetoM31andtheangulardistanceonthesky mag so as to avoidany adverseeffects fromcrowdingat
between the two galaxies yields a 3D distance for Lac I faint magnitudes. The free parameters for our expo-
of 264±6 kpc from M31. nential profile model are: the central position (α0, δ0),
ellipticity (ǫ, which is defined as 1−b/a, where b is the
4.3. Structural Parameters, Luminosity, and HI Gas
scalelengthalongtheminoraxisandaisthescalelength
Content
along the major axis), position angle (PA; θ), half-light
We fitted an exponential profile distribution to the
radius (r ) and background surface density (Σ ). Un-
h b
surface density profile of Lac I, utilizing the maximum
certainties on each parameter were calculated via 1000
likelihood technique described by Martin et al. (2008),
bootstrap resamples of the data, from which 68% confi-
asimplementedbySand et al. (2012). Whilerealsatel-
dence limits were derived. The resulting structural pa-
lites often have a complexity that cannot be encapsu-
rameters for Lac I are presented in Table 2, along with
lated by parameterized models such as the exponential
the other properties we measure for the galaxy. The
profile,suchprofilesareusefulforquantifyingthegalax-
probabilitydistributionfunctionsderivedfromthemax-
ies’basicstructuralpropertiesandfordirectcomparison
imum likelihood analysis are shown in Figure 5.
with other results. The stars selected for the structural
analysis are drawn from the RGB selection box seen in
Properties of Andromeda Satellite Dwarf Lac I 7
transformation of Veljanoski et al. (2013). Our total
20
magnitude is consistent within the uncertainties with
the value presented in the Martin et al. (2013a) dis-
15 coverypaper(MV =−11.7±0.7mag),althoughourun-
certainty is a factor of two smaller. The central surface
ts brightness of Lac I is calculated using the total magni-
n
ou10 tude and the best-fitting exponential profile described
C
earlier, and is µV,0 = 24.8±0.3 mag/arcsec2. Our mea-
5 sured µV,0 value is a full magnitude brighter than the
corresponding value from Martin et al. (2013a) (µV,0
= 25.8±0.8 mag/arcsec2), although the numbers are in
0 agreement to within the uncertainties. As is the case
20.6 20.8 21 21.2 21.4 21.6 21.8
withthetotalmagnitude,theuncertaintyonourcentral
i
0 surfacebrightnessmeasurementissubstantiallyreduced
Figure 4. Luminosity function ofLac I’sRGBstars within comparedtothepreviousmeasurement. (Notethatthis
2rh andwith acolorcutof1.2<(g−i)0 <1.8: theredline increase in surface brightness is not unexpected, since
isthebest-fittingmodelluminosityfunctionappliedinorder
our derived half-light radius is smaller.) The derived
to derivetheTRGB luminosity.
magnitudes and surface brightness values are included
in Table 2.
Our structural parameters are in agreement with the We investigated the neutral gas content of Lac I by
discovery data of Martin et al. (2013a) to within the searching for HI emission along the line-of-sight to the
uncertainties, although our derived half-light radius is galaxy in publicly-available Effelsberg Bonn HI Survey
smaller and slightly more than 1-σ discrepant. The data (EBHIS; Winkel et al. 2016), smoothed to a spec-
structural parameters presented here should not be bi- tral resolution of 15 km s−1. We find no HI emission
ased given the depth of the data, the stellar density in the smoothed spectrum at the systemic velocity for
contrast compared to the background, and the field of Lac I reported by Martin et al. (2014), and compute a
view of the pODI data; our data set meets all of the
5-σ, single-channel upper limit on the HI mass within
criteria determined by Mun˜oz et al. (2012) for deriv- 6′ (1.85 rh) of MHlimI = 1.9 × 105M⊙. This implies
ing accurate structural parameters using our maximum
MHI/LV < 0.06 M⊙/L⊙ for Lac I (see 2), and there-
likelihood technique.
fore that this galaxy is gas-poor like the other dwarf
Weshowaone-dimensionalrepresentationofourbest-
spheroidal galaxies around the Milky Way and M31
fitting stellar profile in the bottom panel of Figure 3. (Grcevich & Putman 2009; Spekkens et al. 2014).
While the binned data points are not used to fit stel-
lar profiles – as the maximum likelihood technique uses
4.4. Photometric Metallicity Distribution Functions
thetwodimensionalunbinneddistributionofstars–the
agreement between the best-fitting model stellar profile We derive photometric metallicities for each individ-
and the data points is excellent, with only minor devia- ual RGB star that is located within our RGB selec-
tions from an exponential profile. tion box (marked in Fig. 2) and also has i0 < 23
Tomeasurethe totalmagnitudeofLacI,wefirstsum mag. Applying this additional faint-magnitude cut re-
thefluxwithinonehalf-lightradiususingtheRGBstars duces contamination significantly and keeps the photo-
within the CMD selectionbox shownin Figure 2. From metric uncertainties below 0.1 mag in magnitude and
this, we subtract offthe flux fromforegroundandback- 0.2 mag in color, to ensure that we are using the best-
groundsourcesusingthefieldregionsmarkedintheup- quality photometric data to yield metallicity informa-
per left panel of Figure 3 and rescaling to match the tion. Photometric metallicities are obtained by linearly
area used for Lac I. We then multiply the remaining interpolatingamongstellarisochroneswithafixedaged
flux by a factor of two to accountfor the flux outside of of 12 Gyr and varying metallicity ([Fe/H]= −2.5 to
Lac I’s half light radius. We correct for stars below our −1.0; Dotter et al. 2008). Under the assumption that
detection limit by using several metal poor ([Fe/H] = the RGB width is mainly driven by metallicity rather
−1.5 to −2.0) and old (10-13 Gyr) Parsec luminosity than age, the color of a RGB star will correspond to
functions (Bressan et al. 2012). From this, we measure an isochrone with a given metallicity (see Fig. 2, and
M = −11.3±0.2 mag and M = −12.0±0.2 mag, and Crnojevi´c et al. 2010 for details). This approximation
g i
convert this to M = −11.4±0.3 mag using the filter is valid in the absence of significant intermediate-age
V
populations, which appears to be a safe assumption for
8 Rhode et al.
Figure 5. Probability distribution functions for the structural parameters derived from the maximum likelihood analysis
described in Section 4.3.
Lac I, based on the appearance of the CMD. (We do star’s equatorial coordinates into standard coordinates
note,however,thatMartin et al. (2014)statethatthey (ξandη;seeFigure3)onaplanetangentialtothecenter
identified “a handful” of carbon stars in Lac I based on of Lac I. We then take these coordinates and use them
the shape of a few of the stellar spectra they obtained, as the X and Y coordinates in the definition of ellipti-
i i
and that the presence of these stars may suggest that cal radius given in Martin et al. (2008) (their Equation
Lac I has at least a modest intermediate-age popula- 4). The three panels in Figure 6 show the [Fe/H] distri-
tion.) This type of approach provides robust results bution of stars with r < r (top panel), r < r < 2r
h h h
in terms of relative quantities such as the derivation (middlepanel),andr >2r (bottompanel). Theouter-
h
of radial metallicity trends (VandenBerg et al. 2006; mostbinincludes starsouttoa radiusof9 arcminutes,
Crnojevi´c et al. 2014). We also explore the effect that i.e., the largest ellipse fully enclosed within the pODI
aslightlyyoungeraverageagewouldhaveonthederived images (which is just short of 3r ). We do not correct
h
metallicities: if we adopt isochrones with a fixed 8 Gyr the derived MDFs for incompleteness, since the RGB
age instead of 12 Gyr, the metallicity values obtained selection box is ∼ 97% complete down to i0 < 23. To
for Lac I (see below) become more metal-rich by about correctforcontaminationinthestellarsample,wederive
0.2dex. (SeealsoCrnojevi´c et al. 2010foranextensive an“MDF”forthefieldregionsaswell(strictlyspeaking,
discussion on the possible effects of prolonged star for- contaminating sources are not RGB stars belonging to
mation on the derivation of photometric metallicities.) thesamepopulation,sothederivedmetallicitiesarenot
In Figure 6 we show the resulting metallicity distri- meaningful), andsubtractit fromthe LacI MDFs after
bution functions (MDFs) for stars separated into three rescaling it to the area of each radial bin. The percent-
regionsbasedontheir ellipticalradius. Tocalculate the age of contaminants in the three radial bins is ∼ 2%,
elliptical radius (r) for each star, we first transform the 9%, and 28%, respectively.
Properties of Andromeda Satellite Dwarf Lac I 9
Weusedtheinformationaboutcontaminationgleaned nounced in the innermost radial bin (top panel of Fig.
fromthefield“MDF”tocorrectnotonlytheLacIMDF 6). Thedistinctionfadesoffinthemiddlebin,whilethe
data in histogram form but also the individual photo- last adopted bin contains few stars due to the rapidly
metric metallicity values of the stars in the three radial decreasingstellardensitybeyondr =2r ,thusanypos-
h
regions shown in Figure 6. We corrected the individual sible trend gets lost in the noise. We stress that the ra-
photometric metallicity measurements by randomly re- dialMDFshaveacomparableshapewhenderivedunder
movingthe appropriatenumber ofstarsfalling within a the assumption of a fixed 8 Gyr age.
given metallicity range in each radial region. In those We carried out the following steps to investigate
caseswhenthenumberofcontaminantsinagivenmetal- whethertheapparentmultiplepeaksintheMDFsmight
licity and radial range was a fraction, the value was actually be statistically significant. The contamination-
roundedtothenearestinteger,andthenthatnumberof corrected MDF data (i.e., the individual photometric
stars was randomly removed from the appropriate data metallicity values ofthe starsinthe three radialregions
file. shown in Figure 6, corrected for contamination) were
We used the contamination-corrected MDF data to evaluated with a series of statistical tests to assess the
calculatethemedianmetallicityofthestarsinthethree likelihoodthat a mixture ofone,two,or three Gaussian
radial ranges shown in Figure 6. Uncertainties on these distributions canproduce the observedvalues. We used
median[Fe/H]values werederivedwith aset ofMC ex- a parametric bootstrap Anderson-Darling (A-D) test
periments. First,themagnitudeandcolorofeachstarin (Anderson & Darling 1952) to independently test each
the MDF was varied within the photometric uncertain- Gaussian mixture as a potential fit to the MDFs. First,
tiesforthatstar. The metallicitywasrederivedforthat a set of one to three Gaussian functions was fitted to
magnitude and color using the same method as for the the input data, and best-fitting means, dispersions,and
original data (interpolation from the isochrones). We mixing proportions for each Gaussian were returned.
did this 1000times for eachstar andcalculatedthe me- The original data were evaluated against the candidate
dian [Fe/H] value for each realization, and within each mixturemodelusingtheA-Dtest. Next,1000synthetic
radial region. The spread of [Fe/H] values computed data sets with the same parameters as the best-fitting
from the MC simulations yields an estimate of the un- mixture model were produced and evaluated with the
certainty in the [Fe/H] derived from the original data. A-D test. The A-D score derived from the observed
The median metallicities for the contamination- data was then compared to the distribution of boot-
correctedMDFsinthethreeradialregionsare[Fe/H]= strapped A-D scores. This testing procedure indicated
−1.66±0.03 dex for the innermost radialregion(inside with high confidence that the observed MDFs for all
r ), [Fe/H] = −1.69±0.03 for stars with r <r <2r , three radial regions are not likely to be drawn from a
h h h
and [Fe/H] = −1.72±0.05 for stars in the outer radial unimodal or bimodal Gaussian distribution. The data
region (outside 2 r ). These values are marked in the in the outermost radial region (r > 2r ) is also not
h h
histogramplotsinFigure6. Combiningallofthe[Fe/H] likely to be drawn from a trimodal Gaussian distribu-
values for stars within 2 r yields a median [Fe/H] of tion. The tests also indicated, however, that there is a
h
−1.68,and combining all three radial regions yields the high probability that the MDF data for the inner two
samemedianvalue; wehavelistedthis value inTable 2. radial regions (r < r and r < r < 2r ) is drawn
h h h
The median [Fe/H] values in all three of the radial from a mixture of three Gaussian distributions. The
regions are more metal-rich than the [Fe/H] value of peak values (and dispersions) of the best-fitting Gaus-
−2.0±0.1 derived by Martin et al. (2014) from their sian functions are [Fe/H] = −1.3 (0.1), −1.8 (0.3), and
spectroscopic observations of 126 RGB stars in Lac I, −2.4 (0.1) and mixing fractions of 31%, 63%, and 6%,
although in some cases the difference is not significant respectively for the stars inside the half-light radius r .
h
whentheuncertaintiesonthesevaluesaretakenintoac- The corresponding values for stars with radii between
count. Thefixed-ageapproximationinherenttothepho- r and 2 r are [Fe/H] = −1.4 (0.1), −1.8 (0.2), and
h h
tometric metallicity derivation method can only partly −2.4 (0.1) and mixing fractions of 25%, 71%, and 5%,
explain this discrepancy. For the discrepancy with the respectively.
Martin et al. (2014) data set to be alleviated, their We performed additional analysis steps to determine
spectroscopicsamplewouldneedtohavemissedthema- whether the parametric bootstrap A-D test was identi-
jority of the metal-rich subsample highlighted by our fying multi-modality simply because of the noise in the
MDFs. A close inspection of our MDFs suggests that data or biases introduced during the conversion from
there could be two metallicity peaks, at [Fe/H]∼ −1.8 photometric measurements to metallicities. We gener-
and [Fe/H]∼ −1.4 respectively, which are most pro- ated a synthetic MDF by populating an isochrone to
10 Rhode et al.
produce a 12-Gyr population with [Fe/H]∼−1.7. We episode of star formation and thus a distinct and more
convolvedthis catalogwiththe photometricerrorsfrom metal-rich population in their central regions.
our data set to obtain an “observed”CMD. We derived
metallicities for RGB stars within the upper ∼2 magni-
5. SUMMARY AND MAIN CONCLUSIONS
tudesofthesyntheticRGB,justaswasdoneforthereal
In this paper we presented results from deep, wide-
data. We then carried out the bootstrap testing proce-
field WIYN pODI g,i imaging of the M31 dwarf satel-
dure on the synthetic [Fe/H] values and found that the
lite galaxy Lac I (And XXXI), acquired in order to in-
best-fitting unimodal, bimodal, and trimodal Gaussian
vestigatethegalaxy’sstructure,stellarpopulations,and
distributions were all unlikely to reproduce the particu-
metallicity. TheCMDofthisgalaxyisdominatedbyan
lar distribution of the test data set at a high confidence
old (∼12 Gyr) stellar population and no intermediate-
level (99.999%, 98.3%, and 99.5% for the unimodal, bi-
age stars (AGB stars) are apparent in our data. We
modal, and trimodal distributions respectively). Since
trace the RGB stars in the Lac I images to a radius
the bootstraptesting rejectednotonlythe bimodaland
of ∼10 arcmin (∼2.25 kpc) from the galaxy center and
trimodal mixture models but also the single-metallicity
use them to derive a distance to the galaxy as well as
model,wecanonlyinferfromthisthattheobservedtri-
its structuralproperties. OurmeasuredTRGBdistance
modality that is implied by the A-D testing on the real
of 773±40 kpc agrees with the Pan-STARRS discovery
data may not be genuine either. Our overall conclu-
paper distance (Martin et al. 2013a). Our derived 3D
sionbasedonthisanalysisisthatalthoughitispossible
distance for Lac I to M31 is 264±6 kpc and we confirm
thatadwarfgalaxywiththepropertiesofLacIcouldin-
thefindingbyMartin et al. (2013a)thatLacIisinthe
deed have multiple stellar populations, our photometric
far western outskirts of the Andromeda galaxy halo.
metallicities are unable to unambiguously demonstrate
Despite its relatively late discovery and distant loca-
their presence or absence.
tion from its host galaxy, Lac I seems in other ways to
The spectroscopic metallicity value reported by
be afairlytypicalLocalGroupdwarfspheroidalgalaxy.
Martin et al. (2014) separates Lac I from the bulk
Our derived half-light radius r and associated uncer-
of Local Group dwarfs on a luminosity-metallicity plot h
tainty for the galaxy, 728±47 pc, are smaller than the
(Fig. 4intheirpaper,whichshowsthepositionsofM31
Pan-STARRS1-measured value (912+124 pc), although
satellitedwarfgalaxiesontheluminosity-metallicity(L- −93
they agree within the uncertainties. Brasseur et al.
Z) relation derived by Kirby et al. (2013) from nearby
(2011) used the measured V-band absolute magnitudes
dwarfs), i.e., it is too metal-poor for its luminosity. We
and half-light radii of dSph satellites of the Galaxy and
cantakeourupdatedabsolutemagnitudemeasurement,
M31 and found that they follow a well-defined size-
M =−11.4±0.3, and our median photometric metal-
V
luminosityrelationandthattherelationsforeachgalaxy
licity estimate of [Fe/H] ∼−1.68 (from all of the stars
(the Milky Way and M31) are statistically the same.
in the contamination-corrected MDFs), and compare
Given its measured M of −11.4 from our pODI data,
these values to the Kirby et al. (2013) L-Z relation V
the derivedhalf-lightradiusofLacIisrightinlinewith
(their Equation 3). Assuming this relation, the pre-
the value predicted by the Brasseur et al. (2011) re-
dicted [Fe/H] value for Lac I given its luminosity is
lation for Andromeda dSph galaxies, 685+213 pc. Our
−1.54. The RMS scatter of the Kirby et al. relation −220
measuredellipticityvalue,ǫ=0.44±0.03isalmostiden-
is 0.16 dex, so our photometric metallicity value is,
tical to the Pan-STARRS1 value, but with a formalun-
interestingly, more in line with the expected value.
certainty that is a factor of two smaller. This elliptic-
Lastly,wealsolookedforthe presenceofametallicity
ity is within the usual range for dSph satellites of An-
gradient in Lac I. We used the photometrically-derived
dromeda; for the dSph galaxies in the M31 sub-group,
metallicitiesforstarswithinoneandtwor . Wedidnot
h
the range of ellipticities is 0.13−0.56, with a mean ǫ of
correct for contamination for this experiment because
0.31 and a dispersion of 0.12 (McConnachie 2012). We
the field-star contamination would be only 2% within
haveconfirmedthatthisgalaxyisgas-poor,withanup-
r and 8% within 2 r . The measured metallicity gra-
h h
per limit on the HI gas to L ratio that is comparable
dient in our data is d[Fe/H]/d(r/r ) = 0.0028±0.0029 V
h
to the most sensitive limits for dSph galaxies orbiting
and −0.0014± 0.0065 dex per r , respectively, which
h
the Milky Way (Spekkens et al. 2014).
is consistent with a flat metallicity profile. The lack
Our investigationofthe MDF ofLac I– whichwede-
of a gradient has also been observed in some dwarf
galaxies of similar luminosity beyond the Local Group rived from photometry of the RGB stars with i0 < 23
mag — indicates that this galaxy is metal-poor, with a
(e.g., Crnojevi´c et al. 2010), which may suggest that
median[Fe/H]of−1.68±0.03forstarswithin2r ,buta
the galaxies are not massive enough to favor a second h
broad range of stellar metallicities, from [Fe/H]∼ −1 to