text:
\section{Introduction}

\begin{figure*}[t]
 \centerline{\psfig{figure=Pritzl.fig01.ps,height=2.50in,width=4.50in}}
 \caption{And~I (a) and And~III (b) color-magnitude diagrams using the
  photometry of DACS00 and DAC02 except for the
  variable stars identified in this work which are plotted as plus
  signs.  The anomalous Cepheids or Population~II Cepheids occur above
  the level of the horizontal branch.  In addition, we note the presence
  of two fainter RR~Lyrae in the And~I color-magnitude diagram.}
 \label{Fig01}
\end{figure*}

\begin{figure*}[t]
  \centerline{\psfig{figure=Pritzl.fig02a.eps,height=3.25in,width=3.50in}}
  \caption{Finding charts for the And~I variable stars.  The WFC2
   ($1.2\arcmin$x$1.3\arcmin$), WFC3 ($1.3\arcmin$x$1.2\arcmin$),
   and WFC4 ($1.2\arcmin$x$1.2\arcmin$) images are each shown in a
   panel.  North and east directions are shown with the arrow pointing
   toward the north.}
  \label{Fig02a}
\end{figure*}

\begin{figure*}[t]
  \figurenum{2 cont}
  \centerline{\psfig{figure=Pritzl.fig02b.eps,height=3.25in,width=3.50in}}
  \caption{Finding charts for the And~I variable stars.  The WFC2
   ($1.2\arcmin$x$1.3\arcmin$), WFC3 ($1.3\arcmin$x$1.2\arcmin$),
   and WFC4 ($1.2\arcmin$x$1.2\arcmin$) images are each shown in a
   panel.  North and east directions are shown with the arrow pointing
   toward the north.}
  \label{Fig02b}
\end{figure*}

\begin{figure*}[t]
  \figurenum{2 cont}
  \centerline{\psfig{figure=Pritzl.fig02c.eps,height=3.25in,width=3.50in}}
  \caption{Finding charts for the And~I variable stars.  The WFC2
   ($1.2\arcmin$x$1.3\arcmin$), WFC3 ($1.3\arcmin$x$1.2\arcmin$),
   and WFC4 ($1.2\arcmin$x$1.2\arcmin$) images are each shown in a
   panel.  North and east directions are shown with the arrow pointing
   toward the north.}
  \label{Fig02c}
\end{figure*}

\begin{figure*}[t]
  \centerline{\psfig{figure=Pritzl.fig03a.eps,height=3.35in,width=3.50in}}
  \caption{Finding charts for the And~III variable stars.  The PC
   ($0.5\arcmin$x$0.5\arcmin$), WFC2
   ($1.2\arcmin$x$1.3\arcmin$), WFC3 ($1.3\arcmin$x$1.2\arcmin$),
   and WFC4 ($1.2\arcmin$x$1.2\arcmin$) images are each shown in a
   panel.  North and east directions are shown with the arrow pointing
   toward the north.}
  \label{Fig03a}
\end{figure*}

\begin{figure*}[t]
  \figurenum{3 cont}
  \centerline{\psfig{figure=Pritzl.fig03b.eps,height=3.35in,width=3.50in}}
  \caption{Finding charts for the And~III variable stars.  The PC
   ($0.5\arcmin$x$0.5\arcmin$), WFC2
   ($1.2\arcmin$x$1.3\arcmin$), WFC3 ($1.3\arcmin$x$1.2\arcmin$),
   and WFC4 ($1.2\arcmin$x$1.2\arcmin$) images are each shown in a
   panel.  North and east directions are shown with the arrow pointing
   toward the north.}
  \label{Fig03b}
\end{figure*}

\begin{figure*}[t]
  \figurenum{3 cont}
  \centerline{\psfig{figure=Pritzl.fig03c.eps,height=3.25in,width=3.50in}}
  \caption{Finding charts for the And~III variable stars.  The PC,
   ($0.5\arcmin$x$0.5\arcmin$), WFC2
   ($1.2\arcmin$x$1.3\arcmin$), WFC3 ($1.3\arcmin$x$1.2\arcmin$),
   and WFC4 ($1.2\arcmin$x$1.2\arcmin$) images are each shown in a
   panel.  North and east directions are shown with the arrow pointing
   toward the north.}
  \label{Fig03c}
\end{figure*}

\begin{figure*}[t]
  \figurenum{3 cont}
  \centerline{\psfig{figure=Pritzl.fig03d.eps,height=3.25in,width=3.50in}}
  \caption{Finding charts for the And~III variable stars.  The PC
   ($0.5\arcmin$x$0.5\arcmin$), WFC2
   ($1.2\arcmin$x$1.3\arcmin$), WFC3 ($1.3\arcmin$x$1.2\arcmin$),
   and WFC4 ($1.2\arcmin$x$1.2\arcmin$) images are each shown in a
   panel.  North and east directions are shown with the arrow pointing
   toward the north.}
  \label{Fig03d}
\end{figure*}

The Galactic dwarf spheroidal (dSph) galaxies are known to have a diversity
of star formation histories, from mainly old (age $>$ 10~Gyr) stellar populations such
as Ursa Minor (e.g., Olszewski \& Aaronson 1985), to Fornax which had star
formation as late as 0.3-0.4 Gyrs ago (Saviane, Held, \& Bertelli 2000).
While there have been many studies of the Galactic dSph galaxies, until
recently little was known about the stellar populations of the M31 dSph
galaxies.  In fact, it was only in the past few years that half of the
known M31 dSph galaxies were discovered (Andromeda~V:  Armandroff, Davies,
\& Jacoby 1998; Andromeda~VI [Pegasus]:  Armandroff, Jacoby, \&
Davies 1999, Karachentsev \& Karachentseva 1999; Andromeda~VII [Cassiopeia]:
Karachentsev \& Karachentseva 1999).

A series of observations of the M31 dSph galaxies with the {\it Hubble
Space Telescope} (HST) Wide Field Planetary Camera~2 (WFPC2) has been used
to investigate their stellar populations to levels fainter than the
horizontal branch (HB).  We are also able to use these observations to
investigate the variable star content of these dSph galaxies.
The variable star content is important because it provides
insight to the age, metallicity, and distance to the galaxy in which the variables
are found.  We have already discussed the variable stars in Andromeda~VI
(And~VI; Pritzl et al.\ 2002; henceforth Paper~I) and Andromeda~II (And~II;
Pritzl et al.\ 2004; henceforth Paper~II)\@.  In this third paper of the
series, we investigate the variable stars in Andromeda~I (And~I) and
Andromeda~III (And~III).

Of the M31 dSph companions, And~I lies closest to M31.  It is also on the
high end of the metallicities for dSph galaxies ($\langle{\rm [Fe/H]}\rangle
= -1.46\pm0.12$; Da~Costa et al.\ 2000, henceforth DACS00).  The
color-magnitude diagram (CMD) shows the typical properties seen in other
dSph galaxies such as a predominantly red HB and an internal abundance
spread.  A radial gradient in the HB stars was also detected where there
are relatively more blue HB stars beyond the core radius of the galaxy
(Da~Costa et al.\ 1996; henceforth DACS96).

And~III also lies in the outer halo of M31 and is the next closest dSph to M31
after And~I.  The HB in the CMD for this dSph galaxy is significantly
redder than that seen in the other M31 dSph galaxies that have been observed.
And~III is also one of the most metal-poor
of the M31 dSph companions ($\langle{\rm [Fe/H]}\rangle = -1.88\pm0.11$;
Da~Costa, Armandroff, \& Caldwell 2002, henceforth DAC02).  Further, while
there is
also an internal abundance spread in And~III, it is low compared to most other
dSph galaxies.

The variable star content of And~I was initially investigated in DACS96
and later in more detail in Da~Costa et al.\
(1997), while that for And~III was investigated in DAC02.  In this paper we
expand upon those works bringing to bear the techniques described below and
in Paper~I\@.  After describing the processing of the data, we discuss
the variable star contents of these galaxies and compare them with those for
other dSph galaxies.  We also discuss how the variable star
populations reflect the properties of And~I and And~III.

\section{Observations and Reductions}

Observations of And~I were taken by the HST/WFPC2 as part of the GO Program
5325 on 1994 August 11 and 16, using the same orientation.
Three 1800~s integrations through the F555W filter and six 1800~s
integrations through the F450W filter were taken in the first set of
observations.  Identical exposure times were used for the second set of
observations, but there were four F555W and six F450W integrations.

For And~III, the observations were taken for the GO Program 7500 on 1999
February 22 and 26 with the same orientation.  Each set of observations
had four observations of 1200~s in F555W and eight observations of 1300s
in F450W\@.  As for And~I, the two sets of observations were slightly offset
from each other to minimize the impact of instrumental defects.  For
And~III, the
field center was offset from the center of the dSph galaxy to avoid
bright foreground stars (see Fig.~1 of DAC02).

The point-spread function fitting photometry was performed with {\sc allframe}
(Stetson 1994) as described in Paper~I\@.  Similarly, the aperture and
charge-transfer efficiency corrections along with the $B$,$V$ calibrations
were carried out in the same fashion.  As with And~II, we have the
photometry used in creating the color-magnitude diagrams (CMDs) so we may
compare our photometry with that of DACS00 and DAC02.
We list in Table~1 the mean differences between the two sets of photometry.
There are obvious systematic differences that are of
similar size and sign as those found for And~II in Paper~II\@.  The origin
of these systematic differences is unclear, although it likely is due to the
different techniques and calibration processes.  Fortunately they appear
to be just zero point offsets:  there is no dependance of these
differences on magnitude.  We have applied them to our data in order to
keep the present photometry consistent with the earlier work.  It should
also be noted that DAC02 found their HST $V$-band photometry to be consistent
with ground-based observations of And~III.

\begin{figure*}[t]
  \centerline{\psfig{figure=Pritzl.fig04a.ps,height=7.00in,width=5.00in}}
  \caption{And~I variable star light curves.  The observations are shown
   as filled circles and the fitted templates are displayed as curves.}
  \label{Fig04}
\end{figure*}

\begin{figure*}[t]
  \figurenum{4 cont}
  \centerline{\psfig{figure=Pritzl.fig04b.ps,height=7.00in,width=5.00in}}
  \caption{And~I variable star light curves.  The observations are shown
   as filled circles and the fitted templates are displayed as curves.}
  \label{Fig04}
\end{figure*}

\begin{figure*}[t]
  \figurenum{4 cont}
  \centerline{\psfig{figure=Pritzl.fig04c.ps,height=7.00in,width=5.00in}}
  \caption{And~I variable star light curves.  The observations are shown
   as filled circles and the fitted templates are displayed as curves.}
  \label{Fig04}
\end{figure*}

\begin{figure*}[t]
  \figurenum{4 cont}
  \centerline{\psfig{figure=Pritzl.fig04d.ps,height=7.20in,width=5.00in}}
  \caption{And~I variable star light curves.  The observations are shown
   as filled circles and the fitted templates are displayed as curves.}
  \label{Fig04}
\end{figure*}

\begin{figure*}[t]
  \figurenum{4 cont}
  \centerline{\psfig{figure=Pritzl.fig04e.ps,height=1.75in,width=2.50in}}
  \caption{And~I variable star light curves.  The observations are shown
   as filled circles and the fitted templates are displayed as curves.}
  \label{Fig04}
\end{figure*}

\begin{figure*}[t]
  \centerline{\psfig{figure=Pritzl.fig05a.ps,height=7.00in,width=5.00in}}
  \caption{And~III variable star light curves.  The observations are shown
   as filled circles and the fitted templates are displayed as curves.}
  \label{Fig05}
\end{figure*}

\begin{figure*}[t]
  \figurenum{5 cont}
  \centerline{\psfig{figure=Pritzl.fig05b.ps,height=7.00in,width=5.00in}}
  \caption{And~III variable star light curves.  The observations are shown
   as filled circles and the fitted templates are displayed as curves.}
  \label{Fig05}
\end{figure*}

\begin{figure*}[t]
  \figurenum{5 cont}
  \centerline{\psfig{figure=Pritzl.fig05c.ps,height=4.50in,width=2.50in}}
  \caption{And~III variable star light curves.  The observations are shown
   as filled circles and the fitted templates are displayed as curves.}
  \label{Fig05}
\end{figure*}

\section{Variable Stars}

As was done in Papers~I and II, the photometry of the individual images was
searched for variable stars using {\sc daomaster}, a routine created by
P. B. Stetson.  {\sc daomaster} compares the rms scatter in the photometric
values with that expected from the photometric errors returned by the
{\sc allframe} program.  For And~I, we do not include the PC data since only a
small number of RR~Lyrae (RRL) stars were found and no candidate anomalous
Cepheids (ACs).  On the other hand, we did find one AC on the PC for And~III.
Therefore we include the RRL stars found on that chip in our analysis.
Period searches of the variable stars were done using the routines
created by A. C. Layden as outlined in Papers~I and II.  The routines determine
the most likely period from the $\chi^2$ minima by fitting the photometry of the
variable star with 10 templates over a selected range of periods.  A cubic spline
was fitted to each template light curve to determine the mean magnitudes and colors.
The amplitudes derive from the template fits.

As discussed in Paper~I, the nature of the observations makes the determination of
precise periods and magnitudes a challenge.  The data for both filters are
combined to allow for more accurate magnitudes and periods (see Paper~I for
more details).  As was done in the previous papers in this series, we used the
period-amplitude diagram to test the periods of the RRL stars.  When one of these
stars was scattered from the majority in the period-amplitude daigram we revised the
period to reduce the scatter.  Although there is a slight possibility that a
small number of And~I and And~III RRL stars may have an alias period, the combination of the
template-fitting program and the period-amplitude diagram reduces the likelihood
of this happening.

Figure~1 shows the CMDs of DACS00 (And~I) and DAC02 (And~III) in which we have
replaced their photometry with that derived here for all the stars found to be
variable in our survey.  Further, we checked all the DACS00 and DAC02 stars in
Figure~1 that fall in the region of the instability strip along the HB or brighter
for variability.  However, no additional variables were found.  Each variable is plotted
according to its intensity-weighted $V$ magnitude and magnitude-weighted
$(\bv)$ color.  Table~2 lists the photometric data for the variable stars
in And~I, while Table~3 lists these for And~III.  For both tables,
column~1 lists the star's ID, while the next two columns give the RA and
Dec.  Column~4 lists the period of each star.  The intensity-weighted
$\langle V \rangle$ and $\langle B \rangle$ magnitudes along with the
magnitude-weighted colors $(\bv)_{\rm mag}$ are shown in columns 5 - 7.
Columns~8 and 9 give the $V$ and $B$ amplitudes of the variable stars.
The classifications of the variable stars are listed in column~12.  The
remaining columns will be discussed later in the paper.  Figures~2 and 3
are the finding charts for And~I and And~III, respectively, while
Tables~4 - 7 give the photometric $B$ and $V$ data for And~I and And~III\@.
The light curves for the variable stars in And~I are shown in Figure~4,
while those for And~III are in Figure~5.

For And~I, there is one clear supra-HB variable star in the CMD (Fig.\ 1a).
This
star may be a Population~II Cepheid (P2C) and is discussed in the following
section.  There are also two variable stars that are
clearly fainter than the HB\@.  These stars will be discussed in \S5.1.1.

The And~III CMD in Fig.~1b shows five variable stars brighter than
the RRL along the HB\@.  DAC02 discovered two of these stars and suggested
one (V08$=$WF2-1398 in DAC02) may be a P2C\@.  This possibility is also
discussed in the next section.  The two CMDs also show that And~III,
despite having a lower mean metallicity than And~I, has a redder HB
(cf.\ DAC02).

\section{Anomalous Cepheids and Population~II Cepheids}

As mentioned above, And~I has one supra-HB variable star and And~III has five.
Following the prescription used in Paper~I, we list the absolute magnitudes
for these stars in Table~8 assuming a distance modulus and visual absorption of
$24.49\pm0.06$~mag and $0.16\pm0.03$ for And~I (DACS00) and $24.38\pm0.06$~mag
and $0.17\pm0.03$ for And~III (DAC02).  The period-luminosity relation shown
in Figure~6 plots the ACs from Paper~I and Paper~II along with the supra-HB
variable stars in And~I and And~III\@.
Four of the supra-HB variable stars in And~III fit in well with the other ACs
in this Figure confirming their classification as ACs.  These ACs are also
found to be consistent with the other ACs in a period-amplitude diagram.

In addition to the AC period-luminosity (P-L) relation lines, we plot
in Figure~6 the P2C P-L relation for $P<10$~days using equation~11 in McNamara
(1995).  Clearly, V01 in And~I and V08 in And~III fall near the P2C
line for their given magnitude and period.  The way the data were taken
and the relatively long apparent periods for these stars combine to
generate significant gaps in their light curves.
This leads to higher uncertainty in their periods and magnitudes compared
to the rest of our data.  If V01 in And~I is a P2C, then it will mean that
we have been unable to find a definite AC in this dSph galaxy.  And~I might
then become the first dSph galaxy without an AC,
though we have not by any means surveyed all of the galaxy for variable
stars (see Table~9).  We also note, as was first shown by DAC02 using
a different ``shorter" period,  that it is possible to fit the
observations for And~III V08 with a period as short as $P=0.655$~d.
This would make the star an AC, although this is not the best $\chi^2$
fit according to the template fitting program we have employed.  Given
the lack of phase coverage, we do not feel comfortable forcing a change in the
period soley to make it an AC.  The mean magnitudes we find for this short
period would place the variable on the fundamental mode period-luminosity
relation line for the ACs.  We were unable to find a viable ``AC-like''
period for And~I V01.

Do we expect to see P2C variables in dSph galaxies?  In Galactic globular
clusters, the main property associated with the presence of P2Cs are
strong blue HBs (e.g., DAC02; Wallerstein 2002).  In particular, the
shorter period P2Cs, known as BL~Her stars, which And~I V01 and And~III V08
would be classified as, are assumed to be post blue HB stars evolving
through the instability strip towards the asymptotic giant branch.  Of
the Galactic dSph galaxies, only Fornax has been shown to contain P2Cs
(Bersier \& Wood 2002).  It may be that Fornax has a significant population
of blue HB stars that could provide a source for P2Cs, but it is difficult
to infer this from the CMD as the blue HB region is severely contaminated
by main sequence stars.  On the other hand, the CMDs for And~I and
And~III clearly do not contain strong blue HB populations (see Figure~1)
and this would seem to argue against the P2C interpretation.  We are
forced to conclude that further observations of these stars are
needed to clarify their periods and light curve shapes, and thus their
classification.

\begin{figure*}[t]
  \centerline{\psfig{figure=Pritzl.fig06.ps,height=2.50in,width=4.50in}}
  \caption{Period-luminosity diagrams for anomalous Cepheids for both the
   (a) $B$ and (b) $V$ filters.  The anomalous Cepheid fundamental
   and first-overtone mode period-luminosity relations from Pritzl et al.\ (2002)
   are shown as dashed lines.  The Population~II Cepheid period-luminosity line
   from McNamara (1995) is shown as a dotted-dashed line.}
  \label{Fig06}
\end{figure*}

\subsection{The Frequency of Anomalous Cepheids in dSph Galaxies}

Mateo et al.\ (1995) pointed out that the specific frequency of
ACs (the number of ACs per $10^5 L_{V,\odot}$) correlates with both
(visual) luminosity and mean abundance for the Galactic dSphs.  In Paper~II
we updated the Galactic dSph data and found that the M31 dSphs And~II and
And~VI apparently follow the same correlations.  We now explore whether
this result applies also to And~I and And~III\@.  In Table~9 we list the data
used in calculating the specific frequency of ACs for
And~I and And~III (cf.\ Table~5 of Paper~II).  We note that in this
discussion, the supra-HB variable stars in And~I and And~III that
may be ACs or P2Cs, have been assumed to be ACs.  Without this assumption,
And~I would have no ACs and And~III would have a specific frequency of 1.7
per $10^5 L_{V,\odot}$.  Figure~7 plots the logarithm of specific frequency
against M$_{V}$ and mean metallicity for And~I and And~III along with the
data from Paper~II\@.  We also include the
specific frequency value for the Phoenix dwarf irregular galaxy from
Gallart et al.\ (2004).  Clearly, like And~II and And~VI (cf. Paper~II),
And~I and III fall near the line defined by
the Galactic dSph galaxies, as does Phoenix (cf.\ Gallart et al.\ 2004).
Consequently,
it appears that the correlation between AC specific
frequency and either (visual) luminosity or metallicity seen in the
Galactic dSph galaxies applies also to the M31 systems.

As pointed out by Mateo et al.\ (1995) and in Paper~II, it is perhaps
surprising to see a strong correlation between the specific frequency of
ACs and the total luminosity of the dSph galaxies given the stellar
population differences among the dSphs, and the fact that there are two
different mechanisms that can create ACs, one
from younger stars and the other from mass-transfer in binaries.  Both
mechanisms are complicated and both can occur in a dSph galaxy, as
discussed by Bono et al.\ (1997) using various stellar models.  However,
as noted by Mateo et al.\ (1995) and in Paper~II, the mean abundances
of dSph galaxies are well correlated with their luminosities, with the
lower luminosity systems having lower abundances.  Thus, since regardless
of the mechanism creating the AC the star needs to be metal-poor to
enter the instability strip, it may simply be that it is easier to
generate ACs in a more metal-poor environment.

We now comment briefly on the observed lack of ACs in the M31 halo field
surveyed for variable stars by Brown et al.\ (2004).
Given the results of Durrell, Harris, \& Pritchet (2004), for example, we
can assume that the mean metallicity for the surveyed region is
approximately $\langle {\rm [Fe/H]} \rangle = -0.8$.  Then assuming that
the relation between AC specific
frequency and mean abundance shown in Figure~7 can be extended to mean
abundances of this order, the linear fit shown gives $\log\,S\sim-1.55$
per $10^5 L_V$.  The mean surface brightness and area of the region
(Brown et al.\ 2004), then yield, assuming $(m-M)_V=24.5\pm0.1$~mag,
a visual luminosity for the region of $7.4 \times 10^5 L_V$.  Therefore,
the number of ACs expected in the field is $\sim0.2$.  This is certainly
consistent with the fact that Brown et al.\ (2004) found none.  However,
we know that ACs derive from metal-poor stellar populations
(${\rm [Fe/H]}<-1.3$; Demarque \& Hirshfeld 1975).  Consequently, using
a mean metallicity of ${\rm [Fe/H]}=-0.8$ may not be the most appropriate
approach.
Using Eq.~2 of Alcock et al.\ (2000), Brown et al.\ (2004) found that the RRL
population in their field has a mean metallicity of $-1.79$.  For this
metallicity, Figure~7 gives $\log\,S\sim-0.1$ per $10^5 L_V$.  However, in this
situation, we cannot apply the total visual luminosity for the surveyed
region.  Brown et al.\ (2003) argue that, in this region, the old, metal-poor
stellar population makes up at most 30\% of the total
(cf.\ Durrell et al.\ 2004).  Scaling the total luminosity by this
fraction then predicts 1.8 ACs in the surveyed field.  This
number is not inconsistent with the observed lack of ACs
given small number statistics and the uncertainty in the luminosity
fraction generated by the metal-poor population.  Clearly further variable
star
searches over larger areas are required to more fully investigate
whether or not ACs exist in the M31 halo.  A confirmed lack of
such stars would add  strength to the contention that the disruption
of dwarf galaxies
comparable to the existing M31 dSph companions was not a major contributor
to the build-up of the M31 halo.

\begin{figure*}[t]
  \centerline{\psfig{figure=Pritzl.fig07.ps,height=2.50in,width=4.50in}}
  \caption{Specific frequency of anomalous Cepheids in dwarf spheroidal galaxies
   as a function of the absolute visual magnitude (left panel),
   and the mean metallicity of the dwarf galaxy (right panel).  The Galactic dwarf
   spheroidal galaxies are shown as open circles, while the M31 ones are shown as
   filled circles.  The Phoenix dwarf galaxy is shown as a filled square.  In both plots,
   there are clear trends that the Galactic dwarf spheroidal galaxies follow
   as shown by the least squares fit to the data.  The M31 dSph
   galaxies follow these trends, including And~I and And~III\@.  Note that we have
   assumed that the two supra-HB variables stars And~I V01 and And~III V08 to
   be anomalous Cepheids, although their classification is uncertain.}
  \label{Fig07}
\end{figure*}

\subsection{Anomalous Cepheids $=$ Short-Period Cepheids?}

Recently, the number of variable star surveys of dwarf galaxies has
increased, especially for dwarf irregular galaxies such as IC~1613
(Dolphin et al.\ 2001), Leo~A (Dolphin et al.\ 2002), Sextans~A
(Dolphin et al.\ 2003), NGC~6822 (Clementini et al.\ 2003) and
Phoenix (Gallart et al.\ 2004).  These studies have revealed a number of short-period
(Classical) Cepheids.  Given that these variables
have periods similar to the ACs and comparable magnitudes,
there is some question as to the distinction between the two classes of
variables.  Using the OGLE Small Magellanic Cloud database (Udalski et al.\ 1999),
Dolphin et al.\ (2002) found the P-L relations for Cepheids with periods
of two days or less was similar to the AC P-L relations of Nemec, Nemec,
\& Lutz (1994).  Therefore, they concluded that there was no clear distinction between
ACs and short-period Cepheids in terms of their position
in the P-L relations.  The only difference between these two
classes would be that short-period Cepheids are predominantly found in
systems with young stars (ages$<100$~Myr) while ACs preferentially
occur in systems that lack such young stars.

Baldacci et al.\ (2003) were the first to show that the short-period
Cepheids in dwarf irregular galaxies, including the Large and Small
Magellanic Clouds, have P-L relations different than those of ACs as
given in Paper~I\@.  They also comment that Phoenix and NGC~6822 may have their
instability strip continuously populated from the RRL stars, through the ACs
to the short-period Cepheids.  Marconi, Fiorentino, \& Caputo (2004) and Gallart et al.\
(2004) took this a step further claiming that some of the short-period
Cepheids in dwarf galaxies such as Leo~A and Sextans~A may actually be
ACs.

Following the same method as outlined in \S4 of Paper~I, we determined the absolute
magnitudes of the short-period Cepheids in IC~1613, Leo~A, and
Sextans~A using the tip of the red giant branch as the distance
indicator.  This is to ensure consistency between the absolute magnitudes
found for the ACs and the short-period Cepheids.  We
plot the absolute magnitude of the short-period Cepheids against their
periods in Figure~8 along with the lines for
the AC P-L relations as determined in Paper~I (cf.\ Eqns.~4 and 5).  Looking
first at the fundamental mode variables, which are found at a fainter
magnitude than the first-overtone variables for a given period, the
short-period Cepheids are clearly found at higher luminosity than the
ACs at a given period.  For
the first-overtone Cepheids, the case isn't as clear.  However for a set
period, these stars are still offset toward brighter absolute magnitudes
than the first-overtone ACs, especially at short periods.  There are some
stars which are located near the AC P-L lines, but this may be due to the
uncertainties in the periods and magnitudes of the stars.  The higher
luminosity at fixed period for the short-period Cepheids relative to
the ACs indicates that these stars have higher masses than the ACs.  This
is not unexpected given that these dwarf irregular galaxies have on-going
star formation which the dSph galaxies lack.

Our analysis agrees with Baldacci et al.\ (2003), Marconi et al.\ (2004),
and Gallart et al.\ (2004) as regards to the existence of a difference
between the P-L relations for ACs and short-period Cepheids.  In essence,
the reason we do not see as many short-period Cepheids lying along the AC
P-L relations as do Dolphin et al.\ (2001, 2002, 2003) lies with their
use of the Nemec, Nemec, \& Lutz (1994) AC P-L relations rather than
those of Paper~I.\@  This does not mean, however, that dwarf galaxies such as
Leo~A and Sextans~A do not contain both short-period and anomalous
Cepheids.  Indeed, we encourage further observations of these and
other dwarf irregular galaxies to search for such stars.

\begin{figure*}[t]
 \centerline{\psfig{figure=Pritzl.fig08.ps,height=3.50in,width=3.50in}}
 \caption{$V$-band absolute magnitude versus the logarithm of the period
  for short period Cepheids in Sextans~A (plusses),
  IC~1613 (open circles), and Leo~A (open stars).  The solid lines are
  the period-luminosity relations representing the fundamental and
  first-overtone mode anomalous Cepheids (Pritzl et al.\ 2002).  This plot
  clearly illustrates that the short period Cepheids are found at higher
  luminosities than the anomalous Cepheids at a given period.}
 \label{Fig08}
\end{figure*}

\section{RR Lyrae Stars}

\subsection{And~I}

We detected 99 RRL stars in our field-of-view of And~I, with 72 pulsating in
the fundamental mode (RRab) and 26 pulsating in the first-overtone mode (RRc).
This nearly doubles the number of RRL stars found by Da~Costa et al.\ (1997),
who detected 50 RRL stars.  One variable, V04, remains unclassified due to a lack
of F555W data because of a chip defect.  It is likely an RRL star given its
F450W magnitude.  The presence of the RRL stars indicates that
And~I contains a stellar population with an age $> 10$~Gyr.  It should be noted
that due to the low amplitudes of the RRc stars, we may not have detected all
of the possible stars pulsating in this mode.

We find the mean period of the And~I RRab and RRc stars to be 0.575~day and
0.388~day, respectively.  The ratio of RRc stars to the total number of
RRLs, $N_c/N_{RR}$, is 0.27.  If we place these values in Table~6 of Paper~I
according
to the metallicity given in DACS00, $\langle {\rm [Fe/H]} \rangle = -1.46 \pm
0.12$, we find that they are consistent with those found for other
dSph galaxies.  With this metallicity, the RRL stars in And~I also follow
the mean period - metallicity relation defined by the Galactic globular
clusters,
as is shown in Figure~9.  The mean period for the RRab stars in And~I is close
to the value found for And~II which has a very similar mean metallicity
to And~I (DACS00).  It is interesting to note that this is the case even
though there is a large spread among the And~II RRab stars in the
period-amplitude diagram (see Fig.~7 in Paper~II).

\begin{figure*}[t]
 \centerline{\psfig{figure=Pritzl.fig09.ps,height=3.25in,width=3.50in}}
 \caption{Mean period for the RRab stars versus the mean metallicity of the
  parent system.  The Andromeda dwarf spheroidal galaxies
  are shown as open squares.  The Galactic dwarf spheroidals are indicated
  by open circles.  Galactic globular clusters with at least 15 RRab stars
  are shown as filled circles, along with $\omega$~Centauri (filled square).
  Large Magellanic Cloud globular clusters with a minimum of 15 RRab stars
  are shown as open triangles.}
 \label{Fig09}
\end{figure*}

The mean magnitude of the And~I RRL stars, not including the two fainter
RRL stars, is found to be $\langle V_{\rm RR} \rangle = 25.14\pm0.04$~mag,
where the uncertainty is the aperture correction uncertainty, the photometry
zeropoint uncertainty in the DAC02 photometry, and the uncertainty in the
mean RRL instrumental magnitude derived from the spline-fitting routine added
in quadrature to the standard error of the mean.  This matches the value
determined by DACS00 of $V_{\rm HB} = 25.23\pm0.04$~mag.  Given $\langle {\rm [Fe/H]}
\rangle = -1.46 \pm 0.12$, the equation $M_{V,{\rm RR}} = 0.17{\rm [Fe/H]} + 0.82$
from Lee, Demarque, \& Zinn (1990) yields $M_{V,{\rm RR}} = +0.57$ and thus a
true distance modulus of $24.42 \pm 0.07$~mag for the adopted reddening.
This corresponds to a distance of $765\pm25$~kpc in good accord with the distance,
$790\pm25$~kpc, found by DACS00.

\subsubsection{M31 Halo RR~Lyrae Stars?}

\begin{figure*}[t]
  \centerline{\psfig{figure=Pritzl.fig10.ps,height=2.50in,width=4.50in}}
  \caption{Period-amplitude diagram for the RR~Lyrae stars in And~I (left panel)
   and And~III (right panel) for the $B$ filter.}
  \label{Fig10}
\end{figure*}

According to DACS96 and DACS00, the line-of-sight distance between M31 and
And~I is $0\pm70$~kpc and the true distance of And~I from the center of M31
is somewhere between $\sim 45$ and $\sim 85$~kpc.  This makes And~I
the closest dSph to M31 leading to the possibility that there may
be contamination of the CMD from M31 halo stars.  In fact,  DACS96 showed that a
number of stars somewhat fainter and redder than the And~I red giant branch
(RGB) in their
CMD were likely to be from the M31 halo.

Variable stars V76 and V100 in And~I are both clearly fainter than the rest
of the RRL in this dSph galaxy.  We checked the images for any defects
near these stars which may have affected their photometry and none
were found.  DACS96 drew attention to a population of faint blue stars
in And~I which they suggested might be blue straggler stars analogous to
those found in globular clusters.  Some blue straggler stars are known to
be short period variables ($\delta$~Scuti), but the periods of the And~I
faint variables are too long for them to be interpreted in this way.
Therefore, it appears that V76 and V100 must originate from a stellar
population not associated with And~I\@.  The only logical interpretation
of this is that they are part of the M31 halo.

We can attempt to verify this assertion by making use of the recent study
of RRL stars in the halo of M31 of Brown et al.\ (2004).  These authors
used the Advanced Camera for Surveys on HST to provide a complete census of
RRL stars in a halo
field approximately 51 arcmin from the center of M31 on the minor axis.
In their field the density of RRab variables is 2.24 per ${\rm arcmin}^2$.
Brown et al.\ (2004) also give the surface brightness of the M31 halo at
the location of their field as 26.3 $V$ mag per ${\rm arcsec}^2$.  Using
the Pritchet \& van den Bergh (1994) surface brightness profile, DACS96
estimated
the M31 halo surface brightness in the vicinity of And~I as approximately
29.5 $V$ mag per ${\rm arcsec}^2$.  Then assuming no change in the stellar
population
with radius, these figures imply a M31 halo RRab density at the location of
And~I
of approximately 0.12 per ${\rm arcmin}^2$.  Combined with the area of the
field studied
here, this density predicts only 0.6 M31 halo RRab should be present in our
data, rather than the two observed.  Consequently, even allowing for small
number statistics, it appears that these two fainter RRL may be associated
with a region of moderately enhanced density in the halo of M31.  This conclusion is
strengthened by looking at the magnitude distribution of the RRab stars in the
Brown et al.\ (2004) M31 halo field.  The 29 stars have a mean $V$ magnitude,
corrected to the reddening of the And~I, of $\langle V \rangle=25.18$ mag,
with a standard deviation of 0.11 mag (in F606W, which for this purpose we
can equate with $\sigma_V$).  The largest excursion from this mean on the
faint side is only 0.24 mag.  Consequently, the two fainter RRab stars in the
And~I field are both more than 3$\sigma$ fainter than the mean, increasing the
likelyhood that they are associated with a distinct feature, rather than the
general field in the outer halo of M31.

This indeed may be the case.  McConnachie et al.\ (2003) have used the CHF12k
CCD mosaic camera to map the giant stellar stream in the halo of M31
(Ibata et al.\ 2001; Ferguson et al.\ 2002) to larger radial distances.  They
find the stream extends to the South-East of M31 for at least 4.5$^\circ$,
and using the tip of the red giant branch as a distance indicator,
McConnachie et al.\ demonstrate that the Stream is on the far side of M31,
increasingly so as the angular distance from M31 increases.  Coincidently,
And~I is
projected close to this Stream on the sky, and, based on Fig.\ 7 of
McConnachie et al., we estimate that the Stream lies approximately 150 kpc
beyond M31 (and And~I, which is at the same distance as M31 [DAC02]) at the
location of And~I\@.  This corresponds to a total distance of $\sim$875 kpc
or an apparent visual distance modulus of approximately 24.9~mag.  If the two
faint RRL stars are members of this Stream, then their absolute visual
magnitudes would be $\sim$0.7 (V76) and $\sim$0.9 (V100).  Such values are
not unexpected given the apparent metal-rich nature of the Stream
(Ibata et al.\ 2001; Ferguson et al.\ 2002; McConnachie et al.\ 2003).
We conclude then that it is quite possible that the two faint RRL stars
observed in the field of And~I are associated with the recently identified
Stream in the halo of M31, rather than with the general M31 halo field.
The existence of RRL stars in the Stream immediately indicates that its
progenitor must have contained an old stellar population, and such variables
may provide a further means to map both the location of the Stream and to
investigate its stellar population.

\subsection{And~III}

For And~III, we found a total of 51 RRL, 39 pulsating in the fundamental mode
and 12 in the first-overtone mode.  As
mentioned above, it is more difficult to detect the RRc stars due to their
smaller amplitudes.  Therefore not all of the RRc stars within our
field-of-view may have been detected.

The mean periods are 0.657~day and 0.402~day for the RRab and RRc stars,
respectively.  The $N_c/N_{RR}$ ratio is found to be 0.24, although
this number and the mean period for the RRc stars may be uncertain due to
undetected RRc stars.  As was done above for And~I, we can place these values
in Table~6 of Paper~I according to And~III's metallicity of $\langle {\rm [Fe/H]}
\rangle = -1.88\pm0.11$.  We find that in comparison to the other dSph
galaxies, And~III has unusually long periods for its RRab and RRc stars.
This can clearly be seen in the mean period - metallicity diagram of Figure~9
where And~III lies to the right of
the other dSph galaxies and globular clusters with similar abundances.
A possible reason for this will be discussed in \S5.3.

The mean magnitude for the And~III RRL stars is $\langle V_{\rm RR} \rangle =
25.01\pm0.04$~mag.  DAC02 found the mean $V$ magnitude of the HB of And~III
to be $25.06\pm0.04$~mag.  Given $\langle {\rm [Fe/H]} \rangle =
-1.88\pm0.11$, $E(\bv)=0.06\pm0.01$, and the equations used above, we find
$M_{V,{\rm RR}} = +0.50$ and $A_V = 0.17\pm0.03$.  This yields a distance
of $740\pm20$~kpc, which matches quite well with the estimate of
$750\pm20$~kpc by DAC02.

\subsection{RR~Lyrae Period-Amplitude Diagrams}

Figure~10 plots the $B$-amplitude of the RRL stars against their adopted
period for And~I and And~III\@.  As discussed in Paper~I, the scatter in these
diagrams was reduced by revising the period of a small number of stars where
it was apparent that A. C. Layden's period-finding routines had picked out an
alias of the probable true period.  For And~I the longer duration of the
observation set meant that there were only minimal period revisions for this
dSph.
Figure~10a also shows that in And~I there are a number of longer period RRc
stars which overlap with similar period, but higher amplitude, RRab stars.

In Figure~10b, we see that the RRab stars in And~III have mostly smaller
amplitudes and longer periods.  In direct contrast to And~I, there is a
notable lack of shorter period, higher amplitude RRab
stars.  It is this lack of shorter period RRab stars that results in
a relatively long mean period, thus displacing the And~III point in the
mean period - metallicity diagram (Figure~9) to the right.

The explanation may lie with the morphology of the horizontal branch
in this dSph.  It is clear from the CMD of And~III (see Fig.~1b; Fig.~3 in
DAC02) that the horizontal branch is lacking in stars bluer than the
instability strip.  A majority of the stars are located toward the
red side of the horizontal branch and therefore, more of the red side
of the instability strip is filled.  As a consequence, longer period
RRab and RRc stars are likely.  A similar situation is
thought to occur for the RRL variables in the globular cluster Ruprecht~106
(Catelan 2004), a cluster which also has a very red HB.

\begin{figure*}[t]
 \centerline{\psfig{figure=Pritzl.fig11.ps,height=7.00in,width=5.00in}}
 \caption{Period distribution plots for the RR~Lyrae stars in dwarf spheroidal
  galaxies.  The plots are arranged so that the mean metallicity
  of the parent system increases from the top down.  RRab stars are shown as
  open histograms while RRc stars are shown as filled histograms.}
 \label{Fig11}
\end{figure*}

\begin{figure*}[t]
 \centerline{\psfig{figure=Pritzl.fig12.ps,height=2.50in,width=4.50in}}
 \caption{Period shift versus period for the RRab stars in (a) And~I and
  (b) And~III\@.  The dashed lines represent the zone in which few
  RRab stars from Galactic globular clusters are found.}
 \label{Fig12}
\end{figure*}

\begin{figure*}[t]
 \centerline{\psfig{figure=Pritzl.fig13.ps,height=5.25in,width=3.50in}}
 \caption{Upper panel:  [Fe/H] distribution plot for the RRab stars in
  And~I\@.  The individual [Fe/H] values were calculated using Eq.\ 2 and have
  an uncertainty of $\sim0.3$~dex.  The dashed line is a gaussian fit to these data.
  It has a mean of ${\rm [Fe/H]}=-1.44$ and a standard deviation of
  0.51~dex.  Lower panel:  [Fe/H] distribution plot for red giant branch stars in And~I
  from DACS00.  The individual [Fe/H] values have uncertainties of $\sim0.1$~dex.}
 \label{Fig13}
\end{figure*}

\begin{figure*}[t]
 \centerline{\psfig{figure=Pritzl.fig14.ps,height=5.25in,width=3.50in}}
 \caption{Upper panel:  [Fe/H] distribution plot for the RRab stars in And~III\@.
  The individual [Fe/H] values were calculated using Eq.\ 2 and have
  an uncertainty of $\sim0.3$~dex.  The dashed line is a gaussian fit to these
  data.  The curve has a mean of ${\rm [Fe/H]}=-1.79$ and a standard
  deviation of 0.37~dex.  Lower panel:  [Fe/H] distribution plot for red giant branch
  stars in And~III from DAC02.  The individual [Fe/H] values have uncertainties of $\sim0.1$~dex.}
 \label{Fig14}
\end{figure*}

\subsection{RR~Lyrae Period Shift}

Another way to compare the RRL populations is to view their period
distribution.  In Figure~11 we plot the RRL period distribution for a number
of dSph galaxies according to their mean metallicity.  As with the mean
RRab periods discussed above, there is a trend for the RRab distribution to
shift toward shorter periods as the metallicity increases.  For And~III,
the distribution has a marked discontinuity in the RRL numbers at $P \sim 0.6$~day,
a further manifestation of the lack of shorter period, higher amplitude RRab stars
in this dSph galaxy.

The shift in period among the RRab stars in globular clusters was first
noticed by Sandage, Katem, \& Sandage (1981) and was later found to be
dependent on metallicity by Sandage (1981; 1982a,b).  With M3 as the fiducial
cluster, the period shifts of RRab stars were determined to follow the
relation:
\begin{equation}
\Delta\log\,P = -(0.129A_B + 0.088 + \log\,P)
\end{equation}
\noindent
by Sandage (1982a,b).  Using this equation, Sandage found that more metal-rich
globular clusters have $\langle\Delta\log\,P\rangle \ge -0.01$, while the more
metal-poor clusters have $\langle\Delta\log\,P\rangle \le -0.05$ with few
globular cluster RRab stars found between these values.  However, a number
of RRab stars in dSph galaxies have been found
in this gap (Sextans:  Mateo, Fischer, \& Krzeminski 1995; Leo~II:  Siegel \& Majewski
2000; Andromeda~VI:  Paper~I; Andromeda~II:  Paper~II).  The presence of
these stars in the gap indicates that the RRL populations in dSph galaxies
are not simply superpositions of two separate populations, one being
metal-rich and the other metal-poor.  In column~10 of Tables~2 and 3,
we list the $\Delta\log\,P$ values for the RRab stars of And~I and
And~III\@.  These values are plotted against the corresponding
$\log\,P$ values in Figure~12.  Clearly, like the other dSph galaxies, both
And~I and And~III have a substantial number of RRab stars within the gap.
This figure also shows the lack of short period RRab stars in And~III\@.
The mean period shift is +0.01 for And~I and --0.02 for And~III\@.  Using
$\Delta\log\,P = 0.116 {\rm [Fe/H]} + 0.173$ from Sandage (1982a), we
find ${\rm [Fe/H]} = -1.41$ for And~I and $-1.66$ for And~III\@.  The
value determined for And~I is close to that found by DACS00
($\langle{\rm [Fe/H]}\rangle = -1.46\pm0.12$) based on the colors of RGB
stars.  On the other hand, the
estimate for And~III is somewhat more metal-rich than that given by DAC02 from
the color of the RGB ($\langle{\rm [Fe/H]}\rangle = -1.88\pm0.11$).  This
discrepancy is reduced with the metallicity estimates made in the following
section using different methods.

\subsection{Metallicity Estimates from the RR~Lyrae Stars}

We found in Papers~I and II that the equation:
\begin{equation}
{\rm [Fe/H]}_{\rm ZW} = -8.85(\log\,P_{ab} + 0.15A_V) - 2.60
\end{equation}
\noindent
derived by Alcock et al.\ (2000) using the RRab stars in M3, M5, and M15
yields a mean metallicity for the RRL in And~II and And~VI similar
to those found using the mean colors of the RGB\@.  The accuracy of
this equation is $\sigma_{\rm [Fe/H]} = 0.31$ per star (Alcock et al. 2000).
Using
this equation, we derived individual metallicities for the RRab stars and
these are
listed in column~11 in Tables~2 and 3 for And~I and And~III, respectively.

The upper panel of Figure~13 plots the abundance distribution for the RRab stars
in And~I using the individual abundances derived from Eq.~2.  The mean and
median of the values are ${\rm [Fe/H]} = -1.49$ and $-1.46$, respectively.
A gaussian fit to these data is also shown which has a mean of
${\rm [Fe/H]} = -1.44\pm0.03$ (standard error of the mean).  These RRab
based abundances agree well with the mean And~I abundance, ${\rm [Fe/H]}=-1.46\pm0.12$,
determined by DACS00 from the colors of the red giant branch stars.  As noted
in Paper~II, because not every red giant branch star evolves to become
an RRab, there is no obvious reason to expect these mean abundances to agree.

The gaussian fit shown in the upper panel of Fig.~13 has a standard deviation of 0.51~dex.
Given that the individual RRL abundances have uncertainties of order 0.3~dex,
this suggests the presence of a real abundance dispersion among the And~I
RRab stars, with $\sigma_{{\rm [Fe/H], int}}\sim0.4$~dex.  This value is somewhat
larger than the abundance dispersion found by DACS00 from the And~I red giant
branch ($\sigma_{{\rm [Fe/H], int}}\sim0.21$) though, again recognizing that not
every red giant branch star evolves to become a RRab star, it is difficult
to compare these dispersions in a meaningful way.  The lower panel of Fig.~13
shows the red giant branch abundance distribution for And~I from DACS00.
Given that the individual red giant branch abundance determinations have substantially
lower uncertainties than the RRab values, the distributions appear quite
comparable.  Both distributions appear to be sharply limited
on the metal-rich side.  The And~I results are similar to the situation for
And~II, where both the RRab and the red giant branch stars show substantial
abundance ranges, larger indeed than those found here for And~I (Paper~II).

For And~III, the distribution of the individual metallicity estimates for the
RRab stars is shown in the upper panel of Figure~14.  Here the mean and
median metallicity values are $-1.81$ and $-1.77$, respectively.  The gaussian fit to the
data has a mean value of $-1.79\pm0.03$ (standard error of the mean).
Once again, despite the fact that only a relatively small fraction of the red
giant branch stars evolve to become RRab stars (cf.\, Fig.~1), these RRab
based abundance values agree well with the red giant branch based determination
of the mean abundance, ${\rm [Fe/H]}=-1.88\pm0.11$, given by DAC02.

The gaussian fit shown in Fig.~14 has a standard deviation of 0.37~dex,
considerably smaller than was found for And~I, and barely larger than that
expected on the basis of the individual errors alone ($\sim0.3$~dex).
There is therefore no compelling case for the existence of a substantial
abundance spread among the And~III RRab stars.  This result is similar
to that found for the RRab in And~VI (Paper~I).  Again while there is no
reason to expect this to be the case, the small abundance dispersion for the
And~III RRab stars is consistent with the results for the red giant branch:
DAC02 give $\sigma_{{\rm [Fe/H], int}}=0.12$ from their analysis of the
red giant branch colors.  The lower panel of Fig.~14 reinforces this conclusion:
it shows the red giant branch abundance distribution from DAC02.  As for
Fig.~13, given the larger uncertainty in the individual RRab values, the
distribution in the upper and lower panels appear quite similar.

Now that we have used the Alcock et al.\ (2000) equation (Eq.~2) to estimate
the mean metallicity for the RRL in four of the M31 dSph galaxies, it is
worthwhile to evaluate the outcome of this process.  Even though the
metallicity estimate for any individual RRL from this equation is of
limited accuracy, for each of the four dSph galaxies the mean metallicity
derived from the RRL stars is in excellent accord with that determined
from the RGB\@.  Indeed, for these four systems, the standard deviation of
the differences between the RRL and RGB metallicity estimates is only
0.05~dex.  Since not every RGB star evolves into an RRL, there is no
{\it a priori} reason to expect this good agreement.  Yet clearly the RRL stars,
 and the use of Eq.~2, are providing valid estimates of the mean
metallicities of these four systems.  Consequently, application of Eq.~2
may prove worthwhile in those situations where information is available
only for RRL stars.  Further applications to other dSph galaxies and globular
clusters will be important to test the application of this equation.

\section{Summary \& Conclusions}

We have presented the results of variable star surveys of the M31 dSph
galaxies And~I and And~III using the HST/WFPC2.  And~I was found
to contain 72 fundamental mode and 26 first-overtone mode RRL stars
with mean periods of 0.575~day and 0.388~day, respectively, with one
unclassified RRL star.  We also found that two of the RRL in the
And~I field are fainter than the HB; these stars
may be associated with the recently discovered stellar stream in the halo
of M31.  In And~III, we discovered 39 fundamental mode and 12
first-overtone mode RRL stars with mean periods of 0.657~day and 0.402~day,
respectively.  The mean period of the RRab stars in And~I is consistent
with the Galactic globular cluster RRL mean period - metallicity relation.  For
And~III, the mean period of the RRab stars is longer than that expected
for the mean metallicity of the galaxy.  This discrepancy arises from a
lack of shorter period, higher amplitude RRab stars in And~III
compared to other dSphs.  This effect may be related to the very red
morphology of the HB in this dSph.
We also find for both dSph galaxies that the mean magnitudes of the RRL
imply distances similar to those previously determined from the mean
magnitude of the horizontal branch.

We found five variable stars that are brighter than the HB in And~III, four
of which are ACs.  These stars have properties consistent with ACs
found in other dSph galaxies in terms of their P-L and
period-amplitude relations.  The other star, and the single supra-HB star in
And~I, may be P2C variables rather than ACs.  Further observations are
needed to clarify their nature though we note that in the Galactic globular
cluster population, P2Cs are found only in those clusters with strong blue
HB morphology, which both And~I and And~III lack.  Assuming that these
two stars are ACs, we have included the resulting AC specific frequencies
for And~I and And~III with the data for other dSph galaxies from Paper~II\@.
These AC specific frequencies follow the trends defined by the other dSphs when
plotted against both (visual) luminosity and mean abundance.  As we
concluded in Paper~II, there is a clear correlation between the AC
specific frequency and dSph luminosity (and mean abundance) as first
noted by Mateo et al.\ (1995).

For the RRab stars in And~I, we found $\langle {\rm [Fe/H]} \rangle = -1.49$
from the Alcock et al.\ (2000) equation that relates the metallicity of a
RRab star to its period and amplitude.  This mean abundance estimate agrees
well with that of DACS00, $\langle {\rm [Fe/H]} \rangle = -1.46\pm0.12$,
determined from the colors of the red giant branch stars.  For And~III,
applying the same method yields $\langle {\rm [Fe/H]} \rangle = -1.81$
from the RRab stars, which again agrees well with the mean abundance from the red
giant branch, $\langle {\rm [Fe/H]} \rangle = -1.88\pm0.11$ (DAC02).
Indeed, we have found that the Alcock et al.\ (2000) equation provides
a good estimate for the mean metallicity for all the four systems we have
surveyed despite the fact that not all red giant branch stars evolve to become
RRL stars.  It remains to be seen how well this equation applies to other
dwarf galaxies or globular clusters.

In agreement with Baldacci et al.\ (2003), Marconi et al.\ (2004), and
Gallart et al.\ (2004), we find that the short-period Cepheids in dwarf
galaxies such as Leo~A, Sextans~A, and IC~1613 do not follow the same P-L
relations as found for the ACs.  The short-period Cepheids
typically have higher luminosities than the ACs at fixed period.

In summary, our search for variable stars in the M31 dSph companions has,
up to this point, revealed that their variable star populations are basically
indistinguishable from those of their Galactic counterparts.  In particular,
the properties and specific frequencies of the
ACs in the M31 dSph galaxies are similar to those found in the Galactic
dSph galaxies.  Further, the properties of the RRL stars are consistent with
those found in the Galactic dSphs, and have been shown to be good indicators
for the distance and, perhaps surprisingly, also the mean metallicity for
these M31 dSph companions.

\acknowledgements

This research was supported in part by NASA through grant number GO-08272
from the Space Telescope Science Institute, which is operated by AURA, Inc.,
under NASA contract NAS 5-26555.

Thank you to the referee for the valuable comments for this paper.
We would like to thank P. B. Stetson for graciously sharing his PSFs for
the WFPC2 and for the use of his data reduction programs.  Thanks to A. C.
Layden for the use of his light curve analysis programs.  GDaC is
grateful to Andrew Drake for his efforts in carrying out the initial
analysis of the variable stars in And~I\@.  Thanks also to M. Catelan and
H. A. Smith for discussions on the RRL period distribution in And~III.

\clearpage

redpajama_set_name: RedPajamaArXiv


Overview: The GDC Microtalks returns with ten short talks about the philosophy, history and futures of the design, art and culture of games and play, all packed into a single hour. The concept is simple: each speaker gets 20 slides, each of which will be displayed for exactly 16 seconds before automatically advancing, giving the speaker exactly five minutes and 20 seconds to make their point. Join our nine amazing speakers along with curator and MC Richard Lemarchand, to receive a rapid-fire mind-blast of original, inspirational, challenging and entertaining takes on the state of the art in games and play.


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Woodworking husband-and-wife duo Andrea Brugi and Samina Langholz invite you into their magical world, where their Scandinavian sensibility for clean design is balanced with organic and aged imperfection inspired by their Tuscan home. Discover some of their key woodworking techniques through twenty simple projects for useful and decorative objects for the home—from cutting boards and simple doorstops to benches and dining tables. With striking photography, step-by-step instructions, and information on the types of wood and tools required for each project, you'll have everything you need to start handcrafting your own woodworking masterpieces that celebrate the beauty of uniqueness and combine modern design with rustic warmth.


text:
EclipseGeeks.com
Types of Eclipse
Geometry of a Lunar Eclipse
Geometry of a Solar Eclipse
Total Lunar Eclipse Jan 2018
EclipseGeeks.com - All you ever wanted to know about eclipses and other celstial bodies
The Prime Meridian is the line of 0° of longitude which divides the Earth into the Eastern and Western Hemispheres.
All world time zones are either set in front or behind the Prime Meridian at Greenwich, London, England.
Astronomical data, National Observatories, International Space Organisations and other Astronomical Services use Universal Time 'UT' when predicting astronomical events. It avoids ambiguity and confusion across the World's Time Zones. Everyone knows exactly when an event will occur. Use the map below to add or suntract your time zone from the Prime Meridian at Greenwich London, England.
Astronomical data, computers, computer servers, world wide web standards, network time protocols, aircraft navigation, nautical positioning systems, GPS systems, satellites, weather forecasts, flight plans, air traffic control, and civilian time zones throughout the world all use a single reference time which is measured from the Prime Meridian at Greenwich London England. The Prime Meridian is the line of 0° of longitude which divides the Earth into the Eastern and Western Hemispheres. All world time zones are either set in front or behind the Prime Meridian at Greenwich.
Greenwich Meantime (GMT) is also known as Universal Time UT and uses a 24 hour clock system with a new day beginning at midnight. Although UT and GMT exact definitions differ, for most everyday situations, one can assume that Universal Time is comparable to Greenwich Meantime (GMT). .
Universal Time 'UT' also refers to a time scale called Coordinated Universal Time 'UTC' which is the basis for the worldwide system of civil time. This time scale is kept by National Physical Laboratories and Institutions around the world using high accurate caesium atomic clocks.
International Astronomical Data and Astronomy Events are normally given in UT – Universal Time / GMT – Greenwich Meantime. Using a single reference time avoids ambiguity when describing when an astronomical event will occur; you can use this map to calculate your own time zone with reference to UT/GMT.
Global World Time Map:
Courtesy of the University of Texas Libraries, The University of Texas, Austin, USA.
Time Zones World Map
The Prime Meridian
The Prime Meridian is the line of 0° longitude which divides the Earth into the Eastern and Western Hemispheres.
Greenwich Mean Time is the same as Universal Time (UT), a standard astronomical concept used in many technical fields.
UT – Universal Time / GMT – Greenwich Meantime
International Astronomical Data and Astronomical Events are normally given in: UT. Universal Time / GMT. Greenwich Meantime.
Using a single reference time avoids ambiguity when describing when an astronomical event will occur.
Please use this map to calculate your own time zone with reference to UT/GMT.
Click World Time Zone Map to enlarge
Astronomical events are normally given in: UT/GMT.
Using a single reference time avoids ambiguity; you can use this world map see your own time.
Penumbral Lunar Eclipse, 11th February 2017 Penumbral Lunar Eclipse, 28th February 2012 Solar Eclipse, 26th February 2017
eclipsegeeks.com All rights reserved © 2010 - 2018
Site Map - index
Transit of Venus 2012
Eclipse predictions acknowledgment: Fred Espenak, NASA's GSFC"

redpajama_set_name: RedPajamaCommonCrawl


Unable to find a 50th vote for a GOP plan to overhaul Obamacare, Republicans on Tuesday announced they would hold hearings in the Senate after Labor Day, in hopes of spurring a bipartisan agreement in Congress on short term plans to stabilize markets for individual insurance policies, just before insurance companies set their premiums for 2018.
"We will hear from state insurance commissioners, patients, governors, health care experts and insurance companies," said Sen. Lamar Alexander (R-TN), the Chairman of the Senate Health, Education, Labor and Pensions Committee.
"For the short term, the proposal is by mid-September to see if we can agree on a way to stabilize the individual insurance market," Alexander added.
The decision was a big turnaround for Republicans, who had steadfastly avoided hearings on their plan to overhaul the Obama health law.
"I'm glad to get to work on health care with Sen. Alexander," said the top Democrat on that panel, Sen. Patty Murray (D-WA). "We've tackled tough issues together before."
"I'm very excited by that," said Sen. Susan Collins (R-ME) about the announcement of the bipartisan hearings. "I think that's the direction we should have gone in the first place."
Like Collins, the idea of more hearings, and a deeper explanation of what's involved on health care also resonated with another of the Republican "No" votes as well.
"I like process; I think process is good for all of us," said Sen. Lisa Murkowski (R-AK) on Monday. "I think it makes us a better institution."
Alexander said the process of developing some kind of interim health care plan would not only be bipartisan, but would involve more than just the members of his committee, as Republicans changed their tune on working with Democrats from where things stood a week ago, when the GOP 'skinny' bill was defeated.
Senate Majority Leader Mitch McConnell - for a second straight day - didn't even mention health care on the floor of the Senate, as he talked about what he hoped to get the Senate to accomplish during the first two weeks of August.
Meanwhile, some Republicans were still exploring ways to find 50 votes - only from Republicans - for a GOP health care bill.
"I like the idea that we are not quitting," said Sen. Lindsey Graham (R-SC) to reporters just off the Senate floor. "We haven't tried all options yet."
Down at the White House, officials were still publicly urging GOP leaders not to give up.
"We know that Obamacare is failing, we know that inaction is not okay," said incoming Press Secretary Sarah Huckabee Sanders.
But for now, the push to get something done that is wide-ranging, seems to be going on the back burner - though Republicans still remain just one vote away from getting enough support for a broader package in the Senate.


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text:
Delta Foreclosures
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Delta, Iowa
Delta is a city in Keokuk County, Iowa, United States. The population was 328 at the 2010 census.
Delta is located at 41°19′27″N 92°19′46″W (41.324112, -92.329481).
According to the United States Census Bureau, the city has a total area of 0.93 square miles (2.41 km2), all of it land.
As of the census of 2010, there were 328 people, 157 households, and 78 families living in the city. The population density was 352.7 inhabitants per square mile (136.2/km2). There were 172 housing units at an average density of 184.9 per square mile (71.4/km2). The racial makeup of the city was 97.0% White, 1.8% African American, 0.3% Native American, 0.3% from other races, and 0.6% from two or more races. Hispanic or Latino of any race were 0.6% of the population.
There were 157 households, of which 27.4% had children under the age of 18 living with them, 36.3% were married couples living together, 9.6% had a female householder with no husband present, 3.8% had a male householder with no wife present, and 50.3% were non-families. 45.2% of all households were made up of individuals, and 18.5% had someone living alone who was 65 years of age or older. The average household size was 2.09 and the average family size was 2.91.
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text:
Obama ends day of Indian pageantry with $4B pledge
Published Mon, Jan 26 2015 6:21 PM EST Updated Mon, Jan 26 2015 6:43 PM EST
Obama returns to India
Power Lunch
U.S. President Barack Obama ended a landmark day in India on Monday with a pledge of $4 billion in investments and loans, seeking to release what he called the "untapped potential" of a business and strategic partnership between the world's largest democracies.
Earlier in the day, at the invitation of Prime Minister Narendra Modi, Obama was the first U.S. president to attend India's annual Republic Day parade, a show of military might that has been associated with Cold War anti-Americanism.
It rained as troops, tanks and cultural floats filed through the heart of New Delhi, but excitement nevertheless ran high over Obama's visit, which began on Sunday with a clutch of deals to unlock billions of dollars in nuclear trade and to deepen defense ties.
Both sides hope to build enough momentum to forge a relationship that will help balance China's rise by catapulting democratic India into the league of major world powers.
The significance of US-India nuclear trade progress
Street Signs Asia
The leaders talked on first name terms, recorded a radio program together and spent hours speaking at different events, but despite the bonhomie, Obama and Modi reminded business leaders, including the head of PepsiCo, that trade ties were still fragile.
India accounts for only 2 percent of U.S. imports and one percent of its exports, Obama said. While annual bilateral trade had reached $100 billion, that is less than a fifth of U.S. trade with China.
"We are moving in the right direction ... That said, we also know that the U.S.-India relationship is defined by so much untapped potential," Obama told the Indian and U.S. business leaders. "Everyone here will agree, we've got to do better."
Read MoreBig change in India on its way: Finance Minister
Modi said U.S. investment in India had doubled in the past four months and vowed to do more to slash the country's notorious red tape and make it one of the world's easiest places for business.
Obama said that U.S. Export-Import Bank would finance $1 billion in exports of 'Made-in-America' products. The U.S. Overseas Private Investment Corporation will lend $1 billion to small- and medium-sized enterprises in rural areas of India.
Regarding renewable energy, a key focus for Modi, $2 billion will be committed by the U.S. Trade and Development Agency for renewable energy, Obama said.
Most significant was an agreement on issues that, despite a groundbreaking 2006 pact, had stopped U.S. companies from setting up nuclear reactors in India and had become one of the major irritants in bilateral relations.
"Mobama breaks N-deadlock," ran the front-page headline of the Mail Today newspaper, which carried a photograph of Modi and Obama hugging each other warmly.
Obama and Modi sat behind a rain-spotted screen as the parade unfolded along Rajpath, an elegant lawn-bordered boulevard dating from the British colonial era that connects the presidential palace to India Gate.
Helicopters showered petals on the crowds, and then tanks, missiles, stiffly saluting soldiers, brass bands and dancers filed past the guests.
Obama's presence at the parade signals Modi's willingness to end India's traditional reluctance to get too close to any big power. Instead, he is seeking close ties with them all, even as he pushes back against China and take sides on other global issues.
Modi has injected a new vitality into the economy and foreign relations since his May elections.
Obama's second visit to India is the latest upturn in a roller-coaster relationship with Washington that a year ago was scarred by protectionism and a fiery diplomatic spat.
The United States views India as a vast market and potential counterweight to China's assertiveness, but has been frustrated with the pace of New Delhi's economic reforms.
"There are still too many barriers, hoops to jump through, bureaucratic restrictions that make it hard to start a business, or to export, to import, to close a deal, deliver on a deal," Obama told a forum of CEOs from both countries in New Delhi.
In a joint statement that made a veiled reference to China's territorial claims, Modi and Obama stated their commitment to freedom of navigation in the South China Sea.
India could even play a role in battling Islamic State, the White House said on Monday, underlining the confidence that New Delhi is increasingly prepared to engage with global security.
"The leaders agreed to exchange information on individuals returning from these conflict zones and to continue to cooperate in protecting and responding to the needs of civilians caught up in these conflicts," the two sides said in a joint statement.
They also agreed to a 10-year framework for defense ties and struck deals on cooperation that included joint production of drone aircraft and equipment for Lockheed Martin C-130 military transport plane.
PepsiCo Inc.


Mizen Information and e-Mizen Centre is on Main Street, Goleen.
On your way to or from Mizen Head, call in for Visitor Information, Free Wifi, Hot Desks, Business Services, Coffee, Gift Shop, Public Restrooms.
Come in for a coffee and a chat! Free Car Parking with play park at the back of the village with a path down past Goleen Play school to Main Street.
Take a break in your journey and visit Goleen, the village you pass through on your way to Mizen Head. Last pubs before the most Southwesterly point! The Lobster Pot, Denny O'Meara's, The Fastnet and Norma's. Buckets and spades and provisions at Dermot Sheehan Mini-Market. Homemade Cakes and coffee at Sarah Jane's Along the Way. Don't forget to visit the village of Crookhaven too.
Mizen Head Office. All enquiries to 028-35000 during opening times.
The E Centres Initiative is funded through Cork County Council's Economic Development Fund to provide support to local communities in establishing business incubation or "COCOON" facilities.
A Hot Desk will suit you if you are starting a business, working remotely, downsizing your business or working from home and wish to move to a professional dedicated working environment.


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In this highly interactive session participants will be using technology to reflect on the different types of assessment and the benefits they bring as they try out a couple of tools which are appropriate for low-tech contexts. We will also be thinking about how to turn assessments into valuable information to help both learners and teachers move forward.
British Council, Ente accreditato dal MIUR per la formazione del personale della scuola ai sensi della Direttiva 170 del 21/3/2016, articolo 1, comma 5.


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Pictured: Face painting courtesy of Simply Circus provided some pre-movie entertainment at the Guardians of the Galaxy Vol 2 screening at Glen Forrest Oval.
WITH two movies down, and three to go, there's still time to enjoy free outdoor films this summer as part of the Shire of Mundaring's Cinema Under Starlight series.
The season kicked-off with Guardians of the Galaxy Vol 2 at Glen Forrest Oval, followed by family favourite Moana at Chidlow Oval.
Cinema Under Starlight coordinator Tracey Peacock said that the cost-free, community events were a great way to spend the weekend with family and friends.
"Cinema Under Starlight is a great way to entertain the family without having to travel outside of the local area. Along with our sponsors Lotterywest, Linley Valley Pork, Acciona Trility Joint Venture and Mundaring Community Bank Branch - Bendigo Bank, Shire of Mundaring is pleased to be able to offer these free events to the community," Ms Peacock said.
"Support from our sponsors has also enabled the Shire to extend the movie series this year to include a fifth event, offering further opportunities for residents to enjoy the warm summer evenings."
With the first cinema event in January drawing an impressive crowd of 350 people, Ms Peacock said there were three more opportunities in 2018 to enjoy a special cinema experience.
"We really want to encourage people to make the most of the program this summer," she said.
"There's lots on offer before each movie including food and beverages for sale as well as activities such as face-painting and other children's entertainment."
Next up is Cars 3 (rated G), which will show at Mundaring Recreation Ground on Saturday 17 February. Gates open at 6.30pm for an 8pm movie start.
Movie goers are encouraged to bring a picnic blanket or low-backed chairs to sit on.
Please contact Cinema Under Starlight coordinator Tracey Peacock with any enquiries.